Please write clearly in block capitals.
Centre number
Candidate number
Surname
Forename(s)
Candidate signature
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 1 Technical Principles
Friday 7 June 2019
Morning
Time allowed: 2 hours 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
• normal writing and drawing instruments
• a scientific calculator.
Pages
2–3
4–5
Instructions
•
•
•
•
•
•
Mark
Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided.
Do not write outside the box around each page or on blank pages.
Do all rough work in this book. Cross through any work you do not want to be
marked.
6–8
9
10–11
12
13–15
16–17
18–19
Information
20–21
• The marks for questions are shown in brackets.
• The maximum mark for this paper is 120.
22
TOTAL
*Jun197552101*
IB/G/Jun19/E16
7552/1
2
Do not write
outside the
box
Answer all questions in the spaces provided.
0 1
Explain why ‘potatopak’ is a suitable material for the manufacture of disposable cutlery.
[3 marks]
0 2
Explain how BSI certification impacts on the purchase of a child’s car seat by a consumer.
[6 marks]
*02*
IB/G/Jun19/7552/1
3
0 3
Give three benefits of using stock forms of material for a manufacturer.
Do not write
outside the
box
[3 marks]
1
2
3
0 4
PAR is a stock form of timber. What does PAR stand for?
[1 mark]
13
Turn over for the next question
Turn over ►
*03*
IB/G/Jun19/7552/1
4
0 5
Do not write
outside the
box
Figure 1 shows a children’s climbing frame.
Figure 1
Explain why powder coating is an appropriate finish for the climbing frame shown in
Figure 1.
[6 marks]
*04*
IB/G/Jun19/7552/1
5
0 6
Do not write
outside the
box
Define each of the following terms:
• copyright
• trademark
• patent.
[3 marks]
Copyright
Trademark
Patent
9
Turn over for the next question
Turn over ►
*05*
IB/G/Jun19/7552/1
6
0 7
Do not write
outside the
box
Figures 2 and 3 show rolls of adhesive tape.
Figure 2
Figure 3
Core
A roll with an ABS core
Core
A roll with a cardboard core
Compare the environmental impact of the materials used to manufacture the cores of the
adhesive tapes shown.
[6 marks]
*06*
IB/G/Jun19/7552/1
7
0 8
Do not write
outside the
box
Figure 4 shows the dimensions of a component to be made using 3D printing.
Figure 4
All dimensions in mm
Not drawn to scale
Front view
Side view
Completed component
Material costs
Material
ABS
Printed density
(grams per mm3)
Cost per 500 g
0.000 448 g
£18
Calculate the material cost of manufacturing 50 units.
Show your working out.
[5 marks]
Turn over ►
*07*
IB/G/Jun19/7552/1
8
Do not write
outside the
box
0 9
Name a specific application for each of the following compliant materials:
• bleed proof paper
• duplex card
• moulded paper pulp.
[3 marks]
Bleed proof paper
Duplex card
Moulded paper pulp
14
*08*
IB/G/Jun19/7552/1
9
1 0
Do not write
outside the
box
Evaluate the following techniques for rendering a design:
• using computer aided design (CAD)
• hand generated.
[6 marks]
6
Turn over for the next question
Turn over ►
*09*
IB/G/Jun19/7552/1
10
1 1
Figure 5 shows an aluminium seat clamp. Figure 6 shows the dimensions of a block of
aluminium.
Figure 5
Figure 6
All dimensions in mm
Not drawn to scale
The seat clamp is currently manufactured by wastage from the aluminium block shown in
Figure 6.
The manufacturer wants to produce the clamp using a redistribution process.
Compare the cost of each manufacturing process if 5000 units are to be produced.
Show your working out.
Volume of the seat clamp
Cost of aluminium
Cost of manufacturing a mould for the
redistribution process
7280 mm3
£4 per 100 000 mm3
£3000
[6 marks]
*10*
IB/G/Jun19/7552/1
Do not write
outside the
box
11
Do not write
outside the
box
1 2
Explain the safe work practices necessary to protect workers when using solvent
adhesives.
[6 marks]
Turn over ►
*11*
IB/G/Jun19/7552/1
12
12
1 3
Explain why neoprene is a suitable material to manufacture a case to carry a laptop.
[8 marks]
Do not write
outside the
box
8
*12*
IB/G/Jun19/7552/1
13
1 4
Do not write
outside the
box
Figure 7 shows a lift interface.
Figure 7
All dimensions in mm
Not drawn to scale
Evaluate how well the lift interface has been designed to be inclusive to all users.
[6 marks]
Turn over ►
*13*
IB/G/Jun19/7552/1
14
Do not write
outside the
box
1 5
A manufacturer is producing a glass reinforced plastic (GRP) moulding.
Calculate the volume of hardener needed.
Show all of your working.
Size of GRP mat needed for moulding
Ratio of resin to hardener
Total volume of liquid (resin and hardener)
needed per m2 of GRP matting
2 metres × 5 metres
3:2
3 litres per m2
[4 marks]
*14*
IB/G/Jun19/7552/1
15
Do not write
outside the
box
1 6
Explain why industrial tests are more accurate than workshop tests when testing material
properties.
[2 marks]
1 7
Describe how a specific industrial test is undertaken to measure material hardness.
[4 marks]
16
Turn over ►
*15*
IB/G/Jun19/7552/1
16
1 8
Do not write
outside the
box
Figure 8 and Figure 9 show two bicycle frames.
Figure 8
Figure 9
Aluminium TIG welded bicycle frame
CFRP lay-up bicycle frame
Evaluate the suitability of the materials and manufacturing methods used for each of the
bicycle frames shown.
[12 marks]
*16*
IB/G/Jun19/7552/1
17
Do not write
outside the
box
12
Turn over for the next question
Turn over ►
*17*
IB/G/Jun19/7552/1
18
1 9
Figure 10 shows a component to be cut on a computer numerically controlled (CNC)
router.
Figure 10
All dimensions in mm
Not drawn to scale
Material
Depth of cut per pass
Rate of cut
12 mm MDF
6 mm
6 metres per minute
12 mm plywood
4 mm
4.5 metres per minute
Calculate how long it would take to machine the shape in each of the materials.
Show your working out.
[6 marks]
*18*
IB/G/Jun19/7552/1
Do not write
outside the
box
19
Do not write
outside the
box
6
Turn over for the next question
Turn over ►
*19*
IB/G/Jun19/7552/1
20
2 0
Do not write
outside the
box
Figures 11, 12 and 13 show pieces of self-assembly furniture.
Figure 11
Figure 12
Figure 13
Cot frame using barrel nuts
and bolts
Shelf unit frame using cam
locks
Bookcase shelf using dowels
Barrel nut and bolt
Cam lock
Dowel
Explain why the knock down fittings named above are appropriate for each of the specific
applications.
[3 × 2 marks]
Barrel nut and bolt
Cam lock
Dowel
*20*
IB/G/Jun19/7552/1
21
2 1
Explain the importance of the efficient supply of materials and components in a Just In
Time (JIT) manufacturing process.
[9 marks]
Do not write
outside the
box
15
Turn over ►
*21*
IB/G/Jun19/7552/1
22
2 2
Give three reasons why a kitchen work surface may have a melamine formaldehyde layer
applied.
[3 marks]
Do not write
outside the
box
Reason 1
Reason 2
Reason 3
2 3
Describe the process of forming a timber product using lamination.
[6 marks]
9
END OF QUESTIONS
*22*
IB/G/Jun19/7552/1
23
Do not write
outside the
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
*23*
IB/G/Jun19/7552/1
24
Do not write
outside the
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Copyright information
For confidentiality purposes, from the November 2015 examination series, acknowledgements of third-party copyright material are published in a separate
booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available
for free download from www.aqa.org.uk after the live examination series.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and
AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House,
Guildford, GU2 7XJ.
Copyright © 2019 AQA and its licensors. All rights reserved.
*24*
*196a7552/1*
IB/G/Jun19/7552/1
Please write clearly in block capitals.
Centre number
Candidate number
Surname
Forename(s)
Candidate signature
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 2 Designing and Making Principles
Friday 14 June 2019
Morning
Time allowed: 1 hour 30 minutes
For Examiner’s Use
Materials
For this paper you must have:
• normal writing and drawing instruments
• a scientific calculator.
Question
1
2
Instructions
•
•
•
•
•
•
Mark
Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided.
Do not write outside the box around each page or on blank pages.
Do all rough work in this book. Cross through any work you do not want to be
marked.
Information
3
4
5
6
7
8
9
10
• The marks for questions are shown in brackets.
• The maximum mark for this paper is 80.
• There are 30 marks in Section A and 50 marks in Section B.
11
12
13
14
15
TOTAL
*jun197552201*
IB/G/Jun19/E16
7552/2
2
Do not write
outside the
box
Section A – Product Analysis
Answer all questions in this section.
0 1
Figures 1 and 2 show two power drills.
Figure 1
Figure 2
2
1
Figure 1
Die cast mains powered
drill
Figure 2
Injection moulded
cordless drill
Casing material
Die cast aluminium
Injection moulded ABS
Power supply
230 V mains power
9.6 V rechargeable battery
pack
Chuck operation
Chuck key
Keyless chuck
Casing joined by
Flat head screws
Security fasteners
Labelled 1
Labelled 2
Centre of mass
*02*
IB/G/Jun19/7552/2
3
Do not write
outside the
box
Compare the two drills shown. In your answer you should refer to:
• ergonomic factors
• design safety.
[12 marks]
Turn over ►
*03*
IB/G/Jun19/7552/2
4
Do not write
outside the
box
12
0 2
Evaluate the impact of the Waste Electrical and Electronic Equipment (WEEE) Directive on
manufacturers of portable electronic hand tools.
[6 marks]
6
*04*
IB/G/Jun19/7552/2
5
0 3
Explain four ways that cordless power tools can be designed to be disassembled.
Do not write
outside the
box
[4 × 2 marks]
1
2
3
4
8
Turn over for the next question
Turn over ►
*05*
IB/G/Jun19/7552/2
6
0 4
The battery life of a rechargeable battery was tested in a handheld electronic device. The
test was repeated 11 times with a new battery each time.
Do not write
outside the
box
The results are shown in the table below.
Battery life
(in minutes)
1
2
3
4
5
6
7
8
9
10
11
65
110
180
130
90
220
150
75
90
190
210
On the grid below draw a box plot to show the results.
[4 marks]
4
*06*
IB/G/Jun19/7552/2
7
Do not write
outside the
box
Section B – Commercial Manufacture
Answer all questions in this section.
0 5
When producing a die cut package, three different, independently occurring faults are
possible with these probabilities:
Fault A: 1/100
Fault B: 1/100
Fault C: 1/500
A and B are minor faults which must be monitored but will only fail quality control if both
faults are seen on a single product.
C is a critical fault and any product suffering from this fault will fail quality control.
If a batch of 10 000 packages are produced, calculate how many products would be
expected to fail quality control.
[3 marks]
3
Turn over for the next question
Turn over ►
*07*
IB/G/Jun19/7552/2
8
0 6
State four ways a manufacturer may use quality assurance procedures and policies to
reduce the rate of errors during die cutting of packaging nets.
[4 marks]
Do not write
outside the
box
1
2
3
4
4
*08*
IB/G/Jun19/7552/2
9
0 7
Do not write
outside the
box
Figure 3 shows a submarine.
Figure 3
Explain the specific virtual modelling techniques that may be used to test the design of a
submarine before production.
[6 marks]
Turn over ►
*09*
IB/G/Jun19/7552/2
10
Do not write
outside the
box
6
0 8
Define the term Total Quality Management (TQM).
[2 marks]
2
0 9
For a specific application, give two reasons why a go no-go gauge would be used.
[3 marks]
3
1 0
State three characteristics associated with products from the Memphis postmodern design
group.
[3 marks]
1
2
3
3
*10*
IB/G/Jun19/7552/2
11
1 1
Describe the methods used by manufacturers to conserve energy and materials during
product development and manufacture.
[9 marks]
Do not write
outside the
box
9
Turn over ►
*11*
IB/G/Jun19/7552/2
12
1 2
Do not write
outside the
box
Figure 4 shows a low carbon steel component with a volume of 11 100 mm3
The density of low carbon steel is 7.85 g/cm3
The component is to be hot dip galvanised.
The galvanising process increases the mass of the component by 5%
Calculate the mass of the galvanised component in grams.
Show your working out.
[3 marks]
Figure 4
Isometric view
3
*12*
IB/G/Jun19/7552/2
13
1 3
Do not write
outside the
box
Compare the two radios shown in Figures 5 and 6.
In your answer you should refer to developments in:
• microelectronics
• materials.
[12 marks]
Figure 5
Figure 6
Figure 5
Fabricated plywood valve
radio (1950s)
Figure 6
Injection moulded digital
radio (2015)
Button/control material
Thermoset polymer
TPE
Electronics
Thermionic valves
Integrated circuits
Fabricated plywood
Injection moulded
thermoplastic
No display
LCD screen
Main casing material
Information display
Turn over ►
*13*
IB/G/Jun19/7552/2
14
Do not write
outside the
box
12
*14*
IB/G/Jun19/7552/2
15
1 4
State three reasons why a designer may use a focus group.
Do not write
outside the
box
[3 marks]
1
2
3
3
Turn over for the next question
Turn over ►
*15*
IB/G/Jun19/7552/2
16
1 5
Do not write
outside the
box
Figure 7 shows a label often found on electronic products.
Explain the meaning of the label shown in Figure 7.
[2 marks]
Figure 7
2
END OF QUESTIONS
Copyright information
For confidentiality purposes, from the November 2015 examination series, acknowledgements of third-party copyright material are published in a separate
booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available
for free download from www.aqa.org.uk after the live examination series.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and
AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House,
Guildford, GU2 7XJ.
Copyright © 2019 AQA and its licensors. All rights reserved.
*16*
*196a7552/2*
IB/G/Jun19/7552/2
Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 1
Technical Principles
Friday 5 June 2020
Morning
Time allowed: 2 hours 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.
Information


The marks for questions are shown in brackets.
The maximum mark for this paper is 120.
Mark
1– 4
5
6
7
8
9–10
11
12
13
14
15
16
17
18
19
20
21–22
TOTAL
(JUN207552101)
G/TI/Jun20/E3
7552/1
2
Do not write
outside the
box
Answer all questions in the spaces provided.
0
1
Give three reasons why polymorph may be used in the modelling of an
ergonomic grip.
[3 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
3 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
0
2
Define the following material properties:
malleability
elasticity.
[2 marks]
Malleability _______________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Elasticity _________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(02)
G/Jun20/7552/1
3
0
3
State three ways that manufacturers are improving sustainability throughout product
manufacture.
[3 marks]
Do not write
outside the
box
1 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
3 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
0
4
Explain why high speed steel would be a suitable material for a metal drill bit.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over 8
(03)
G/Jun20/7552/1
____
14
4
0
Do not write
outside the
box
5
Figure 1
Not drawn to scale. All dimensions in mm.
42
24
9
Component A
33
15
21
Component B
30
6
57
3
15
3
24
Component C
30
42
33
Figure 2
Fabricated Acrylic component
(04)
G/Jun20/7552/1
5
0 5
.
1
Figure 1 shows the dimensions of the components required to produce Figure 2.
The component parts are cut from a 90 mm × 70 mm × 3 mm sheet of acrylic.
Calculate the percentage (%) of waste from the acrylic sheet.
Show your working.
[4 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Percentage (%) of waste = ________________________
Question 5 continues on the next page
Turn over 8
(05)
G/Jun20/7552/1
Do not write
outside the
box
6
0 5
.
Do not write
outside the
box
2
The product shown in Figure 3 has been laser cut and fabricated. An alternative
method is to form it in one piece using injection moulding.
Figure 3
Compare and evaluate the suitability of each manufacturing method for this product.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(06)
G/Jun20/7552/1
____
10
7
Do not write
outside the
box
0
6
Describe the main stages in the process of soft soldering.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
(07)
G/Jun20/7552/1
____
6
8
0
7
Explain how the data gained from Electronic Point Of Sale (EPOS) systems can be
used.
[6 marks]
Do not write
outside the
box
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(08)
G/Jun20/7552/1
____
6
9
Do not write
outside the
box
0
8
Figure 4
Silicone oven mitt
Explain why silicone is an appropriate material for the manufacture of the oven mitt
shown in Figure 4.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
(09)
G/Jun20/7552/1
____
6
10
0
9
Analyse and evaluate the suitability of phosphorescent pigment for use in indoor
emergency signage.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(10)
G/Jun20/7552/1
Do not write
outside the
box
11
1
0
Do not write
outside the
box
Describe the purpose of risk assessment in a manufacturing environment.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
(11)
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____
12
12
1
Do not write
outside the
box
1
Figure 5
Concrete table tennis table
Explain why concrete is a suitable material for the manufacture of the outdoor
table tennis table shown in Figure 5.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(12)
G/Jun20/7552/1
____
6
13
Do not write
outside the
box
Turn over for the next question
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Turn over 8
(13)
G/Jun20/7552/1
14
1 2
.
1
Do not write
outside the
box
Table 1 shows information on the number of pledges and funds raised by
a crowd-funding campaign for a new product.
Using the data provided in Table 1, complete the histogram in Figure 6.
[4 marks]
Table 1
Backer’s pledge (£p)
Number of backers
0 < x ≤ 20
20 < x ≤ 40
20
40 < x ≤ 60
16
60 < x ≤ 100
20
Figure 6
Frequency
density
0
(14)
20
40
60
Pledge amount in £
80
100
G/Jun20/7552/1
15
1 2
.
2
Calculate the percentage (%) of people who supported the campaign with a pledge
of £20 or less.
[2 marks]
Do not write
outside the
box
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Percentage (%) of people = ________________________
1
3
____
6
Explain why bio-batch may be added to a polymer used in the manufacture of
single-use carrier bags.
[2 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
1
4
____
2
State two reasons why Danish oil is used as a surface finish for timber.
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over 8
(15)
G/Jun20/7552/1
____
2
16
1
5
Describe how physical and virtual prototypes can be used during the development of
a product.
Do not write
outside the
box
Include the benefits of each kind of prototype to the designer in your answer.
[9 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(16)
G/Jun20/7552/1
____
9
17
Do not write
outside the
box
1
6
A student wishes to route a symmetrical V-shaped channel in a piece of timber to
the dimensions provided in Figure 7.
Figure 7
30
20
a
Not drawn to scale
Cross section of timber
All dimensions in mm
Calculate cutter angle a.
Show your working.
[4 marks]
___________________________________________________________________________________
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___________________________________________________________________________________
Cutter angle = ________________________________ degrees
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1
7
Figure 8 and Figure 9 show children’s toys.
Figure 8
Figure 9
Beech toy
(hand shaped)
Acrylonitrile Butadiene
Styrene (ABS) toy
(injection moulded)
Analyse and evaluate the suitability of the materials and manufacturing methods
used for each of the children’s toys.
[12 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
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1
8
____
12
Explain why polypropylene (PP) is an appropriate material for the manufacture of an
ice cream container.
[6 marks]
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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Figure 10 shows the internal view of an injection moulded component.
Figure 10
Snap fitting
Rib
Moulded boss
State the function of each of the labelled features.
[3 marks]
Moulded boss ____________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Rib _______________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Snap fitting _______________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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2
0
Figure 11 shows a chocolate bar packaging. Figure 12 shows a larger
mathematically similar promotional version.
80
12
0
10
80
E
T
A
L
O
C
O
CH
10
Figure 11
300
Not drawn to scale
All dimensions in mm
11
88
E
T
A
L
O
C
O
H
C
11
Figure 12
Not drawn to scale
All dimensions in mm
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Use the information on the diagrams to calculate the percentage (%) increase in
volume of the new promotional packaging in Figure 12, from the original packaging
in Figure 11.
[6 marks]
Do not write
outside the
box
___________________________________________________________________________________
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___________________________________________________________________________________
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___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Percentage (%) increase in volume = __________________________________
Turn over for the next question
Turn over 8
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24
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1
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Compare and contrast the suitability of producing vehicle signage using either a
digital printed image or plotter cut vinyl.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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2
2
Explain why foam board is a suitable material for the manufacture of an architectural
model.
[4 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
END OF QUESTIONS
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Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet.
This booklet is published after each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have
been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact
the Copyright Team.
Copyright © 2020 AQA and its licensors. All rights reserved.
(28)
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Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 2
Designing and Making Principles
Friday 12 June 2020
Morning
Time allowed: 1 hour 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.
Information



The marks for questions are shown in brackets.
The maximum mark for this paper is 80.
There are 30 marks for Section A and 50 marks for Section B.
Mark
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TOTAL
(JUN207552201)
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7552/2
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Section A – Product Analysis
Answer all questions in this section.
0
1
Figures 1 and 2 show two camping lanterns.
Figure 1
Figure 2
Metal and glass oil lantern
Thermoplastic LED lantern
Figure 1
Figure 2
Power source
Burning oil
Solar panel
Operation of light
Match
Button
Materials
Low carbon steel sheet and
glass
Acrylonitrile Butadiene
Styrene (ABS), Thermoplastic
Elastomer (TPE) and
Polycarbonate
Manufacture
Deformation and fabrication
Redistribution and fabrication
Compare the two camping lanterns.
In your answer you should refer to:
suitability
of materials
manufacturing processes
power sources.
[12 marks]
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___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
Turn over 8
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4
0
2
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Figures 3 and 4 show two packages for camping lanterns.
Figure 3
Figure 4
1970s Camping lantern packaging
2017 Camping lantern packaging
Explain how the packaging for electronic products has changed over time and
possible reasons for this.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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5
0
3
Explain how the work of Philippe Starck reflects the postmodern design movement.
[6 marks]
Do not write
outside the
box
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
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6
0
4
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Figures 5, 6 and 7 show an electric shower.
Figure 5
Figure 6
Figure 7
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Discuss how well the shower has been designed to be inclusive to all users.
[6 marks]
Do not write
outside the
box
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for Section B
Turn over 8
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8
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Section B – Commercial Manufacture
Answer all questions in this section.
0
5
Figure 8 shows the performance of a Direct Current (DC) motor under different
loads (torque).
Figure 8
1500
1400
1300
1200
1100
1000
900
Revolutions 800
per minute
700
(RPM)
600
500
400
300
200
100
0
(08)
0
1
2
3
4
5 6 7 8
Torque (Nm)
9 10 11 12 13
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Calculate the equation of the red line in Figure 8.
Use this to calculate the stall torque (torque when the motor stops spinning) in Nm.
[3 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Answer ___________________________________
Turn over for the next question
Turn over 8
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10
0
6
Figure 9 shows the cross section of a low carbon steel blank used to press form a
section of a motor casing.
Do not write
outside the
box
The blank is a regular hexagon with a central through hole.
The blank has a volume of 12 500 mm3
Figure 9
50
All dimensions in mm
Not drawn to scale
R15
Calculate the thickness of the blank to two decimal places.
[4 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Answer ___________________________________
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11
0
7
Explain how increased accuracy within production processes can reduce waste and
improve efficiency.
[6 marks]
Do not write
outside the
box
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
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12
0
8
Give two reasons why X-ray testing would be a suitable post-production test for a
welded bridge structure.
[2 marks]
Do not write
outside the
box
Reason 1 _________________________________________________________________________
___________________________________________________________________________________
Reason 2 _________________________________________________________________________
___________________________________________________________________________________
0
9
____
2
Explain how developments in manufacturing techniques affected the work of
Bauhaus designers.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
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1
0
Give four effective uses of project management systems that can benefit designers
and manufacturers.
[4 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
3 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
4 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
1
1
____
4
Define what is meant by an iterative design process.
[2 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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14
1
2
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Figure 10 shows drawing views of a zinc alloy component.
Figure 10
B
B
Section B – B
Describe the pre-production procedures a manufacturer would go through to prepare
for die casting 100 000 copies of the component.
In your answer you should refer to:
design
modifications
preparation
how a manufacturer would use computer modelling for quality assurance (QA).
[6 marks]
machinery
___________________________________________________________________________________
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___________________________________________________________________________________
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1
3
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Figures 11 and 12 show a cantilever chair component formed from laminated
veneers.
Figure 11
Figure 12
All dimensions in mm
Not drawn to scale
340.00
0
100°
R4
0.0
0
R
90
.0
330.00
290.00
90°
90°
R
385.00
3D CAD representation
90
.0
0
2D side view
When forming the chair an allowance of 5% must be added to the length.
Calculate the length of laminated veneer (represented by the red line) needed to
form the chair in a single piece to the nearest mm.
For this calculation you should ignore material thickness.
The component is constructed from straight lines and circular arcs.
[3 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Answer ___________________________________
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16
1 4
.
1
Analyse and evaluate the success of two portable MP3 players using the data shown
in the Product Life Cycle (PLC) graph in Figure 13.
[6 marks]
Figure 13
MP3 player B
50
40
Sales
(millions) 30
20
10
MP3 player A
13
20
12
20
11
20
10
20
09
20
20
08
07
20
06
20
05
20
04
20
03
20
02
20
20
01
0
Year
___________________________________________________________________________________
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17
1 4
.
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2
Explain how a manufacturer of music players can prevent the decline in sales of
their product.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
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1
5
Give two reasons why companies conform to International Standards Organisation
(ISO) standards.
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
END OF QUESTIONS
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22
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box
(23)
G/Jun20/7552/2
24
Do not write
outside the
box
There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet. This booklet is published after
each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful
and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team.
Copyright © 2020 AQA and its licensors. All rights reserved.
(24)
(206A7552/2)
G/Jun20/7552/2
Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 1
Technical Principles
Time allowed: 2 hours 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
1
2
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.

3–4
5
6
7–8
9–11
12
13–14
15
Information

Mark
The marks for questions are shown in brackets.
The maximum mark for this paper is 120.
16–18
19–20
21
22–23
TOTAL
(JUN217552101)
G/TI/Jun21/E6
7552/1
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Answer all questions in the spaces provided.
0
1
Identify each of the following Control of Substances Hazardous to Health (COSHH)
symbols.
[3 marks]
_________________________________________________
_________________________________________________
_________________________________________________
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0
2
Describe the process of die cutting.
[6 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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0
3
Figure 1 and Figure 2 show freestanding signage.
Figure 1
Sign type
Method of manufacture
Material
Style of hinge
Figure 2
Figure 1
Figure 2
Safety sign
Novelty sign
Injection moulded
Vacuum formed
High density polyethylene
(HDPE)
High impact polystyrene
(HIPS)
Integrated hinge
Riveted hinge
Compare and evaluate the suitability of the manufacturing processes used for each
sign.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
0
4
Give three reasons why a product may have an anodised finish.
[3 marks]
Reason 1 _________________________________________________________________________
___________________________________________________________________________________
Reason 2 _________________________________________________________________________
___________________________________________________________________________________
Reason 3 _________________________________________________________________________
___________________________________________________________________________________
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0
Calculate the area of the face shown in the packaging in Figure 3.
5
[6 marks]
Figure 3
r7.5
r3
126
29
Euroslot cut out dimensions using
straight lines and semicircles
145
Not drawn to scale
All dimensions in mm
___________________________________________________________________________________
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___________________________________________________________________________________
Answer ____________________________ mm2
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6
Discuss the advantages and disadvantages of buying a bespoke item of furniture for
the home.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
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0
7
The costs of manufacturing a component using two different methods are shown in
the tables below.
Calculate the total number of products that could be produced by 3D printing before
injection moulding becomes a more cost-effective method of manufacture.
[4 marks]
3D printing
Material cost per unit
30p
Injection moulding
Cost of mould
Material cost per unit
£8000
3p
___________________________________________________________________________________
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___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Answer ____________________________
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Explain why injection moulding is not a suitable manufacturing method for large
products.
[6 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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9
Name the following metal stock forms.
[2 marks]
_________________________________________________
_________________________________________________
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1
0
Compare and evaluate the suitability of the materials used to manufacture the
dishwasher detergent packaging shown in Figure 4 and Figure 5.
[6 marks]
Figure 4
Figure 5
Lactide
Individual tablet
with foil-based packaging
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1
1
Figure 6 and Figure 7 show mug holders.
Figure 6
Figure 7
Figure 6
Figure 7
Beech
Low-carbon steel
CNC turned
Cold formed
Fabricated and glued
Fabricated and welded
Material
Method of Manufacture
Method of Assembly
Analyse and evaluate the two mug holders.
In your answer you should refer to:


the suitability of the materials used
the manufacturing methods used.
[12 marks]
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
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___________________________________________________________________________________
___________________________________________________________________________________
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1
2
A hemispherical bowl is to be turned on a lathe from the prepared wooden cylinder
in Figure 8. A flat base would be added after turning.
[6 marks]
Figure 8
140
Ø218
Not drawn to scale
All dimensions in mm
Calculate the percentage waste created if the turned bowl has an external diameter
of 218 mm and a wall thickness of 10 mm.
4
Formula: volume of a sphere V = 3 πr 3
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Percentage waste ____________________________ %
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1
3
Describe how modular/cell production has improved efficiency in high-volume
manufacture.
[9 marks]
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1
4
Explain how the inclusion of smart materials in electronic products aids the
end-of-life disassembly.
[4 marks]
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13
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1
5
Table 1 shows the number of aluminium offcuts stored for use in a workshop.
Table 1
Length of offcut (mm)
x < 30
24
x < 40
27
x < 50
26
v
50
12
v
40
x < 20
v
30
4
v
20
x < 10
v
10
v
0
Frequency
x < 60
7
Cumulative Frequency
Lengths that are longer than 37 mm are needed for a particular job.
Complete the cumulative frequency curve and then estimate the number of lengths
of aluminium over 37 mm long.
[4 marks]
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100
90
80
70
60
Cumulative
frequency
50
40
30
20
10
0
0
10
20
30
40
Length in mm
50
60
Number of lengths over 37 mm ____________________________
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1
6
Explain why manufacturers of flat-pack furniture provide customers with exploded
diagrams.
[6 marks]
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1
7
Define the term ‘composite’.
[2 marks]
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1
8
Describe the role of a master production schedule (MPS) as part of production,
planning and control networking.
[6 marks]
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1
9
Name a specific application for each of the following composites:
[3 marks]
Aluminium composite board _______________________________________________________
___________________________________________________________________________________
Glass reinforced polymer (GRP) ___________________________________________________
___________________________________________________________________________________
Glulam ___________________________________________________________________________
___________________________________________________________________________________
2
0
Define the following material properties:
[2 marks]
Thermal conductivity ______________________________________________________________
___________________________________________________________________________________
Toughness _______________________________________________________________________
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2
1
Explain the manufacturing processes that would be used to manufacture the
stainless steel ruler shown in Figure 9.
[6 marks]
Figure 9
Stainless steel ruler
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2
2
Explain why cedar is commonly used in outdoor cladding such as the example
shown in Figure 10.
[6 marks]
Figure 10
Cedar clad property
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2
3
Explain why high density polyethylene (HDPE) and thermoplastic elastomer (TPE)
are suitable materials for the manufacture of the polymer clothes peg shown in
Figure 11.
[6 marks]
Figure 11
TPE inserts
HDPE body
Polymer clothes peg
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END OF QUESTIONS
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Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet. This booklet is published after
each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and
AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team.
Copyright © 2021 AQA and its licensors. All rights reserved.
(32)
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Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 2
Designing and Making Principles
Time allowed: 1 hour 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
1
2
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.
Information



Mark
The marks for questions are shown in brackets.
The maximum mark for this paper is 80.
There are 30 marks for Section A and 50 marks for Section B.
3
4
5
6
7
8
9
10
11
12
13
14
15
TOTAL
(JUN217552201)
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Section A – Product Analysis
Answer all questions in this section.
0
1
Figures 1 and 2 show two step ladders.
Figure 1
Wooden step ladder
Main manufacture
process
Joining methods
Applied finish
Figure 2
Aluminium step ladder
Figure 1
Figure 2
Wood wastage techniques
Aluminium extrusion
Adhesive and screws
Nuts and bolts
Clear varnish
Self-finishing
Compare and evaluate the two step ladders shown.
In your answer you should refer to:
design
safety
ergonomic
(02)
factors.
[12 marks]
G/Jun21/7552/2
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Figure 3 shows a 2D view of a 2 metre step ladder.
Figure 3
Not drawn to scale
2000
15°
300
The step ladder is angled at 15 degrees from the vertical wall and stands on a
horizontal floor.
The ladder has 5 steps with even spacing of 300 mm between each step.
The first step is 300 mm from the bottom of the ladder.
Calculate the vertical height of the 5th step from the floor to the nearest mm.
[4 marks]
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Answer ___________________________________ mm
0
3
____
4
Describe the testing procedures required during product development to ensure a
step ladder is safe for sale.
[6 marks]
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Figure 4 shows a range of safety instructions used on a loft ladder.
4
Figure 4
1
2
Use in accordance with the
manufacturer’s instructions.
Never use damaged
equipment.
3
Ensure installation is in
accordance with the
manufacturer’s instructions.
4
WARNING!
ENSURE ALL LOCKS ARE
ENGAGED PRIOR TO USE.
Ensure both feet of ladder
are firm and level.
5
TOP STOPS MUST BE DOWN
AGAINST LOFT GUIDES.
6
VERTICAL
CLEARANCE
HORIZONTAL
CLEARANCE
Check clearance at top and
access to the loft.
7
Keep a secure grip at all
times.
8
Never have more than one
person on a ladder at a time.
Avoid electrical hazards.
Analyse and evaluate how the images shown in Figure 4 effectively communicate
the safety instructions to the user.
[6 marks]
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0
5
____
6
State two specific forms of anthropometric data used in the development of a
step ladder.
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
Turn over for Section B
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Section B – Commercial Manufacture
Answer all questions in this section.
0
6
State the two types of nutrient associated with the circular economy.
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
0
7
____
2
Outline how a manufacturer could personalise a mass-produced product to an
individual customer’s requirements.
[6 marks]
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9
0
8
Explain the benefits of using laser scanning for quality control in mass production.
[6 marks]
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Turn over for the next question
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0
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Figure 5 shows some packaging for biscuits.
Figure 5
Component
Material
Box
Carton board
Polymer wrapper
Biscuit tray
Low density polyethylene (LDPE) film
Polyethylene terephthalate (PET)
Analyse and evaluate the environmental impact of the three packaging components
shown.
In your answer you should refer to:

raw
materials

product
manufacture

disposal/end
of life.
[12 marks]
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1
0
State two reasons why a barcode is used on packaging.
____
12
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
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Figure 6 represents the coverage of different printing ink colours on some
packaging.
1
Figure 6
Black
Cyan
Yellow
30°
60°
135°
135°
Magenta
Table 1 shows the cost of different cartridges and the ink areas each cartridge can
cover.
Table 1
Colour
Cartridge cost (£)
Surface coverage
per cartridge (m2)
Black
10.50
8 m2
Cyan
16.00
12 m2
Magenta
16.00
12 m2
Yellow
16.00
12 m2
The packaging has a surface area of 0.6 m2
1 1
.
1
Show that five yellow cartridges will be needed for 1000 packages.
[3 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
1 1
.
2
Calculate the total cost of full cartridges needed for 1000 packages.
[3 marks]
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Answer £ ___________________________________
Turn over for the next question
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14
1 2
.
1
Define the purpose of the RoHS directive.
Do not write
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box
[2 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
1 2
.
2
State two specific materials that are restricted under the RoHS directive.
[2 marks]
1 _________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
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15
1
3
Identify the following labels and state what they mean.
Figure 7
Do not write
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[4 marks]
Figure 8
Figure 7 __________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Figure 8 __________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Turn over for the next question
Turn over 8
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16
1
4
Outline the impact of the work of Charles and Ray Eames on furniture design.
You should refer to specific examples in your answer.
Do not write
outside the
box
[6 marks]
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17
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5
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Figure 9 shows steel beam supports for a wooden floor.
Give two reasons why an I-beam cross-section is ideal for the main support.
[2 marks]
Figure 9
Steel I-beam
cross-section
1 _________________________________________________________________________________
___________________________________________________________________________________
2 _________________________________________________________________________________
___________________________________________________________________________________
END OF QUESTIONS
(17)
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____
2
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(19)
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20
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Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet.
This booklet is published after each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have
been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact
the Copyright Team.
Copyright © 2021 AQA and its licensors. All rights reserved.
(20)
(216A7552/2)
G/Jun21/7552/2
Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 1
Technical Principles
Time allowed: 2 hours 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
1– 2
3– 4
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.
5
6
7
8–9
10–11
12–13
14–15
Information
16

17

Mark
The marks for questions are shown in brackets.
The maximum mark for this paper is 120.
18
19–20
21–22
TOTAL
(JUN227552101)
G/TI/Jun22/E6
7552/1
2
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Answer all questions in the spaces provided.
0
State three reasons why Precious Metal Clay (PMC) may be used in the
manufacture of a decorative pendant for a necklace.
1
[3 marks]
Reason 1 _________________________________________________________________________
___________________________________________________________________________________
Reason 2 _________________________________________________________________________
___________________________________________________________________________________
Reason 3 _________________________________________________________________________
___________________________________________________________________________________
0
A purple component is to be produced using a pigmented resin.
2
Use the data to calculate the maximum number of these components that could be
produced.
You may assume unlimited supplies of clear resin and magenta pigment.
[4 marks]
Cyan pigment available
10 ml
Single component volume
Ratios for Purple Resin
5965 mm3
Clear Resin
Cyan Pigment
Magenta Pigment
80
4
1
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Answer ____________________________ components
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0
3
Figure 1 shows a low carbon steel shopping basket with a chrome plated finish.
Figure 1
Analyse and evaluate the suitability of the material and finish used for the shopping
basket.
[6 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
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0
4
Explain how rapid prototyping has impacted on traditional manufacture.
[9 marks]
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.
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1
Table 1 shows a series of coordinates used by a laser cutter to produce a
component.
The external and internal cutting paths are shown.
Table 1
External Path
Internal Path
(10,10)
(30,20)
(70,10)
(60,20)
(70,80)
(60,70)
(30,80)
(40,70)
(10,10)
(30,20)
Plot the external and internal paths on the grid below.
[1 mark]
y
90
80
70
60
50
40
30
20
10
0
(06)
0
10
20
30
40
50
60
70
80
90
x
G/Jun22/7552/1
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.
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2
Figure 2 shows the path of a laser cutter used to cut the shape below.
Figure 2
y
90
80
70
Laser cutter path
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
x
Grid spacing in mm
Calculate the shaded area.
[2 marks]
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___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Total shaded area ____________________________ mm2
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0
6
Figure 3 shows the current dimensions of a school desk.
If all existing components are used, calculate how much closer together Bracket A
and Bracket B would be at a new desk height of 720 mm.
Assume that when fully extended the end of each leg is vertically in line with the
bracket on the underside of the desk.
[7 marks]
Figure 3
60°
Bracket B
700
Bracket A
Not drawn to scale
Dimension in mm
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0
7
Explain why galvanising is an appropriate finish for the low carbon steel scaffold
shown in Figure 4.
[6 marks]
Figure 4
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8
State three different stimuli that can cause a change in the property of a smart
material.
[3 marks]
Stimulus 1 ________________________________________________________________________
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Stimulus 2 ________________________________________________________________________
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0
9
Name a specific application for each of the following materials:
[3 marks]
Cellulose acetate _________________________________________________________________
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Fluted polypropylene ______________________________________________________________
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Styrofoam ________________________________________________________________________
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0
Styrofoam and high-density modelling foam are often used in modelling.
Compare and evaluate the suitability of each material for the manufacture of a
block model that represents aesthetic appearance to a potential client.
[6 marks]
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1
Explain why die casting is an appropriate manufacturing method for the model toy
vehicle shown in Figure 5.
[6 marks]
Figure 5
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2
Describe the purpose of the following polymer additives:


fillers
plasticisers.
[2 x 2 marks]
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1
3
Give two reasons why outdoor decking may be pressure treated before use.
[2 marks]
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2 _________________________________________________________________________________
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4
A polymer extrusion process has been used to produce the rigid polyvinyl chloride
(PVC) cable trunking shown in Figure 6.
Describe the main stages of the polymer extrusion process.
[6 marks]
Figure 6
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5
Describe the advantages to a manufacturer of using bought-in components.
[6 marks]
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6
Figure 7 shows an acrylic tube that will have a section cut out on a laser cutter.
The section to be removed is one quarter of the circumference of the tube.
Figure 7
Laser cutter path
r10 on all curved corners
20
20
All dimensions in mm
Length of Cylinder
200 mm
Diameter of Cylinder
75 mm
Cutting Speed
2200 mm per minute
Use the data provided to calculate the time taken to cut the path shown on the
acrylic tube.
[6 marks]
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Total time taken in seconds ____________________________
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1
7
Figure 8 and Figure 9 show two novelty moneyboxes, each with a slot for coins
located at the top.
Figure 8
Figure 9
Blow moulded, low density
polyethylene (LDPE) moneybox
Injection moulded,
polymethylmethacrylate (PMMA)
moneybox
Analyse and evaluate the suitability of the materials and manufacturing methods
used for each of the moneyboxes shown.
[12 marks]
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8
Describe and explain the stages that timber undergoes from felling through to the
creation of the planed square edge (PSE) stock form.
[6 marks]
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Describe two ways that a jig can be used to improve accuracy in manufacture.
[2 x 2 marks]
1 _________________________________________________________________________________
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2
0
Justify why Finite Element Analysis (FEA) may be used to improve efficiency during
product development.
[6 marks]
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1
Explain why tungsten carbide is an appropriate material for the manufacture of a
centre lathe cutting tool.
[6 marks]
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2
Outline how and why a company would use social media to market their product.
[6 marks]
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Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet.
This booklet is published after each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have
been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact
the Copyright Team.
Copyright © 2022 AQA and its licensors. All rights reserved.
(32)
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Please write clearly in block capitals.
Centre number
Candidate number
Surname
________________________________________________________________________
Forename(s)
________________________________________________________________________
Candidate signature
________________________________________________________________________
I declare this is my own work.
A-level
DESIGN AND TECHNOLOGY:
PRODUCT DESIGN
Paper 2
Designing and Making Principles
Time allowed: 1 hour 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
 normal writing and drawing instruments
 a scientific calculator.
Question
1
2–3
Instructions






Use black ink or black ball-point pen. Use pencil only for drawing.
Fill in the boxes at the top of this page.
Answer all questions.
You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
Do all rough work in this book. Cross through any work you do not want
to be marked.
4
5
6
7
8
9–10
11
12
Information
13

14


Mark
The marks for questions are shown in brackets.
The maximum mark for this paper is 80.
There are 30 marks for Section A and 50 marks for Section B.
15
16
17
TOTAL
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Section A – Product Analysis
Answer all questions in this section.
0
1
Figures 1 and 2 show two screwdrivers.
Figure 1
Figure 2
Jeweller’s screwdriver
General purpose screwdriver
Figure 1
Figure 2
Handle material(s)
Aluminium
Thermoplastic and elastomer
Handle formed by
Casting
Injection moulding
Screwdriver tip
Fixed tip
Interchangeable magnetic attachment
Compare the two screwdrivers shown.
In your answer you should refer to:
ergonomics
material
product
suitability
function.
[12 marks]
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2
Explain how different prototyping methods may be used in the development of a
screwdriver handle.
[4 marks]
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3
A screwdriver handle has a volume of 55 000 mm3
The handle is formed from two materials:
Material
Density
Percentage of handle
A
1.4 g/cm3
85%
B
1.1 g/cm3
15%
Calculate the mass of the handle in grams.
[4 marks]
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Answer ___________________________________ g
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Explain how the Art Deco design style was influenced by:
historical
design styles
socio-economic
factors.
[6 marks]
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Outline the concept of eco-labelling and the impact on customer buying preferences.
[4 marks]
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Section B – Commercial Manufacture
Answer all questions in this section.
0
Table 1 shows sales of new vehicles from 2016–2019
6
Plot the data shown in the table to compare % sales of each fuel type from
2016–2019
[4 marks]
Table 1
Year
Petrol
Diesel
Electric Vehicles (all types)
Total Sales
2016
1 319 423
1 292 496
80 781
2 692 700
2017
1 371 924
1 067 052
101 624
2 540 600
2018
1 491 273
733 801
142 026
2 367 100
2019
1 502 215
623 997
184 888
2 311 100
100
90
80
70
60
50
40
30
20
10
0
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Discuss the issues associated with the development of electric vehicles.
[6 marks]
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8
Fully dimension the drawing shown in Figure 3 to minimise dimensional
inaccuracies.
Use the 5 mm grid and the datum labelled in red for your task.
[4 marks]
Figure 3
____
4
Datum
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Outline the ways a design team can reduce the time from idea conception to
product release.
[6 marks]
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1
0
State four of Dieter Rams’ principles of good design.
[4 marks]
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3 _________________________________________________________________________________
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4 _________________________________________________________________________________
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Explain why utility furniture was introduced after the Second World War.
[4 marks]
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1
2
____
4
State two stages found on a product life cycle graph.
[2 marks]
1 _________________________________________________________________________________
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2 _________________________________________________________________________________
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Figures 4 and 5 show two different drawing types.
State the drawing type used in each figure.
[2 marks]
Figure 5
Figure 4
Plan view
Front view
Side view
Figure 4 __________________________________________________________________________
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Figure 5 __________________________________________________________________________
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1
4
____
2
Name two primary research methods.
[2 marks]
1 _________________________________________________________________________________
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2 _________________________________________________________________________________
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1
5
Figures 6 and 7 show two mobility aids used to increase stability when standing
and walking.
Figure 7
Figure 6
Frame material
Braking
Height adjustment
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Figure 6
Figure 7
Aluminium tube
Aluminium casting
None
Cable brakes with lever
Telescopic tube and press button
None
Compare the suitability of the mobility aids for use around the home and garden.
[6 marks]
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Figure 8 shows a water pump used in an isolated village.
Figure 8
Feature
Power
Fabrication
Description
Hand-operated mechanical pump
Standardised nuts and bolts
Material
Low-carbon steel sheet
Design
Open-sourced
Finish
Galvanising
Analyse and evaluate the suitability of the water pump design for this isolated village.
[6 marks]
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1
7
____
6
Explain the impact of a product recall on a manufacturer of electrical goods.
[4 marks]
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END OF QUESTIONS
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There are no questions printed on this page
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Copyright information
For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet. This booklet is published after
each live examination series and is available for free download from www.aqa.org.uk.
Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful
and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team.
Copyright © 2022 AQA and its licensors. All rights reserved.
(20)
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GCE A LEVEL
A602U10-1
O20-A602U10-1
MONDAY, 12 OCTOBER – MORNING
DESIGN AND TECHNOLOGY – A level component 1
Product Design
A 6 0 2U101
01
3 hours
ADDITIONAL MATERIALS
In addition to this paper you will need:
a WJEC pink 16-page answer booklet, a calculator, ruler, pencil and coloured pencils.
INSTRUCTIONS TO CANDIDATES
Use black ink or black ball-point pen.
Answer all questions.
Write your answers in the separate answer booklet provided.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
CJX*(O20-A602U10-1)
2
Answer all questions.
1.
Materials can broadly be classified into groups.
(a)
Provide a definition of each of the three material classification groups given below:
(i)
(ii)
(iii)
[3]
Synthetic
Natural
Regenerated
(b)
The image shown below is of a car body made from GRP (Glass Reinforced Plastic).
Describe the stages of laminating a GRP product by hand.
[6]
(c)
The bicycle wheel and water bottle shown below are made from anodised aluminium.
Explain what is meant by the term ‘anodising’.
[2]
(d)
Describe in detail four benefits of anodising as a finish for aluminium.
© WJEC CBAC Ltd.
(A602U10-1)
[4]
3
2.
Charts like the one shown below are often used to help manage complex projects.
PROJECT SCHEDULE
Task list
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Task name
12-Feb
27-Jul
12-Feb
27-Jul
SOLUTION DESIGN
SOLUTION DEVELOPMENT
SOLUTION TESTING
3.
Show
(a)
Name the type of chart shown above, then compare and contrast the features of this
project management system with a flowchart.
[5]
(b)
The chart above includes a critical path. Explain the purpose of a critical path.
[2]
A patent is an example of intellectual property protection. Analyse and describe, using examples,
the conditions that must be met if a creation is to be patented.
[6]
© WJEC CBAC Ltd.
(A602U10-1)
Turn over.
A 6 0 2U101
03
Task detail panel
4
4.
Shown below is a student’s design for a modern shelving unit. The shelves will be made from a
natural timber and the triangular frame from a composite board.
22˚
Triangular frame
1500.0mm
b
Bottom shelf
a
Isometric view
Front elevation
The bottom shelf is 1200 mm long. The shelves above decrease in length by 10% at each
height. Calculate the length of each shelf to the nearest mm.
[4]
(Show all calculations.)
(a)
The shelves are 365 mm wide. The natural wood planks used to make them are supplied
in planks measuring 144 mm wide which require edge gluing to make up to 365 mm.
Calculate how many linear metres of wood planks would be needed to make all of the
shelves.
[3]
(Show all calculations.)
(b)
The top shelf is 200 mm from the top of the triangular frame. Each shelf is 18 mm thick and
evenly spaced. Calculate the space between each shelf to the nearest mm.
[2]
(Show all calculations.)
(c)
(d) Calculate the missing dimensions of the triangular frame identified as ‘a’ and ‘b’.
(Show all calculations.)
[4]
The student has decided to increase the overall size of the product. The new bottom shelf
will measure 1500 mm. If the size ratio remains the same, calculate the new height of the
shelving unit to the nearest mm.
[2]
(Show all calculations.)
(e)
© WJEC CBAC Ltd.
(A602U10-1)
5
5.
Promotion is one of the 4 Ps of the marketing mix.
4Ps
Marketing
Mix
Promotion
6.
7.
(a)
Identify the other three Ps.
[3]
(b)
Discuss the various methods that can be used to promote products.
[6]
Health and safety is a key element in any workshop environment.
(a)
Identify and describe each of the steps in a five-stage risk assessment.
[5]
(b)
Describe and justify four ways in which risks can be reduced when using a pillar drill. [4]
Fad products, such as the products shown below have a short Product Life Cycle.
(a)
Draw and label a typical life cycle graph for a fad product.
(b)
Evaluate the ways in which designers can increase the time at which a product is at peak
sales.
[5]
© WJEC CBAC Ltd.
(A602U10-1)
[4]
Turn over.
6
8.
Some manufacturers are using wind power as the main energy source to power their factories.
Analyse the benefits and limitations of wind power for manufacturing.
[9]
9.
Designers use a range of strategies to encourage creative outcomes. Two of these are
morphological analysis and brainstorming. Explain how these strategies promote creativity in
the design process.
[9]
10. Evaluate the impact that Product Champions and Entrepreneurs play in the development and
delivery of innovative products.
[12]
END OF PAPER
© WJEC CBAC Ltd.
(A602U10-1)
7
BLANK PAGE
© WJEC CBAC Ltd.
(A602U10-1)
GCE A LEVEL
A602U10-1
O21-A602U10-1
MONDAY, 11 OCTOBER 2021 – MORNING
DESIGN AND TECHNOLOGY – A level component 1
Product Design
A 6 0 2U101
01
3 hours
ADDITIONAL MATERIALS
In addition to this paper you will need:
a WJEC pink 16-page answer booklet, a calculator, ruler, pencil and coloured pencils.
INSTRUCTIONS TO CANDIDATES
Use black ink or black ball-point pen.
Answer all questions.
Write your answers in the separate answer booklet provided.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
MK*(Y20-A602U10-1)
2
Answer all questions.
1.
Shown below are images of a range of consumer products evident in most homes.
(Images are not to scale.)
(a)
Describe two ways in which the designer can consider ease of maintenance by the
consumer in products such as those shown above.
[4]
(b)
Explain how making a product easy to maintain can help build brand loyalty with the
consumer.
[4]
© WJEC CBAC Ltd.
(A602U10-1)
3
Below is a table showing anthropometric information for hand lengths of boys aged 13-16 in the
United Kingdom.
Hand length (nearest mm)
Number of boys in sample
146-150
7
151-155
10
156-160
13
161-165
18
166-170
36
171-175
79
176-180
98
181-185
79
186-190
36
191-195
18
196-200
13
201-205
10
206-210
7
A 6 0 2U101
03
2.
Calculate the range of hand lengths that would need to be included to cover boys
from the 5th to the 95th percentile.
(Show all calculations.)
[3]
(a)
(i)
(ii)
Gloves will be made from a material that could stretch 15 mm in hand length.
Calculate the maximum sample that could be accommodated for a single glove as
a percentage.
(Show all calculations. State your answer to the nearest whole number.)
[3]
(b)
Describe the relationship between anthropometric data and ergonomic design.
(c)
Explain where it would be appropriate to use the data for the 5th percentile and 95th
percentile when designing products.
[2]
(d)
Discuss the importance to the designer of applying ergonomic principles when designing
a wireless computer mouse.
[4]
© WJEC CBAC Ltd.
(A602U10-1)
[2]
Turn over.
4
3.
The image below shows a cylinder head for a motorcycle.
(a)
Describe in detail the sequences of high pressure die casting used to produce the cylinder
head shown above.
[6]
(b)
Explain why sand casting is suitable for one-off or very low volume components.
© WJEC CBAC Ltd.
(A602U10-1)
[2]
5
4.
The table below shows the densities of metals commonly used for jewellery.
Metal
Density (g/mm3)
Gold
0.01932
Platinum
0.02415
Silver
0.01049
Pewter
0.00728
Strap
m
m
40
3mm
Pendant
m
40
m
Pendant dimensions 40 mm, 40 mm, 3 mm
(a)
(i)
The pendant shown above is produced in silver and pewter. Calculate the difference
in weight.
(Show all calculations.)
[4]
(ii)
When casting the jewellery in pewter 3 in every 100 fail to pour correctly and
2 in every 100 tarnish because of the mould properties. These outcomes are
independent of one another. State the probability of one cast suffering from both of
the issues.
[1]
A manufacturer has decided to laser cut the pendants from a sheet of aluminium. Calculate
the maximum number of pendants that can be laser cut from a sheet 0.5 m × 0.7 m.
(Show all calculations.)
[4]
(b)
(c)
Qualitative testing and quantitative testing must be considered when selecting materials
and processes for the design and manufacture of jewellery products.
Explain what you understand by both qualitative testing and quantitative testing in relation
to jewellery products.
[4]
© WJEC CBAC Ltd.
(A602U10-1)
Turn over.
6
5.
6.
The home cinema projector shown below has been designed considering both the needs and
wants of the target market.
(a)
Describe the importance of using a specification when designing a product such as the
home cinema projector.
[5]
(b)
Explain the importance of a ‘User Centred Design’ approach to investigating design
opportunities for products such as the home cinema projector.
[5]
Every year a number of innovative products are brought to market.
Explain why innovation is important to the success of commercial products.
© WJEC CBAC Ltd.
(A602U10-1)
[5]
7
7.
8.
Study the image of the chair shown below which has been cut using a CNC router.
(a)
Analyse the benefits of using a CNC router to cut out the chair frame.
[6]
(b)
Evaluate the environmental impact of using CNC machines to produce commercial
products.
[6]
Client profiles are used by designers when developing design proposals.
Describe the type of information that is gathered when creating a client profile and analyse why
this information is useful to designers.
[9]
9.
Explain how developments in modern material technology have had an impact on the design,
manufacture and use of modern sports equipment.
[9]
10. Evaluate the ways in which a product designer can reduce the environmental impact of their
products at each stage of the product life cycle.
[12]
END OF PAPER
© WJEC CBAC Ltd.
(A602U10-1)
Centre
Number
Surname
Candidate
Number
2
Other Names
GCE AS – NEW
B602U10-1
S18-B602U10-1
DESIGN AND TECHNOLOGY – AS component 1
Product design
MONDAY, 14 MAY 2018 – AFTERNOON
2 hours 30 minutes
For Examiner’s use only
Maximum
Mark
1.
8
2.
14
3.
8
4.
13
5.
10
6.
5
7.
12
ADDITIONAL MATERIALS
8.
9
You will need a ruler and a calculator.
9.
9
10.
12
Total
100
INSTRUCTIONS TO CANDIDATES
Mark
Awarded
B 6 0 2U101
01
Question
Use black ink or black ball-point pen.
Write your name, centre number and candidate number in the spaces at the top of this page.
Answer all questions.
Write your answers in the spaces provided in this booklet. Where the space is not sufficient for your
answer, continue at the back of the book, taking care to number the continuation correctly.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
SM*(S18-B602U10-1)
2
Examiner
only
Answer all questions.
1.
Final detail designing is essential for the manufacture of successful products.
(a)
The image below is of a modern flat-pack drawer unit made from high-density chipboard
with a veneer surface.
Describe two properties of high-density chipboard that make it appropriate for the drawer
unit.
Property 1:
[2]
Property 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
3
(b)
Knock-down fittings, such as the examples shown below are commonly used in the
construction of flat-pack furniture.
Examiner
only
(c)
Explain one feature of effective detail designing.
© WJEC CBAC Ltd.
(B602U10-1)
[2]
Turn over.
B 6 0 2U101
03
Explain one advantage of using knock-down fittings in the flat-pack drawer unit for the
consumer.
[2]
4
2.
Qualitative and quantitative testing is critical to the eventual success of the final product.
With reference to the design and production of the car shown above.
(a)
Explain one qualitative test that the designer will carry out during the development of the
car.
[2]
(b)
Explain one quantitative test that the manufacturer will carry out during the development
of the car.
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
5
(c)
Examiner
only
Explain two reasons why manufacturers use their unique logo on products.
Reason 1:
[2]
Reason 2:
[2]
The images below show a simple plant pot manufactured in polypropylene.
B 6 0 2U101
05
(d)
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
6
(i)
One plant pot costs £1.52 to manufacture. The manufacturer sells the product to the
retailer for £9.99 per pot.
Over a period of one month, the manufacturer makes a profit of £1160.39.
Calculate the number of plant pots that have been supplied to the retailer during this
month.
[2]
Show all calculations.
(ii)
Every time the manufacturer produces 500 or more plant pots the £1.52 per unit
manufacturing cost reduces by 1.5%.
Calculate the gross profit for an order of 8350 plant pots.
Show all calculations.
© WJEC CBAC Ltd.
(B602U10-1)
[4]
Examiner
only
7
3.
The image below is of a modern plug socket with USB connection made from urea formaldehyde.
[4]
B 6 0 2U101
07
(a) The plug socket has been made by the process of injection moulding.
Use notes and diagrams to describe this process.
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
8
(b)
Explain two properties that make urea formaldehyde a suitable material for the modern
plug socket.
Property 1:
[2]
Property 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
9
The external light product shown below features an acrylic dome with a rim.
(a)
Explain why acrylic is a suitable material for this product.
[2]
B 6 0 2U101
09
4.
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
10
The diagrams show a 2D working drawing (all dimensions in mm) and a 3D CAD drawing
of the product. (Both Not to Scale)
All dimensions in mm
0
external radius of dome
30
(b)
cross section
0
35
external radius of rim
© WJEC CBAC Ltd.
(B602U10-1)
6
Examiner
only
11
Examiner
only
2
The formula for calculating the surface area of a hemisphere is A = 2πr .
Using the formula, calculate the surface area of the dome and the rim in m2 to 3
[5]
decimal places. Show all calculations.
(ii)
The formula V =
4
3
B 6 0 2U101
11
(i)
× π × r3 is used to calculate the volume of a sphere.
Calculate the volume of material used to make the acrylic dome without the rim in
mm3.
[4]
(Rounded to a whole number.)
Show all calculations.
(c)
Describe why vacuum forming could be used to manufacture the acrylic dome.
© WJEC CBAC Ltd.
(B602U10-1)
[2]
Turn over.
12
5.
(a)
Explain the meaning of the term ‘Just in Time’ manufacturing (JIT).
(b)
The design of the packaging has a significant impact on the success of a product.
(i)
[2]
Describe two reasons why a company would conduct consumer market research
when developing packaging for a new mobile phone.
Reason 1:
[2]
Reason 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
13
(ii)
Smart materials such as thermochromic inks are widely used in the packaging of
food and drink products such as the drinks cans below.
Describe two advantages of using thermochromic inks in product packaging to the
consumer.
Advantage 1:
[2]
Advantage 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
14
6.
Examiner
only
The CE mark is often found on packaging such as the LED Bulb shown below.
Explain how the CE mark protects the consumer when purchasing a LED bulb.
© WJEC CBAC Ltd.
(B602U10-1)
[5]
15
7.
Manufacturers often use standardised parts when manufacturing and assembling products such
as the bike shown below.
(a)
Analyse the advantages and disadvantages of using standardised parts in the design and
production of a mountain bike to the manufacturer.
[6]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
16
(b)
Evaluate how the use of stock forms of hardwoods, softwoods and manufactured boards
affect the manufacturer and the consumer.
[6]
Typical wooden product made from stock forms
© WJEC CBAC Ltd.
(B602U10-1)
Stock forms available from supplier
Examiner
only
17
8.
Quality control and quality assurance are critical to ensure the successful manufacture and sale
of a new product.
Analyse the role that quality control and quality assurance play in the success of a new product,
such as the vacuum cleaner shown.
[9]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
18
9.
Many companies now utilise the benefits of global production when manufacturing products
where different parts, components or materials are sourced internationally.
Evaluate the economic and environmental effects of global production.
© WJEC CBAC Ltd.
(B602U10-1)
[9]
Examiner
only
19
10. Modern sports equipment such as hockey sticks, tennis rackets, cycles and golf clubs are made
using composite materials such as fibreglass, Kevlar and Carbon Fibre Weave.
Describe the advantages and disadvantages of using composite materials in the design of
modern sports equipment.
[12]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
20
Examiner
only
END OF PAPER
© WJEC CBAC Ltd.
(B602U10-1)
21
Examiner
only
For continuation only.
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
22
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
23
BLANK PAGE
© WJEC CBAC Ltd.
(B602U10-1)
Centre
Number
Surname
Candidate
Number
2
Other Names
GCE AS – NEW
B602U10-1
S19-B602U10-1
MONDAY, 13 MAY 2019 – AFTERNOON
DESIGN AND TECHNOLOGY – AS component 1
Product Design
2 hours 30 minutes
For Examiner’s use only
Maximum
Mark
1.
10
2.
14
3.
8
4.
11
5.
10
6.
5
7.
12
ADDITIONAL MATERIALS
8.
9
You will need a ruler and a calculator.
9.
9
10.
12
Total
100
INSTRUCTIONS TO CANDIDATES
Mark
Awarded
B 6 0 2U101
01
Question
Use black ink or black ball-point pen.
Write your name, centre number and candidate number in the spaces at the top of this page.
Answer all questions.
Write your answers in the spaces provided in this booklet. Where the space is not sufficient for your
answer, continue at the back of the book, taking care to number the continuation correctly.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
JD*(S19-B602U10-1)
2
Examiner
only
Answer all questions.
1.
The image below shows a mass produced television remote control made from ABS [Acrylonitrile
Butadiene Styrene].
(a)
Describe two properties of ABS (Acrylonitrile Butadiene Styrene) plastic that make it
appropriate for the remote control.
Property 1:
[2]
Property 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
3
(b)
Examiner
only
Effective aesthetic qualities are critical when designing products.
Explain two aesthetic qualities to be considered when designing the remote control.
Aesthetic quality 1:
[2]
Aesthetic quality 2:
[2]
(c)
Explain one advantage of using rapid prototyping when designing the television remote
control.
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
B 6 0 2U101
03
Rapid prototyping is essential when designing successful products.
4
BLANK PAGE
© WJEC CBAC Ltd.
(B602U10-1)
5
2.
Examiner
only
Fitness for purpose is critical to the eventual success of a final product.
With reference to the design and production of the car shown answer the following.
(a)
Explain two factors that the manufacturer must consider to ensure fitness for purpose
and eventual success of the car.
[2]
Factor 2:
[2]
B 6 0 2U101
05
Factor 1:
(b)
Explain one example of primary processing undertaken during the manufacture of a car.
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
6
(c)
The graph and table shows the top five car manufacturers’ monthly sales for January
2018 to June 2018.
Top Five Car Brand Cumulative Monthly Sales
200000
189966
180000
160000
Sales
140000
120000
100000
101689
80000
60000
40000
36774
20000
0
79543
66867
65776
Jan
Feb
Mar
Apr
May
Jun
Top five brands
Jan
2018
Feb
2018
Mar
2018
Apr
2018
May
2018
Jun
2018
Manufacturer A
19,654
12,046
50,257
20,114
21,136
22,334
Manufacturer B
12,579
7,036
37,843
14,607
18,097
23,224
Manufacturer C
12,652
4,860
37,023
11,214
13,983
18,218
Manufacturer D
9,000
6,744
31,649
9,078
12,940
22,985
Manufacturer E
11,891
6,088
33,194
11,854
13,387
14,928
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
7
(i)
Calculate the mean (average) number of car sales during the 6 month period.
[2]
Examiner
only
Show all workings.
(ii)
Calculate the percentage share Manufacturer B has of the total sales of the top
five brands.
[2]
B 6 0 2U101
07
Show all workings.
(iii)
In January, February, March and April 2019 there has been a 4% increase in car
sales.
In May and June there has been a 8% increase in car sales.
Calculate the new mean (average) for January to June 2019 rounded to the nearest
whole number.
[4]
Show all workings.
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
8
3.
Study the image below showing a decorative modern USB powered lamp.
(a)
Use notes and diagrams to describe how the lamp body has been made from plywood
using the laminating and steam bending process.
[4]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
9
(b)
Examiner
only
Explain two properties that make plywood suitable for this product.
[2]
Property 2:
[2]
B 6 0 2U101
09
Property 1:
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
10
4.
The metal corner brackets pictured below are designed to strengthen corner joints in wooden
structures.
(a)
Explain why mild steel is a suitable material for these corner brackets.
© WJEC CBAC Ltd.
(B602U10-1)
[2]
Examiner
only
11
(b)
(i)
Using the information on the diagram below, calculate the length of side A of a
simple corner bracket.
[3]
Examiner
only
Show all workings.
57
°
8
side A
17
°
B 6 0 2U101
11
90
150
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
12
The diagrams show a 2D working drawing and a 3D CAD drawing of the simple corner
bracket with drilled holes for screw fixing.
(Drawings not to scale)
(i)
Ø8
150
All dimensions are in mm
48
Ø8
Ø8
(ii) Calculate the external total surface area of the bracket in mm2.
Round your answer to a whole number.
Show all workings.
© WJEC CBAC Ltd.
(B602U10-1)
[4]
Examiner
only
13
(c)
Describe why the mild steel bracket would need to be galvanised if it were to be used in
an outdoor wooden product.
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
14
5.
(a)
Explain the meaning of the term ‘Reverse Engineering’.
(b)
The bracelets below are made from aluminium and have been anodised.
[2]
Describe two reasons why anodising is a suitable finish for this product.
Reason 1:
[2]
Reason 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
15
(c)
Examiner
only
Products such as the soft drink cans shown in the image are mass-produced.
Describe two advantages of using mass production when manufacturing the soft drinks
can.
Advantage 1:
[2]
Advantage 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
16
6.
Explain how conducting effective risk assessments can protect employees in factory situations
like the one shown below.
[5]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
17
7.
Cardboard furniture can be used in emergency and disaster relief situations where homes are
damaged and destroyed.
(a)
Analyse and discuss the use of corrugated cardboard furniture in this context.
© WJEC CBAC Ltd.
(B602U10-1)
[6]
Turn over.
Examiner
only
18
(b)
Evaluate how the use of a laser cutter has benefited the manufacturer of flat packed selfassembly furniture such as the product below.
[6]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
19
8.
Ergonomics and anthropometrics play an important part in the successful development of an
office chair such as the one below.
Analyse the role ergonomics and anthropometrics play in the successful development and
design of an office chair.
[9]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
20
9.
The life cycle of a mobile phone can impact on the environment in many different ways.
Using a life cycle analysis, evaluate the environmental impact of the mobile phone shown
above.
[9]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
21
10. Smart materials have had a significant impact in the development of many modern products.
Define the term ‘smart material’ and using specific products, describe the contribution of the
named smart material.
[12]
END OF PAPER
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
22
Examiner
only
For continuation only.
© WJEC CBAC Ltd.
(B602U10-1)
23
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
24
Examiner
only
For continuation only.
© WJEC CBAC Ltd.
(B602U10-1)
GCE AS – NEW
B602U20-1
DESIGN AND TECHNOLOGY
Component 2
Contextual Challenge
1 JUNE 2018
Duration approximately 40 hours
AVAILABLE ONLY TO CANDIDATES ENTERING THE WJEC-EDUQAS
QUALIFICATION ACCREDITED BY OFQUAL
A defining feature of design and technological activity is that it is context dependent, as are the
outcomes of such activities.
The role of the contextual challenge is to provide an external stimulus for learners, from which they
will explore and clarify design problems and opportunities. This will lead to the development of their
own design briefs, which will inform and direct their designing and making activities.
Learners will be assessed on their ability to analyse and respond to contexts, rather than their
knowledge of specific contextual areas.
Learners are required to select one of the following contexts as the basis of their design and make
task:
•
Interpret time as a start point for the development of different contextual challenges.
Learners are expected to use ‘time’ as a starting point to design a new product or redesign a
product from the past that meet the needs of modern society.
•
“Cradle to grave” and “the circular economy” are important concepts for modern designers. Use
these principles to inspire the creation of a product.
Learners are expected to identify a product and consider how the circular economy and its
principles could inspire the development of a product.
•
As people lead increasingly busy lives or find some situations or activities a challenge, design a
product that would give them a ‘helping hand.’
Learners are expected to develop a product that supports a specific target customer in a named
activity or situation.
Centres are reminded of the need to review the guidance on pages 29 - 32 of the specification.
© WJEC CBAC Ltd.
CJ*(S19-B602U20-1)
GCE A LEVEL – NEW
A602U10-1
S19-A602U10-1
FRIDAY, 7 JUNE 2019 – MORNING
DESIGN AND TECHNOLOGY – A level component 1
Product Design
A 6 0 2U101
01
3 hours
ADDITIONAL MATERIALS
In addition to this paper you will need:
a WJEC pink 16-page answer booklet, a calculator, ruler, pencil and coloured pencils.
INSTRUCTIONS TO CANDIDATES
Use black ink or black ball-point pen.
Answer all questions.
Write your answers in the separate answer booklet provided.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
SM*(S19-A602U10-1)
2
Answer all questions.
1.
Below is a picture of a racing drone. It has been made from a composite material.
(a)
Name a composite material that could have been used.
[1]
(b)
Explain why this composite is a suitable choice of material for use in this application. [3]
(c)
State the name of the quality assurance mark that would be displayed on the product to
show that it has passed stringent standard safety tests for use within the UK.
[1]
(d)
Products that are certified by the British Standards Institute (BSI) have passed specific
tests before being available to the consumer.
Describe a test that the drone would need to pass before being made available to the
consumer.
[3]
© WJEC CBAC Ltd.
(A602U10-1)
3
2.
The 3D component shown below (fig. 1) is to be printed on a standard desktop 3D printer using
a reel of filament (fig. 2). All dimensions are in mm.
120
25
75
Ø30
A 6 0 2U101
03
fig. 1 (3D component to be printed)
fig. 2 (filament reel for a 3D printer)
(a)
(i) Calculate the overall volume of the component in fig. 1 using the sizes provided.
Show all calculations.
[3]
(ii)
The component is to be printed at 10 % density (including surface area). Calculate
the volume based on this 10 % density.
[1]
(iii)
If 1 cm of filament prints 125 mm³, calculate how many centimetres of filament will
be needed to complete 4 of these prints. Show all calculations.
[2]
(b)
The manufacturer requires a logo to be spray-painted onto the component for modelling
purposes. Explain how the use of a template would be beneficial.
[2]
(c)
Describe one advantage of producing the component shown in fig. 1 on a 3D printer,
rather than producing it by hand.
[2]
(d)
Discuss the environmental impact of using plastic material for pre-production models. [4]
© WJEC CBAC Ltd.
(A602U10-1)
Turn over.
4
3.
4.
The outer casing of the bluetooth headphones shown below is made from a thermoplastic and
has been injection moulded.
(a)
Describe the sequence of steps used in the injection moulding process.
[4]
(b)
Explain in detail why moulds for injection moulding are often made from steel.
[4]
Cell production systems are typically used when manufacturing consumer electronics such as
e-readers.
(a)
Describe two benefits of cell production to the manufacturer.
[4]
A manufacturer pays production staff £15.32 per hour, and the cell production manager
£17.32 per hour. There are 6 people in the production team (which includes the manager)
and they each work an 8 hour shift. It takes 3 shifts for the production cell to complete
their specified job. Work out how much it costs to pay the whole workforce for this specific
job.
Show all calculations.
[4]
(b)
(c)
(i)
The workforce completed the job and are eligible for a 3.7% pay bonus. Work out
how much extra money each member of the team would be paid, including the cell
production manager.
Show all calculations.
[4]
(ii)
Calculate how much more the cell production manager will be paid after the bonus
in comparison to the cell production staff. Show your answer as a percentage. [1]
© WJEC CBAC Ltd.
(A602U10-1)
5
5.
The trampoline shown below has been made from several different materials, each of which was
chosen for their respective working properties.
(a)
Explain the difference between ‘physical properties’ and ‘mechanical properties’.
[2]
(b)
The trampoline frame is made from galvanised mild steel tubing. Describe the mechanical
properties of galvanised mild steel tubing that make it suitable for use in this product. [4]
(c)
The protective sleeves on the upper frame have been made from high density foam.
Describe the properties of high density foam that make it suitable for use in this product.
[4]
6.
Explain how the use of composite boards has impacted on the design and manufacture of
modern flat-pack furniture items.
[5]
7.
Study the image of the hand drill below.
(a)
Analyse the ways in which the designer has considered consumers’ safety in the design
and manufacture of this product.
[6]
(b)
Many manufacturing plants that make consumer goods are investing in renewable energy
to help power their factories. Evaluate the use of solar energy as the main power source
to the manufacturing plant used to make products such as the hand drill.
[6]
© WJEC CBAC Ltd.
(A602U10-1)
Turn over.
6
8.
Many companies are now reconsidering their environmental and sustainable credentials.
When they design products they often ‘design for maintenance’ by the consumer in order to
extend the product’s life.
Using named examples, explain how designers are making products ‘maintainable’ by the
consumer in order to extend the product’s life and analyse how this impacts on the environment.
[9]
9.
Explain how CAD/CAM technologies have facilitated a truly global workforce in terms of the
design and manufacture of products.
[9]
10. Evaluate the advantages and disadvantages to the designer and manufacturer of using
concurrent engineering for either high volume consumer products such as mobile phones or
large complex one-off projects such as a modern ocean liner.
[12]
END OF PAPER
© WJEC CBAC Ltd.
(A602U10-1)
7
BLANK PAGE
© WJEC CBAC Ltd.
(A602U10-1)
Centre
Number
Surname
Candidate
Number
2
First name(s)
GCE AS
B602U10-1
Z22-B602U10-1
MONDAY, 16 MAY 2022 – AFTERNOON
DESIGN AND TECHNOLOGY – AS component 1
Product Design
For Examiner’s use only
ADDITIONAL MATERIALS
You will need a ruler and a calculator.
INSTRUCTIONS TO CANDIDATES
Question
Maximum
Mark
1.
10
2.
15
3.
8
4.
10
5.
7
6.
10
7.
10
8.
9
9.
9
10.
12
Total
100
Mark
Awarded
B 6 0 2U101
01
2 hours 30 minutes
Use black ink or black ball-point pen. Do not use gel pen or correction fluid.
You may use a pencil for graphs and diagrams only.
Write your name, centre number and candidate number in the spaces at the top of this page.
Answer all questions.
Write your answers in the spaces provided in this booklet. If you run out of space, use the
continuation page(s) at the back of the booklet, taking care to number the question(s) correctly
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
JD*(Y20-B602U10-1)
2
Examiner
only
Answer all questions.
1.
The images below show a soap dispenser made from brushed aluminium.
(a)
Describe two properties of brushed aluminium that make it a suitable material for the
soap dispenser.
Property 1:
[2]
Property 2:
[2]
© WJEC CBAC Ltd.
(B602U10-1)
3
(b)
Examiner
only
Describe two different aesthetic features evident in the soap dispenser.
Aesthetic feature 1:
[2]
Aesthetic feature 2:
[2]
Explain one advantage of obtaining a ‘registered design’ to the manufacturer of the
soap dispenser.
[2]
B 6 0 2U101
03
(c)
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
4
2.
Examiner
only
A 3D printed rapid prototype of a can holder is shown below.
(a)
Justify two advantages to the manufacturer of using a 3D printer to rapid prototype the
can holder.
Advantage 1:
[2]
Advantage 2:
[2]
(b)
Name a material used to 3D print the can holder and explain why this material is
suitable.
© WJEC CBAC Ltd.
(B602U10-1)
[2]
5
(c) The diagram below is a front view of the product showing measurements in millimetres.
Diagram not to scale.
Examiner
only
200
R50
B 6 0 2U101
05
R45
100
Calculate the total surface area of the front view of the product.
(Show all workings.)
© WJEC CBAC Ltd.
(B602U10-1)
[4]
Turn over.
6
(d)
The graph below shows the number of annual sales of the can holder over an eight-year
period.
Sales
8000
6300
7000
6000
4300
5000
4000
7000
5000
4600
3020
3000
3000
5020
2000
1000
0
Series 1
0
0
0
Year 1 Year 2 Year 3 Year 4 Year 5
3000
4300
5000 6300 7000
Year 6 Year 7 Year 8
5020 4600 3020
(i) Calculate the mean sales figures between Year 2 and Year 5 inclusive.
(Show all workings.)
(ii)
Calculate the predicted sales figure for Year 9 if sales continue to drop at the
same rate as Year 8.
(Show all workings and round your answer to the nearest whole number.)
© WJEC CBAC Ltd.
(B602U10-1)
[2]
[3]
Examiner
only
7
Study the image below showing a water bottle spray.
Nozzle
(a)
Use notes and diagrams to describe how the water spray nozzle has been
manufactured using injection moulding.
[4]
(b)
Justify why polypropylene is a suitable material for the water spray nozzle.
[4]
B 6 0 2U101
07
3.
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
8
4.
Examiner
only
The cotton reel storage stand below is made from beech.
(a)
(b)
Explain why beech is a suitable material for this product.
(i)
[2]
The cotton reel storage stand costs £2.43 to manufacture. Calculate the selling
cost of the cotton reel storage stand if the manufacturer makes 30% profit.
[2]
(Show all workings.)
© WJEC CBAC Ltd.
(B602U10-1)
9
(ii) Below is a working drawing of the adjustable leg to enable the product to stand.
Calculate the length of the leg labelled A–B.
[4]
(Show all workings.)
Examiner
only
A
330
A
B
B 6 0 2U101
09
65°
B
All dimensions in mm not to scale.
(c)
The manufacturer uses a jig to drill the holes in the beech cotton reel stand. Explain
one advantage to the manufacturer of using a drilling jig.
[2]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
10
5.
Examiner
only
The images below show bookstands made from sheet steel.
(a)
Describe one reason why stamping the shape out of the sheet steel is a suitable
manufacturing method for this product.
[2]
(b)
Explain the benefits of using standard steel stock forms to the manufacturer of the
bookstands.
[5]
© WJEC CBAC Ltd.
(B602U10-1)
11
6.
(a)
Explain what primary and secondary research strategies a designer could use prior to
redesigning the cordless drill shown below.
[5]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
Examiner
only
12
(b)
Analyse how the international standards information used on the drill offers protection to
the consumer.
[5]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
13
7.
Examiner
only
Composite materials such as fibreglass, carbon fibre and kevlar/aramid are used in many
ways on modern bikes.
(a)
Analyse how composite materials are used when manufacturing modern bikes.
(b)
Evaluate the impact of using bought-in or standardised part-assembled components to
the manufacturer of modern bikes.
[5]
© WJEC CBAC Ltd.
(B602U10-1)
[5]
Turn over.
14
8.
Examiner
only
Quality Control (QC) and Quality Assurance (QA) are critical when manufacturing products.
Explain the difference between Quality Control (QC) and Quality Assurance (QA) when
manufacturing the hair straighteners shown.
© WJEC CBAC Ltd.
(B602U10-1)
[9]
15
9.
Examiner
only
Below are images of two kitchen work surfaces.
Block Hardwood
Veneered Chipboard
Evaluate the environmental advantages and disadvantages of using hardwoods compared to
manufactured materials for products such as kitchen work surfaces.
[9]
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
16
10. Ergonomics and anthropometrics play a key role in the design of products such as those
shown below.
Discuss how ergonomic principles and anthropometric data are used to successfully design
effective products.
[12]
© WJEC CBAC Ltd.
(B602U10-1)
Examiner
only
17
Examiner
only
END OF PAPER
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
18
Examiner
only
For continuation only.
© WJEC CBAC Ltd.
(B602U10-1)
19
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
Turn over.
20
Examiner
only
© WJEC CBAC Ltd.
(B602U10-1)
GCE A LEVEL
A602U10-1
Z22-A602U10-1
THURSDAY, 9 JUNE 2022 – AFTERNOON
DESIGN AND TECHNOLOGY – A level component 1
Product Design
A 6 0 2U101
01
3 hours
ADDITIONAL MATERIALS
In addition to this paper you will need:
a WJEC pink 16-page answer booklet, a calculator, ruler, pencil and coloured pencils.
INSTRUCTIONS TO CANDIDATES
Use black ink or black ball-point pen.
Answer all questions.
Write your answers in the separate answer booklet provided.
INFORMATION FOR CANDIDATES
When and where appropriate, answers should be amplified and illustrated with sketches and/or
diagrams.
The number of marks is given in brackets at the end of each question or part-question. You are
advised to divide your time accordingly.
The number of marks available is 100.
You are reminded of the need for good English and orderly, clear presentation in your answers.
You may use a calculator in this examination.
© WJEC CBAC Ltd.
JD*(X21-A602U10-1)
2
Answer all questions.
1.
The image below is of a mass-produced sideboard made from seasoned timber.
(a)
Name one method used to season timber.
[1]
(b)
Explain why using seasoned timber is necessary to manufacture the sideboard.
[3]
(c)
Describe, in detail, the process of seasoning wood most commonly used for products
such as the mass-produced sideboard.
[4]
© WJEC CBAC Ltd.
(A602U10-1)
3
2.
Below is a CAD drawing of a table design. The design feature on the top will be an epoxy resin
cast with a blue tint.
31°
b
h
c
a
a = 630 mm
b = 800 mm
h = 324mm
Table top plan view
(a)
(i) Calculate the surface area of the epoxy resin cast part of the table.
Show all calculations.
[3]
(ii)
The designer has decided to insert a strip of LED lights around the perimeter of
the epoxy resin cast.
Calculate the length of LED strip lights required.
[3]
Show all calculations.
(b)
The LED strip lights will be bought-in components. Explain what is meant by the term
‘bought-in components’.
[2]
(c)
Describe the benefits to the manufacturer of using bought-in components.
(d)
Explain the risks to the manufacturer of relying on the use of bought-in components. [3]
© WJEC CBAC Ltd.
(A602U10-1)
[3]
Turn over.
A 6 0 2U101
03
CAD drawing
4
3.
The main body of the keyboard shown is made from aluminium.
(a)
Briefly describe the process of extracting aluminium from its natural source.
[2]
(b)
Explain the environmental impact of extracting aluminium.
[6]
© WJEC CBAC Ltd.
(A602U10-1)
5
4.
Below is an image and details of a stool designed by a student. It features 30 mm diameter
mild steel tube legs that have been powder coated.
250
5
5
R7
R4
200
Drawing of leg showing
key measurements
(a)
(i)
Describe the process of powder coating a steel tube.
[2]
(ii)
Explain one benefit of powder coating as a finish for mild steel.
[2]
(b) Calculate the length of steel tubing required to make both legs of the stool.
Show all calculations.
[7]
(c)
The 30 mm diameter mild steel tubing weighs 0.9 kg per linear metre. Using your answer
from 4.(b), calculate the weight of the stool legs.
[2]
Show all calculations.
© WJEC CBAC Ltd.
(A602U10-1)
Turn over.
6
5.
6.
During the design and manufacture of products, such as the scooter pictured below, a range of
tests are carried out.
(a)
Explain the difference between destructive and non-destructive material testing.
(b)
Describe the reasons why designers and manufacturers carry out both types of tests
when designing the scooter.
[4]
(c)
Using notes and sketches, describe an industrial test that could be carried out to assess
a material’s relative toughness for the scooter.
[4]
Explain the benefits of Computer Integrated Manufacturing (CIM) to the designer and
manufacturer when producing products such as an adjustable office chair.
© WJEC CBAC Ltd.
(A602U10-1)
[2]
[5]
7
7.
Study the images of the baby car seats shown below.
Baby car seat from the
1970s.
Baby car seat from the
1990s.
Baby car seat from 2017.
(a)
Analyse how ‘market pull’ forces have impacted on the development of baby car seats
over time.
[6]
(b)
Study the child booster seat shown below and evaluate why polypropylene is a suitable
material for use in this product.
[6]
8.
Analyse the range of methods that can be used to conduct market research when carrying out
‘User-Centred Design’.
[9]
9.
Explain how designers and/or manufacturers carry out feasibility studies for the design and
manufacture of new and innovative products such as hybrid cars or bladeless fans.
[9]
10. The Consumer Protection Act is an example of legislation put in place to protect consumers.
Evaluate how effectively and thoroughly consumers are protected by legislation.
END OF PAPER
© WJEC CBAC Ltd.
(A602U10-1)
[12]
PMT
Oxford Cambridge and RSA
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Question Paper
Wednesday 6 June 2018 – Morning
* 7 0 2 0 5 1 3 4 5 3 *
Time allowed: 2 hours
You must have:
• Printed Answer Booklet
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre
number and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. Additional paper may be used if necessary but you must clearly show your
candidate number, centre number and question number(s).
• Do not write in the barcodes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by g m s–2. Unless otherwise instructed, when
a numerical value is needed, use g = 9.8.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 20 pages. The Question Paper consists of
12 pages.
© OCR 2018 [603/1002/9]
DC (LK/SW) 164528/3
OCR is an exempt Charity
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
1-r
a
S3 =
for r 1 1
1-r
Sn =
Binomial series
^a + bhn = a n + n C 1 a n - 1 b + n C 2 a n - 2 b 2 + f + n C r a n - r b r + f + b n
n
n!
where n C r = n C r = c m =
r
r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
dx
d
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f l^xh = lim
h"0
f ^x + hh - f ^xh
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
e f ^xh
n
n+1
1
; f l^xh`f ^xhj dx = n + 1 `f ^xhj + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
© OCR 2018
H640/01 Jun18
^n ! Nh ,
^ x 1 1, n ! Rh
PMT
3
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan ^A ! Bh =
aA ! B ! ^k + 12h rk
tan A ! tan B
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + y nh + 2 ^y1 + y 2 + f + y n - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = xn f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
or
P ^A Bh =
P ^A k Bh
P ^Bh
Sample variance
s2 =
^/ xih2
1
= / x 2i - nx- 2
S xx where S xx = /^x i - -xh2 = / x i2 n
n-1
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
If X + N ^n, v 2h then X + N cn,
v 2m
n
and
X-n
+ N ^0, 1h
v n
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
0
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut + 12 at 2
s = ut + 12 at 2
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2018
s = 12 ^u + vh t
s = vt - 12 at 2
H640/01 Jun18
Turn over
PMT
4
Answer all the questions
Section A (23 marks)
1
Show that (x - 2) is a factor of 3x 3 - 8x 2 + 3x + 2 .
[3]
2
By considering a change of sign, show that the equation e x - 5x 3 = 0 has a root between 0 and 1.
[2]
3
In this question you must show detailed reasoning.
Solve the equation sec 2 i + 2 tan i = 4 for 0° G i 1 360° .
4
5
[4]
Rory pushes a box of mass 2.8 kg across a rough horizontal floor against a resistance of 19 N. Rory applies a
constant horizontal force. The box accelerates from rest to 1.2 m s–1 as it travels 1.8 m.
(i)
Calculate the acceleration of the box.
[2]
(ii)
Find the magnitude of the force that Rory applies.
[2]
The position vector r metres of a particle at time t seconds is given by
r = (1 + 12t - 2t 2) i + (t 2 - 6t) j.
6
(i)
Find an expression for the velocity of the particle at time t.
[2]
(ii)
Determine whether the particle is ever stationary.
[2]
Aleela and Baraka are saving to buy a car. Aleela saves £50 in the first month. She increases the amount she
saves by £20 each month.
(i)
Calculate how much she saves in two years.
[2]
Baraka also saves £50 in the first month. The amount he saves each month is 12% more than the amount he
saved in the previous month.
(ii)
Explain why the amounts Baraka saves each month form a geometric sequence.
[1]
(iii)
Determine whether Baraka saves more in two years than Aleela.
[3]
© OCR 2018
H640/01 Jun18
PMT
5
Answer all the questions
Section B (77 marks)
7
A rod of length 2 m hangs vertically in equilibrium. Parallel horizontal forces of 30 N and 50 N are applied
to the top and bottom and the rod is held in place by a horizontal force F N applied x m below the top of the
rod as shown in Fig. 7.
30 N
xm
FN
50 N
Fig. 7
8
(i)
Find the value of F.
[1]
(ii)
Find the value of x.
[2]
(i)
Show that 8 sin 2 x cos 2 x can be written as 1 - cos 4x.
[3]
(ii)
Hence find
© OCR 2018
y sin 2 x cos 2 x dx.
[3]
H640/01 Jun18
Turn over
PMT
6
9
A pebble is thrown horizontally at 14 m s–1 from a window which is 5 m above horizontal ground. The
pebble goes over a fence 2 m high d m away from the window as shown in Fig. 9. The origin is on the
ground directly below the window with the x-axis horizontal in the direction in which the pebble is thrown
and the y-axis vertically upwards.
y
Window
14 m s–1
5m
2 m Fence
O
x
dm
Fig. 9
10
(i)
Find the time the pebble takes to reach the ground.
[3]
(ii)
Find the cartesian equation of the trajectory of the pebble.
[4]
(iii)
Find the range of possible values for d.
[3]
Fig. 10 shows the graph of y = (k - x) ln x where k is a constant (k 2 1) .
y
x
O
Fig. 10
Find, in terms of k, the area of the finite region between the curve and the x-axis.
© OCR 2018
H640/01 Jun18
[8]
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7
11
Fig. 11 shows two blocks at rest, connected by a light inextensible string which passes over a smooth pulley.
Block A of mass 4.7 kg rests on a smooth plane inclined at 60° to the horizontal. Block B of mass 4 kg rests
on a rough plane inclined at 25° to the horizontal. On either side of the pulley, the string is parallel to a line
of greatest slope of the plane. Block B is on the point of sliding up the plane.
Block A
Block B
60°
25°
Fig. 11
12
(i)
Show that the tension in the string is 39.9 N correct to 3 significant figures.
[2]
(ii)
Find the coefficient of friction between the rough plane and Block B.
[5]
Fig. 12 shows the circle (x - 1) 2 + (y + 1) 2 = 25 , the line 4y = 3x - 32 and the tangent to the circle at the
point A (5, 2). D is the point of intersection of the line 4y = 3x - 32 and the tangent at A.
y
A
x
O
D
B
E
Fig. 12
(i)
Write down the coordinates of C, the centre of the circle.
[1]
(ii)
(A) Show that the line 4y = 3x - 32 is a tangent to the circle.
[4]
(B) Find the coordinates of B, the point where the line 4y = 3x - 32 touches the circle.
[1]
(iii)
Prove that ADBC is a square.
[3]
(iv)
The point E is the lowest point on the circle. Find the area of the sector ECB.
[5]
© OCR 2018
H640/01 Jun18
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PMT
8
13
The function f (x) is defined by f (x) =
values for f (x) and f l (x) .
3
27 - 8x 3 . Jenny uses her scientific calculator to create a table of
x
0
0.25
0.5
0.75
1
1.25
1.5
f (x)
f l (x)
3
2.9954
2.9625
2.8694
2.6684
2.2490
0
0
–0.056
–0.228
–0.547
–1.124
–1.977
ERROR
(i)
Use calculus to find an expression for f l (x) and hence explain why the calculator gives an error for
[3]
f l (1.5) .
(ii)
Find the first three terms of the binomial expansion of f (x).
(iii)
Jenny integrates the first three terms of the binomial expansion of f (x) to estimate the value of
[3]
y 01 3 27 - 8x 3 dx. Explain why Jenny’s method is valid in this case. (You do not need to evaluate
Jenny’s approximation.)
(iv)
[2]
Use the trapezium rule with 4 strips to obtain an estimate for
The calculator gives 2.921 174 38 for
y 01 3 27 - 8x 3 dx.
[3]
y 01 3 27 - 8x 3 dx. The graph of y = f (x) is shown in Fig. 13.
y
4
2
–1
x
O
1
Fig. 13
(v)
© OCR 2018
Explain why the trapezium rule gives an underestimate.
H640/01 Jun18
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9
14
The velocity of a car, v m s–1 at time t seconds, is being modelled. Initially the car has velocity 5 m s–1 and it
accelerates to 11.4 m s–1 in 4 seconds.
In model A, the acceleration is assumed to be uniform.
(i)
Find an expression for the velocity of the car at time t using this model.
[3]
(ii)
Explain why this model is not appropriate in the long term.
[1]
Model A is refined so that the velocity remains constant once the car reaches 17.8 m s–1.
(iii)
Sketch a velocity-time graph for the motion of the car, making clear the time at which the acceleration
changes.
[3]
(iv)
Calculate the displacement of the car in the first 20 seconds according to this refined model.
[3]
In model B, the velocity of the car is given by
5 + 0.6t 2 - 0.05t 3 for 0 G t G 8,
v='
17.8
for 8 1 t G 20.
(v)
Show that this model gives an appropriate value for v when t = 4 .
(vi)
Explain why the value of the acceleration immediately before the velocity becomes constant is likely
to mean that model B is a better model than model A.
[3]
(vii)
Show that model B gives the same value as model A for the displacement at time 20 s.
END OF QUESTION PAPER
© OCR 2018
H640/01 Jun18
[1]
[3]
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© OCR 2018
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© OCR 2018
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Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2018
H640/01 Jun18
PMT
Oxford Cambridge and RSA
Wednesday 5 June 2019 – Morning
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Time allowed: 2 hours
* 7 6 9 3 2 4 9 4 4 6 *
You must have:
• Printed Answer Booklet
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If additional space is required, you should use the lined page(s) at the end of
the Printed Answer Booklet. The question number(s) must be clearly shown.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by g m s–2. Unless otherwise instructed, when
a numerical value is needed, use g = 9.8.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 20 pages. The Question Paper consists of
8 pages.
© OCR 2019 [603/1002/9]
DC (NF/CGW) 174863/3
OCR is an exempt Charity
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
n
n!
where n C r = n C r = c m =
r
r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2019
H640/01 Jun19
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
aA ! B ! ^k + 12h rk
tan ^A ! Bh =
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih
1
S xx where S xx = /^xi - -xh2 = / x 2i = / x 2i - nx- 2
s =
n
n-1
2
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
X -n
v2
+ N ^0, 1h
If X + N ^n, v 2h then X + N cn, m and
n
v n
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2019
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/01 Jun19
Turn over
PMT
4
Answer all the questions.
Section A (25 marks)
1
In this question you must show detailed reasoning.
Show that
y4 ^2x +
9
xh dx =
233
.
3
[3]
2
Show that the line which passes through the points (2, - 4) and (- 1, 5) does not intersect the line
[3]
3x + y = 10 .
3
The function f (x) is given by f (x) = (1 - ax) -3 , where a is a non-zero constant. In the binomial
expansion of f (x) , the coefficients of x and x 2 are equal.
(a) Find the value of a.
[3]
(b) Using this value for a,
4
(i) state the set of values of x for which the binomial expansion is valid,
[1]
(ii) write down the quadratic function which approximates f (x) when x is small.
[1]
Fig. 4 shows a uniform beam of mass 4 kg and length 2.4 m resting on two supports P and Q. P is at
one end of the beam and Q is 0.3 m from the other end.
Determine whether a person of mass 50 kg can tip the beam by standing on it.
[3]
2.4 m
P
Q
0.3 m
Fig. 4
5
A car of mass 1200 kg travels from rest along a straight horizontal road. The driving force is 4000 N
and the total of all resistances to motion is 800 N.
Calculate the velocity of the car after 9 seconds.
[4]
6
(a) Prove that
sin i
1
= cot i .
1 - cos i sin i
[4]
(b) Hence find the exact roots of the equation
© OCR 2019
sin i
1
= 3 tan i in the interval 0 G i G r.
1 - cos i sin i
[3]
H640/01 Jun19
PMT
5
Answer all the questions.
Section B (75 marks)
7
The velocity v m s -1 of a particle at time t s is given by
v = 0.5t (7 - t) .
Determine whether the speed of the particle is increasing or decreasing when t = 8 .
8
9
[4]
An arithmetic series has first term 9300 and 10th term 3900.
(a) Show that the 20th term of the series is negative.
[3]
(b) The sum of the first n terms is denoted by S. Find the greatest value of S as n varies.
[4]
A cannonball is fired from a point on horizontal ground at 100 m s -1 at an angle of 25° above the
horizontal. Ignoring air resistance, calculate
(a) the greatest height the cannonball reaches,
[3]
(b) the range of the cannonball.
[4]
10 (a) Express 7 cos x - 2 sin x in the form R cos (x + a) where R 2 0 and 0 1 a 1 12 r , giving the
[4]
exact value of R and the value of a correct to 3 significant figures.
(b) Give details of a sequence of two transformations which maps the curve y = sec x onto the
1
.
[3]
curve y =
7 cos x - 2 sin x
11 In this question, the unit vector i is horizontal and the unit vector j is vertically upwards.
A particle of mass 0.8 kg moves under the action of its weight and two forces given by (ki + 5j) N
and (4i + 3j) N . The acceleration of the particle is vertically upwards.
(a) Write down the value of k.
[1]
Initially the velocity of the particle is (4i + 7j) m s -1 .
(b) Find the velocity of the particle 10 seconds later.
© OCR 2019
H640/01 Jun19
[4]
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6
12 Fig. 12 shows a curve C with parametric equations x = 4t 2 , y = 4t . The point P, with parameter t,
is a general point on the curve. Q is the point on the line x + 4 = 0 such that PQ is parallel to the
x-axis. R is the point (4, 0).
y
C
Q
-4
P (4t 2, 8t)
O
R (4, 0)
x
Fig. 12
(a) Show algebraically that P is equidistant from Q and R.
[4]
(b) Find a cartesian equation of C.
[2]
13 A 15 kg box is suspended in the air by a rope which makes an angle of 30° with the vertical. The
box is held in place by a string which is horizontal.
(a) Draw a diagram showing the forces acting on the box.
[1]
(b) Calculate the tension in the rope.
[2]
(c) Calculate the tension in the string.
[2]
© OCR 2019
H640/01 Jun19
PMT
7
14 Fig. 14 shows a circle with centre O and radius r cm. The chord AB is such that angle
AOB = x radians . The area of the shaded segment formed by AB is 5% of the area of the circle.
O
x rad r cm
A
B
Fig. 14
1
(a) Show that x - sin x - 10
r = 0.
[4]
The Newton-Raphson method is to be used to find x.
(b) Write down the iterative formula to be used for the equation in part (a).
[1]
(c) Use three iterations of the Newton-Raphson method with x 0 = 1.2 to find the value of x to a
suitable degree of accuracy.
[3]
15 A model for the motion of a small object falling through a thick fluid can be expressed using the
differential equation
dv
= 9.8 - kv ,
dt
where v m s -1 is the velocity after t s and k is a positive constant.
(a) Given that v = 0 when t = 0 , solve the differential equation to find v in terms of t and k.
[7]
(b) Sketch the graph of v against t.
[2]
Experiments show that for large values of t, the velocity tends to 7 m s -1 .
(c) Find the value of k.
[2]
(d) Find the value of t for which v = 3.5.
[1]
© OCR 2019
H640/01 Jun19
Turn over
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8
16 A particle of mass 2 kg slides down a plane inclined at 20° to the horizontal. The particle has an
initial velocity of 1.4 m s -1 down the plane. Two models for the particle’s motion are proposed.
In model A the plane is taken to be smooth.
(a) Calculate the time that model A predicts for the particle to slide the first 0.7 m.
[5]
(b) Explain why model A is likely to underestimate the time taken.
[1]
In model B the plane is taken to be rough, with a constant coefficient of friction between the
particle and the plane.
(c) Calculate the acceleration of the particle predicted by model B given that it takes 0.8 s to slide
the first 0.7 m.
[2]
(d) Find the coefficient of friction predicted by model B, giving your answer correct to 3 significant
figures.
[6]
END OF QUESTION PAPER
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2019
H640/01 Jun19
PMT
Oxford Cambridge and RSA
Wednesday 07 October 2020 – Afternoon
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Time allowed: 2 hours
* 8 1 6 8 8 2 9 2 2 4 *
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2020 [603/1002/9]
DC (PQ/SW) 186980/3
OCR is an exempt Charity
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2020
H640/01 Jun20
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
aA ! B ! ^k + 12h rk
tan ^A ! Bh =
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih
1
S xx where S xx = /^xi - -xh2 = / x 2i = / x 2i - nx- 2
s =
n
n-1
2
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v 2O
2h
K
^
+ N ^0, 1h
If X + N n, v then X + N Kn, O and
n
v n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2020
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/01 Jun20
Turn over
PMT
4
Answer all the questions.
Section A (22 marks)
1
27 3 x 4
Simplify c 9 m # c m .
9
x
2
Express
3
J 3N
J- 1N
K O
K O
The points A and B have position vectors a = K 2O and b = K 4O respectively.
K O
K O
L- 1P
L 8P
2
[2]
a+ 2
in the form p + q 2 , giving p and q in terms of a.
3- 2
[3]
Show that the exact value of the distance AB is 101.
[3]
4
Find the second derivative of ^x 2 + 5h , giving your answer in factorised form.
[5]
5
A child is running up and down a path. A simplified model of the child’s motion is as follows:
4
• he first runs north for 5 s at 4 m s -1 ;
• he then suddenly stops and waits for 8 s;
• finally he runs in the opposite direction for 7 s at 3.5 m s -1 .
(a) Taking north to be the positive direction, sketch a velocity-time graph for this model of the
child’s motion.
[2]
Using this model,
(b) calculate the total distance travelled by the child,
[2]
(c) find his final displacement from his original position.
[1]
© OCR 2020
H640/01 Jun20
PMT
5
6
A uniform ruler AB has mass 28 g and length 30 cm. As shown in Fig. 6, the ruler is placed on a
horizontal table so that it overhangs a point C at the edge of the table by 25 cm.
A downward force of F N is applied at A. This force just holds the ruler in equilibrium so that the
contact force between the table and the ruler acts through C.
25 cm
A
B
C
Fig. 6
(a) Complete the force diagram in the Printed Answer Booklet, labelling the forces and all relevant
distances.
[2]
(b) Calculate the value of F.
© OCR 2020
[2]
H640/01 Jun20
Turn over
PMT
6
Answer all the questions.
Section B (78 marks)
7
In this question you must show detailed reasoning.
The function f (x) is defined by f (x) = x 3 + x 2 - 8x - 12 for all values of x.
8
(a) Use the factor theorem to show that (x + 2) is a factor of f (x) .
[2]
(b) Solve the equation f (x) = 0 .
[4]
Fig. 8.1 shows the cross-section of a straight driveway 4 m wide made from tarmac.
4m
Fig. 8.1
0.2
The height h m of the cross-section at a displacement x m from the middle is modelled by h =
1 + x2
for - 2 G x G 2 .
A lower bound of 0.3615 m2 is found for the area of the cross-section using rectangles as shown in
Fig. 8.2.
h
–2
–1.5
–1
–0.5
0
0.5
1
1.5
2
x
Fig. 8.2
(a) Use a similar method to find an upper bound for the area of the cross-section.
y
2
[3]
0.2
.
[2]
2 dx
0 1+x
(c) The driveway is 10 m long. Use your answer in part (b) to find an estimate of the volume of
tarmac needed to make the driveway.
[2]
(b) Use the trapezium rule with 4 strips to estimate
© OCR 2020
H640/01 Jun20
PMT
7
9
A particle is moving in a straight line. The acceleration a m s -2 of the particle at time t s is given by
a = 0.8t + 0.5. The initial velocity of the particle is 3 m s -1 in the positive x-direction.
Determine whether the particle is ever stationary.
[6]
10 In this question you must show detailed reasoning.
Fig. 10 shows the curve given parametrically by the equations x =
1
1 1
2 , y = 3 - t , for t 2 0 .
t
t
y
x
O
Fig. 10
(a) Show that
dy 3 - t 2
.
=
2t
dx
[3]
(b) Find the coordinates of the point on the curve at which the tangent to the curve is parallel to
the line 4y + x = 1.
[3]
(c) Find the cartesian equation of the curve. Give your answer in factorised form.
[3]
11 A block of mass 2 kg is placed on a rough horizontal table. A light inextensible string attached to
the block passes over a smooth pulley attached to the edge of the table. The other end of the string
is attached to a sphere of mass 0.8 kg which hangs freely.
The part of the string between the block and the pulley is horizontal. The coefficient of friction
between the table and the block is 0.35. The system is released from rest.
(a) Draw a force diagram showing all the forces on the block and the sphere.
[3]
(b) Write down the equations of motion for the block and the sphere.
[2]
(c) Show that the acceleration of the system is 0.35 m s -2 .
[4]
(d) Calculate the time for the block to slide the first 0.5 m. Assume the block does not reach the
pulley.
[2]
© OCR 2020
H640/01 Jun20
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8
12 A function is defined by f (x) = x 3 - x .
(a) By considering
f (x + h) - f (x)
, show from first principles that f l (x) = 3x 2 - 1.
h
(b) Sketch the gradient function f l (x) .
[4]
[2]
(c) Show that the curve y = f (x) has a single point of inflection which is not a stationary point.
[3]
13 A projectile is fired from ground level at 35 m s -1 at an angle of i° above the horizontal.
(a) State a modelling assumption that is used in the standard projectile model.
[1]
(b) Find the cartesian equation of the trajectory of the projectile.
[4]
The projectile travels above horizontal ground towards a wall that is 110 m away from the point of
projection and 5 m high. The projectile reaches a maximum height of 22.5 m.
(c) Determine whether the projectile hits the wall.
[6]
14 Douglas wants to construct a model for the height of the tide in Liverpool during the day, using a
cosine graph to represent the way the height changes.
He knows that the first high tide of the day measures 8.55 m and the first low tide of the day
measures 1.75 m.
Douglas uses t for time and h for the height of the tide in metres. With his graph-drawing software
set to degrees, he begins by drawing the graph of h = 5.15 + 3.4 cos t .
(a) Verify that this equation gives the correct values of h for the high and low tide.
[1]
Douglas also knows that the first high tide of the day occurs at 1 am and the first low tide occurs
at 7.20 am. He wants t to represent the time in hours after midnight, so he modifies his equation to
h = 5.15 + 3.4 cos (at + b) .
(b) (i) Show that Douglas’s modified equation gives the first high tide of the day occurring at
the correct time if a + b = 0 .
[1]
(ii) Use the time of the first low tide of the day to form a second equation relating a and b.
[1]
(iii) Hence show that a = 28.42 correct to 2 decimal places.
[2]
(c) Douglas can only sail his boat when the height of the tide is at least 3 m.
Use the model to predict the range of times that morning when he cannot sail.
[3]
(d) The next high tide occurs at 12.59 pm when the height of the tide is 8.91 m.
Comment on the suitability of Douglas’s model.
© OCR 2020
H640/01 Jun20
[2]
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9
15 Fig. 15 shows a particle of mass m kg on a smooth plane inclined at 30° to the horizontal. Unit
vectors i and j are parallel and perpendicular to the plane, in the directions shown.
j
i
30°
Fig. 15
(a) Express the weight W of the particle in terms of m, g, i and j.
[2]
The particle is held in equilibrium by a force F, and the normal reaction of the plane on the particle
is denoted by R. The units for both F and R are newtons.
(b) Write down an equation relating W, R and F.
[1]
(c) Given that F = 6i + 8j,
• show that m = 1.22 correct to 3 significant figures,
• find the magnitude of R.
END OF QUESTION PAPER
© OCR 2020
H640/01 Jun20
[6]
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BLANK PAGE
© OCR 2020
H640/01 Jun20
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© OCR 2020
H640/01 Jun20
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12
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2020
H640/01 Jun20
PMT
Oxford Cambridge and RSA
Wednesday 6 October 2021 – Afternoon
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Time allowed: 2 hours
* 8 9 7 9 4 3 5 3 2 5 *
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2021 [603/1002/9]
DC (ST/SW) 300398/5
OCR is an exempt Charity
Turn over
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2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2021
H640/01 Oct21
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
aA ! B ! ^k + 12h rk
tan ^A ! Bh =
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih
1
S xx where S xx = /^xi - -xh2 = / x 2i = / x 2i - nx- 2
s =
n
n-1
2
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v 2O
2h
K
^
+ N ^0, 1h
If X + N n, v then X + N Kn, O and
n
v n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2021
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/01 Oct21
Turn over
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4
Answer all the questions.
Section A (21 marks)
1
Beth states that for all real numbers p and q, if p 2 2 q 2 then p 2 q .
Prove that Beth is not correct.
2
[2]
An unmanned spacecraft has a weight of 5200 N on Earth. It lands on the surface of the planet
Mars where the acceleration due to gravity is 3.7 m s -2 .
Calculate the weight of the spacecraft on Mars.
3
[3]
(a) The diagram shows the line y = x + 5 and the curve y = 8 - 2x - x 2 . The shaded region is the
finite region between the line and the curve. The curved part of the boundary is included in the
region but the straight part is not included.
Write down the inequalities that define the shaded region.
[2]
y
10
8
6
4
2
–6
–4
–2
0
2
4
x
–2
(b) In this question you must show detailed reasoning.
Solve the inequality 8 - 2x - x 2 2 x + 5 giving your answer in exact form.
© OCR 2021
H640/01 Oct21
[3]
PMT
5
4
(a) The first four terms of a sequence are 2, 3, 0, 3 and the subsequent terms are given by
ak + 4 = ak .
(i) State what type of sequence this is.
[1]
200
(ii) Find
/a .
k =1
[1]
k
(b) A different sequence is given by u n = b n where b is a constant and n H 1.
5
(i) State the set of values of b for which this is a divergent sequence.
[2]
(ii) In the case where b = 13 , find the sum of all the terms in the sequence.
[2]
ABCD is a rectangular lamina in which AB is 30 cm and AD is 10 cm.
Three forces of 20 N and one force of 30 N act along the sides of the lamina as shown in the
diagram.
20 N
FN
A
x cm
20 N
D
B
C
20 N
30 N
An additional force F N is also applied at right angles to AB to a point on the edge AB x cm from A.
(a) Given that the lamina is in equilibrium, calculate the values of F and x.
[3]
The point of application of the force F N is now moved to B, but the magnitude and direction of the
force remain the same.
(b) Explain the effect of the new system of forces on the lamina.
© OCR 2021
H640/01 Oct21
[2]
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6
Answer all the questions.
Section B (79 marks)
6
(a) The diagram shows part of the graph of y = cosec x , where x is in radians.
State the equations of the three vertical asymptotes that can be seen.
[1]
y
O
x
The tangent to the graph at the point P with x-coordinate
r
3
meets the x-axis at Q.
r
(b) Show that the x-coordinate of Q is + 3 . (You may use without proof the result that the
3
derivative of cosec x is - cosec x cot x .)
[6]
7
In this question you must show detailed reasoning.
The points A (-1, 4) and B (7, -2) are at opposite ends of a diameter of a circle.
(a) Find the equation of the circle.
[4]
(b) Find the coordinates of the points of intersection of the circle and the line y = 2x + 5.
[3]
(c) Q is the point of intersection with the larger y-coordinate.
Calculate the area of the triangle ABQ.
© OCR 2021
H640/01 Oct21
[3]
PMT
7
8
Kareem wants to solve the equation sin 4x + e -x + 0.75 = 0 . He uses his calculator to create the
following table of values for f (x) = sin 4x + e -x + 0.75.
x
f (x)
0
1
2
3
4
5
6
1.750
0.361
1.875
0.263
0.480
1.670
-0.153
He argues that because f (6) is the first negative value in the table, there is a root of the equation
between 5 and 6.
(a) Comment on the validity of his argument.
[1]
The diagram shows the graph of y = sin 4x + e -x + 0.75.
y
2
1
–1
0
1
2
3
4
5
6
x
(b) Explain why Kareem failed to find other roots between 0 and 6.
[1]
Kareem decides to use the Newton-Raphson method to find the root close to 3.
(c) (i) Determine the iterative formula he should use for this equation.
[2]
(ii) Use the Newton-Raphson method with x0 = 3 to find a root of the equation f (x) = 0.
Show three iterations and give your answer to a suitable degree of accuracy.
[3]
Kareem uses the Newton-Raphson method with x0 = 5 and also with x0 = 6 to try to find the root
which lies between 5 and 6. He produces the following tables.
x0
5
x0
6
x1
3.97288
x1
6.09036
x2
4.12125
x2
6.07110
(d) (i) For the iteration beginning with x0 = 5, represent the process on the graph in the Printed
Answer Booklet.
[2]
© OCR 2021
(ii) Explain why the method has failed to find the root which lies between 5 and 6.
[2]
(iii) Explain how Kareem can adapt his method to find the root between 5 and 6.
[1]
H640/01 Oct21
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PMT
8
9
The diagram shows a toy caterpillar consisting of a head and three body sections each connected
by a light inextensible ribbon. The head has a mass of 120 g and the body sections each have a
mass of 90 g.
The toy is pulled on level ground using a horizontal string attached to the head. The tension in the
string is 12 N. There are resistances to motion of 2.5 N for the head and each section of the body.
Body sections
Head
(a) (i) State the equation of motion for the toy caterpillar modelled as a single particle.
(ii) Calculate the acceleration of the toy caterpillar.
[2]
[1]
(b) Draw a diagram showing all the forces acting on the head of the toy caterpillar.
[3]
(c) Calculate the tension in the ribbon that joins the head to the body.
[2]
10 A ball is thrown upwards with a velocity of 29.4 m s -1 .
(a) Show that the ball reaches its maximum height after 3 s.
[1]
(b) Sketch a velocity-time graph for the first 5 s of motion.
[2]
(c) Calculate the speed of the ball 5 s after it is thrown.
[3]
A second ball is thrown at u m s -1 at an angle of a° above the horizontal. It reaches the same
maximum height as the first ball.
(d) Use this information to write down
• the vertical component of the second ball’s initial velocity,
• the time taken for the second ball to reach its greatest height.
[2]
This second ball reaches its greatest height at a point which is 48 m horizontally from the point of
projection.
(e) Calculate the values of u and a.
© OCR 2021
[3]
H640/01 Oct21
PMT
9
11 A balloon is being inflated. The balloon is modelled as a sphere with radius x cm at time t s. The
volume V cm 3 is given by V = 43 rx 3 .
The rate of increase of volume is inversely proportional to the radius of the balloon. Initially, when
t = 0, the radius of the balloon is 5 cm and the volume of the balloon is increasing at a rate of
21 cm 3 s -1 .
(a) Show that x satisfies the differential equation
dx
105
=
.
d t 4r x 3
[5]
(b) Find the radius of the balloon after two minutes.
[5]
(c) Explain why the model may not be suitable for very large values of t.
[1]
12 A box of mass m kg slides down a rough slope inclined at 15° to the horizontal. The coefficient of
friction between the box and the slope is 0.4. The box has an initial velocity of 1.2 m s -1 down the
slope.
Calculate the distance the box travels before coming to rest.
[7]
13 In this question i and j are unit vectors in the x- and y-directions respectively.
The velocity of a particle at time t s is given by (3t 2 i + 7j) m s -1 . At time t = 0 the position of the
particle with respect to the origin is (-i + 2j) m.
(a) Determine the distance of the particle from the origin when t = 2.
(b) Show that the cartesian equation of the path of the particle is x = c
[6]
y-2 3
m - 1.
7
[3]
(c) At time t = 2, the magnitude of the resultant force acting on the particle is 48 N.
Find the mass of the particle.
[4]
END OF QUESTION PAPER
© OCR 2021
H640/01 Oct21
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10
BLANK PAGE
© OCR 2021
H640/01 Oct21
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11
BLANK PAGE
© OCR 2021
H640/01 Oct21
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12
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2021
H640/01 Oct21
PMT
1
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Sample Question Paper
Version 2
Date – Morning/Afternoon
Time allowed: 2 hours
You must have:
• Printed Answer Booklet
en
You may use:
• a scientific or graphical calculator
0
0
0
0
0
0
*
im
*
Sp
ec
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number and
candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer Booklet.
Additional paper may be used if necessary but you must clearly show your candidate number,
centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by g m s-2. Unless otherwise instructed, when a
numerical value is needed, use g = 9.8.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Booklet consists of 20 pages. The Question Paper consists of 12 pages.
© OCR 2018
603/1002/9
H640/01
B10025/5.0
Turn over
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2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
Sn 12 n(a l ) 12 n{2a (n 1)d}
Geometric series
Sn
S
a(1 r n )
1 r
a
for r
1 r
1
Binomial series
an
where n Cr
(1 x) n
n
C1 a n 1b
n
n Cr
n
C2 a n 2b2
n!
r !(n r )!
r
n(n 1) 2
x
2!
n(n 1)
Cr a n r b r
Differentiation
f ( x)
(n r 1) r
x
r!
f ( x)
tan kx
ec
k sec 2 kx
sec x tan x
sec x
cot x
Quotient Rule y
cosec 2 x
cosec x cot x
Sp
cosec x
u dy
,
v dx
v
du
dv
u
dx
dx
v2
Differentiation from first principles
f ( x h) f ( x )
f ( x) lim
h 0
h
Integration
f ( x)
dx ln f ( x)
f ( x)
c
1
n
f ( x) f ( x) dx
n 1
u
Integration by parts
f ( x)
n 1
dv
dx uv
dx
c
v
du
dx
dx
Small angle approximations
sin
bn
im
1 nx
n
, cos
© OCR 2018
1
1
2
2
, tan
(n
en
(a b)n
where θ is measured in radians
H640/01
x
1, n
),
PMT
3
Trigonometric identities
sin( A B) sin A cos B cos A sin B
cos( A B) cos A cos B sin A sin B
tan A tan B
1 tan A tan B
tan( A B)
1
)
2
( A B (k
)
Numerical methods
b
Trapezium rule:
a
y dx
1
2
h{( y0
yn ) 2( y1
y2
… yn 1 ) }, where h
The Newton-Raphson iteration for solving f( x) 0 : xn
Probability
P( A B) P( A) P( B) P( A
B)
B)
or
P( A) P( B | A) P( B) P( A | B )
P( A | B)
Sample variance
Standard deviation, s
( xi
x
variance
The binomial distribution
If X ~ B(n, p) then P( X
x)
r)
n
Cr p r q n
r
2
xi2 nx 2
n
where q 1 p
Sp
Mean of X is np
xi
2
i
im
n 1
S xx where S xx
2
P( A B)
P(B )
ec
s
1
2
f( xn )
f ( xn )
xn
en
P( A
1
b a
n
Hypothesis testing for the mean of a Normal distribution
2
If X ~ N
,
2
then X ~ N
,
n
and
X
/ n
~ N(0, 1)
Percentage points of the Normal distribution
p
z
10
1.645
5
1.960
2
2.326
1
2.576
Kinematics
Motion in a straight line
v u at
s ut 12 at 2
u v t
s
1
2
v 2 u 2 2as
s vt 12 at 2
s
vt
© OCR 2018
H640/01
s
1
2
Motion in two dimensions
v u at
s ut 12 at 2
u v t
1
at 2
2
Turn over
PMT
4
Answer all the questions
Section A (23 marks)
1
Fig. 1 shows a sector of a circle of radius 7 cm. The area of the sector is 5 cm2.
7 cm
Fig. 1
[2]
A geometric series has first term 3. The sum to infinity of the series is 8.
Find the common ratio.
ec
im
2
in radians.
en
Find the angle
Solve the inequality 2 x 1
4
Differentiate the following.
4.
[4]
Sp
3
[3]
(a)
1 3x 2
[3]
x2
(b)
3x 2
© OCR 2018
[3]
H640/01
PMT
5
5
A woman is pulling a loaded sledge along horizontal ground. The only resistance to motion of the
sledge is due to friction between it and the ground.
100 N
32°
Fig. 5
im
(b)
Determine the frictional force between the ground and the sledge.
Give your answer correct to 3 significant figures.
[2]
Next she pulls with a force of 100 N inclined at a smaller angle to the horizontal. The sledge
still does not move.
ec
(a)
en
At first, she pulls with a force of 100 N inclined at 32° to the horizontal, as shown in Fig.5, but the
sledge does not move.
Sp
Compare the frictional force in this new situation with that in part (a), justifying your answer.
[2]
© OCR 2018
H640/01
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6
6
Fig. 6 shows a partially completed spreadsheet.
This spreadsheet uses the trapezium rule with four strips to estimate
1
2
3
4
5
6
7
8
0
0.125
0.25
0.375
0.5
B
x
0.0000
0.3927
0.7854
1.1781
1.5708
C
sin x
0.0000
0.3827
0.7071
0.9239
1.0000
D
y
1.0000
1.1759
1.3066
1.3870
1.4142
Fig. 6
im
(a) Show how the value in cell B3 is calculated.
0
1 sin x dx .
E
0.5000
1.1759
1.3066
1.3870
0.7071
5.0766
en
A
1
2
(b) Show how the values in cells D2 to D6 are used to calculate the value in cell E7.
1
2
0
Sp
Give your answer to 3 significant figures.
© OCR 2018
[1]
1 sin x dx .
ec
(c) Complete the calculation to estimate
[1]
H640/01
[2]
PMT
7
Answer all the questions
Section B (77 marks)
7
In this question take g = 10.
A small stone is projected from a point O with a speed of 26 m s –1 at an angle θ above the
horizontal. The initial velocity and part of the path of the stone are shown in Fig. 7.
12
You are given that sin
.
13
After t seconds the horizontal displacement of the stone from O is x metres and the vertical
displacement is y metres.
y
θ
O
x
Fig. 7
Using the standard model for projectile motion,
show that y
ec
(a)
en
–1
im
26 m s
24t 5t 2 ,
find an expression for x in terms of t.
[4]
Sp
The stone passes through a point A. Point A is 16 m above the level of O.
(b) Find the two possible horizontal distances of A from O.
[4]
A toy balloon is projected from O with the same initial velocity as the small stone.
(c)
© OCR 2018
Suggest two ways in which the standard model could be adapted.
H640/01
[2]
Turn over
PMT
8
x 2 e2 x d x .
8
Find
[7]
9
In an experiment, a small box is hit across a floor. After it has been hit, the box slides without
rotation.
The box passes a point A. The distance the box travels after passing A before coming to rest is S
metres and the time this takes is T seconds.
The only resistance to the box’s motion is friction due to the floor. The mass of the box is m kg and
the frictional force is a constant F N.
(ii)
Show that S
kT 2 where k
F
.
2m
en
Find the equation of motion for the box while it is sliding.
[4]
Given that k = 1.4, find the value of the coefficient of friction between the box and the floor.
[4]
Sp
ec
(b)
(i)
im
(a)
© OCR 2018
H640/01
Turn over
PMT
9
10
In a certain region, the populations of grey squirrels, PG and red squirrels PR, at time t years are
modelled by the equations:
PG
10 000 1 e kt
PR
20 000e kt
where t
(a)
(i)
On the axes in your Printed Answer Book, sketch the graphs of PG and PR on the same
axes.
(ii)
Give the equations of any asymptotes.
What does the model predict about the long term population of
grey squirrels
red squirrels?
[4]
[2]
im
en
(b)
0 and k is a positive constant.
Grey squirrels and red squirrels compete for food and space. Grey squirrels are larger and more
successful than red squirrels.
ec
(c) Comment on the validity of the model given by the equations, giving a reason for your answer.
[1]
Show that, according to the model, the rate of decrease of the population of red squirrels is
always double the rate of increase of the population of grey squirrels.
[4]
(e)
When t = 3, the numbers of grey and red squirrels are equal. Find the value of k.
© OCR 2018
Sp
(d)
H640/01
[4]
PMT
10
11
Fig. 11 shows the curve with parametric equations
x 2cos , y sin , 0
The point P has parameter
1
4
2 .
. The tangent at P to the curve meets the axes at A and B.
y
A
P
Fig. 11
Fig. 11
x
Show that the equation of the line AB is x 2 y
(b)
Determine the area of the triangle AOB.
2 2.
ec
im
(a)
A model boat has velocity v =
2t 2 i
Sp
12
B
en
O
[6]
[3]
2t 2 j m s –1 for t
0 , where t is the time in seconds.
i is the unit vector east and j is the unit vector north.
When t 3 , the position vector of the boat is (3i + 14j) m.
13
(a)
Show that the boat is never instantaneously at rest.
[2]
(b)
Determine any times at which the boat is moving directly northwards.
[2]
(c)
Determine any times at which the boat is north-east of the origin.
[5]
In this question you must show detailed reasoning.
Determine the values of k for which part of the graph of y
x2 kx 2k appears below the x-axis.
[4]
© OCR 2018
H640/01
PMT
11
14
Blocks A and B are connected by a light rigid horizontal bar and are sliding on a rough horizontal
surface.
A light horizontal string exerts a force of 40 N on B.
This situation is shown in Fig. 14, which also shows the direction of motion, the mass of each of the
blocks and the resistances to their motion.
direction of motion
side view
10 N
bar
A
6 kg
5N
string
40 N
B
4 kg
(a)
en
Fig. 14
Calculate the tension in the bar.
[4]
[5]
Fig. 15 shows a uniform shelf AB of weight W N.
The shelf is 180 cm long and rests on supports at points C and D. Point C is 30 cm from A and point
D is 60 cm from B.
Sp
15
Determine
the magnitude of the new force in the bar,
whether the bar is in tension or in compression.
ec
(b)
im
The string breaks while the blocks are sliding. The resistances to motion are unchanged.
side view
30 cm C
60 cm
30 cm
D
60 cm
B
A
WN
Fig. 15
Determine the range of positions a point load of 3 W could be placed on the shelf without the shelf
tipping.
[6]
END OF QUESTION PAPER
© OCR 2018
H640/01
PMT
12
Sp
ec
im
en
BLANK PAGE
Copyright Information:
OCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials. OCR has attempted to
identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to
candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements booklet. This is produced for each
series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct
its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations
Syndicate (UCLES), which is itself a department of the University of Cambridge.
© OCR 2018
H640/01
PMT
Oxford Cambridge and RSA
A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Question Paper
Wednesday 13 June 2018 – Morning
* 7 0 2 0 8 8 5 5 3 7 *
Time allowed: 2 hours
You must have:
• Printed Answer Booklet
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre
number and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. Additional paper may be used if necessary but you must clearly show your
candidate number, centre number and question number(s).
• Do not write in the barcodes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 16 pages. The Question Paper consists of
12 pages.
© OCR 2018 [603/1002/9]
DC (LEG/TP) 164684/3
OCR is an exempt Charity
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
1-r
a
S3 =
for r 1 1
1-r
Sn =
Binomial series
^a + bhn = a n + n C 1 a n - 1 b + n C 2 a n - 2 b 2 + f + n C r a n - r b r + f + b n
n
n!
where n C r = n C r = c m =
r
r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
dx
d
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f l^xh = lim
h"0
f ^x + hh - f ^xh
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
e f ^xh
n
n+1
1
; f l^xh`f ^xhj dx = n + 1 `f ^xhj + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
© OCR 2018
H640/02 Jun18
^n ! Nh ,
^ x 1 1, n ! Rh
PMT
3
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan ^A ! Bh =
aA ! B ! ^k + 12h rk
tan A ! tan B
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + y nh + 2 ^y1 + y 2 + f + y n - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = xn f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
or
P ^A Bh =
P ^A k Bh
P ^Bh
Sample variance
s2 =
^/ xih2
1
= / x 2i - nx- 2
S xx where S xx = /^x i - -xh2 = / x i2 n
n-1
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
If X + N ^n, v 2h then X + N cn,
v 2m
n
and
X-n
+ N ^0, 1h
v n
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut + 12 at 2
s = ut + 12 at 2
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2018
s = 12 ^u + vh t
s = vt - 12 at 2
H640/02 Jun18
Turn over
PMT
4
Answer all the questions
Section A (21 marks)
27 + 192 = a b , where a and b are prime numbers to be determined.
1
Show that
2
Solve the inequality 2x + 1 1 5 .
3
The probability that Chipping FC win a league football match is P(W) = 0.4.
(i)
[2]
[3]
Calculate the probability that Chipping FC fail to win each of their next two league football matches.
[1]
The probability that Chipping FC lose a league football match is P(L) = 0.3.
(ii)
4
Explain why P(W) + P(L) ≠ 1.
[1]
A survey of the number of cars per household in a certain village generated the data in Fig. 4.
Number of cars
0
1
2
3
4
Number of households
8
22
31
27
7
Fig. 4
5
(i)
Calculate the mean number of cars per household.
[1]
(ii)
Calculate the standard deviation of the number of cars per household.
[1]
(i)
(A) Sketch the graph of y = 3x.
[1]
(B) Give the coordinates of any intercepts.
[1]
The curve y = f(x) is the reflection of the curve y = 3x in the line y = x.
6
(ii)
Find f(x).
[1]
(i)
Express 7cosx ‒ 24sin x in the form R cos(x + α), where 0 < α <
(ii)
Write down the range of the function
f(x) = 12 + 7cosx ‒ 24sin x ,
r
.
2
[3]
0 G x G 2r.
[2]
7
Find y c4 x -
© OCR 2018
6
m dx .
x3
[4]
H640/02 Jun18
PMT
5
Answer all the questions
Section B (79 marks)
8
9
Every morning before breakfast Laura and Mike play a game of chess. The probability that Laura wins
is 0.7. The outcome of any particular game is independent of the outcome of other games. Calculate the
probability that, in the next 20 games,
(i)
Laura wins exactly 14 games,
[2]
(ii)
Laura wins at least 14 games.
[2]
At the end of each school term at North End College all the science classes in year 10 are given a test. The
marks out of 100 achieved by members of set 1 are shown in Fig. 9.
3
4
5
6
7
8
9
Key 5
5
0
2
0
0
3
5
9
3
1
1
4
5
6
3
2
6
5
5
5
6
6
6
6 8 9 9
8 8 9
7
2 represents a mark of 52
Fig. 9
(i)
Describe the shape of the distribution.
[1]
(ii)
The teacher for set 1 claimed that a typical student in his class achieved a mark of 95.
How did he justify this statement?
[1]
Another teacher said that the average mark in set 1 is 76. How did she justify this statement?
[1]
(iii)
Benson’s mark in the test is 35. If the mark achieved by any student is an outlier in the lower tail of the
distribution, the student is moved down to set 2.
(iv)
© OCR 2018
Determine whether Benson is moved down to set 2.
H640/02 Jun18
[2]
Turn over
PMT
6
10
The screenshot in Fig. 10 shows the probability distribution for the continuous random variable X, where
X + N ^n, v 2h .
Fig. 10
The area of each of the unshaded regions under the curve is 0.025. The lower boundary of the shaded region
is at 16.452 and the upper boundary of the shaded region is at 21.548.
11
(i)
Calculate the value of n.
[1]
(ii)
Calculate the value of v 2 .
[3]
(iii)
Y is the random variable given by Y = 4X + 5.
(A) Write down the distribution of Y.
[3]
(B) Find P(Y > 90).
[1]
The discrete random variable X takes the values 0, 1, 2, 3, 4 and 5 with probabilities given by the formula
P(X = x) = k(x + 1)(6 ‒ x) .
(i)
Find the value of k.
[2]
In one half-term Ben attends school on 40 days. The probability distribution above is used to model X, the
number of lessons per day in which Ben receives a gold star for excellent work.
(ii)
Find the probability that Ben receives no gold stars on each of the first 3 days of the half-term and two
gold stars on each of the next 2 days.
[2]
(iii)
Find the expected number of days in the half-term on which Ben receives no gold stars.
© OCR 2018
H640/02 Jun18
[2]
PMT
7
12
You must show detailed reasoning in this question.
In the summer of 2017 in England a large number of candidates sat GCSE examinations in both mathematics
and English. 56% of these candidates achieved at least level 4 in mathematics and 80% of these candidates
achieved at least level 4 in English. 14% of these candidates did not achieve at least level 4 in either
mathematics or English.
Determine whether achieving level 4 or above in English and achieving level 4 or above in mathematics
were independent events.
[5]
13
Each weekday Keira drives to work with her son Kaito. She always sets off at 8.00 a.m. She models her
journey time, x minutes, by the distribution X + N ^15, 4h .
Over a long period of time she notes that her journey takes less than 14 minutes on 7% of the journeys, and
takes more than 18 minutes on 31% of the journeys.
(i)
Investigate whether Keira’s model is a good fit for the data.
[3]
Kaito believes that Keira’s value for the variance is correct, but realises that the mean is not correct.
(ii)
Find, correct to two significant figures, the value of the mean that Keira should use in a refined model
which does fit the data.
[2]
Keira buys a new car. After driving to work in it each day for several weeks, she randomly selects the
journey times for n of these days. Her mean journey time for these n days is 16 minutes. Using the refined
model she conducts a hypothesis test to see if her mean journey time has changed, and finds that the result is
significant at the 5% level.
(iii)
© OCR 2018
Determine the smallest possible value of n.
H640/02 Jun18
[5]
Turn over
PMT
8
14
The pre-release material includes data on unemployment rates in different countries. A sample from this
material has been taken. All the countries in the sample are in Europe. The data have been grouped and are
shown in Fig 14.1.
Unemployment rate
0–
5–
10–
15–
20–
35–50
Frequency
15
21
5
5
2
2
Fig. 14.1
A cumulative frequency curve has been generated for the sample data using a spreadsheet. This is shown in
Fig. 14.2.
Unemployment rates in Europe
Cumulative frequency
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
45
Unemployment rate
Fig. 14.2
Hodge used Fig. 14.2 to estimate the median unemployment rate in Europe. He obtained the answer 5.0.
The correct value for this sample is 6.9.
(i)
(A) There is a systematic error in the diagram.
•
Identify this error.
•
State how this error affects Hodge’s estimate.
[2]
(B) There is another factor which has affected Hodge’s estimate.
•
Identify this factor.
•
State how this factor affects Hodge’s estimate.
[2]
(ii)
Use your knowledge of the pre-release material to give another reason why any estimation of the
[1]
median unemployment rate in Europe may be unreliable.
(iii)
Use your knowledge of the pre-release material to explain why it is very unlikely that the sample has
been randomly selected from the pre-release material.
[1]
© OCR 2018
H640/02 Jun18
PMT
9
The scatter diagram shown in Fig. 14.3 shows the unemployment rate and life expectancy at birth for the 47
countries in the sample for which this information is available.
Life expectancy at birth
Scatter diagram to show life expectancy at birth against
unemployment rate
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
Unemployment rate
Fig. 14.3
The product moment correlation coefficient for the 47 items in the sample is ‒ 0.2607.
The p-value associated with r = ‒ 0.2607 and n = 47 is 0.0383.
(iv)
Does this information suggest that there is an association between unemployment rate and life
expectancy at birth in countries in Europe?
[2]
Hodge uses the spreadsheet tools to obtain the equation of a line of best fit for this data.
(v)
15
The unemployment rate in Kosovo is 35.3, but there is no data available on life expectancy. Is it
reasonable to use Hodge’s line of best fit to estimate life expectancy at birth in Kosovo?
[1]
You must show detailed reasoning in this question.
The equation of a curve is
y 3 - xy + 4 x = 4 .
Find the gradient of the curve at each of the points where y = 1.
© OCR 2018
H640/02 Jun18
[9]
Turn over
PMT
10
16
In the first year of a course, an A-level student, Aaishah, has a mathematics test each week. The night before
each test she revises for t hours. Over the course of the year she realises that her percentage mark for a test,
p, may be modelled by the following formula, where A, B and C are constants.
p = A ‒ B( t ‒ C)2
•
Aaishah finds that, however much she revises, her maximum mark is achieved when she does 2 hours
revision. This maximum mark is 62.
•
Aaishah had a mark of 22 when she didn’t spend any time revising.
(i)
Find the values of A, B and C.
(ii)
According to the model, if Aaishah revises for 45 minutes on the night before the test, what mark will
she achieve?
[2]
(iii)
What is the maximum amount of time that Aaishah could have spent revising for the model to work?
[2]
[3]
In an attempt to improve her marks Aaishah now works through problems for a total of t hours over the
three nights before the test. After taking a number of tests, she proposes the following new formula for p.
p = 22 + 68(1 ‒ e–0.8t)
For the next three tests she recorded the data in Fig. 16.
t
1
3
5
p
59
84
89
Fig. 16
17
(iv)
Verify that the data is consistent with the new formula.
(v)
Aaishah’s tutor advises her to spend a minimum of twelve hours working through problems in future.
Determine whether or not this is good advice.
[2]
(i)
Express
(ii)
Express y in terms of x given that
^x 2 - 8x + 9h
in partial fractions.
^x + 1h^x - 2h2
dy y ^x 2 - 8x + 9h
=
and y = 16 when x = 3.
dx ^x + 1h^x - 2h2
END OF QUESTION PAPER
© OCR 2018
H640/02 Jun18
[2]
[5]
[7]
PMT
11
BLANK PAGE
© OCR 2018
H640/02 Jun18
PMT
12
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2018
H640/02 Jun18
PMT
Oxford Cambridge and RSA
Wednesday 12 June 2019 – Morning
A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Time allowed: 2 hours
* 7 6 9 3 7 0 7 5 2 8 *
You must have:
• Printed Answer Booklet
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If additional space is required, you should use the lined page(s) at the end of
the Printed Answer Booklet. The question number(s) must be clearly shown.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 16 pages. The Question Paper consists of
12 pages.
© OCR 2019 [603/1002/9]
DC (SC/TP) 178062/4
OCR is an exempt Charity
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2019
H640/02 Jun19
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2019
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/02 Jun19
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Answer all the questions
Section A (22 marks)
1
Fig. 1 shows the probability distribution of the discrete random variable X.
x
1
2
3
4
5
P (X = x)
0.2
0.1
k
2k
4k
Fig. 1
2
(a) Find the value of k.
[2]
(b) Find P (X ! 4) .
[2]
Given that y = (x 2 + 5) 12 ,
(a) Find
dy
.
dx
[2]
(b) Hence find ; 48x (x 2 + 5) 11 dx .
3
[2]
Fig. 3 shows the time Lorraine spent in hours, t, answering e-mails during the working day. The
data were collected over a number of months.
Time in hours,
0Gt11 1Gt12 2Gt13 3Gt14 4Gt16 6Gt18
t
Number of
days
28
36
42
31
24
12
Fig. 3
(a) Calculate an estimate of the mean time per day that Lorraine spent answering e-mails over this
period.
[1]
(b) Explain why your answer to part (a) is an estimate.
[1]
When Lorraine accepted her job, she was told that the mean time per day spent answering e-mails
would not be more than 3 hours.
(c) Determine whether, according to the data in Fig. 3, it is possible that the mean time per day
Lorraine spends answering e-mails is in fact more than 3 hours.
[1]
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4
Fig. 4 shows the graph of y = 1 + x 3 .
y
1.5
1
0.5
–1 – 0.5 0
x
0.5
1
Fig. 4
(a) Use the trapezium rule with h = 0.5 to find an estimate of ;
1 + x 3 dx , giving your answer
-1
correct to 6 decimal places.
[3]
0
(b) State whether your answer to part (a) is an under-estimate or an over-estimate, justifying your
answer.
[1]
5
Fig. 5 shows the number of times that students at a sixth form college visited a recreational
mathematics website during the first week of the summer term.
Number of visits to website
0
1
2
3
4
5
Number of students
24
38
17
12
4
2
Fig. 5
6
(a) State the value of the mid-range of the data.
[1]
(b) Describe the shape of the distribution.
[1]
(c) State the value of the mode.
[1]
Find <
© OCR 2019
32
ln x dx .
x5
[4]
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Answer all the questions
Section B (78 marks)
7
The area of a sector of a circle is 36.288cm 2 . The angle of the sector is i radians and the radius of
the circle is r cm.
(a) Find an expression for i in terms of r.
[1]
The perimeter of the sector is 24.48cm.
(b) Show that i =
24.48
- 2.
r
[1]
(c) Find the possible values of r.
8
[3]
A team called “The Educated Guess” enter a weekly quiz. If they win the quiz in a particular week,
the probability that they will win the following week is 0.4, but if they do not win, the probability
that they will win the following week is 0.2.
In week 4 The Educated Guess won the quiz.
(a) Calculate the probability that The Educated Guess will win the quiz in week 6.
[3]
Every week the same 20 quiz teams, each with 6 members, take part in a quiz. Every member of
every team buys a raffle ticket. Five winning tickets are drawn randomly, without replacement. Alf,
who is a member of one of the teams, takes part every week.
(b) Calculate the probability that, in a randomly chosen week, Alf wins a raffle prize.
[2]
(c) Find the smallest number of weeks after which it will be 95% certain that Alf has won at least
one raffle prize.
[4]
9
You are given that
f (x) = 2x + 3
g (x) = x 2 - 2x + 1
for x 1 0 and
for x 2 1.
(a) Find gf (x) , stating the domain.
[3]
(b) State the range of gf (x) .
[1]
(c) Find (gf ) -1 (x) .
[5]
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10 Club 65–80 Holidays fly jets between Liverpool and Magaluf. Over a long period of time records
show that half of the flights from Liverpool to Magaluf take less than 153 minutes and 5% of the
flights take more than 183 minutes.
An operations manager believes that flight times from Liverpool to Magaluf may be modelled by
the Normal distribution.
(a) Use the information above to write down the mean time the operations manager will use in his
Normal model for flight times from Liverpool to Magaluf.
[1]
(b) Use the information above to find the standard deviation the operations manager will use in
his Normal model for flight times from Liverpool to Magaluf, giving your answer correct to 1
decimal place.
[3]
(c) Data is available for 452 flights. A flight time of under 2 hours was recorded in 16 of these
flights. Use your answers to parts (a) and (b) to determine whether the model is consistent
with this data.
[3]
The operations manager suspects that the mean time for the journey from Magaluf to Liverpool is
less than from Liverpool to Magaluf. He collects a random sample of 24 flight times from Magaluf
to Liverpool. He finds that the mean flight time is 143.6 minutes.
(d) Use the Normal model used in part (c) to conduct a hypothesis test to determine whether there
is evidence at the 1% level to suggest that the mean flight time from Magaluf to Liverpool is
less than the mean flight time from Liverpool to Magaluf.
[7]
(e) Identify two ways in which the Normal model for flight times from Liverpool to Magaluf
might be adapted to provide a better model for the flight times from Magaluf to Liverpool. [2]
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11 Fig. 11 shows the graph of y = x 2 - 4x + x ln x .
y
8
6
4
2
0
x
2
4
6
–2
Fig. 11
(a) Show that the x-coordinate of the stationary point on the curve may be found from the equation
2x - 3 + ln x = 0 .
[4]
(b) Use an iterative method to find the x-coordinate of the stationary point on the curve
y = x 2 - 4x + x ln x , giving your answer correct to 4 decimal places.
[4]
12 The jaguar is a species of big cat native to South America. Records show that 6% of jaguars are
born with black coats. Jaguars with black coats are known as black panthers. Due to deforestation
a population of jaguars has become isolated in part of the Amazon basin. Researchers believe that
the percentage of black panthers may not be 6% in this population.
(a) Find the minimum sample size needed to conduct a two-tailed test to determine whether there
is any evidence at the 5% level to suggest that the percentage of black panthers is not 6%. [3]
A research team identifies 70 possible sites for monitoring the jaguars remotely. 30 of these sites
are randomly selected and cameras are installed. 83 different jaguars are filmed during the evidence
gathering period. The team finds that 10 of the jaguars are black panthers.
(b) Conduct a hypothesis test to determine whether the information gathered by the research team
provides any evidence at the 5% level to suggest that the percentage of black panthers in this
population is not 6%.
[7]
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13 The population of Melchester is 185 207. During a nationwide flu epidemic the number of new
cases in Melchester are recorded each day. The results from the first three days are shown in Fig. 13.
Day
1
2
3
Number of new cases
8
24
72
Fig. 13
A doctor notices that the numbers of new cases on successive days are in geometric progression.
(a) Find the common ratio for this geometric progression.
[1]
The doctor uses this geometric progression to model the number of new cases of flu in Melchester.
(b) According to the model, how many new cases will there be on day 5?
[1]
(c) Find a formula for the total number of cases from day 1 to day n inclusive according to this
model, simplifying your answer.
[1]
(d) Determine the maximum number of days for which the model could be viable in Melchester.
[3]
(e) State, with a reason, whether it is likely that the model will be viable for the number of days
found in part (d).
[1]
© OCR 2019
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14 The pre-release material includes data concerning crude death rates in different countries of the
world. Fig. 14.1 shows some information concerning crude death rates in countries in Europe and
in Africa.
Europe
Africa
48
56
minimum
6.28
3.58
lower quartile
8.50
7.31
median
9.53
8.71
upper quartile
11.41
11.93
maximum
14.46
14.89
n
Fig. 14.1
(a) Use your knowledge of the large data set to suggest a reason why the statistics in Fig. 14.1
refer to only 48 of the 51 European countries.
[1]
(b) Use the information in Fig. 14.1 to show that there are no outliers in either data set.
[3]
The crude death rate in Libya is recorded as 3.58 and the population of Libya is recorded as
6 411 776.
(c) Calculate an estimate of the number of deaths in Libya in a year.
[1]
The median age in Germany is 46.5 and the crude death rate is 11.42. The median age in Cyprus is
36.1 and the crude death rate is 6.62.
(d) Explain why a country like Germany, with a higher median age than Cyprus, might also be
expected to have a higher crude death rate than Cyprus.
[1]
Fig. 14.2 shows a scatter diagram of median age against crude death rate for countries in Africa and
Fig. 14.3 shows a scatter diagram of median age against crude death rate for countries in Europe.
Median age
Africa
45
40
35
30
25
20
15
10
5
0
0
2
4
6
8
10
Crude death rate
Fig. 14.2
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14
16
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Median age
Europe
60
50
40
30
20
10
0
0
2
4
6
8
10
Crude death rate
12
14
16
Fig. 14.3
The rank correlation coefficient for the data shown in Fig. 14.2 is - 0.281206 .
The rank correlation coefficient for the data shown in Fig. 14.3 is 0.335 215.
(e) Compare and contrast what may be inferred about the relationship between median age and
crude death rate in countries in Africa and in countries in Europe.
[2]
15 You must show detailed reasoning in this question.
The screenshot in Fig. 15 shows the probability distribution for the continuous random variable X,
where X + N (n, v 2) .
20
25
30
35
40
45
50
Fig. 15
The distribution is symmetrical about the line x = 35 and there is a point of inflection at x = 31.
Fifty independent readings of X are made. Show that the probability that at least 45 of these
readings are between 30 and 40 is less than 0.05.
[6]
END OF QUESTION PAPER
© OCR 2019
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12
Oxford Cambridge and RSA
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department of the University of Cambridge.
© OCR 2019
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Oxford Cambridge and RSA
Wednesday 14 October 2020 – Afternoon
A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Time allowed: 2 hours
* 8 2 5 7 6 0 8 4 9 9 *
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. You can use extra paper if you need to, but you must clearly show your
candidate number, the centre number and the question numbers.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 20 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2020 [603/1002/9]
DC (ST/JG) 192267/4
OCR is an exempt Charity
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Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2020
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^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2020
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/02 Jun20
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Answer all the questions.
Section A (23 marks)
1
Fig. 1 shows triangle ABC.
C
22.1 m
133°
A
18.0 m
B
Fig. 1
Calculate the area of triangle ABC, giving your answer correct to 3 significant figures.
2
[2]
Fig. 2 shows a sector of a circle of radius 8 cm.
The angle of the sector is 2.1 radians.
8 cm
L
2.1
radians
Fig. 2
(a) Calculate the length of the arc L.
[1]
(b) Calculate the area of the sector.
[2]
© OCR 2020
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3
You are given that y = 4x + sin 8x .
(a) Find
dy
.
dx
[2]
(b) Find the smallest positive value of x for which
4
dy
= 0 , giving your answer in an exact form.
dx
[2]
Fig. 4 shows a cumulative frequency diagram for the time spent revising mathematics by year 11
students at a certain school during a week in the summer term.
Year 11 Students
250
200
Cumulative 150
Frequency
100
50
0
0
20
40 60 80 100 120 140
Time in Minutes
Fig. 4
(a) Use the diagram to estimate the median time spent revising mathematics by these students. [1]
A teacher comments that 90% of the students spent less than an hour revising mathematics during
this week.
(b) Determine whether the information in the diagram supports this comment.
5
[1]
The first n terms of an arithmetic series are
17 + 28 + 39 + … + 281 + 292.
(a) Find the value of n.
[1]
(b) Find the sum of these n terms.
[2]
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6
1
(a) Find the first three terms in ascending powers of x of the binomial expansion of (1 + 4x) 2 . [3]
(b) State the range of values of x for which this expansion is valid.
7
[1]
You are given that P (A) = 0.6 , P (B) = 0.5 and P (A , B)l = 0.2 .
(a) Find P (A + B) .
[2]
(b) Find P (A B) .
[2]
(c) State, with a reason, whether A and B are independent.
[1]
© OCR 2020
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BLANK PAGE
© OCR 2020
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Answer all the questions.
Section B (77 marks)
8
Rosella is carrying out an investigation into the age at which adults retire from work in the city
where she lives. She collects a sample of size 50, ensuring this comprises of 25 randomly selected
retired men and 25 randomly selected retired women.
(a) State the name of the sampling method she uses.
[1]
Fig. 8.1 shows the data she obtains in a frequency table and Fig. 8.2 shows these data displayed in
a histogram.
Age in years at retirement
45 –
50 –
55 –
60 –
65 –
70 –
75 – 80
Frequency density
0.4
1.8
2.4
2.2
1.8
1.2
0.2
Fig. 8.1
2.5
2.0
1.5
Frequency
Density
1.0
0.5
0
40
50
60
70
Age in Years
80
Fig. 8.2
(b) How many people in the sample are aged between 50 and 55?
[1]
Rosella obtains a list of the names of all 4960 people who have retired in the city during the
previous month.
(c) Describe how Rosella could collect a sample of size 200 from her list using
• systematic sampling such that every item on the list could be selected,
• simple random sampling.
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Rosella collects two simple random samples, one of size 200 and one of size 500, from her list. The
histograms in Fig. 8.3 show the data from the sample of size 200 on the left and the data from the
sample of 500 on the right.
30
12
24
18
Frequency
Density 12
Frequency 8
Density
4
6
0
40
0
50
60
70
Age in Years
Sample size 200
80
40
90
50
60
70
Age in Years
Sample size 500
Fig. 8.3
(d) With reference to the histograms shown in Fig. 8.2 and Fig. 8.3, explain why it appears
reasonable to model the age of retirement in this city using the Normal distribution.
[1]
Summary statistics for the sample of 500 are shown in Fig. 8.4.
Statistics
n
Mean
500
60.0515
σ
s
Σx
6.5717
6.5783
30025.7601
1824686.322
36.0793
Min
55.2573
Q1
Median 59.9202
64.4239
Q3
81.742
Max
Σx2
Fig. 8.4
(e) Use an appropriate Normal model based on the information in Fig. 8.4 to estimate the number
of people aged over 65 who retired in the city in the previous month.
[4]
(f) Identify a limitation in using this model to predict the number of people aged over 65 retiring
in the following month.
[1]
© OCR 2020
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9
A company supplies computers to businesses. In the past the company has found that computers
are kept by businesses for a mean time of 5 years before being replaced. Claud, the manager of the
company, thinks that the mean time before replacing computers is now different.
(a) Describe how Claud could obtain a cluster sample of 120 computers used by businesses the
company supplies.
[1]
Claud decides to conduct a hypothesis test at the 5% level to test whether there is evidence to
suggest that the mean time that businesses keep computers is not 5 years. He takes a random sample
of 120 computers. Summary statistics for the length of time computers in this sample are kept are
shown in Fig. 9.
Statistics
n
Mean
120
4.8855
σ
s
Σx
2.6941
2.7054
Σx2
Min
Q1
Median
Q3
586.2566
3735.1475
0.1213
2.5472
4.8692
7.0349
Max
9.9856
Fig. 9
(b) In this question you must show detailed reasoning.
• State the hypotheses for this test, explaining why the alternative hypothesis takes the form
it does.
• Use a suitable distribution to carry out the test.
© OCR 2020
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10 In this question you must show detailed reasoning.
The equation of a curve is
y=
sin 2x - x
.
x sin x
(a) Use the small angle approximation given in the list of formulae on pages 2–3 of this question
paper to show that
0.05
y
y dx . ln 5 .
[4]
0.01
(b) Use the same small angle approximation to show that
dy
.- 10000 at the point where x = 0.01.
dx
[2]
The equation y = 0 has a root near x = 1. Joan uses the Newton-Raphson method to find this root.
The output from the spreadsheet she uses is shown in Fig. 10.1.
n
0
xn
1
1
2
3
0.958509 0.950084 0.948261
4
0.94786
5
6
7
0.947772 0.947753 0.947748
Fig. 10.1
Joan carries out some analysis of this output. The results are shown in Fig. 10.2.
x
y
0.9477475
–7.79967E–07
0.9477485
–2.90821E‒06
x
y
0.947745
4.54066E–06
0.947755
–1.67417E–05
Fig. 10.2
(c) Consider the information in Fig. 10.1 and Fig. 10.2.
• Write 4.54066E‒06 in standard mathematical notation.
• State the value of the root as accurately as you can, justifying your answer.
© OCR 2020
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[3]
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11 The pre-release material contains information concerning median house prices over the period
2004 – 2015. A spreadsheet has been used to generate a time series graph for two areas: the London
borough of “Barking and Dagenham” and “North West”. This is shown together with the raw data
in Fig. 11.1.
Median House Price
300 000
250 000
200 000
150 000
100 000
50 000 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Barking and Dagenham 160 000 163 000 168 000 185 000 190 000 160 000 171 000 170 000 174 995 180 995 215 000 243 500
North West
107 000 118 000 127 000 134 750 129 950 130 000 130 000 127 000 130 000 131 000 138 500 140 000
Barking and Dagenham
North West
Fig. 11.1
Dr Procter suggests that it is unusual for median house prices in a London borough to be consistently
higher than those in other parts of the country.
(a) Use your knowledge of the large data set to comment on Dr Procter’s suggestion.
[1]
Dr Procter wishes to predict the median house price in Barking and Dagenham in 2016. She uses
the spreadsheet function LINEST to find the equation of the line of best fit for the given data. She
obtains the equation
P = 4897Y - 9 657 847, where P is the median house price in pounds and Y is the calendar year, for
example 2015.
(b) Use Dr Procter’s equation to predict the median house price in Barking and Dagenham in
• 2016
• 2017.
[2]
Professor Jackson uses a simpler model by using the data from 2014 and 2015 only to form a
straight-line model.
(c) Find the equation Professor Jackson uses in her model.
[2]
(d) Use Professor Jackson’s equation to predict the median house price in Barking and Dagenham
in
• 2016
• 2017.
© OCR 2020
[2]
H640/02 Jun20
PMT
13
Professor Jackson carries out some research online. She finds some information about median
house prices in Barking and Dagenham, which is shown in Fig. 11.2.
2016
2017
£290 000
£300 000
Fig. 11.2
(e) Comment on how well
• Dr Procter’s model fits the data,
• Professor Jackson’s model fits the data.
[2]
(f) Explain which, if any, of the models is likely to be more reliable for predicting median house
prices in Barking and Dagenham in 2020.
[1]
12 In this question you must show detailed reasoning.
A 5-sided spinner can give scores of 1, 2, 3, 4 or 5. After observing a large number of spins, Elaine
models the probability distribution of X, the score on the spinner, as shown in Fig. 12.
x
P(X = x)
1
2
3
4
5
0.2
0.3
p
p
q
Fig. 12
When the spinner is spun twice, the probability of obtaining a total score of 9 is 0.06.
(a) Given that q 1 2p, determine the values of p and q.
[6]
(b) The spinner is spun 10 times. Calculate the probability that exactly one 5 is obtained.
[2]
Elaine’s teacher believes that the probability that the spinner shows a 1 is greater than 0.2. The
spinner is spun 100 times and gives a score of 1 on 28 occasions.
(c) Conduct a hypothesis test at the 5% level to determine whether there is any evidence to suggest
that the probability of obtaining a score of 1 is greater than 0.2.
[7]
© OCR 2020
H640/02 Jun20
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13 The pre-release material contains information concerning median house prices, recycling rates and
employment rates. Fig. 13.1 shows a scatter diagram of recycling rate against employment rate for
a random sample of 33 regions.
55
50
45
40
Recycling 35
Rate
30
25
20
15
10
60
65
70
75
Employment Rate
80
85
Fig. 13.1
The product moment correlation coefficient for this sample is 0.37154 and the associated p-value is
0.033.
Lee conducts a hypothesis test at the 5% level to test whether there is any evidence to suggest there
is positive correlation between recycling rate and employment rate. He concludes that there is no
evidence to suggest positive correlation because 0.033 . 0 and 0.37154 2 0.05.
(a) Explain whether Lee’s reasoning is correct.
[2]
Fig. 13.2 shows a scatter diagram of recycling rate against median house price for a random sample
of 33 regions.
55
50
45
40
Recycling 35
Rate
30
25
20
15
10
120 000
320 000
520 000 720 000 920 000
Median House Price
Fig. 13.2
© OCR 2020
H640/02 Jun20
1 120 000 1 320 000
PMT
15
The product moment correlation coefficient for this sample is -0.33278 and the associated p-value
is 0.058.
Fig. 13.3 shows summary statistics for the median house prices for the data in this sample.
Statistics
n
Mean
33
465467.9697
σ
s
Σx
201236.1345
204356.2606
Σx2
Min
Q1
Median
Q3
15360443
8486161617387
243500
342500
410000
521000
Max
1200000
Fig. 13.3
(b) Use the information in Fig. 13.3 and Fig. 13.2 to show that there are at least two outliers. [2]
(c) Describe the effect of removing the outliers on
• the product moment correlation coefficient between recycling rate and median house price,
• the p-value associated with this correlation coefficient,
in each case explaining your answer.
[2]
All 33 items in the sample are areas in London. A student suggests that it is very unlikely that only
areas in London would be selected in a random sample.
(d) Use your knowledge of the pre-release material to explain whether you think the student’s
suggestion is reasonable.
[1]
© OCR 2020
H640/02 Jun20
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16
14 In this question you must show detailed reasoning.
1
2
Fig. 14 shows the graphs of y = sin x cos 2x and y =
- sin2x cosx.
y
1
y = 12 – sin2x cosx
0.5
0
0.5
1
x
y = sin x cos 2x
–0.5
Fig. 14
Use integration to find the area between the two curves, giving your answer in an exact form. [8]
© OCR 2020
H640/02 Jun20
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17
15 Functions f (x) and g (x) are defined as follows.
f (x) = x for x 2 0 and g (x) = x 3 - x - 6 for x 2 2.
The function h (x) is defined as
h (x) = fg (x).
(a) Find h (x) in terms of x and state its domain.
[2]
(b) Find h (3).
[1]
Fig. 15 shows h (x) and h -1 (x) , together with the straight line y = x.
y
h -1 (x)
x
h (x)
Fig. 15
(c) Determine the gradient of y = h -1 (x) at the point where y = 3.
END OF QUESTION PAPER
© OCR 2020
H640/02 Jun20
[4]
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BLANK PAGE
© OCR 2020
H640/02 Jun20
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BLANK PAGE
© OCR 2020
H640/02 Jun20
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20
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2020
H640/02 Jun20
PMT
Oxford Cambridge and RSA
Wednesday 13 October 2021 – Afternoon
A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Time allowed: 2 hours
* 8 9 7 9 6 7 7 9 7 5 *
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2021 [603/1002/9]
DC (RW/FC) 301024/6
OCR is an exempt Charity
Turn over
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2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2021
H640/02 Oct21
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2021
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/02 Oct21
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Answer all the questions.
Section A (23 marks)
1
The equation of a curve is y = 4x 2 + 8x + 1.
The curve is stretched parallel to the x-axis with scale factor 2.
Find the equation of the new curve, giving your answer in the form y = ax 2 + bx + c , where a, b
and c are integers to be determined.
[2]
2
(a) Write 65° in radians, giving your answer in the form kr , where k is a fraction in its lowest
terms.
[2]
(b) Write 0.211 radians in degrees, giving your answer correct to 1 decimal place.
[1]
3
Draw a number line to show the values of x which belong to the set {x: x H 2} + {x: x 1 7}.
[3]
4
Sketch the graph of y = 2x - 3 .
[3]
5
It is known that 40% of people in Britain carry a certain gene.
A random sample of 32 people is collected.
(a) Calculate the probability that exactly 12 people carry the gene.
[1]
(b) Calculate the probability that at least 8 people carry the gene, giving your answer correct to
3 decimal places.
[2]
6
You are given that v = 2a + 3b , where a and b are the position vectors
-1
5
a = c m and b = c m .
6
3
7
(a) Determine the magnitude of v.
[3]
1
(b) Determine the angle between v and the vector c m.
0
[2]
The parametric equations of a circle are
x = 7 + 5 cos i ,
y = 5 sin i - 3 , for 0 G i G 2r .
(a) Find a cartesian equation of the circle.
[3]
(b) State the coordinates of the centre of the circle.
[1]
© OCR 2021
H640/02 Oct21
PMT
5
Answer all the questions.
Section B (77 marks)
8
The Normal variable X is transformed to the Normal variable Y.
The transformation is y = a + bx , where a and b are positive constants.
You are given that X + N (42, 6.8) and Y + N (57.2, 11.492) .
Determine the values of a and b.
9
[4]
Labrador puppies may be black, yellow or chocolate in colour. Some information about a litter of
9 puppies is given in the table.
male
female
black
1
3
yellow
2
1
chocolate
1
1
Four puppies are chosen at random to train as guide dogs.
(a) Determine the probability that exactly 3 females are chosen.
[3]
(b) Determine the probability that at least 3 black puppies are chosen.
[3]
(c) Determine the probability that exactly 3 females are chosen given that at least 3 black puppies
are chosen.
[3]
(d) Explain whether the 2 events
‘choosing exactly 3 females’ and ‘choosing at least 3 black puppies’
are independent events.
© OCR 2021
[1]
H640/02 Oct21
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6
10 Ben has an interest in birdwatching.
For many years he has identified, at the start of the year, 32 days on which he will spend an hour
counting the number of birds he sees in his garden.
He divides the year into four using the Meteorological Office definition of seasons. Each year
he uses stratified sampling to identify the 32 days on which he will count the birds in his garden,
drawn equally from the four seasons.
Ben’s data for 2019 are shown in the stem and leaf diagram in Fig. 10.1.
0
1
2
3
4
5
6
3
0
0
0
0
1
0
5
0
1
0
3
9
1
4
2
6
9 9
1 2 4 5 6 7 8 9
6 7 8 9
3
Fig. 10.1
(a) Suggest a reason why Ben chose to use stratified sampling instead of simple random sampling.
[1]
(b) Describe the shape of the distribution.
[1]
(c) Explain why the mode is not a useful measure of central tendency in this case.
[1]
(d) For Ben’s sample, determine
• the median,
• the interquartile range.
[3]
Ben found a boxplot for the sample of size 32 he collected using stratified sampling in 2015.
The boxplot is shown in Fig. 10.2.
0
10
20
30
40
50
Number of birds
Fig. 10.2
© OCR 2021
H640/02 Oct21
60
70
PMT
7
In 2016 Ben replaced his hedge with a garden fence.
Ben now believes that
• he sees fewer birds in his garden,
• the number of birds he sees in his garden is more variable.
(e) With reference to Fig. 10.2 and your answer to part (d), comment on whether there is any
evidence to support Ben’s belief.
[2]
Jane says she can tell that the data for 2015 is definitely uniformly distributed by looking at the
boxplot.
(f) Explain why Jane is wrong.
[1]
11 In 2010 the heights of adult women in the UK were found to have mean n = 161.6 cm and variance
v 2 = 1.96 cm 2 .
It is believed that the mean height of adult women in 2020 in the UK is greater than in 2010.
In 2020 a researcher collected a random sample of the heights of 200 adult women in the UK.
The researcher calculated the sample mean height and carried out a hypothesis test at the 5% level
to investigate whether there was any evidence to suggest that the mean height of adult women in
the UK had increased.
The researcher assumed that the variance was unaltered.
(a) • State suitable hypotheses for the test, defining any variables you use.
• Explain whether the researcher conducted a 1-tail or a 2-tail test.
[3]
(b) Determine the critical region for the test.
[2]
The researcher found that the sample mean was 161.9 cm and made the following statements.
• The sample mean is in the critical region.
• The null hypothesis is accepted.
• This proves that the mean height of adult women in the UK is unaltered at 161.6 cm.
(c) Explain whether each of these statements is correct.
© OCR 2021
H640/02 Oct21
[3]
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8
12 Fig. 12.1 shows an excerpt from the pre-release material.
A
B
C
D
E
F
G
H
1
Sex
Age
Marital
Weight
Height
BMI
Waist
Pulse
2
Female
34
Married
60.3
173.4
20.05
82.5
74
3
Female
85
Widowed
64.7
161.2
24.9
#N/A
#N/A
4
Female
48
Divorced
100.6
171.4
34.24
105.6
92
5
Male
61
Married
70.9
169.5
24.68
92.2
70
6
Male
68
Divorced
96.8
181.6
29.35
112.9
68
Fig. 12.1
There was no data available for cell H3.
(a) Explain why #N/A is used when no data is available.
[1]
Fig. 12.2 shows a scatter diagram of pulse rate against BMI (Body Mass Index) for females.
All the available data was used.
Pulse rate against BMI for females
140
120
100
Pulse
rate
80
60
40
20
0
0
10
20
30
40
50
BMI
Fig. 12.2
There are two outliers on the diagram.
(b) On the copy of Fig. 12.2 in the Printed Answer Booklet, ring these outliers.
[1]
(c) Use your knowledge of the pre-release material to explain whether either of these outliers
should be removed.
[2]
(d) State whether the diagram suggests there is any correlation between pulse rate and BMI.
© OCR 2021
H640/02 Oct21
[1]
PMT
9
The product moment correlation coefficient between waist measurement, w, in cm and BMI, b,
for females was found to be 0.912. All the available data was used.
(e) Explain why a model of the form w = mb + c for the relationship between waist measurement
and BMI is likely to be appropriate.
[1]
The LINEST function on a spreadsheet gives m = 2.16 and c = 33.0 .
(f) Calculate an estimate of the value for cell G3 in Fig. 12.1.
[1]
13 At a certain factory Christmas tree decorations are packed in boxes of 10.
The quality control manager collects a random sample of 100 boxes of decorations and records the
number of decorations in each box which are damaged.
His results are displayed in Fig. 13.1.
Number of damaged decorations
0
1
2
3
4
5 or more
Number of boxes
19
35
28
13
5
0
Fig. 13.1
(a) Calculate
• the mean number of damaged decorations per box,
• the standard deviation of the number of damaged decorations per box.
[2]
It is believed that the number of damaged decorations in a box of 10, X, may be modelled by a
binomial distribution such that X + B (n, p) .
(b) State suitable values for n and p.
[1]
(c) Use the binomial model to complete the copy of Fig. 13.2 in the Printed Answer Booklet,
giving your answers correct to 1 decimal place.
[3]
Number of damaged decorations
0
1
2
3
4
5 or more
Observed number of boxes
19
35
28
13
5
0
Expected number of boxes
Fig. 13.2
(d) Explain whether the model is a good fit for these data.
© OCR 2021
H640/02 Oct21
[1]
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10
14 The equation of a curve is
y = x 2 (x - 2) 3 .
(a) Find
dy
, giving your answer in factorised form.
dx
(b) Determine the coordinates of the stationary points on the curve.
In part (c) you may use the result
[4]
[4]
d2y
2
2 = 4 (x - 2) (5x - 8x + 2) .
dx
(c) Determine the nature of the stationary points on the curve.
[3]
(d) Sketch the curve.
[2]
3
15 (a) Show that
/ 0.99 r - 1 # 0.01 = 1 .
[3]
r =1
Kofi is a very good table tennis player. Layla is determined to beat him.
Every week they play one match of table tennis against each other. They will stop playing when
Layla wins the match for the first time.
X is the discrete random variable “the number of matches they play in total”.
Kofi models the situation using the probability function
P (X = r) = 0.99 r - 1 # 0.01
r = 1, 2, 3, 4, f
Kofi states that he is 95% certain that Layla will not beat him within 6 years.
(b) Determine whether Kofi’s statement is consistent with his model.
[3]
In between matches, Layla practises, but Kofi does not.
(c) Explain why Layla might disagree with Kofi’s model.
[1]
Layla models the situation using the probability function
P (X = r) = kr 2
r = 1, 2, 3, 4, 5, 6, 7, 8.
(d) Explain how Layla’s model takes into account the fact that she practises between matches, but
Kofi’s does not.
[1]
Layla states that she is 95% certain that she will beat Kofi within the first 6 matches.
(e) Determine whether Layla’s statement is consistent with her model.
© OCR 2021
H640/02 Oct21
[3]
PMT
11
16 In this question you must show detailed reasoning.
Find
y 1 +x
x
dx .
[8]
END OF QUESTION PAPER
© OCR 2021
H640/02 Oct21
PMT
12
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2021
H640/02 Oct21
PMT
A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Sample Question Paper
Version 2
Date – Morning/Afternoon
Time allowed: 2 hours
You must have:
• Printed Answer Booklet
Sp
ec
im
en
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer Booklet.
Additional paper may be used if necessary but you must clearly show your candidate number,
centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Book consists of 20 pages. The Question Paper consists of 16 pages.
© OCR 2018
603/1002/9
H640/02
B10026/5.2
Turn over
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2
Formulae A Level Mathematics B (MEI) H640
Arithmetic series
Sn  12 n(a  l )  12 n{2a  (n 1)d}
Geometric series
a(1  r n )
1 r
a
S 
for r  1
1 r
Sn 
Binomial series
(a  b)n  a n  n C1 a n1b  n C2 a n2b2 
 n Cr a n r b r 
 bn
en
n
n!
where n Cr  n Cr    
 r  r !(n  r )!
n(n  1) 2
n(n  1) (n  r  1) r
(1  x) n  1  nx 
x 

x 
2!
r!
Sp
ec
im
Differentiation
f ( x)
tan kx
sec x
cot x
cosec x
du
dv
u
u dy
Quotient Rule y  ,
 dx 2 dx
v dx
v
k sec 2 kx
sec x tan x
 cosec 2 x
 cosec x cot x
Differentiation from first principles
f ( x  h)  f ( x )
f ( x)  lim
h0
h
Integration
f ( x)
dx  ln f ( x)  c
f ( x)


n
Integration by parts
1
n 1
 f ( x)   c
n 1

u
dv
du
dx  uv  v dx
dx
dx

Small angle approximations
sin    , cos   1  12  2 , tan    where θ is measured in radians
© OCR 2018
x
f ( x)
v
f ( x)  f ( x)  dx 
(n  ) ,
H640/02
 1, n 

PMT
3
Trigonometric identities
sin( A  B)  sin A cos B  cos A sin B
cos( A  B)  cos A cos B
tan( A  B) 
sin A sin B
tan A  tan B
1 tan A tan B
( A  B  (k  12 ) )
Numerical methods
b
a y dx  12 h{( y0  yn )  2( y1  y2  …  yn1) }, where h 
Trapezium rule:
The Newton-Raphson iteration for solving f( x)  0 : xn1  xn 
ba
n
f( xn )
f ( xn )
Probability
P( A  B)  P( A)  P( B)  P( A  B)
or
Sample variance
P( A | B) 
P( A  B)
P(B )
en
P( A  B)  P( A) P( B | A)  P( B) P( A | B )
  xi   x2  nx 2
1
s 
S xx where S xx   ( xi  x )2   xi2 
i
n 1
n
Sp
ec
im
2
2
Standard deviation, s  variance
The binomial distribution
If X ~ B(n, p) then P( X  r )  n Cr p r q nr where q  1  p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution

 2
X 
If X ~ N  ,  2 then X ~ N   ,
~ N(0, 1)
 and
n 
/ n



Percentage points of the Normal distribution
p
z
10
1.645
5
1.960
2
2.326
1
2.576
Kinematics
Motion in a straight line
v  u  at
s  ut  12 at 2
Motion in two dimensions
v  u  at
s  ut  12 at 2
v 2  u 2  2as
s  vt  12 at 2
s  vt  12 at 2
© OCR 2018
H640/02
s  12  u  v  t
s  12  u  v  t
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PMT
4
Answer all the questions.
Section A (23 marks)
1
In this question you must show detailed reasoning.
Find the coordinates of the points of intersection of the curve y  x2  x and the line 2 x  y  4 . [5]
Given that f ( x)  x3 and g( x)  2 x3  1 , describe a sequence of two transformations which maps
the curve y  f ( x) onto the curve y  g( x) .
[4]

4
Evaluate

cos 3 x dx , giving your answer in exact form.
Sp
ec
im
3
12
en
2
0
[3]
The function f ( x) is defined by f ( x)  x3  4 for 1  x  2.
For f 1 ( x) , determine


5
the domain
the range.
In a particular country, 8% of the population has blue eyes. A random sample of 20 people is
selected from this population.
Find the probability that exactly two of these people have blue eyes.
© OCR 2018
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[5]
[2]
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5
Each day, for many years, the maximum temperature in degrees Celsius at a particular location is
recorded. The maximum temperatures for days in October can be modelled by a Normal
distribution. The appropriate Normal curve is shown in Fig. 6.
5
10
15
en
6
20
25
Maximum temperature (°C)
Sp
ec
im
Fig. 6
(a) (i) Use the model to write down the mean of the maximum temperatures.
[1]
(ii) Explain why the curve indicates that the standard deviation is approximately 3 degrees
Celsius.
[1]
Temperatures can be converted from Celsius to Fahrenheit using the formula F  1.8C  32 ,
where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
(b)
© OCR 2018
For maximum temperature in October in degrees Fahrenheit, estimate

the mean

the standard deviation.
H640/02
[2]
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6
Answer all the questions.
Section B (77 marks)
7
Two events A and B are such that P( A)  0.6 , P( B)  0.5 and P( A  B)  0.85 . Find P( A | B) .
[4]
8
Alison selects 10 of her male friends. For each one she measures the distance between his eyes.
The distances, measured in mm, are as follows:
51 57 58 59 61 64 64 65 67 68
en
The mean of these data is 61.4. The sample standard deviation is 5.232, correct to 3 decimal
places.
Sp
ec
im
One of the friends decides he does not want his measurement to be used. Alison replaces his
measurement with the measurement from another male friend. This increases the mean to 62.0 and
reduces the standard deviation.
Give a possible value for the measurement which has been removed and find the measurement
which has replaced it.
[3]
9
A geyser is a hot spring which erupts from time to time. For two geysers, the duration of each
eruption, x minutes, and the waiting time until the next eruption, y minutes, are recorded.
(a) For a random sample of 50 eruptions of the first geyser, the correlation coefficient between x
and y is 0.758.
The critical value for a 2-tailed hypothesis test for correlation at the 5% level is 0.279.
Explain whether or not there is evidence of correlation in the population of eruptions.
[2]
© OCR 2018
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7
The scatter diagram in Fig. 9 shows the data from a random sample of 50 eruptions of the second
geyser.
Waiting time, y
100
90
80
70
60
50
40
30
20
10
0
1
2
3
4
Fig. 9
5
6
en
0
Duration of eruption, x
10
Sp
ec
im
(b) Stella claims the scatter diagram shows evidence of correlation between duration of eruption
and waiting time. Make two comments about Stella’s claim.
[2]
A researcher wants to find out how many adults in a large town use the internet at least once a
week. The researcher has formulated a suitable question to ask.
For each of the following methods of taking a sample of the adults in the town, give a reason why
the method may be biased.
Method A: Ask people walking along a particular street between 9 am and 5 pm on one Monday.
Method B: Put the question through every letter box in the town and ask people to send back answers.
Method C: Put the question on the local council website for people to answer online.
© OCR 2018
H640/02
[3]
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8
11
Suppose x is an irrational number, and y is a rational number, so that y 
where m and n are integers and n  0 .
Prove by contradiction that x + y is not rational.
12
m
,
n
[4]
Fig. 12 shows the curve 2 x3  y3  5 y .
Sp
ec
im
en
y
x
O
Fig. 12
(a)
Find the gradient of the curve 2 x3  y3  5 y at the point (1, 2) , giving your answer in exact
form.
[4]
(b) Show that all the stationary points of the curve lie on the y-axis.
13
Evaluate
© OCR 2018

1
0
[2]
1
dx , giving your answer in the form a  b ln c , where a, b and c are integers.
1 x
[6]
H640/02
PMT
9
14
In a chemical reaction, the mass m grams of a chemical at time t minutes is modelled by the
differential equation
dm
m
.

dt t (1  2t )
At time 1 minute, the mass of the chemical is 1 gram.
(a)
Solve the differential equation to show that m 
(b)
Hence
3t
.
(1  2t )
[8]
[2]
(ii) show what happens to the mass of the chemical as t becomes large.
[2]
15
Sp
ec
im
en
(i) find the time when the mass is 1.25 grams,
A quality control department checks the lifetimes of batteries produced by a company.
The lifetimes, x minutes, for a random sample of 80 ‘Superstrength’ batteries are shown in the table
below.
Lifetime 160 ≤ x < 165 165 ≤ x < 168 168 ≤ x < 170 170 ≤ x < 172 172 ≤ x < 175 175 ≤ x < 180
Frequency
5
14
20
21
16
4
(a)
Estimate the proportion of these batteries which have a lifetime of at least 174.0 minutes.
[2]
(b)
© OCR 2018
Use the data in the table to estimate

the sample mean,

the sample standard deviation.
H640/02
[3]
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10
The data in the table on the previous page are represented in the following histogram, Fig 15:
Frequency
density
155
160
165
170
Lifetime (minutes)
Fig. 15
175
180
185
en
12
11
10
9
8
7
6
5
4
3
2
1
0
Sp
ec
im
A quality control manager models the data by a Normal distribution with the mean and standard
deviation you calculated in part (b).
(c) Comment briefly on whether the histogram supports this choice of model.
(d)
(i)
(ii)
[2]
Use this model to estimate the probability that a randomly selected battery will have a
lifetime of more than 174.0 minutes.
Compare your answer with your answer to part (a).
[3]
The company also manufactures ‘Ultrapower’ batteries, which are stated to have a mean lifetime of
210 minutes.
(e)
A random sample of 8 Ultrapower batteries is selected. The mean lifetime of these batteries
is 207.3 minutes.
Carry out a hypothesis test at the 5% level to investigate whether the mean lifetime is as high
as stated. You should use the following hypotheses H 0 :   210 , H1 :   210 , where μ
represents the population mean for Ultrapower batteries.
You should assume that the population is Normally distributed with standard deviation 3.4.
[5]
© OCR 2018
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12
16
Fig. 16.1, Fig. 16.2 and Fig. 16.3 show some data about life expectancy, including some from the
pre-release data set.
Life expectancy at birth 1974 for 193 countries
30
Sweden is in
this interval
25
Percent
20
15
(70 - 75 years)
10
Ethiopia is in
this interval
5
0
30
35
40
45
50
55
60
65
70
75
80
85
Life expectancy at birth (years)
en
(35 - 40 years)
Source: CIA
World Factbook
Fig. 16.1
Sp
ec
im
Life expectancy at birth 2014 for 222 countries
30
25
Percent
20
15
10
5
0
30
35
40
45
50
55
60
65
70
75
Life expectancy at birth (years)
80
85
90
Source:
Gapminder
Fig. 16.2
-10
0
10
20
30
Increase in life expectancy from 1974 to 2014
(years)
Source: CIA World
Factbook and
Gapminder
© OCR 2018
Fig. 16.3
H640/02
Increase in life expectancy for
193 countries from 1974 to 2014
Number of values
193
Minimum
- 4.618
Lower quartile
6.9576
Median
9.986
Upper quartile
15.873
Maximum
30.742
PMT
13
(a)
Comment on the shapes of the distributions of life expectancy at birth in 2014 and 1974.
[2]
(b)
(i)
The minimum value shown in the box plot is negative.
What does a negative value indicate?
[1]
(ii) What feature of Fig 16.3 suggests that a Normal distribution would not be an
appropriate model for increase in life expectancy from one year to another year?
[1]
(iii) Software has been used to obtain the values in the table in Fig. 16.3.
Decide whether the level of accuracy is appropriate. Justify your answer.
[1]
Decide whether the maximum increase in life expectancy from 1974 to 2014 is an outlier.
Justify your answer.
[3]
Sp
ec
im
(c)
en
(iv) John claims that for half the people in the world their life expectancy has improved by
10 years or more.
Explain why Fig. 16.3 does not provide conclusive evidence for John’s claim.
[1]
Here is some further information from the pre-release data set.
Country
(d)
Life expectancy
at birth in 2014
Ethiopia
60.8
Sweden
81.9
(i)
(ii)
Estimate the change in life expectancy at birth for Ethiopia between 1974 and 2014.
Estimate the change in life expectancy at birth for Sweden between 1974 and 2014.
(iii) Give one possible reason why the answers to parts (i) and (ii) are so different.
[4]
© OCR 2018
H640/02
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14
Fig. 16.4 shows the relationship between life expectancy at birth in 2014 and 1974.
Life expectancy
at birth 2014 (years)
85
80
75
70
65
60
55
50
40.0
50.0
60.0
Life expectancy at birth 1974 (years)
70.0
80.0
Sp
ec
im
40
30.0
Source: CIA World
Factbook and
Gapminder
en
45
Fig. 16.4
A spreadsheet gives the following linear model for all the data in Fig 16.4.
(Life expectancy at birth 2014) = 30.98 + 0.67 × (Life expectancy at birth 1974)
The life expectancy at birth in 1974 for the region that now constitutes the country of South Sudan
was 37.4 years. The value for this country in 2014 is not available.
(e)
(i)
(ii)
Use the linear model to estimate the life expectancy at birth in 2014 for South Sudan.
[2]
Give two reasons why your answer to part (i) is not likely to be an accurate estimate for
the life expectancy at birth in 2014 for South Sudan.
You should refer to both information from Fig 16.4 and your knowledge of the large
data set.
[2]
(f) In how many of the countries represented in Fig. 16.4 did life expectancy drop between 1974
and 2014? Justify your answer.
[3]
END OF QUESTION PAPER
© OCR 2018
H640/02
PMT
Oxford Cambridge and RSA
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Insert
Friday 15 June 2018 – Afternoon
* 7 0 8 8 4 3 6 9 3 9 *
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INFORMATION FOR CANDIDATES
• This Insert contains the article for Section B.
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INSTRUCTION TO EXAMS OFFICER/INVIGILATOR
Do not send this Insert for marking; it should be retained in the centre or recycled.
Please contact OCR Copyright should you wish to re-use this document.
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2
Arithmetic and Geometric Means
Arithmetic and geometric mean of two numbers
a+b
. For two
2
non-negative real numbers a and b, the geometric mean of the two numbers is defined to be ab.
For two real numbers a and b, the arithmetic mean of the numbers is defined to be
Squares of real numbers cannot be negative, so we know that (a - b) 2 H 0. It follows that a 2 + b 2 H 2ab and
so (a + b) 2 H 4ab. Hence the arithmetic mean of two real non-negative numbers is greater than, or equal to,
their geometric mean.
5
a+b
H ab for a, b H 0
2
This result is known as the inequality of the arithmetic and geometric means. If the two numbers a and b are
equal then the arithmetic mean equals the geometric mean.
10
a+b
, b form an arithmetic sequence. The three non-negative real numbers a,
The three real numbers a,
2
ab, b form a geometric sequence.
Constructing the arithmetic and geometric mean of two numbers
Lengths representing the arithmetic and geometric mean of two positive numbers can be constructed with a
straight edge and compasses.
15
Fig. C1.1 shows a straight line ACB with AC of length a and CB of length b.
D
A
a
C
b
B
A
Fig. C1.1
a
C
b
B
Fig. C1.2
The line AB is first bisected, to locate its midpoint. A semicircle with AB as diameter is then drawn, and a
line at C perpendicular to the diameter is constructed. Fig. C1.2 shows this semicircle, with the perpendicular
line through C meeting the semicircle at D.
The radius of the semicircle is the arithmetic mean of a and b, and the length of CD is the geometric mean
of a and b.
To prove that the length of CD is the geometric mean of a and b, consider triangles ACD and BCD, as
shown in Fig. C1.3. Letting angle CBD = i, it follows that angle CDA is also i. Finding expressions for
tan i in each of triangles ACD and BCD leads to h = ab, where h is the length of CD.
© OCR 2018
H640/03/I Jun18
20
PMT
3
D
h
i
A
a
C
b
B
Fig. C1.3
The relationship between a, b and h in Fig. C1.3 means that a square with side CD has the same area as a
rectangle with sides equal to AC and CB. Fig. C2 shows the square and a rectangle ACFG with CF equal
in length to CB. This diagram illustrates how a straight edge and compasses can be used to construct a
square with area equal to that of a given rectangle. This method appears in Euclid’s books on Geometry (the
‘Elements’) which were published around 2300 years ago.
25
D
A
C
G
F
B
Fig. C2
Areas of rectangles
30
The inequality of arithmetic and geometric means implies that the square has the smallest perimeter of all
rectangles with the same area.
Consider a rectangle of given area A that has sides of lengths x and y, so that xy = A. The perimeter of this
x+y
H xy so
rectangle is 2(x + y). From the inequality of arithmetic and geometric means, we know that
2
that 2 (x + y) H 4 xy. But the right-hand side of this last inequality has the fixed value 4 A whatever x and
y are. For a square of area A, each side has length A and so 4 A is the perimeter of this square. Therefore,
the perimeter of any rectangle of area A is not less than this, so the square has the smallest perimeter of all
rectangles with given area.
© OCR 2018
H640/03/I Jun18
35
PMT
4
Oxford Cambridge and RSA
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Oxford Cambridge and RSA
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Question Paper
Friday 15 June 2018 – Afternoon
* 7 0 2 1 0 2 3 2 5 0 *
Time allowed: 2 hours
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• Complete the boxes provided on the Printed Answer Booklet with your name, centre
number and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If additional space is required, you should use the lined page(s) at the end of
the Printed Answer Booklet. The question number(s) must be clearly shown.
• Do not write in the barcodes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
The total mark for this paper is 75.
The marks for each question are shown in brackets [ ].
You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 20 pages. The Question Paper consists of
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2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = n ^a + lh = n "2a + ^n - 1h d ,
1
2
1
2
Geometric series
Sn =
a ^1 - r nh
1-r
S3 =
a
for r 1 1
1-r
Binomial series
^a + bhn = a n + n C 1 a n - 1 b + n C 2 a n - 2 b 2 + ... + n C r a n - r b r + ... + b n
n
n!
where n C r = n C r = c m =
r
r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h ... ^n - r + 1h r
n ^n - 1h 2
x + ... +
x + ...
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
dx
d
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f l (x) = lim
h "0
f ^x + hh - f (x)
h
Integration
c f l (x)
dd
dx = ln ; f (x) ;+ c
e f (x)
1
n
n+1
; f l (x) ^f (x)h dx = n + 1 ^f (x)h + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
© OCR 2018
H640/03 Jun18
^n ! Nh ,
^ x 1 1, n ! Rh
PMT
3
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan ^A ! Bh =
aA ! B ! ^k + 12h rk
tan A ! tan B
1 " tan A tan B
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + y nh + 2 ^y1 + y 2 + f + y n - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = xn f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
or
P ^A Bh =
P ^A k Bh
P ^Bh
Sample variance
s2 =
^/ xih2
1
= / x 2i - nx- 2
S xx where S xx = /^x i - -xh2 = / x i2 n
n-1
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
If X + N ^n, v 2h then X + N cn,
v 2m
n
and
X-n
+ N ^0, 1h
v n
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
0
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut + 12 at 2
s = ut + 12 at 2
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2018
s = 12 ^u + vh t
s = vt - 12 at 2
H640/03 Jun18
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PMT
4
Answer all the questions.
Section A (60 marks)
1
Triangle ABC is shown in Fig. 1.
A
85°
14 cm
C
32 cm
B
Fig. 1
Find the perimeter of triangle ABC.
2
3
[3]
1
The curve y = x 3 - 2x is translated by the vector c m . Write down the equation of the translated curve. [2]
-4
Fig. 3 shows a circle with centre O and radius 1 unit. Points A and B lie on the circle with angle
AOB = i radians. C lies on AO, and BC is perpendicular to AO.
A
B
C
i
O
Fig. 3
Show that, when i is small, AC . 12 i 2 .
© OCR 2018
[2]
H640/03 Jun18
PMT
5
4
In this question you must show detailed reasoning.
A curve has equation y = x - 5 +
1
. The curve is shown in Fig. 4.
x-2
y
x
O
Fig. 4
(i)
Determine the coordinates of the stationary points on the curve.
[5]
(ii)
Determine the nature of each stationary point.
[3]
(iii)
Write down the equation of the vertical asymptote.
[1]
(iv)
Deduce the set of values of x for which the curve is concave upwards.
[1]
© OCR 2018
H640/03 Jun18
Turn over
PMT
6
5
A social media website launched on 1 January 2017. The owners of the website report the number of users
the site has at the start of each month. They believe that the relationship between the number of users, n, and
the number of months after launch, t, can be modelled by n = a # 2 kt where a and k are constants.
(i)
Show that, according to the model, the graph of log 10 n against t is a straight line.
[2]
(ii)
Fig. 5 shows a plot of the values of t and log 10 n for the first seven months. The point at t = 1 is for
1 February 2017, and so on.
log10 n
4
3
2
1
t
0
0
1
2
3
4
5
6
7
8
Fig. 5
Find estimates of the values of a and k.
6
[4]
(iii)
The owners of the website wanted to know the date on which they would report that the website had
half a million users. Use the model to estimate this date.
[4]
(iv)
Give a reason why the model may not be appropriate for large values of t.
1 15
Find the constant term in the expansion of cx 2 + m .
x
© OCR 2018
H640/03 Jun18
[1]
[2]
PMT
7
7
In this question you must show detailed reasoning.
Fig. 7 shows the curve y = 5x - x 2 .
y
x
O
Fig. 7
The line y = 4 - kx crosses the curve y = 5x - x 2 on the x-axis and at one other point.
Determine the coordinates of this other point.
8
A curve has parametric equations x =
(i)
(ii)
9
10
[8]
t2
t
=
,
y
, where t ! -1.
1 + t3
1 + t3
In this question you must show detailed reasoning.
Determine the gradient of the curve at the point where t = 1.
[5]
Verify that the cartesian equation of the curve is x 3 + y 3 = xy.
[3]
The function f (x) =
ex
is defined on the domain x d R , x ! 0.
1- ex
(i)
Find f -1(x) .
[3]
(ii)
Write down the range of f -1(x) .
[1]
a
4
Point A has position vector f b p where a and b can vary, point B has position vector f 2 p and point C has
0
0
2
position vector f 4 p . ABC is an isosceles triangle with AC = AB.
2
(i)
Show that a - b + 1 = 0.
[4]
(ii)
Determine the position vector of A such that triangle ABC has minimum area.
[6]
© OCR 2018
H640/03 Jun18
Turn over
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8
Answer all the questions.
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before attempting
the questions.
11
12
a+b
Line 8 states that
H ab for a, b H 0. Explain why the result cannot be extended to apply in each of
2
the following cases.
(i)
One of the numbers a and b is positive and the other is negative.
[1]
(ii)
Both numbers a and b are negative.
[1]
a+b
H ab. Starting from (a - b) 2 H 0, give a detailed
Lines 5 and 6 outline the stages in a proof that
2
proof of the inequality of arithmetic and geometric means.
[3]
13
Consider a geometric sequence in which all the terms are positive real numbers. Show that, for any three
consecutive terms of this sequence, the middle one is the geometric mean of the other two.
[3]
14
(i)
In Fig. C1.3, angle CBD = i. Show that angle CDA is also i, as given in line 23.
[2]
(ii)
Prove that h = ab, as given in line 24.
[2]
15
It is given in lines 31–32 that the square has the smallest perimeter of all rectangles with the same area.
Using this fact, prove by contradiction that among rectangles of a given perimeter, 4L, the square with side
L has the largest area.
[3]
END OF QUESTION PAPER
Oxford Cambridge and RSA
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A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Insert
* 7 7 9 0 9 0 0 3 7 4 *
Time allowed: 2 hours
INFORMATION
• This Insert contains the article for Section B.
• This document consists of 4 pages.
INSTRUCTION TO EXAMS OFFICER/INVIGILATOR
• Do not send this Insert for marking; it should be retained in the centre or recycled.
Please contact OCR Copyright should you wish to re-use this document.
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2
Modelling a tube
Products such as toothpaste and hand cream are often sold in tubes which have a circular
cross-section at the end which has the opening for the product to be dispensed. The other end of
the tube is closed and is a straight line. The front view and side view of such a tube are shown in
Fig. C1. The circular end will be defined to be the bottom end of the tube and the straight line end
will be defined to be the top end.
Front view
5
Side view
Fig. C1
There is no simple formula for the volume of a tube of this shape, but a good approximation can be
derived using mathematical modelling.
The cross-section at the bottom of the tube is a circle; the cross-section at the top is a straight line.
Observation of tubes suggests that they are made by starting with a cylinder and closing one end by
bringing the sides together in a straight line. This means that the tube will have a volume smaller 10
than the cylinder that was used when making it. If the base radius of the tube is r, the height is h
and the volume is V then
V 1 rr 2 h .
Modelling assumptions
The following table lists the modelling assumptions which will be made, together with some 15
comments justifying each of them.
Modelling assumption
Comments
The perimeter of the cross-section of the
tube is constant all the way up.
This follows from starting with a cylinder to
make the tube.
The nozzle at the bottom of the tube and the
cap will be ignored.
Experience suggests that the nozzle and cap are
not filled with the product when the tube is first
opened so their volumes are not relevant.
The front width of the tube increases at a
constant rate from the bottom end to the top
end.
Observation suggests that this is a good
approximation.
The side width of the tube decreases at a
constant rate from the bottom end to the top
end.
This situation is shown in Fig. C2; observation
suggests that this is a close approximation for
tubes of typical sizes.
© OCR 2019
H640/03/I Jun19
3
Modelling the cross-section
y
Taking the y-axis as the axis of symmetry of the tube and
looking at the tube from the side, as shown in Fig. C2,
means that the side width of the tube is 2x at height y.
h
20
When y = 0, x = r and when y = h, x = 0 .
Assuming that the relationship between x and y is linear
means that the side width decreases at a constant rate as y
increases; this leads to ry + hx = hr .
The cross-section at the bottom of the tube is a circle, as
shown in Fig. C3.1; at the top of the tube, the cross-section
is a line, as shown in Fig. C3.3.
O
r
x
25
Fig. C2
l
r
2x
rr
Fig. C3.1
Fig. C3.2
Fig. C3.3
The exact ‘oval’ shape of the cross-section at intermediate points is not easy to determine, so a
simple approximation for the shape is used.
When the width of the tube is 2x, the cross-section will be modelled as a rectangle with semicircular 30
ends, as shown in Fig. C3.2. The radius of the semicircular ends is x. To ensure that the total
perimeter of the cross-section is a constant, the length, l, of the rectangular part of the cross-section
is given by l = r (r - x) . It can be shown that this ensures that the front width of the tube increases
at a constant rate as y increases, as required by the modelling assumptions.
Calculating the volume
35
Finding the area of the cross-section shown in Fig. C3.2 and using ry + hx = hr gives the
rr 2
cross-sectional area in terms of y as 2 (h 2 - y 2) .
h
Imagine slicing the tube into thin horizontal slices, with cross-section as shown in Fig. C3.2 and
thickness dy. The volume of the tube is given by
h
/ rhr (h - y ) dy;
2
2
2
2
since r and h are constants
0
for the tube, this can be written as
rr
h
2 h
2
/ (h - y ) d y .
2
2
0
Taking the limit as dy " 0 and evaluating the resulting integral gives V = 23 rr 2 h . This is less than
the volume of the cylinder, rr 2 h, as expected.
© OCR 2019
H640/03/I Jun19
40
4
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Friday 14 June 2019 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Time allowed: 2 hours
* 7 6 9 4 6 0 8 7 6 4 *
You must have:
• Printed Answer Booklet
• Insert
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If additional space is required, you should use the lined page(s) at the end of
the Printed Answer Booklet. The question number(s) must be clearly shown.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail
of the working to indicate that a correct method is used. You should communicate your
method with correct reasoning.
• The Printed Answer Booklet consists of 16 pages. The Question Paper consists of
8 pages.
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Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2019
H640/03 Jun19
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2019
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/03 Jun19
Turn over
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4
Answer all the questions.
Section A (60 marks)
1
The function f (x) is defined for all real x by
f (x) = 3x - 2.
2
3
(a) Find an expression for f - 1 (x) .
[2]
(b) Sketch the graphs of y = f (x) and y = f - 1 (x) on the same diagram.
[2]
(c) Find the set of values of x for which f (x) 2 f - 1 (x) .
[2]
(a) Find the transformation which maps the curve y = x 2 to the curve y = x 2 + 8x - 7 .
[4]
(b) Write down the coordinates of the turning point of y = x 2 + 8x - 7 .
[1]
(a) Express
1
in partial fractions.
(x + 2) (x + 3)
[3]
1
dx in the form ln ^f (x)h + c, where c is the constant of integration and f (x)
(b) Find <
(x + 2 ) ( x + 3 )
is a function to be determined.
[3]
4
In this question you must show detailed reasoning.
Show that
© OCR 2019
1
1
1
3
.
+
+
=
10 + 11
11 + 12
12 + 13
10 + 13
H640/03 Jun19
[3]
PMT
5
5
A student’s attempt to prove by contradiction that there is no largest prime number is shown below.
If there is a largest prime, list all the primes.
Multiply all the primes and add 1.
The new number is not divisible by any of the primes in the list and so it
must be a new prime.
The proof is incorrect and incomplete.
Write a correct version of the proof.
6
[3]
A circle has centre C (10, 4). The x-axis is a tangent to the circle, as shown in Fig. 6.
y
C (10, 4)
x
O
Fig. 6
7
(a) Find the equation of the circle.
[2]
(b) Show that the line y = x is not a tangent to the circle.
[4]
(c) Write down the position vector of the midpoint of OC.
[1]
In this question you must show detailed reasoning.
(a) Express ln 3 # ln 9 # ln 27 in terms of ln 3.
[2]
(b) Hence show that ln 3 # ln 9 # ln 27 2 6 .
[2]
© OCR 2019
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6
8
In this question you must show detailed reasoning.
A is the point (1, 0), B is the point (1, 1) and D is the point where the tangent to the curve y = x 3 at
B crosses the x-axis, as shown in Fig. 8. The tangent meets the y-axis at E.
y
B (1, 1)
D A (1, 0)
O
x
E
Fig. 8
(a) Find the area of triangle ODE.
[6]
(b) Find the area of the region bounded by the curve y = x 3, the tangent at B and the y-axis.
[4]
© OCR 2019
H640/03 Jun19
PMT
7
9
In this question you must show detailed reasoning.
The curve xy + y 2 = 8 is shown in Fig. 9.
y
O
x
Fig. 9
Find the coordinates of the points on the curve at which the normal has gradient 2.
10 Show that f (x) =
ex
is an increasing function for all values of x.
1 + ex
c x
dx .
11 By using the substitution u = 1 + x, find dd
e1+ x
© OCR 2019
H640/03 Jun19
[6]
[4]
[6]
Turn over
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8
Answer all the questions.
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before
attempting the questions.
12 Show that the equation of the line in Fig. C2 is ry + hx = hr, as given in line 24.
[2]
(i) Show that the cross-sectional area in Fig. C3.2 is rx (2r - x) .
[2]
13 (a)
(ii) Hence show that the cross-sectional area is
(b) Verify that the formula
rr
h
2
2
rr
h
2
2
(h 2 - y 2), as given in line 37.
[2]
(h 2 - y 2) for the cross-sectional area is also valid for
(i) Fig. C3.1,
[1]
(ii) Fig. C3.3.
[1]
h
14 (a) Express lim / (h 2 - y 2) dy as an integral.
dy"0
[1]
0
(b) Hence show that V = 23 rr 2 h, as given in line 41.
[3]
15 A typical tube of toothpaste measures 5.4 cm across the straight edge at the top and is 12 cm high. It
contains 75 ml of toothpaste so it needs to have an internal volume of 75 cm 3 .
Comment on the accuracy of the formula V = 23 rr 2 h, as given in line 41, for the volume in this
case.
[3]
END OF QUESTION PAPER
Oxford Cambridge and RSA
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Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
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© OCR 2019
H640/03 Jun19
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Oxford Cambridge and RSA
Monday 19 October 2020 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension Insert
Time allowed: 2 hours
* 8 1 6 8 1 3 7 9 9 3 *
INSTRUCTIONS
• Do not send this Insert for marking. Keep it in the centre or recycle it.
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• This Insert contains the article for Section B.
• This document has 4 pages.
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2
Which is bigger?
Which is bigger: r e or e r ? Using a calculator confirms that e r is the larger, but how can this be
proved without the use of a calculator?
Simpler examples
It is often helpful in mathematics to consider simpler examples. It is easy to work out that 3 4 2 4 3 .
In the expression 3 4 , 3 is the base and 4 is the exponent. Working with integers greater than 1, it is
easy to find many examples where a b 2 b a if a 1 b . That is, using the smaller base and the larger
exponent gives the larger result. This might lead us to conjecture that a b 2 b a if a 1 b and both
a and b are integers greater than 1. However, it is also possible to find counter examples to this
conjecture.
5
p
q
Exponents can also be rational numbers, and in general x q denotes ^ x h where p and q are integers 10
and q is positive. So, any rational power of a positive number, x, can be defined. However, both e
and r are irrational numbers. Considering the original question about r e and e r raises the issue of
what is meant by an irrational power of a number.
p
Extending the definition of power to irrational numbers
What, for example, is meant by 2 r ?
15
An irrational number corresponds to a non-recurring infinite decimal. Rounding the decimal gives
a rational approximation to the irrational number. For example, the following sequence gives
increasingly accurate approximations to r.
3, 3.1, 3.14, 3.142, 3.1416, 3.14159, …
Using a spreadsheet gives a sequence of approximations to 2 r , as shown in Fig. C1. The limit of this 20
sequence of approximations is the value of 2 r . This limit cannot be evaluated with a spreadsheet
but it is, in principle, possible to find the value to any required degree of accuracy.
A
B
2k
1 k
3
2
8
3
3.1 8.574188
4
3.14 8.815241
3.142
5
8.82747
6
3.1416 8.825023
7
3.14159 8.824962
Fig. C1
2 x and x 2 are increasing functions of x for x 2 0 and this allows us to deduce that r 2 2 2 r , as
follows.
© OCR 2020
H640/03/I Jun20
PMT
3
25
We know that r is between 3 and 3.142
r 1 3.142 & 2 r 1 2 3.142 = 8.827 47
r 2 3 & r2 2 32 = 9
So r 2 2 9 2 8.827 47 2 2 r
Hence r 2 2 2 r
Which is bigger: r e or e r ?
30
An indirect method, using calculus, enables us to prove that e r is larger than r e . Fig. C2 shows
1
the curve y = in the first quadrant together with the rectangle with vertices at the points (e, 0),
x
1
1
ce, m, cr, m and (r, 0). We use the fact that the area under the curve between e and r is less than
e
e
the area of this rectangle.
y
y=
1
x
e
O
r
x
Fig. C2
The area of the rectangle is
y
e
r
1
(r - e)
e
35
1
1
dx 1 (r - e)
x
e
ln r - 1 1
ln r 1
r
e
-1
r
e
e x is an increasing function for all values of x
r
hence r 1 e e
40
Assuming that the usual rules of indices apply to irrational powers of irrational numbers, raising
both sides of the inequality to the power e gives the desired result.
Using a similar method, it can be shown that e a 2 a e for any positive number a ! e .
An alternative method for showing that e a 2 a e for any positive number a is to show that the only
ln x
45
(a maximum) occurs where x = e .
stationary point on the curve y =
x
© OCR 2020
H640/03/I Jun20
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4
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2020
H640/03/I Jun20
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Oxford Cambridge and RSA
Monday 19 October 2020 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Time allowed: 2 hours
* 8 1 6 7 0 7 1 1 9 0 *
You must have:
• the Printed Answer Booklet
• the Insert
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2020 [603/1002/9]
DC (ST/FC) 185726/3
OCR is an exempt Charity
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Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2020
H640/03 Jun20
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2020
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/03 Jun20
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Answer all the questions.
Section A (60 marks)
5
1
Find the value of
/ 2 r (r - 1 ) .
[2]
r =1
2
The graph of y = 1 - x - 2 is shown in Fig. 2.
y
x
O
Fig. 2
Determine the set of values of x for which 1 - x 2 2 .
3
[4]
A particular phone battery will last 10 hours when it is first used. Every time it is recharged, it will
only last 98% of its previous time.
Find the maximum total length of use for the battery.
© OCR 2020
H640/03 Jun20
[3]
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5
4
Fig. 4 shows the regular octagon ABCDEFGH.
F
E
G
D
H
C
A
B
Fig. 4
AB = i , CD = j, where i is a unit vector parallel to the x-axis and j is a unit vector parallel to the
y-axis.
Find an exact expression for BC in terms of i and j.
© OCR 2020
H640/03 Jun20
[3]
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6
5
Fig. 5 shows part of the curve y = cosec x together with the x- and y-axes.
y
x
O
Fig. 5
(a) For the section of the curve which is shown in Fig. 5, write down
(i) the equations of the two vertical asymptotes,
[2]
(ii) the coordinates of the minimum point.
[1]
(b) Show that the equation x = cosec x has a root which lies between x = 1 and x = 2.
[2]
(c) Use the iteration x n + 1 = cosec (x n) , with x0 = 1, to find
(i) the values of x1 and x2 , correct to 5 decimal places,
[1]
(ii) this root of the equation, correct to 3 decimal places.
[1]
(d) There is another root of x = cosec x which lies between x = 2 and x = 3.
Determine whether the iteration x n + 1 = cosec (x n) with x 0 = 2.5 converges to this root.
[1]
(e) Sketch the staircase or cobweb diagram for the iteration, starting with x 0 = 2.5, on the diagram
in the Printed Answer Booklet.
[3]
© OCR 2020
H640/03 Jun20
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7
6
(a) (i) Write down the derivative of e kx , where k is a constant.
[1]
(ii) A business has been running since 2009. They sell maths revision resources online.
Give a reason why an exponential growth model might be suitable for the annual profits
for the business.
[1]
Fig. 6 shows the relationship between the annual profits of the business in thousands of pounds (y)
and the time in years after 2009 (x). The graph of ln y plotted against x is approximately a straight
line.
ln y
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
10
x
Fig. 6
(b) Show that the straight line is consistent with a model of the form y = Ae kx , where A and k are
constants.
[2]
(c) Estimate the values of A and k.
[4]
(d) Use the model to predict the profit in the year 2020.
[3]
(e) How reliable do you expect the prediction in part (d) to be? Justify your answer.
[1]
© OCR 2020
H640/03 Jun20
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8
7
(a) Express
1
1
as a single fraction.
+
x A-x
[1]
The population of fish in a lake is modelled by the differential equation
dx x (400 - x)
=
400
dt
where x is the number of fish and t is the time in years.
When t = 0, x = 100.
(b) In this question you must show detailed reasoning.
Find the number of fish in the lake when t = 10, as predicted by the model.
8
(a) The curve y =
[8]
1
is shown in Fig. 8.
^1 + x 2h2
y
x
O
Fig. 8
d 2 y 20x 2 - 4
(i) Show that 2 =
.
dx
( 1 + x 2) 4
[5]
(ii) In this question you must show detailed reasoning.
Find the set of values of x for which the curve is concave downwards.
(b) Use the substitution x = tan i to find the exact value of
© OCR 2020
H640/03 Jun20
y
[3]
1
1
dx .
2 2
-1 ^1 + x h
[8]
PMT
9
Answer all the questions.
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before
attempting the questions.
9
(a) Show that if a = 1 and b 2 1 then a b 1 b a .
[2]
(b) Find integer values of a and b with b 2 a 2 1 and a b not greater than b a (a counter example
to the conjecture given in lines 7–8).
[1]
10 In this question you must show detailed reasoning.
Show that
y
e
r
1
dx = ln r - 1 as given in line 37.
x
11 Show that e x is an increasing function for all values of x, as stated in line 39.
[2]
[2]
ln x
12 (a) Show that the only stationary point on the curve y =
occurs where x = e, as given in
x
line 45.
[3]
(b) Show that the stationary point is a maximum.
[3]
(c) It follows from part (b) that, for any positive number a with a ! e ,
ln e ln a
2
.
e
a
Use this fact to show that e a 2 a e .
[2]
END OF QUESTION PAPER
© OCR 2020
H640/03 Jun20
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© OCR 2020
H640/03 Jun20
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BLANK PAGE
© OCR 2020
H640/03 Jun20
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Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2020
H640/03 Jun20
PMT
Oxford Cambridge and RSA
Monday 18 October 2021 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Insert
* 8 9 8 0 4 0 8 4 9 2 *
Time allowed: 2 hours
INSTRUCTIONS
• Do not send this Insert for marking. Keep it in the centre or recycle it.
INFORMATION
• This Insert contains the article for Section B.
• This document has 4 pages.
© OCR 2021 [603/1002/9]
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Adding arctangents
Where does the name ‘arctangent’ come from?
The two commonly used ways to denote the angle which has a tangent x are tan -1 x and arctan x .
The first of these is related to inverse function notation, f -1 (x) . Arctangent comes from radian
measure, where an angle is represented by an arc on a unit circle; arctan x is the arc whose tangent
is x.
5
An interesting result
1
1
It can be shown that arctan c m + arctan c m = arctan 1.
2
3
C
Consider the diagram in Fig. C1.
Triangle ABC is right-angled at B.
AB = BC = 1 cm.
D is the midpoint of BC.
0.5 cm
10
D
DB 1
1
= so a = arctan c m.
BA 2
2
0.5 cm
Using triangle ABC, tan ^a + bh = 1 so a + b = arctan 1.
B
Using triangle ABD, tan a =
Hence tan ^a + bh =
b
a
tan a + tan b
= 1.
1 - tan a tan b
1 cm
A
Fig. C1
1
1
and finding tan b , it follows that b = arctan c m,
2
3
1
1
which gives the required result that arctan c m + arctan c m = arctan 1.
2
3
Using tan a =
15
Generalising the result
C
E
x cm
z
i
B
1 cm
A
Fig. C2
Triangle ABC in Fig. C2 is the same as triangle ABC in Fig. C1 but E is a point on BC such that
EB = x cm and i = arctan x .
Following the same method as above, arctan x + arctan c
© OCR 2021
1-x
m = arctan 1 .
1+x
H640/03/I Oct21
20
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The arctan addition formula
The arctangent addition formula is a further generalization:
arctan x + arctan y = arctan c
x+y
m, as long as xy 1 1.
1 - xy
tan a + tan b
This result is equivalent to the addition formula tan (a + b) =
where a = arctan x
1 - tan a tan b
25
and b = arctan y .
To see why the restriction xy 1 1 is necessary, consider what happens if xy H 1.
Clearly,
x+y
is undefined when xy = 1, so the formula does not apply in this case.
1 - xy
1
Suppose next that xy 2 1, and that x and y are both positive; in this case y 2 .
x
r
1
For any positive x, arctan x + arctan c m = .
2
x
r
1
1
y 2 & arctan y 2 arctan c m so it follows that arctan x + arctan y 2 .
2
x
x
30
However, arctan c
x+y
m cannot be greater than r as the range of the arctan function is a- r , rk.
1 - xy
2
2 2
x+y
m therefore cannot be valid in this case.
The formula arctan x + arctan y = arctan c
1 - xy
A similar argument can be used to show that the formula cannot be valid when xy 2 1 and x and y
are both negative.
If xy 2 1, the arctangent addition formula needs to be adapted, as shown below.
arctan x + arctan y = arctan c
x+y
m - r , when xy 2 1 and x, y 1 0
1 - xy
arctan x + arctan y = arctan c
x+y
m + r , when xy 2 1 and x, y 2 0
1 - xy
35
Some additional results
•
For n a positive integer, arctan c
1
1
1
m + arctan c 2
m = arctan c m; this follows directly
n+1
n
n +n+1
from the arctan addition formula in line 23.
•
r
1
arctan 1 + arctan 2 + arctan 3 = r. This can be proved by using arctan x + arctan c m =
2
x
1
1
together with arctan c m + arctan c m = arctan 1.
2
3
© OCR 2021
H640/03/I Oct21
40
PMT
4
Oxford Cambridge and RSA
Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible
opportunity.
For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2021
H640/03/I Oct21
PMT
Oxford Cambridge and RSA
Monday 18 October 2021 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Time allowed: 2 hours
* 8 9 8 0 6 7 3 1 3 6 *
You must have:
• the Printed Answer Booklet
• the Insert
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2021 [603/1002/9]
DC (LK/SG) 300394/4
OCR is an exempt Charity
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Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
S n = 12 n ^a + lh = 12 n "2a + ^n - 1h d ,
Geometric series
a ^1 - r nh
Sn =
1-r
a
for r 1 1
S3 =
1-r
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n
JnN
n!
n
where C r = n C r = KK OO =
r
L P r! ^n - rh !
^1 + xhn = 1 + nx +
n ^n - 1h f ^n - r + 1h r
n ^n - 1h 2
x +f+
x +f
2!
r!
Differentiation
f ^xh
f l^xh
tan kx
k sec 2 kx
sec x
sec x tan x
cot x
- cosec 2 x
cosec x
- cosec x cot x
du
dv
v -u
u dy
d
dx
x
Quotient Rule y = ,
=
2
v dx
v
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0
h
Integration
c f l^xh
dd
dx = ln f ^xh + c
h
^
f
x
e
n
n+1
1
; f l^xhaf ^xhk dx = n + 1 af ^xhk + c
dv
du
Integration by parts ; u dx = uv - ; v dx
dx
dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
© OCR 2021
H640/03 Oct21
^n ! Nh,
^ x 1 1, n ! Rh
PMT
3
Trigonometric identities
sin ^A ! Bh = sin A cos B ! cos A sin B
cos ^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan ^A ! Bh =
1 " tan A tan B
aA ! B ! ^k + 12h rk
Numerical methods
Trapezium rule: ; y dx . 12 h "^y0 + ynh + 2 ^y 1 + y2 + f + yn - 1h, , where h =
a
f ^x nh
The Newton-Raphson iteration for solving f ^xh = 0: x n + 1 = x n f l^x nh
b
b-a
n
Probability
P ^A j Bh = P ^Ah + P ^Bh - P ^A k Bh
P ^A k Bh = P ^Ah P ^B Ah = P ^Bh P ^A Bh
P ^A Bh =
or
P ^A k Bh
P ^Bh
Sample variance
^/ xih2
1
2
2
s =
S where S xx = /^xi - xh = / x i = / x 2i - nx- 2
n
n - 1 xx
2
Standard deviation, s = variance
The binomial distribution
If X + B ^n, ph then P ^X = rh = n C r p r q n - r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J
N
X -n
v2
If X + N ^n, v 2h then X + N KKn, OO and
+ N ^0, 1h
n
v
n
L
P
Percentage points of the Normal distribution
p
10
5
2
1
z
1.645
1.960
2.326
2.576
1 p%
2
1 p%
2
z
Kinematics
Motion in a straight line
Motion in two dimensions
v = u + at
v = u + at
s = ut +
1 2
2 at
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2021
s = ut + 12 at 2
s = 12 ^u + vh t
s = vt - 12 at 2
H640/03 Oct21
Turn over
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4
Answer all the questions.
Section A (60 marks)
1
(a) Express x 2 + 8x + 2 in the form (x + a) 2 + b .
[2]
(b) Write down the coordinates of the turning point of the curve y = x 2 + 8x + 2 .
[1]
(c) State the transformation(s) which map(s) the curve y = x 2 onto the curve y = x 2 + 8x + 2 .
[2]
2
Solve the equation sin 2x = 0.3 for 0° G x G 180° . Give your answer(s) correct to 1 decimal place.
[2]
3
(a) Determine, in terms of k, the coordinates of the point where the lines with the following
equations intersect.
x+y = k
2x - y = 1
[3]
(b) Determine, in terms of k, the coordinates of the points where the line x + y = k crosses the
[4]
curve y = x 2 + k .
4
x -x
The diagram shows points A and B on the curve y = c m .
4
The x-coordinate of A is 1 and the x-coordinate of B is 1.1.
y
A
O
B
x
(a) Find the gradient of chord AB. Give your answer correct to 2 decimal places.
[2]
(b) Give the x-coordinate of a point C on the curve such that the gradient of chord AC is a better
approximation to the gradient of the tangent to the curve at A.
[1]
© OCR 2021
H640/03 Oct21
PMT
5
5
(a) The diagram shows the curve y = e x .
y
O
x
On the axes in the Printed Answer Booklet, sketch graphs of
(i)
dy
against x,
dx
[1]
(ii)
dy
against y.
dx
[2]
(b) Wolves were introduced to Yellowstone National Park in 1995.
The population of wolves, y, is modelled by the equation
y = Ae kt ,
where A and k are constants and t is the number of years after 1995.
(i) Give a reason why this model might be suitable for the population of wolves.
[1]
(ii) When t = 0 , y = 21 and when t = 1, y = 51.
Find values of A and k consistent with the data.
[3]
(iii) Give a reason why the model will not be a good predictor of wolf populations many years
after 1995.
[1]
© OCR 2021
H640/03 Oct21
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6
6
In this question you must show detailed reasoning.
3
Show that
/
r=1
1
= 1.
r+1 + r
[4]
y x cos 2x dx .
[3]
7
Determine
8
For a particular value of a, the curve y =
a
passes through the point (3, 1).
x2
Find the coordinates of all the other points on the curve where both the x-coordinate and the
y-coordinate are integers.
[3]
9
The diagram shows the curve y = 3 - x .
y
5
4
3
2
1
–1
0
1
2
3
4
5
6
7
8
x
–1
–2
(a) Draw the line y = 5x - 1 on the copy of the diagram in the Printed Answer Booklet.
[1]
(b) In this question you must show detailed reasoning.
Determine the exact area of the region bounded by the curve y = 3 - x , the lines y = 5x - 1
[10]
and x = 4 and the x-axis.
© OCR 2021
H640/03 Oct21
PMT
7
10 (a) Express
1
in partial fractions.
(4x + 1) (x + 1)
[3]
(b) A curve passes through the point (0, 2) and satisfies the differential equation
dy
y
=
,
d x (4x + 1) (x + 1)
for x 2 - 14 .
Show by integration that y = A c
4x + 1 B
m where A and B are constants to be determined.
x+1
[6]
11 In this question you must show detailed reasoning.
The diagram shows triangle ABC, with BC = 8 cm and angle BAC = 45°.
The point D on AC is such that DC = 5 cm and BD = 7 cm.
A
45°
D
7 cm
5 cm
B
8 cm
C
Determine the exact length of AB.
© OCR 2021
[5]
H640/03 Oct21
Turn over
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8
Answer all the questions.
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before
attempting the questions.
1
12 Show that b = arctan c m, as given in line 15.
3
[3]
r
1
13 (a) Use triangle ABE in Fig. C2 to show that arctan x + arctan c m = , as given in line 29.
2
x
[1]
(b) Sketch the graph of y = arctan x .
[1]
1
(c) What property of the arctan function ensures that y 2
x
line 30?
& arctan y 2 arctan c1m, as given in
x
[1]
14 (a) Show that
arctan c
1
1
1
1
1
m + arctan c 2
m = arctan c m & arctan c m + arctan c m = arctan 1.
n+1
n
2
3
n +n+1
[1]
(b) Use the arctan addition formula in line 23 to show that
arctan c
1
1
1
m + arctan c 2
m = arctan c m, as given in line 39.
n+1
n
n +n+1
15 Prove that arctan 1 + arctan 2 + arctan 3 = r, as given in line 41.
[4]
[4]
END OF QUESTION PAPER
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© OCR 2021
H640/03 Oct21
PMT
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Sample Insert
Version 2
Date – Morning/Afternoon
ci
m
en
Time allowed: 2 hours
INFORMATION FOR CANDIDATES
Sp
e
This insert contains the article for Section B
This document consists of 4 pages. Any blank pages are indicated.
INSTRUCTION TO EXAMS OFFICER/INVIGILATOR
Do not send this Insert for marking, it should be retained in the centre or recycled. Please
contact OCR Copyright should you wish to re-use this document.
© OCR 2018
603/1002/9
H640/03/I
Turn over
PMT
2
Archimedes’s approximation of π
The constant
5
10
is defined to be the circumference of a circle divided by its diameter.
The value of has been determined to an accuracy of more than twelve trillion
decimal places. To the non-mathematician this may appear strange since it is not possible to
measure the circumference and diameter of a circle to that degree of accuracy; this article
explains how one of the greatest mathematicians of all time found the value of to a high
degree of accuracy without requiring any physical measurement.
Archimedes (287-212 BC) lived in Syracuse, Sicily. He developed many branches of
mathematics, including calculus, in which he devised methods for finding areas under
parabolas nearly 2000 years before Newton and Leibniz, and mechanics, in which he found
the centres of gravity of various plane figures and solids and devised a method for calculating
the weight of a body immersed in a liquid.
Archimedes’s method for determining the value of
is described below.
m
15
en
Whilst absorbed in a mathematical problem, Archimedes was killed by a soldier during the
capture of Syracuse by the Romans.
Fig. C1 shows a circle with unit radius and two regular hexagons.
ci
The smaller regular hexagon has its vertices on the circle; it is called an inscribed polygon. Its
perimeter is 6.
20
Sp
e
The larger regular hexagon has the midpoints of its edges on the circle; it is called an escribed
polygon. Its perimeter is 4 3 .
Fig. C1
The circumference of the circle is greater than the perimeter, ABCDEF, of the smaller
hexagon but less than the perimeter, A'B'C'D'E'F' , of the larger hexagon.
© OCR 2018
H640/03/I
PMT
3
Dividing the perimeters by the diameter of the circle gives lower and upper bounds for
of 3 and 2 3 , so that 3
25
To find tighter bounds, Archimedes repeatedly doubled the number of edges in the two
regular polygons, from 6 to 12, 24, 48 and finally 96. The process of doubling the number of
edges is described below.
Fig. C2 shows two adjacent vertices, P and Q, of a regular polygon inscribed in a circle with
unit radius and centre O. PQ has length a. M is the midpoint of PQ. OM is extended to meet
the circle at R. MR has length h. PR and RQ are adjacent edges of a regular polygon which
has twice as many edges as the polygon which has PQ as an edge. PR has length b.
ci
m
en
30
2 3.
Sp
e
Fig. C2
Applying Pythagoras’ Theorem
a2
2
1 h ,
4
a2
to triangle PMR gives b2
h2 .
4
to triangle OMP gives 1
35
For the inscribed regular hexagon, a 1 . Substituting a 1 in the equations above gives
h
2
3
2
and b
2
3 . This can be written in the equivalent form b
6
2
2
Therefore a regular polygon with 12 edges inscribed in a unit circle has edge length
.
6
2
2
Archimedes repeated this process to find the edge lengths of inscribed regular polygons with
24, 48 and 96 edges. He then used a similar technique for escribed regular polygons.
40
The inscribed and escribed regular polygons with 96 edges provide bounds for
now write, using decimal notation, as
3.14103...
3.14271... .
© OCR 2018
H640/03/I
which we
.
PMT
4
Summary of Updates
Version
2
Change
We’ve reviewed the look and feel of our papers through
text, tone, language, images and formatting. For more
information please see our assessment principles in our
“Exploring our question papers” brochures on our website.
Sp
e
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m
en
Date
October 2018
Copyright Information:
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attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of
answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements booklet. This is produced for each series of examinations and is freely available to download from our
public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be
happy to correct its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge,
CB2 9EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© OCR 2018
H640/03/I
PMT
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Sample Question Paper
Version 2
Date – Morning/Afternoon
Time allowed: 2 hours
You may use:
• a scientific or graphical calculator
en
You must have:
• Printed Answer Booklet
• the Insert
0
0
0
0
0
0
*
im
*
Sp
ec
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number and
candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer Booklet.
Additional paper may be used if necessary but you must clearly show your candidate number,
centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by g m s-2. Unless otherwise instructed, when a
numerical value is needed, use g = 9.8.
INFORMATION
• The total number of marks for this paper is 75.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Booklet consists of 20 pages. The Question Paper consists of 12 pages.
© OCR 2018
603/1002/9
H640/03
B10027/5.2
Turn over
PMT
2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
Sn 12 n(a l ) 12 n{2a (n 1)d}
Geometric series
Sn
S
a(1 r n )
1 r
a
for r
1 r
1
Binomial series
an
where n Cr
(1 x) n
n
C1 a n 1b
n
n Cr
n
C2 a n 2b2
n!
r !(n r )!
r
n(n 1) 2
x
2!
n(n 1)
Differentiation
f ( x)
tan kx
sec x
cot x
cosec x
f ( x)
ec
k sec 2 kx
sec x tan x
cosec 2 x
cosec x cot x
u dy
,
v dx
v
du
dv
u
dx
dx
v2
Differentiation from first principles
f ( x h) f ( x )
f ( x) lim
h 0
h
Integration
f ( x)
dx ln f ( x)
f ( x)
c
1
n
f ( x) f ( x) dx
n 1
u
Integration by parts
f ( x)
n 1
dv
dx uv
dx
c
v
du
dx
dx
Small Angle Approximations
sin
, cos
© OCR 2018
bn
(n r 1) r
x
r!
Sp
Quotient Rule y
Cr a n r b r
im
1 nx
n
1
1
2
2
, tan
(n
en
(a b)n
where θ is measured in radians
H640/03
x
1, n
),
PMT
3
Trigonometric identities
sin( A B) sin A cos B cos A sin B
cos( A B) cos A cos B sin A sin B
tan A tan B
1 tan A tan B
tan( A B)
1
)
2
( A B (k
)
Numerical methods
Trapezium rule:
b
a
1
2
y dx
h{( y0
yn ) 2( y1
y2
… yn 1 ) }, where h
The Newton-Raphson iteration for solving f( x) 0 : xn
Probability
P( A B) P( A) P( B) P( A
B)
B)
P( A) P( B | A) P( B) P( A | B )
or
P( A | B)
Sample Variance
Standard deviation, s
x )2
( xi
xi2
variance
The Binomial Distribution
If X ~ B(n, p) then P( X
r)
n
Cr p r q n
r
Sp
Mean of X is np
(
xi )2
xi2 nx 2
im
n 1
S xx where S xx
P( A B)
P(B )
n
ec
1
s2
f( xn )
f ( xn )
xn
en
P( A
1
b a
n
where q 1 p
Hypothesis testing for the mean of a Normal distribution
2
If X ~ N
,
2
then X ~ N
,
n
and
X
/ n
~ N(0, 1)
Percentage points of the normal distribution
p
z
10
1.645
5
1.960
2
2.326
1
2.576
Kinematics
Motion in a straight line
v u at
s ut 12 at 2
u v t
s
1
2
v 2 u 2 2as
s vt 12 at 2
s
vt
© OCR 2018
H640/03
s
1
2
Motion in two dimensions
v u at
s ut 12 at 2
u v t
1
at 2
2
Turn over
PMT
4
Answer all the questions
Section A (60 marks)
2
5
as a single fraction.
x 1 2x 1
1
Express
[2]
2
Find the first four terms of the binomial expansion of 1 2x 2 .
1
[4]
im
en
State the set of values of x for which the expansion is valid.
Show that points A (1, 4, 9), B (0, 11, 17) and C (3, –10, –7) are collinear.
4
Show that
4
r 1
© OCR 2018
r
ln 5 .
Sp
ln
ec
3
r 1
H640/03
[4]
[3]
PMT
5
5
In this question you must show detailed reasoning.
Fig. 5 shows the circle with equation ( x 4)2 ( y 1)2 10 .
The points (1, 0) and (7, 0) lie on the circle. The point C is the centre of the circle.
C
en
y
(7, 0)
x
ec
im
O (1,0)
Sp
Fig. 5
Find the area of the part of the circle below the x-axis.
© OCR 2018
H640/03
[5]
Turn over
PMT
6
6
Fig. 6 shows the curve with equation y
x4 6x2 4x 5 .
y
x
im
en
O
ec
Fig. 6
7
[5]
Sp
Find the coordinates of the points of inflection.
By finding a counter example, disprove the following statement.
If p and q are non-zero real numbers with p q , then
© OCR 2018
H640/03
1
p
1
.
q
[2]
PMT
7
8
In Fig. 8, OAB is a thin bent rod, with OA = 1 m, AB = 2 m and angle OAB = 120 .
Angles , and h are as shown in Fig. 8.
y
B
2m
120°
1m
C
O
x
im
A
θ
en
hm
D
ec
E
Fig. 8
Show that h sin
2sin(
60 ) .
Sp
(a)
The rod is free to rotate about the origin so that
h in part (a) holds for all values of
(b)
Find an angle
© OCR 2018
[3]
and
vary. You may assume that the result for
.
for which h 0 .
[5]
H640/03
Turn over
PMT
8
9
(a) Express cos
2sin
in the form R cos(
) , where 0
1
2
and R is positive and given
in exact form.
[4]
1
The function f( ) is defined by f( )
k cos
3
(b)
The maximum value of f( ) is
2sin
, 0
2 , k is a constant.
5
.
4
Find the value of k.
x4
x3 2 x 2 4 x 2 .
(a)
Show that x
(b)
Show that another root of f( x) 0 lies between x 1 and x
(c)
Show that f( x) ( x 1)g( x) , where g( x)
determined.
im
1 is a root of f( x) 0.
en
The function f( x) is defined by f( x)
2.
[2]
ec
x3 ax b and a and b are integers to be
[3]
(d)
Without further calculation, explain why g( x) 0 has a root between x 1 and x 2.
(e)
Use the Newton-Raphson formula to show that an iteration formula for finding roots
of g( x) 0 may be written
xn
1
[1]
2 xn 3 2
.
3 xn 2 2
Determine the root of g( x) 0 which lies between x 1 and x
figures.
© OCR 2018
[1]
Sp
10
[3]
H640/03
2 correct to 4 significant
[3]
PMT
9
11
The curve y
(a)
(i)
f ( x) is defined by the function f( x) e x sin x with domain 0
Show that the x-coordinates of the stationary points of the curve y
x 4 .
f ( x) ,
when arranged in increasing order, form an arithmetic sequence.
(ii)
[9]
Would the result still hold with a larger domain? Give reasons for your answer.
Sp
ec
im
en
(b)
Show that the corresponding y-coordinates form a geometric sequence.
© OCR 2018
H640/03
Turn over
[1]
PMT
10
Answer all the questions
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before
attempting the questions.
Explain why the smaller regular hexagon in Fig. C1 has perimeter 6.
[1]
13
Show that the larger regular hexagon in Fig. C1 has perimeter 4 3 .
[3]
14
Show that the two values of b given on line 36 are equivalent.
Sp
ec
im
en
12
© OCR 2018
H640/03
[3]
PMT
11
15
Fig. 15 shows a unit circle and the escribed regular polygon with 12 edges.
en
1
(a)
Show that the perimeter of the polygon is 24 tan15 .
[2]
(b)
Using the formula for tan(
[3]
ec
) show that the perimeter of the polygon is 48 24 3 .
Sp
16
im
Fig. 15
On a unit circle, the inscribed regular polygon with 12 edges gives a lower bound for
escribed regular polygon with 12 edges gives an upper bound for
Calculate the values of these bounds for
(i)
(ii)
, and the
.
, giving your answers:
in surd form
correct to 2 decimal places.
[3]
END OF QUESTION PAPER
© OCR 2018
H640/03
Turn over
PMT
Sp
ec
im
en
12
Copyright Information:
OCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials. OCR has attempted to
identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to
candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements booklet. This is produced for each
series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct
its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 9EA.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations
Syndicate (UCLES), which is itself a department of the University of Cambridge.
© OCR 2018
H640/03
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/11
PHYSICS
Paper 1 Multiple Choice
May/June 2018
1 hour 15 minutes
Additional Materials:
*5399269005*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages.
IB18 06_9702_11/3RP
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
9702/11/M/J/18
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2018
9702/11/M/J/18
[Turn over
4
1
What is a unit for stress?
A
2
kg m–1 s–2
B
kg m–2 s–2
C
N m–1
D
Nm
Physical quantities can be classed as vectors or as scalars.
Which pair of quantities consists of two vectors?
3
A
kinetic energy and force
B
momentum and time
C
velocity and electric field strength
D
weight and temperature
Two dogs pull a sledge along an icy track, as shown.
dog X pulls with
a force of 200 N
track
65°
forward
force
sledge
45°
dog Y pulls with
a force of 120 N
Dog X pulls with a force of 200 N at an angle of 65° to the front edge of the sledge. Dog Y pulls
with a force of 120 N at an angle of 45° to the front edge of the sledge.
What is the resultant forward force on the sledge exerted by the two dogs?
A
80 N
© UCLES 2018
B
170 N
C
270 N
9702/11/M/J/18
D
320 N
5
4
In the circuit shown, an analogue ammeter is to be recalibrated as a thermometer. The ammeter
is connected in series with a thermistor. The thermistor is a component with a resistance that
varies with temperature. The graph shows how the resistance R of the thermistor changes with
temperature T.
R / kΩ
A
0
thermistor
100
T / °C
Which diagram could represent the temperature scale on the ammeter?
A
20
0
B
40 6
0 80
100
0 20
4 0 60
°C
5
C
80
80
100
D
60
100
°C
40
20
0
°C
100
40
80 60
20
0
°C
The sides of a cube are measured with calipers.
The measured length of each side is (30.0 ± 0.1) mm.
The measurements are used to calculate the volume of the cube.
What is the percentage uncertainty in the calculated value of the volume?
A
0.01%
© UCLES 2018
B
0.3%
C
1%
9702/11/M/J/18
D
3%
[Turn over
6
6
A tennis ball falls freely, in air, from the top of a tall building.
Which graph best represents the variation with time t of the distance s fallen?
A
B
s
s
0
0
t
0
t
0
C
D
s
s
0
0
t
0
7
t
0
The graph shows the variation with mass of the weight of objects on a particular planet.
4
weight / N
3
2
1
0
0
1
2
mass / kg
What is the value of the acceleration of free fall on the planet?
A
0.63 m s–2
© UCLES 2018
B
1.6 m s–2
C
3.2 m s–2
9702/11/M/J/18
D
9.8 m s–2
7
8
The momentum of a car of mass m increases from p1 to p2.
What is the increase in the kinetic energy of the car?
A
9
( p 22 − p12)
2m
B
( p 2 − p1)2
2m
p 2 − p1
2m
C
D
p1 − p 2
2m
Two similar spheres, each of mass m and travelling with speed v, are moving towards each other.
v
v
m
m
The spheres have a head-on elastic collision.
Which statement is correct?
A
The spheres stick together on impact.
B
The total kinetic energy after impact is mv 2.
C
The total kinetic energy before impact is zero.
D
The total momentum before impact is 2mv.
10 A horizontal metal bar PQ of length 50.0 cm is hinged at end P. The diagram shows the metal bar
viewed from above.
16.0 N
30°
Q
5.0 N
P
50.0 cm
Two forces of 16.0 N and 5.0 N are in the horizontal plane and act on end Q as shown in the
diagram.
What is the total moment about P due to the two forces?
A
1.5 N m
© UCLES 2018
B
4.4 N m
C
6.5 N m
9702/11/M/J/18
D
9.4 N m
[Turn over
8
11 Blocks P, Q, R and S are made from material of the same density. Block T is made from a
material of twice the density of the material of the other blocks.
The cross-sectional area and height of each of the blocks are shown.
2h
h
P
h
R
2h
S
h
Q
T
ground
A
2A
A
2A
A
Which two blocks exert the same pressure on the ground?
A
P and T
B
Q and R
C
Q and S
D
S and T
12 Two parallel forces, each of magnitude F, act on a rod of length 5d.
Which diagram shows the positions of the two forces that will produce the largest torque on the
rod?
A
d
B
F
F
F
F
C
D
F
2d
2d
F
© UCLES 2018
F
9702/11/M/J/18
F
9
13 Liquids X and Y are stored in large open tanks. Liquid X has a density of 800 kg m–3 and liquid Y
has a density of 1200 kg m–3.
At which depths are the pressures equal?
depth in
liquid X / m
depth in
liquid Y / m
A
8
20
B
10
15
C
15
10
D
20
8
14 A train of mass 3.3 × 106 kg is moving at a constant speed up a slope inclined at an angle of 0.64°
to the horizontal. The engine of the train is producing a useful output power of 14 MW.
Assume that there are no frictional forces opposing the motion of the train.
What is the speed of the train?
A
0.43 m s–1
B
4.2 m s–1
C
39 m s–1
D
380 m s–1
15 A cannon-ball of mass 3.50 kg is fired at a speed of 22.0 m s–1 from a gun on a ship at a height of
6.00 m above sea level.
The total energy of the cannon-ball is the sum of the gravitational potential energy relative to the
surface of the sea and the kinetic energy.
What is the total energy of the cannon-ball as it leaves the gun?
A
206 J
B
641 J
C
847 J
D
1050 J
16 An aircraft travels at a constant velocity of 90 m s–1 in horizontal flight. The diagram shows some
of the forces acting on the aircraft.
drag
2400 N
thrust
weight
The mass of the aircraft is 2000 kg.
What is the power produced by the thrust force?
A
1.8 × 105 W
© UCLES 2018
B
2.2 × 105 W
C
1.8 × 106 W
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D
2.0 × 106 W
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17 An electrical generator is started at time zero. The total electrical energy generated during the
first 5 seconds is shown in the graph.
50
energy / J
40
30
20
10
0
0
1
2
3
4
5
time / s
What is the maximum electrical power generated at any instant during these first 5 seconds?
A
10 W
B
13 W
C
30 W
D
50 W
18 The diagram shows a wire of diameter D and length L that is firmly clamped at one end between
two blocks of wood. A load is applied to the wire which extends its length by x.
blocks of wood
wire
load
A second wire is made of the same material, but of diameter 2D and length 3L. Both wires obey
Hooke’s law.
What is the extension of the second wire when the same load is applied?
A
2x
3
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B
3x
4
C
4x
3
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D
3x
2
11
19 Two wires, one made of brass and the other of steel, are stretched in an experiment. Both wires
obey Hooke’s law during this experiment.
The Young modulus for brass is less than the Young modulus for steel.
Which graph shows how the stress varies with strain for both wires in this experiment?
A
B
steel
stress
steel
stress
brass
brass
0
0
0
strain
0
C
strain
D
brass
stress
brass
stress
steel
steel
0
0
0
© UCLES 2018
strain
0
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strain
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20 A transverse progressive wave is set up on a string.
The graph shows the variation with time of displacement for a point on this string.
displacement
X
0
Y
time
0
The separation XY on the graph represents the ««1«« of the wave.
X and Y have equal ««2«« .
Which words correctly complete gaps 1 and 2?
1
2
A
time period
amplitudes
B
time period
displacements
C
wavelength
amplitudes
D
wavelength
displacements
21 Which region of the electromagnetic spectrum includes waves with a frequency of 107 MHz?
A
infra-red waves
B
radio waves
C
ultraviolet waves
D
X-rays
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13
22 A longitudinal wave has vibrations parallel to the direction of transfer of energy by the wave.
The wave can be represented on a graph showing the variation of the displacement of the
particles with distance from the source.
Which point on the graph is the centre of a compression?
direction of
transfer of energy
A
displacement
away from source
B
0
D
0
distance
from source
displacement
towards source
C
23 What can be deduced from a table of wavelengths of the waves in the electromagnetic spectrum?
A
Green light has a shorter wavelength than X-rays.
B
Red light has a shorter wavelength than green light.
C
The wavelength range for radio waves is less than that for infra-red waves.
D
The wavelength range for X-rays is less than that for radio waves.
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24 A binary star consists of two stars rotating around a common centre. Light from one of the stars is
observed on the Earth.
binary
star
observer
on Earth
The observed frequency of the light varies between a minimum frequency fmin and a maximum
frequency fmax, as shown.
observed
frequency
fmax
fmin
time
0
The rate of rotation of the binary star increases.
What is the change to fmax and the change to fmin?
fmax
fmin
A
decreases
decreases
B
decreases
increases
C
increases
decreases
D
increases
increases
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15
25 A teacher sets up the apparatus shown to demonstrate a double-slit interference pattern on the
screen.
source
of light
screen
double
slit
single
slit
q
r
p
Which change to the apparatus will increase the fringe spacing?
A
decreasing the distance p
B
decreasing the distance q
C
decreasing the distance r
D
decreasing the wavelength of the light
26 The diagram shows two sources of waves S1 and S2. The sources oscillate with a phase
difference of 180°.
S2
S1
5 cm
13 cm
P
The sources each generate a wave of wavelength 2.0 cm. Each source produces a wave that has
amplitude x0 when it reaches point P.
What is the amplitude of the oscillation at P?
A
0
© UCLES 2018
B
x0
2
C
x0
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D
2x0
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27 A pipe, closed at one end, has a loudspeaker at the open end. A stationary sound wave is formed
in the air within the pipe with an antinode at the open end of the pipe.
0.85 m
loudspeaker
pipe
The length of the pipe is 0.85 m.
The speed of sound in air is 340 m s–1.
Which frequency of sound from the loudspeaker would not produce a stationary wave?
A
100 Hz
B
200 Hz
C
300 Hz
D
500 Hz
28 A particle has a charge of +2.0 mC and is in a vertical uniform electric field. An electric force of
1.0 × 10–2 N acts upwards on the particle.
What is the electric field strength?
A
0.20 V m–1 downwards
B
0.20 V m–1 upwards
C
5.0 V m–1 downwards
D
5.0 V m–1 upwards
29 A charged particle is in the electric field between two horizontal metal plates connected to a
battery, as shown. There is a force F on the particle due to the electric field.
charged particle
The separation of the plates is doubled.
What is the new force on the particle?
A
F
4
© UCLES 2018
B
F
2
C
F
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D
2F
17
30 The current I in a metal wire is given by the expression shown.
I = Anvq
What does the symbol n represent?
A
the number of atoms per unit volume of the metal
B
the number of free electrons per atom in the metal
C
the number of free electrons per unit volume of the metal
D
the total number of electrons per unit volume of the metal
31 The circuit diagrams show two lamps X and Y each connected to a cell. The current in lamp X is
0.50 A and its resistance is 9.6 Ω. The current in lamp Y is 3.0 A and its resistance is 1.2 Ω.
0.50 A
What is the ratio
A
0.22
3.0 A
lamp X
lamp Y
9.6 Ω
1.2 Ω
power in lamp X
?
power in lamp Y
B
0.75
C
1.3
D
4.5
32 A cylindrical piece of a soft, electrically-conducting material has resistance R. It is rolled out so
that its length is doubled but its volume stays constant.
What is its new resistance?
A
R
2
B
R
C
2R
D
4R
33 The sum of the electrical currents into a point in a circuit is equal to the sum of the currents out of
the point.
Which statement is correct?
A
This is Kirchhoff’s first law, which results from the conservation of charge.
B
This is Kirchhoff’s first law, which results from the conservation of energy.
C
This is Kirchhoff’s second law, which results from the conservation of charge.
D
This is Kirchhoff’s second law, which results from the conservation of energy.
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34 In the circuit shown, the batteries have negligible internal resistance.
15 V
I1
9V
I2
2.0 Ω
2.0 Ω
I3
2.0 Ω
What are the values of the currents I1, I2 and I3?
I1 / A
I2 / A
I3 / A
A
–5.5
1.0
6.5
B
0.5
4.0
3.5
C
3.5
4.0
0.5
D
6.5
1.0
–5.5
35 A battery of electromotive force (e.m.f.) 6.0 V and negligible internal resistance is connected to
three resistors as shown.
4.0 kΩ
6.0 V
4.0 kΩ
X
4.0 kΩ
Each resistor has a resistance of 4.0 kΩ.
What is the current in resistor X?
A
0.25 mA
© UCLES 2018
B
0.50 mA
C
0.75 mA
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D
1.0 mA
19
36 A uniform resistance wire XY of length 100 cm is connected in series with a cell L. Another cell M
is connected in series with resistors of resistances 5.00 Ω, 10.0 Ω and 15.0 Ω.
L
100 cm
X
Y
12.5 cm
resistance wire
A
5.00 Ω
P
10.0 Ω
Q
15.0 Ω
R
S
M
The potential difference (p.d.) between P and Q is balanced against 12.5 cm of the resistance
wire, so that the ammeter reads zero.
The p.d. across the other resistors is then balanced against other lengths of the resistance wire.
Which balanced lengths of resistance wire correspond to the connection points given in the
table?
balanced length / cm
connection
points
A
B
C
D
Q and R
12.5
25.0
25.0
25.0
Q and S
62.5
62.5
75.0
62.5
P and R
37.5
37.5
37.5
12.5
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37 A motor is required to operate at a distance of 800 m from its power supply. The motor requires a
potential difference (p.d.) of 16.0 V and a current of 0.60 A to operate.
Two wires are used to supply power to the motor as shown.
wires
power
supply
motor
800 m
The resistance of each of these wires is 0.0050 Ω per metre.
What is the minimum output p.d. of the power supply?
A
11.2 V
B
16.0 V
C
18.4 V
D
20.8 V
D
5
38 Which elementary particle is a lepton?
A
proton
B
neutron
C
electron
D
quark
39 How many down quarks are in a nucleus of hydrogen-3, 31H ?
A
2
B
3
C
4
40 What is the correct equation for β+ decay?
A
neutron → proton + electron + electron antineutrino
B
neutron → proton + electron + electron neutrino
C
proton → neutron + positron + electron antineutrino
D
proton → neutron + positron + electron neutrino
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/11/M/J/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
May/June 2018
1 hour 15 minutes
Additional Materials:
*4462866466*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages.
IB18 06_9702_12/3RP
© UCLES 2018
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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4
1
A sheet of gold leaf has a thickness of 0.125 µm. A gold atom has a radius of 174 pm.
Approximately how many layers of atoms are there in the sheet?
A
2
4
B
7
C
400
D
700
The drag coefficient Cd is a number with no units. It is used to compare the drag on different cars
at different speeds. Cd is given by the equation
Cd =
2F
v nρ A
where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the
car and v is the speed of the car.
What is the value of n?
A
3
1
B
2
C
3
D
4
A student measures the current through a resistor and the potential difference (p.d.) across it.
There is a 4% uncertainty in the current reading and a 1% uncertainty in the p.d. reading. The
student calculates the resistance of the resistor.
What is the percentage uncertainty in the calculated resistance?
A
4
0.25%
B
3%
C
4%
D
5%
A student applies a potential difference V of (4.0 ± 0.1) V across a resistor of resistance R of
(10.0 ± 0.3) Ω for a time t of (50 ± 1) s.
The student calculates the energy E dissipated using the equation below.
2
2
E = V t = 4.0 × 50 = 80 J
R
10.0
What is the absolute uncertainty in the calculated energy value?
A
1.5 J
© UCLES 2018
B
3J
C
6J
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D
8J
5
5
The velocity of an object changes with time t as shown.
velocity
0
0
t
Which graph best shows the variation with time t of the displacement s of the object?
A
B
s
s
0
0
0
t
0
C
D
s
s
0
0
0
© UCLES 2018
t
t
0
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t
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6
6
A projectile is launched at an angle to the horizontal at time t = 0. It travels over horizontal
ground, as shown.
path of projectile
ground
Assume that air resistance is negligible.
Which graph best shows the variation with t of the speed of the projectile from when it is launched
to when it lands on the ground?
A
B
speed
speed
0
0
0
0
t
C
D
speed
speed
0
0
0
© UCLES 2018
t
0
t
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t
7
7
A sky-diver falls vertically from a helicopter and reaches constant (terminal) velocity. The graph
shows the variation with time t of the speed v of the sky-diver.
v
0
t
0
Which graph shows the variation with time t of the distance d fallen by the sky-diver?
A
B
d
d
0
D
d
0
t
0
8
C
d
0
t
0
0
t
0
0
t
A tennis ball of mass 55 g is travelling horizontally with a speed of 30 m s–1. The ball makes
contact with a wall before rebounding in the horizontal direction with a speed of 20 m s–1. The ball
is in contact with the wall for a time of 5.0 × 10–3 s.
What is the average force exerted on the wall by the ball?
A
9
110 N
B
220 N
C
330 N
D
550 N
An elastic collision occurs between two bodies X and Y. The mass of body X is m and the mass
of body Y is 4m. Body X travels at speed v before the collision and speed 3v in the opposite
5
direction after the collision. Body Y is stationary before the collision.
3v
5
v
X
Y
X
Y
m
4m
m
4m
before
after
What is the kinetic energy of body Y after the collision?
A
8 mv 2
10
© UCLES 2018
B
34 mv 2
50
C
16 mv 2
50
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D
1 mv 2
5
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10 The density of water is 1.0 g cm–3 and the density of glycerine is 1.3 g cm–3.
Water is added to a measuring cylinder containing 40 cm3 of glycerine so that the density of the
mixture is 1.1 g cm–3. Assume that the mixing process does not change the total volume of the
liquid.
What is the volume of water added?
40 cm3
A
B
44 cm3
C
52 cm3
D
80 cm3
11 An astronaut throws a stone horizontally near to the surface of the Moon, where there is no
atmosphere.
Which row describes the horizontal and vertical forces acting on the stone after release?
horizontal force
vertical force
A
non-zero and constant
constant
B
non-zero and constant
decreasing
C
zero
constant
D
zero
decreasing
12 A cylindrical block of wood has cross-sectional area A and weight W. It is totally immersed in
water with its axis vertical. The block experiences pressures pt and pb at its top and bottom
surfaces respectively.
Which expression is equal to the upthrust on the block?
A
(pb – pt)
B
(pb – pt)A
C
(pb – pt)A – W
D
(pb – pt)A + W
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9
13 A uniform diving-board is held by two fixed rods at points P and Q. A person stands at end R of
the diving-board, as shown.
rod
Q
P
R
rod
The forces exerted by the rods on the board are vertical. The board remains in equilibrium as the
person slowly moves towards point Q from end R.
Which row describes the changes to the forces exerted by the rods on the board?
force at P
force at Q
A
decreases
decreases
B
decreases
increases
C
increases
decreases
D
increases
increases
14 Two forces, each of magnitude F, act in opposite directions on a rod.
F
P
d
d
F
Each force acts on the rod at a distance d from the pivot P.
What is the torque of this couple about P?
A
0
© UCLES 2018
B
F×d
C
2F × d
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D
2F × 2d
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15 The vector diagram shows three coplanar forces acting on an object at P.
3N
P
4N
4N
The magnitude of the resultant of these three forces is 1 N.
What is the direction of this resultant force?
A
B
C
D
16 In ‘normal driving conditions’, an electric car has a range of 150 km. This uses all of the 200 MJ of
energy stored in its batteries.
With the batteries initially fully charged, the car is driven 100 km in ‘normal driving conditions’. The
batteries are then recharged from a household electrical supply delivering a constant current of
13.0 A at a potential difference of 230 V.
What is the minimum time required to recharge the batteries?
A
0.95 hours
B
12.4 hours
C
18.6 hours
D
27.9 hours
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11
17 The diagram shows a ball of weight W hanging in equilibrium from a string.
θ
T
string
ball
P
rod
W
The string is at an angle θ to the vertical. The tension in the string is T. The ball is held away from
the wall by a horizontal force P from a metal rod.
What is the relationship between the magnitudes of T, P and W ?
A
P = T cosθ and W = T sinθ
B
T=P+W
C
T2 = P2 + W2
D
W = P tanθ and W = T cosθ
18 A steel sphere is dropped vertically onto a horizontal metal plate. The sphere hits the plate with
speed u, leaves it at speed v, and rebounds vertically to half of its original height. Ignore air
resistance.
Which expression gives the value of v ?
u
A
1
22
© UCLES 2018
B
1
2
C
1
2
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D
1– 1
2
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19 A car of mass 500 kg is at rest at point X on a slope, as shown.
The car’s brakes are released and the car rolls down the slope with its engine switched off. At
point Y the car has moved through a vertical height of 30 m and has a speed of 11 m s–1.
mass = 500 kg
speed = 0 m s–1
X
30 m
speed = 11 m s–1
Y
What is the energy dissipated by frictional forces when the car moves from X to Y?
A
3.0 × 104 J
1.2 × 105 J
B
C
1.5 × 105 J
D
1.8 × 105 J
20 An elastic material with Young modulus E is subjected to a tensile stress S. Hooke’s law is
obeyed.
What is the expression for the elastic energy stored per unit volume of the material?
2
E
2S
2
A
2E
S2
B
C
S2
E
D
S
2E
21 The graph shows the length of a spring as it is stretched by an increasing load.
15
length / cm
10
5
0
0
0.1
0.2
0.3
0.4
0.5
load / N
What is the spring constant of the spring?
A
0.080 N m–1
© UCLES 2018
B
0.13 N m–1
C
2.7 N m–1
9702/12/M/J/18
D
8.0 N m–1
13
22 Two lasers emit light in a vacuum. One laser emits red light and the other emits green light.
Which property of the two laser beams must be different?
A
amplitude
B
frequency
C
intensity
D
speed
23 The diagram shows the screen of a cathode-ray oscilloscope (c.r.o.) displaying a wave.
The time-base of the c.r.o. is set at 10 ms / division.
What is the frequency of the wave?
A
0.24 Hz
B
4.2 Hz
C
12 Hz
D
24 Hz
24 A string is fixed at one end and the other end is attached to a vibrator. The frequency of the
vibrator is slowly increased from zero. A series of stationary waves is formed. Assume that for a
stationary wave there is a node at point P.
string
P
fixed
vibrator
L
What are the first five wavelengths of the stationary waves that could be formed?
A
2L ,2L ,2L ,2L ,2L
1
2
3
4
5
B
2L ,2L ,2L ,2L ,2L
2
3
4
5
6
C
4L ,4L ,4L ,4L ,4L
1
2
3
4
5
D
4L ,4L ,4L ,4L ,4L
1
3
5
7
9
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25 Which region of the electromagnetic spectrum has waves of wavelength 1000 times smaller than
the wavelength of visible light?
A
infra-red
B
microwaves
C
ultraviolet
D
X-rays
26 The diagram shows apparatus for the measurement of the frequency of a sound wave.
D
microphone
source
of sound
metal
plate
Sound of the unknown frequency is reflected back from a metal plate. A microphone placed at a
distance D from the metal plate detects the sound intensity. A minimum intensity is detected with
D = 12.0 cm. The plate is moved further away from the microphone until the next minimum is
detected with D = 15.0 cm.
The speed of sound in air is 336 m s–1.
What is the frequency of the sound?
A
56 Hz
B
112 Hz
C
5600 Hz
D
11 200 Hz
27 An astronomer observes the light from a star that is moving away from the Earth.
For the observed light, what has been increased due to the star’s motion?
A
amplitude
B
frequency
C
speed
D
wavelength
© UCLES 2018
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15
28 The diagram shows a stationary wave, at time t = 0, that has been set up on a string fixed
between points P and S.
X
Y
P
Q
S
R
The nodes of the stationary wave occur on the string at P, Q, R and S. Point X is moving down at
time t = 0. The points on the string vibrate with time period T and maximum amplitude 2 cm.
The displacement s is positive in the upward direction.
Which graph best shows the variation with t of the displacement s of point Y on the string?
A
B
2
2
s / cm
s / cm
0
0
0
T
2
t
0
–2
T
2
t
T
2
t
–2
C
D
2
2
s / cm
s / cm
0
0
0
T
2
0
t
–2
–2
29 A two-source interference experiment uses the apparatus shown.
lamp
single
slit
double
slit
screen
What is the main purpose of the single slit?
A
to make a narrow beam of light
B
to make the same amplitude of light incident on each slit
C
to provide coherent light
D
to provide monochromatic light
© UCLES 2018
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16
30 Two large parallel metal plates X and Y are situated in a vacuum as shown.
+
plate X
positively
charged
particle
plate Y
–
Plates X and Y carry equal and opposite charges.
What happens to the force on a positively charged particle as it moves from plate X to plate Y?
A
It decreases because the positively charged particle is moving away from the positively
charged plate.
B
It decreases because the positively charged particle is moving in the direction of the electric
field between the plates.
C
It increases because the positively charged particle is moving closer to a negatively charged
plate.
D
It remains constant because the positively charged particle is in the uniform electric field
between the plates.
31 Four diagrams representing the electric field between two oppositely-charged point charges are
shown.
Which diagram correctly shows the electric field lines?
A
+
B
–
+
C
+
© UCLES 2018
–
D
–
+
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–
17
32 The power output of an electrical supply is 2.4 kW at a potential difference (p.d.) of 240 V. The
two wires between the supply and a kettle each have a resistance of 0.50 Ω, as shown.
supply
kettle
0.50 Ω
240 V
2.4 kW
0.50 Ω
What is the power supplied to the kettle and what is the p.d. across the kettle?
power / kW
p.d. / V
A
2.3
230
B
2.3
235
C
2.4
230
D
2.4
235
33 Which graph shows the variation of voltage V with current I for a semiconductor diode?
A
B
V
V
0
0
0
0
I
C
D
V
V
0
0
0
© UCLES 2018
I
0
I
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I
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18
34 Four different resistors are arranged as shown.
A current of 1.5 A enters the network at junction X and leaves through junction Y.
1.5 A
Y
1.5 A
70 Ω
60 Ω
50 Ω
30 Ω
X
What is the current in the resistor of resistance 30 Ω?
A
0.21 A
B
0.50 A
C
0.75 A
D
1.0 A
35 A cell of constant electromotive force drives a current I through an external resistor of
resistance R. The terminal potential difference (p.d.) across the cell is V.
V
r
cell
I
R
When the internal resistance r of the cell increases, what is the effect on V and on I?
V
I
A
decreases
decreases
B
decreases
increases
C
increases
decreases
D
increases
increases
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19
36 In the circuits shown, the batteries are identical and all have negligible internal resistance. All of
the resistors have the same resistance. The diodes have zero resistance when conducting and
infinite resistance when not conducting.
In which circuit is the current in the battery greatest?
A
B
C
D
37 A thermistor is an electrical component with a resistance that varies with temperature. A
thermistor T is used in a fire alarm system. The alarm is triggered when the potential difference
between X and Y is 4.5 V.
12 V
150 Ω
T
X
Y
What is the resistance of T when the alarm is triggered?
A
90 Ω
© UCLES 2018
B
150 Ω
C
250 Ω
9702/12/M/J/18
D
400 Ω
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20
38 In the α-particle scattering experiment, a beam of α-particles is aimed at a thin gold foil. Most of
the α-particles go straight through or are deflected by a small angle. A very small proportion are
deflected through more than 90°, effectively rebounding towards the source of the α-particles.
Which conclusion about the structure of atoms cannot be drawn from this experiment alone?
A
Most of the atom is empty space.
B
Most of the mass of an atom is concentrated in the nucleus.
C
The nucleus contains both protons and neutrons.
D
The nucleus is charged.
39 Radon-211,
211
86 Rn ,
francium-210,
210
87 Fr
, and radium-212,
212
88 Ra ,
are three nuclides.
How many neutrons does each nuclide have in its nucleus?
radon-211
francium-210
radium-212
A
86
87
88
B
125
123
124
C
211
210
212
D
297
297
300
40 A neutron is composed of one up (u) quark and two down (d) quarks. When the neutron decays
to a proton, there is β-emission.
What is the change in the quark structure of the neutron due to the β-emission?
(The symbol for a neutrino is νe and for an antineutrino is νe .)
A
d → u + β– + νe
B
d → u + β– + νe
C
u → d + β+ + νe
D
u → d + β+ + νe
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/12/M/J/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/13
PHYSICS
Paper 1 Multiple Choice
May/June 2018
1 hour 15 minutes
Additional Materials:
*4741131482*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages.
IB18 06_9702_13/3RP
© UCLES 2018
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
9702/13/M/J/18
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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4
1
2
3
What is the best way of describing a physical quantity?
A
a quantity with a magnitude and a direction but no unit
B
a quantity with a magnitude and a unit
C
a quantity with a magnitude but no direction
D
a quantity with a unit but no magnitude
Which pair includes a vector quantity and a scalar quantity?
A
displacement and acceleration
B
force and kinetic energy
C
power and speed
D
work and potential energy
A force F acts at an angle θ to the horizontal.
F
θ
horizontal
What are the horizontal and the vertical components of the force?
4
horizontal
component
vertical
component
A
F cosθ
F cos (90° – θ )
B
F cosθ
F sin (90° – θ )
C
F sinθ
F cosθ
D
F sinθ
F cos (90° – θ )
What will reduce the systematic errors when taking a measurement?
A
adjusting the needle on a voltmeter so that it reads zero when there is no potential difference
across it
B
measuring the diameter of a wire at different points and taking the average
C
reducing the parallax effects by using a marker and a mirror when measuring the amplitude
of oscillation of a pendulum
D
timing 20 oscillations, rather than a single oscillation, when finding the period of a pendulum
© UCLES 2018
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5
5
In an experiment to determine the Young modulus E of the material of a wire, the measurements
taken are shown.
mass hung on end of wire
m = 2.300 ± 0.002 kg
original length of wire
l = 2.864 ± 0.005 m
diameter of wire
d = 0.82 ± 0.01 mm
extension of wire
e = 7.6 ± 0.2 mm
The Young modulus is calculated using
E
=
4mgl
πd 2 e
where g is the acceleration of free fall.
The calculated value of E is 1.61 × 1010 N m–2.
How should the calculated value of E and its uncertainty be expressed?
6
A
(1.61 ± 0.04) × 1010 N m–2
B
(1.61 ± 0.05) × 1010 N m–2
C
(1.61 ± 0.07) × 1010 N m–2
D
(1.61 ± 0.09) × 1010 N m–2
A rock on the surface of Mars is projected vertically upwards with an initial speed of 9.4 m s–1. The
rock rises to a height of 12 m above the surface.
Assume there is no atmosphere on Mars.
What is the acceleration of free fall near the surface of Mars?
A
0.39 m s–2
© UCLES 2018
B
3.7 m s–2
C
7.4 m s–2
9702/13/M/J/18
D
9.8 m s–2
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6
7
Two masses, M and m, are connected by an inextensible string which passes over a frictionless
pulley. Mass M rests on a frictionless slope, as shown.
M
m
frictionless slope
θ
The slope is at an angle θ to the horizontal.
The two masses are initially held stationary and then released. Mass M moves down the slope.
Which expression must be correct?
A
sinθ < m
M
cosθ < m
M
B
C
sinθ > m
M
D
cosθ > m
M
A sky-diver falls from a stationary balloon at time t = 0. As the sky-diver falls, her speed and the
air resistance increase until the force of the air resistance is equal to her weight.
8
Which graph best shows the variation with time t of the displacement s for the motion of the
sky-diver?
A
B
s
C
s
0
0
© UCLES 2018
t
D
s
0
0
t
s
0
0
9702/13/M/J/18
t
0
0
t
7
9
A ball of mass 0.20 kg, travelling in the x-direction at a speed of 0.50 m s–1, collides with a ball of
mass 0.30 kg travelling in the y-direction at a speed of 0.40 m s–1.
The two balls stick together after the collision, travelling at an angle θ to the x-direction.
0.30 kg
0.40 m s–1
x-direction
–1
0.50 m s
θ
0.20 kg
y-direction
What is the value of θ ?
A
39°
B
40°
C
50°
D
51°
10 Four cuboids with identical lengths, breadths and heights are immersed in water. The cuboids are
held at the same depth and in identical orientations by vertical rods, as shown.
W
X
Y
Z
4ρ
2ρ
ρ
0.5ρ
Water has density ρ.
Cuboid W is made of material of density 4ρ.
Cuboid X is made of material of density 2ρ.
Cuboid Y is made of material of density ρ.
Cuboid Z is made of material of density 0.5ρ.
Which statement is correct?
A
The upthrust of the water on each of the cuboids is the same.
B
The upthrust of the water on W is twice the upthrust of the water on X.
C
The upthrust of the water on X is twice the upthrust of the water on W.
D
The upthrust of the water on Y is zero.
© UCLES 2018
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11 A rectangular block of lead of density 1.13 × 104 kg m–3 has sides of length 12.0 cm, 15.0 cm and
10.0 cm.
What is the maximum pressure the block can exert when resting on a table?
A
1.13 kPa
B
1.70 kPa
C
11.1 kPa
D
16.6 kPa
12 Which diagram shows a couple formed by two forces, each of magnitude F, acting on a rod?
B
A
F
F
F
F
F
C
D
F
F
F
13 Full-fat milk is made up of fat-free milk mixed with fat.
A volume of 1.000 × 10–3 m3 of full-fat milk has a mass of 1.035 kg. It contains 4.00% fat by
volume.
The density of fat-free milk is 1.040 × 103 kg m–3.
What is the density of fat?
A
1.25 × 102 kg m–3
B
9.15 × 102 kg m–3
C
9.28 × 102 kg m–3
D
1.16 × 103 kg m–3
© UCLES 2018
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9
14 Gas is trapped inside a cylinder by a piston of cross-sectional area A. The piston is not
frictionless.
P
r
Q
gas
atmospheric
pressure
s
The gas is heated and this causes it to expand, pushing back the piston through distance r from
position P to position Q. The length of the gas column is then s.
Which expression represents the amount of work done by the gas against the atmosphere during
this expansion?
A
(atmospheric pressure) × Ar
B
(atmospheric pressure) × As
C
(pressure inside the gas) × Ar
D
(pressure inside the gas) × As
15 Water from a reservoir is fed to the turbine of a hydroelectric system at a rate of 510 kg s–1. The
reservoir is 280 m above the level of the turbine.
The electrical output from the generator driven by the turbine is a current of 205 A at a potential
difference of 5800 V.
What is the efficiency of the system?
A
8.3%
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B
12%
C
83%
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D
85%
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16 A ball is thrown vertically up into the air. It rises to the top of its path before beginning to fall
vertically downwards.
top of path
midpoint of path
starting position
Assume that the gravitational potential energy of the ball is zero at its starting position.
Which statement about the ball is not correct?
A
As it rises, its kinetic energy is transferred to gravitational potential energy.
B
At the midpoint of its path, its gravitational potential energy is equal to its initial kinetic
energy.
C
At the top of its path, its kinetic energy is zero.
D
At the top of its path, its total energy is less than its initial total energy.
17 A force of 1000 N is needed to lift the hook of a crane at a constant velocity. The crane is then
used to lift a load of mass 1000 kg at a constant velocity of 0.50 m s–1.
What is the power needed to lift the hook and the load?
A
4.9 kW
B
5.4 kW
C
20 kW
D
22 kW
18 Data for a steel wire on an electric guitar are listed.
diameter = 5.0 × 10–4 m
Young modulus = 2.0 × 1011 Pa
tension = 20 N
The wire snaps and contracts elastically. Assume the wire obeys Hooke’s law.
By what percentage does the length l of a piece of the wire contract?
A
1.3 × 10–4 %
© UCLES 2018
B
5.1 × 10–4 %
C
1.3 × 10–2 %
9702/13/M/J/18
D
5.1 × 10–2 %
11
19 The graph shows how the extension of a spring varies with the force used to stretch it.
4.0
extension / cm
2.0
0
0
10
20
30
force / kN
What is the strain energy in the spring when the extension is 4.0 cm?
A
60 J
B
120 J
C
600 J
D
1200 J
20 The displacement-distance graph for a transverse progressive wave is shown.
X
displacement
0
distance
0
Y
The phase difference between points X and Y can be expressed as (180 n)°.
What is the value of n?
A
1.5
© UCLES 2018
B
2.5
C
3.0
9702/13/M/J/18
D
6.0
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21 The four graphs represent a progressive wave on a stretched string. Graphs A and B show how
the displacement d varies with distance x along the string at one instant. Graphs C and D show
how the displacement d varies with time t at a particular value of x.
The labels on the graphs are intended to show the wavelength λ, the period T and the amplitude
a of the wave, but only one graph is correctly labelled.
Which graph is correctly labelled?
A
B
λ
T
d
d
a
0
0
x
0
0
a
x
C
D
λ
d
T
d
a
0
a
0
t
0
t
0
22 A cathode-ray oscilloscope (c.r.o.) is used to determine the frequency of a sound wave.
The diagram shows the waveform on the screen.
The time-base setting is 5.0 ms / div.
What is the frequency of the sound wave?
A
57 Hz
© UCLES 2018
B
71 Hz
C
114 Hz
9702/13/M/J/18
D
143 Hz
13
23 A police car travels at a velocity of 30.0 m s–1 directly towards a stationary observer. The horn of
the car emits sound of frequency 2000 Hz. The speed of sound is 340 m s–1.
What is the frequency of the sound heard by the observer?
A
1840 Hz
B
2000 Hz
C
2180 Hz
D
2190 Hz
24 A vibrating tuning fork is held over a measuring cylinder, as shown.
tuning fork
water
Water is then gradually poured into the measuring cylinder. A much louder sound is first heard
when the water level is 2.9 cm above the base of the measuring cylinder. A second much louder
sound is heard when the water level reaches a height of 67.3 cm above the base.
The speed of sound in air is 330 m s–1.
What is the frequency of the tuning fork?
A
128 Hz
B
256 Hz
C
512 Hz
D
1024 Hz
25 A water wave in a ripple tank is diffracted as it passes through a gap in a barrier.
Which two factors affect the angle of diffraction of the wave?
A
the amplitude and frequency of the incident wave
B
the amplitude of the incident wave and the width of the gap
C
the wavelength and amplitude of the incident wave
D
the wavelength of the incident wave and the width of the gap
26 A double-slit interference pattern using red light of wavelength 7.0 × 10–7 m has a fringe spacing
of 3.5 mm.
Which fringe spacing would be observed for the same arrangement of apparatus but using blue
light of wavelength 4.5 × 10–7 m?
A
2.3 mm
© UCLES 2018
B
3.5 mm
C
5.4 mm
9702/13/M/J/18
D
9.0 mm
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27 Two parallel metal plates are situated 20 cm apart in a vacuum. They are connected to two
sources of potential difference as shown.
proton
+
+
–
–
800 V
20 cm
300 V
A proton is released in the space between the plates.
What is the magnitude and direction of the acceleration of the proton?
A
2.4 × 1011 m s–2 downwards
B
2.4 × 1011 m s–2 upwards
C
5.3 × 1011 m s–2 downwards
D
5.3 × 1011 m s–2 upwards
28 A particle having mass m and charge +q enters a uniform electric field with speed v.
Initially, the particle is travelling at right-angles to the electric field.
During its movement through the field, the particle is deflected through distance d, as shown.
path of particle
d
region of uniform
electric field
A second particle of mass 2m, charge +q and speed v enters the electric field along the same
path.
What is the distance through which this particle is deflected in the electric field?
A
d
4
© UCLES 2018
B
d
2
C
2d
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D
4d
15
29 What is a possible charge on a particle?
A
6.40 × 10–20 C
B
4.00 × 10–19 C
C
1.12 × 10–18 C
D
9.11 × 10–18 C
30 A slice of germanium of cross-sectional area 1.0 cm2 carries a current of 56 µA. The number
density of charge carriers in the germanium is 2.0 × 1013 cm–3. Each charge carrier has a charge
equal to the charge on an electron.
slice of
germanium
area 1.0 cm2
current
56 µA
What is the average drift velocity of the charge carriers in the germanium?
A
0.18 m s–1
B
18 m s–1
C
180 m s–1
D
1800 m s–1
31 A cell of electromotive force (e.m.f.) E and internal resistance r is connected to an external
resistor of resistance R, as shown.
E
r
R
What is the power dissipated in the external resistor?
A
E 2(R + r )
R2
© UCLES 2018
B
E 2R
(R + r )2
C
E 2(R + r )
r2
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D
E 2r
(R + r )2
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32 The graph shows the I-V characteristic of an electrical component.
I
0
0
V
What is the component?
A
a filament lamp
B
a metallic conductor at constant temperature
C
a resistor
D
a semiconductor diode
33 A metal wire of length 1.4 m has a uniform cross-sectional area of 7.8 × 10–7 m2.
The resistivity of the metal is 1.7 × 10–8 Ω m.
What is the resistance of the wire?
A
0.016 Ω
© UCLES 2018
B
0.031 Ω
C
33 Ω
9702/13/M/J/18
D
64 Ω
17
34 A battery of electromotive force (e.m.f.) 6.0 V and negligible internal resistance is connected to
three resistors each of resistance 6.0 Ω.
Which circuit will produce a current through the battery of 0.67 A?
A
B
6.0 V
6.0 V
6.0 Ω
6.0 Ω
6.0 Ω
6.0 Ω
6.0 Ω
6.0 Ω
6.0 Ω
C
D
6.0 V
6.0 V
6.0 Ω
6.0 Ω
6.0 Ω
6.0 Ω
© UCLES 2018
6.0 Ω
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35 The diagram shows a network of three resistors. Two of these, marked R, are identical. The other
resistor has a resistance of 5.0 Ω.
Y
R
5.0 Ω
X
R
Z
The resistance between Y and Z is found to be 2.5 Ω.
What is the resistance between X and Y?
0.30 Ω
A
B
0.53 Ω
C
1.9 Ω
D
3.3 Ω
36 The diagram shows a battery, a fixed resistor, an ammeter and a variable resistor connected in
series.
A voltmeter is connected across the fixed resistor.
V
A
The resistance of the variable resistor is reduced.
Which row describes the changes in the readings of the ammeter and of the voltmeter?
ammeter
voltmeter
A
decrease
decrease
B
decrease
increase
C
increase
decrease
D
increase
increase
© UCLES 2018
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19
37 The circuit diagram shows a battery of electromotive force (e.m.f.) 9.0 V and negligible internal
resistance. It is connected to two resistors of resistances 160 Ω and R. The output potential
difference Vout is 4.0 V.
160 Ω
9.0 V
Vout = 4.0 V
R
What is the resistance R ?
A
32 Ω
B
49 Ω
C
71 Ω
D
128 Ω
38 In the circuit shown, XY is a length L of uniform resistance wire. A potential difference is applied
across XY. R1 and R2 are unknown resistors. J is a sliding contact that joins the junction of R1 and
R2 to points on XY through a lamp S.
L
–
x
X
Y
+
J
S
R2
R1
J is moved along XY to a point at which the lamp is off. This point is at a distance x from X.
The potential difference across R1 is V1 and the potential difference across R2 is V2.
What is the value of the ratio
A
L
x
© UCLES 2018
B
x
L
V1
?
V2
C
L−x
x
9702/13/M/J/18
D
x
L−x
[Turn over
20
39 A nucleus of magnesium-23 undergoes β+ decay, as represented by the nuclear equation shown.
23
12 Mg
→ X + β+ + νe
What is nucleus X?
A
22
11 Na
B
22
13 Al
C
23
11 Na
D
23
13 Al
40 Which list contains only leptons?
A
electron, neutrino, positron
B
electron, neutrino, proton
C
electron, proton, neutron
D
neutrino, neutron, positron
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/13/M/J/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
February/March 2018
1 hour 15 minutes
Additional Materials:
*3331793231*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 19 printed pages and 1 blank page.
IB18 03_9702_12/3RP
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
9702/12/F/M/18
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2018
9702/12/F/M/18
[Turn over
4
1
2
3
Which unit is equivalent to the coulomb?
A
ampere per second
B
joule per volt
C
watt per ampere
D
watt per volt
Which row shows a quantity and an incorrect unit?
quantity
unit
A
efficiency
no unit
B
moment of force
N m–1
C
momentum
Ns
D
work done
J
Two forces of equal magnitude are represented by two coplanar vectors. One is directed towards
the east and the other is directed towards the north.
What is the direction of a single force that will balance these two forces?
4
A
towards the north-east
B
towards the north-west
C
towards the south-east
D
towards the south-west
The density of paper is 800 kg m–3. A typical sheet of paper has a width of 210 mm and a length of
300 mm.
The thickness of a pack of 500 sheets of paper is 50 mm.
What is the mass of a single sheet of paper?
A
0.5 g
© UCLES 2018
B
5g
C
50 g
9702/12/F/M/18
D
500 g
5
5
A person calculates the potential difference across a wire by using the measurements shown.
Which measured quantity has the greatest contribution to the percentage uncertainty in the
calculated potential difference?
6
quantity
value
uncertainty
A
current / A
5.0
± 0.5
B
diameter of wire / mm
0.8
± 0.1
C
length of wire / m
150
±5
D
resistivity of metal in wire / Ω m
1.6 × 10–8
± 0.2 × 10–8
A cathode-ray oscilloscope (c.r.o.) is connected to an alternating voltage. The following trace is
produced on the screen.
1 cm
1 cm
The oscilloscope time-base setting is 0.5 ms cm–1 and the Y-plate sensitivity is 2 V cm–1.
Which statement about the alternating voltage is correct?
A
The amplitude is 3.5 cm.
B
The frequency is 0.5 kHz.
C
The period is 1 ms.
D
The wavelength is 4 cm.
© UCLES 2018
9702/12/F/M/18
[Turn over
6
7
A stone of mass m is dropped from a tall building. There is significant air resistance. The
acceleration of free fall is g.
When the stone is falling at a constant (terminal) velocity, which information is correct?
8
magnitude of
the acceleration
of the stone
magnitude of the
force of gravity
on the stone
magnitude of the
force of air resistance
on the stone
A
g
zero
mg
B
zero
mg
mg
C
zero
zero
mg
D
zero
mg
zero
The velocity-time graph for an object is shown.
velocity
area 1
0
area 2
0
time
How can the total displacement of the object be determined?
A
B
9
area 1 – area 2
(area 1 + area 2)
2
C
area 1 + area 2
D
area 2 – area 1
A girl throws a ball vertically upwards. It takes a time of 3.20 s to return to her hand.
Assume air resistance is negligible.
What is the initial speed with which the ball is thrown?
A
3.07 m s–1
© UCLES 2018
B
7.85 m s–1
C
15.7 m s–1
9702/12/F/M/18
D
31.4 m s–1
7
10 Steel pellets, each with a mass of 0.60 g, fall vertically onto a horizontal plate at a rate of 100
pellets per minute. They strike the plate with a velocity of 5.0 m s–1 and rebound with a velocity of
4.0 m s–1.
What is the average force exerted on the plate by the pellets?
A
0.0010 N
B
0.0054 N
C
0.0090 N
D
0.54 N
11 The diagram shows four forces applied to a circular object.
45 N
30 N
30 N
45 N
Which row describes the resultant force and resultant torque on the object?
resultant force
resultant torque
A
non-zero
non-zero
B
non-zero
zero
C
zero
non-zero
D
zero
zero
12 A charged oil drop is held stationary between two charged parallel plates.
top plate
charged oil drop
bottom plate
Which forces act on the oil drop?
A
both electric and gravitational
B
electric only
C
gravitational only
D
neither electric nor gravitational
© UCLES 2018
9702/12/F/M/18
[Turn over
8
13 In which example is it not possible for the underlined body to be in equilibrium?
A
An aeroplane climbs at a steady rate.
B
An aeroplane tows a glider at a constant altitude.
C
A speedboat changes direction at a constant speed.
D
Two boats tow a ship into harbour.
14 A car of mass 1100 kg is travelling at a constant speed of 15 m s–1 up a slope inclined at 10° to the
horizontal. The combined frictional forces acting on the car are directed down the slope and are
equal to W , where W is the weight of the car.
5
15 m s–1
10°
What is the useful output power of the car’s engine?
A
28 kW
B
32 kW
C
60 kW
D
190 kW
15 An old-fashioned 60 W lamp converts 95% of its energy supply into heat. A 4.0 W modern lamp
has the same power output of light as the old-fashioned lamp.
What is the efficiency of the modern lamp?
A
5.0%
© UCLES 2018
B
6.7%
C
75%
9702/12/F/M/18
D
95%
9
16 A bead is released from rest at point P and slides along a wire, as shown.
P
NOT TO
SCALE
1.4 m s–1
Q
h
40 cm
The track loops around and forms a vertical circle of diameter 40 cm. At point Q, the bead has a
speed of 1.4 m s–1.
Air resistance and friction on the wire are negligible.
What is the height h from which the bead is released?
A
0.30 m
B
0.40 m
C
0.50 m
D
0.60 m
17 A small diesel engine uses a volume of 1.5 × 104 cm3 of fuel per hour to produce a useful power
output of 40 kW. It may be assumed that 34 kJ of energy is transferred to the engine when it uses
1.0 cm3 of fuel.
What is the rate of transfer from the engine of energy that is wasted?
A
102 kW
© UCLES 2018
B
142 kW
C
182 kW
9702/12/F/M/18
D
470 kW
[Turn over
10
18 Two boxes X and Y have the same mass. Box X is lifted vertically through a height h by a force of
magnitude F.
Box Y is pulled along a slope by a force of the same magnitude to reach the same height, as
shown.
h
F
h
F
box X
box Y
Which statement is correct?
A
Both boxes gain the same amount of gravitational potential energy and the same amount of
work is done by the two forces.
B
Both boxes gain the same amount of gravitational potential energy but more work is done by
the force acting on box Y than by the force acting on box X.
C
Box Y gains less gravitational potential energy than box X because the weight of box Y is
less than the weight of box X.
D
Box Y gains more gravitational potential energy than box X as more work is done by the
force acting on box Y than by the force acting on box X.
19 The force-extension graph of a metal wire is shown.
At which point on the graph does the metal wire stop obeying Hooke’s law?
force
C
A
D
B
0
0
© UCLES 2018
extension
9702/12/F/M/18
11
20 The diagram shows a large crane on a construction site lifting a cube-shaped load at a constant
speed.
cable
crane
load
A model is made of the crane, its load and the cable supporting the load.
The material used for each part of the model is the same as that in the full-size crane, cable and
load. The model is one tenth full-size in all linear dimensions.
What is the ratio stress in the cable on the full- size crane ?
stress in the cable on the model crane
A
0.1
B
1
C
10
D
100
21 A wave pulse moves along a stretched rope in the direction shown.
P
Which diagram shows the variation with time t of the displacement s of the particle P in the rope?
A
B
s
s
0
0
0
0
t
C
t
D
s
s
0
0
0
© UCLES 2018
0
t
9702/12/F/M/18
t
[Turn over
12
22 A wave has period T, wavelength λ and amplitude A. The wave is shown on a graph of
displacement x against distance d.
Which graph is correctly labelled?
A
B
x
x
A
A
0
0
d
0
d
0
λ
T
C
D
T
x
x
A
0
d
0
A
0
d
0
λ
23 The table lists possible orders of magnitude of the wavelengths of some of the principal radiations
of the electromagnetic spectrum.
Which row shows the correct orders of magnitude of the wavelengths?
wavelength / m
microwaves
infra-red
ultraviolet
X-rays
A
10–6
10–10
10–12
10–14
B
10–4
10–8
10–10
10–12
C
10–2
10–6
10–8
10–10
D
102
10–4
10–6
10–8
© UCLES 2018
9702/12/F/M/18
13
24 A vehicle carries a microwave transmitter that emits microwaves of a constant frequency. A
stationary observer has a microwave receiver.
The vehicle moves directly towards the observer at constant speed. The observer detects
microwaves of frequency Fo.
The vehicle then accelerates, still moving towards the observer, travels at higher steady speed
for a time and then decelerates until it stops.
What is the variation in the frequency of the microwaves that are detected by the observer?
A
The observed frequency will fall, then remain steady then return to the frequency Fo.
B
The observed frequency will fall, then remain steady then rise to a higher frequency than Fo.
C
The observed frequency will rise, then remain steady then fall to a lower frequency than Fo.
D
The observed frequency will rise, then remain steady then return to the frequency Fo.
25 The diagram shows a cathode-ray oscilloscope display of an electromagnetic wave.
1.0 cm
The time base setting is 0.20 µs cm–1.
Which statement is correct?
A
The frequency of the wave is 2.5 MHz and it lies in the microwave region of the
electromagnetic spectrum.
B
The frequency of the wave is 2.5 MHz and it lies in the radio-wave region of the
electromagnetic spectrum.
C
The frequency of the wave is 5.0 MHz and it lies in the microwave region of the
electromagnetic spectrum.
D
The frequency of the wave is 5.0 MHz and it lies in the radio-wave region of the
electromagnetic spectrum.
26 In a double-slit interference experiment, light of frequency 6.0 × 1014 Hz is incident on a pair of
slits. Bright fringes that are 3.0 mm apart are observed on a screen some distance away.
What is the separation of the bright fringes when the frequency of the light is changed to
5.0 × 1014 Hz?
A
1.8 mm
© UCLES 2018
B
2.5 mm
C
3.0 mm
9702/12/F/M/18
D
3.6 mm
[Turn over
14
27 Monochromatic light is incident on a pair of narrow slits a distance of 0.1 mm apart. A series of
bright and dark fringes are observed on a screen a distance of 2.0 m away. The distance between
adjacent bright fringes is 8.0 mm.
screen
second order dark fringe
monochromatic
light
‘zero’ order bright fringe
distance between
bright fringes = 8.0 mm
2.0 m
(not to scale)
What is the path difference between the light waves from the two slits that meet at the second
order dark fringe?
A
2.0 × 10–7 m
B
4.0 × 10–7 m
C
6.0 × 10–7 m
D
8.0 × 10–7 m
28 A tube of length L is open at both ends. A stationary wave is set up in this tube when a tuning fork
vibrating with frequency fx is held at one end. This is the lowest frequency of stationary wave that
can be formed in this tube.
Another tube of length 2L is closed at one end. A stationary wave is set up in this tube when a
tuning fork vibrating with frequency fy is held at the open end. This is the lowest frequency of
stationary wave that can be formed in this tube.
frequency fx
L
frequency fy
2L
Assume the end correction for each tube is negligible.
Which equation is correct?
A
fx =
© UCLES 2018
fy
4
B
fx =
fy
2
C
fx = 2fy
9702/12/F/M/18
D
fx = 4fy
15
29 Which statement gives a condition that enables diffraction to occur?
A
A source of waves moves towards a stationary observer.
B
A wave is partially blocked by an obstacle.
C
Two coherent waves are superposed.
D
Two waves of equal speed and frequency are travelling through the same part of a medium
in opposite directions.
30 An electron passes into the space between two parallel plates that are 5.0 cm apart and which
are maintained at electric potentials of +2000 V and –500 V, respectively.
+2000 V
5.0 cm
electron
–500 V
What is the electric force on the electron?
A
1.6 × 10–15 N
B
4.8 × 10–15 N
C
6.4 × 10–15 N
D
8.0 × 10–15 N
31 Which statement about electric charges in a uniform electric field is not correct?
A
Electric charges of the same magnitude, whether positive or negative, experience the same
magnitude of force when placed in the same uniform electric field.
B
The direction of the force on a positive charge placed in a uniform electric field is
independent of the magnitude of the charge.
C
The magnitude of the force on a positive charge placed in a uniform electric field is
proportional to the magnitude of the electric field strength.
D
The work done to move a positive charge a certain distance in a uniform electric field is
independent of the direction of the movement.
© UCLES 2018
9702/12/F/M/18
[Turn over
16
32 The diagram shows a simple circuit.
S
R
Which statement is correct?
A
When switch S is closed, the e.m.f. of the battery falls because work is done against the
internal resistance of the battery.
B
When switch S is closed, the e.m.f. of the battery falls because work is done against the
resistance of R.
C
When switch S is closed, the potential difference across the battery falls because work is
done against the internal resistance of the battery.
D
When switch S is closed, the potential difference across the battery falls because work is
done against the resistance of R.
33 A resistor has resistance R. When the potential difference across the resistor is V, the current in
the resistor is I. The power dissipated in the resistor is P. Work W is done when charge Q flows
through the resistor.
What is not a valid relationship between these variables?
A
I= P
V
B
Q= W
V
C
R = P2
I
D
R= V
P
D
76.8 m
34 A wire of resistance 9.55 Ω has a diameter of 0.280 mm.
It is made of metal of resistivity 4.90 × 10–7 Ω m.
What is the length of the wire?
A
1.20 m
B
4.80 m
C
19.0 m
35 Charge carriers, each of charge q, move along a wire of fixed length. The number density of the
charge carriers in the wire is n.
What is also required, for this wire, to determine the average drift velocity of the charge carriers in
terms of n and q?
A
current per unit of cross-sectional area
B
potential difference per unit of length
C
resistance and cross-sectional area
D
resistivity and length
© UCLES 2018
9702/12/F/M/18
17
36 A potential divider circuit is constructed with one variable resistor X and one fixed resistor Y, as
shown.
X
VX
Y
VY
The potential difference across resistor X is VX and the potential difference of resistor Y is VY.
As the resistance of X is increased, what happens to VX and to VY?
VX
VY
A
falls
rises
B
falls
stays the same
C
rises
falls
D
rises
stays the same
37 A cell of electromotive force (e.m.f.) E and negligible internal resistance is connected into a
circuit, as shown.
2Ω
12 Ω
E
4Ω
V
The voltmeter has a very high resistance and reads a potential difference Vout.
What is the ratio
A
1
6
© UCLES 2018
Vout
?
E
B
1
3
C
1
2
9702/12/F/M/18
D
2
3
[Turn over
18
38 Five resistors are connected as shown.
20 Ω
8.0 Ω
6.0 Ω
8.0 Ω
P
Q
7.0 Ω
What is the total resistance between points P and Q?
A
0.25 Ω
B
0.61 Ω
C
4.0 Ω
D
16 Ω
39 A nucleus of neptunium-236 contains 93 protons and 143 neutrons. This nucleus decays with the
emission of an α-particle. The nucleus formed then emits a β– particle.
Which diagram shows the changes in the number P of protons and the number N of neutrons in
these nuclei?
A
B
146
N
146
N
144
144
142
142
140
140
138
138
90
92
94
96
90
92
94
P
C
D
146
N
146
N
144
144
142
142
140
140
138
138
90
92
94
96
P
© UCLES 2018
96
P
90
92
94
96
P
9702/12/F/M/18
19
40 An isolated neutron decays to produce a proton, a β– particle and an antineutrino.
Which row gives the quark composition of the neutron and the proton and the type of force that
gives rise to this reaction?
quark composition
type of force
neutron
proton
A
down, down, up
down, up, up
strong interaction
B
down, down, up
down, up, up
weak interaction
C
down, up, up
down, down, up
strong interaction
D
down, up, up
down, down, up
weak interaction
© UCLES 2018
9702/12/F/M/18
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/12/F/M/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/11
PHYSICS
Paper 1 Multiple Choice
October/November 2018
1 hour 15 minutes
Additional Materials:
*5690949700*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 21 printed pages and 3 blank pages.
IB18 11_9702_11/RP
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
9702/11/O/N/18
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2018
9702/11/O/N/18
[Turn over
4
1
The radius of the Earth is approximately 6.4 × 106 m, and the radius of the Moon is approximately
1.7 × 106 m. A student wishes to build a scale model of the Solar System in the classroom, using
a football of radius 0.12 m to represent the Earth.
Which object would best represent the Moon?
2
A
basketball
B
cherry
C
golf ball
D
tennis ball
When a beam of light is incident on a surface, it delivers energy to the surface. The intensity of
the beam is defined as the energy delivered per unit area per unit time.
What is the unit of intensity, expressed in SI base units?
kg m–2 s–1
A
3
B
kg m2 s–3
C
kg s–2
D
kg s–3
A ship is travelling with a velocity of 8.0 km h–1 in a direction 30° east of north.
What are the components of the ship’s velocity in the east and north directions?
component of velocity
in east direction
/ km h–1
component of velocity
in north direction
/ km h–1
A
4.0
4.0
B
4.0
6.9
C
4.6
6.9
D
6.9
4.0
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4
A micrometer screw gauge is used to measure the diameter of a copper wire.
The reading with the wire in position is shown in diagram 1. The wire is removed and the jaws of
the micrometer are closed. The new reading is shown in diagram 2.
0
15
20
10
15
0
5
diagram 1
10
diagram 2
What is the diameter of the wire?
1.90 mm
A
5
B
2.45 mm
C
2.59 mm
D
2.73 mm
A digital meter has an accuracy of ±1%.
The meter is used to measure the current in an electrical circuit.
The reading on the meter varies between 3.04 A and 3.08 A.
What is the value of the current, with its uncertainty?
6
A
(3.06 ± 0.02) A
B
(3.06 ± 0.04) A
C
(3.06 ± 0.05) A
D
(3.06 ± 0.07) A
A tennis ball is thrown horizontally in air from the top of a tall building.
The effect of air resistance is not negligible.
What happens to the horizontal and to the vertical components of the ball’s velocity?
horizontal component
of velocity
vertical component
of velocity
A
constant
constant
B
constant
increases at a constant rate
C
decreases to zero
increases at a constant rate
D
decreases to zero
increases to a maximum value
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7
Water is pumped through a hose-pipe at a rate of 90 kg per minute. Water emerges horizontally
from the hose-pipe with a speed of 20 m s–1.
What is the minimum force required from a person holding the hose-pipe to prevent it moving
backwards?
A
8
30 N
B
270 N
C
1800 N
D
108 000 N
A ball of mass m is thrown vertically into the air. When the ball has speed v, the air resistance
acting on the ball is F.
What is the magnitude of the acceleration of the ball when its speed is v as it rises and as it falls?
9
acceleration when
ball is rising
acceleration when
ball is falling
A
g– F
m
g– F
m
B
g– F
m
g+ F
m
C
g+ F
m
g– F
m
D
g+ F
m
g+ F
m
What is a statement of the principle of conservation of momentum?
A
A force is equal to the rate of change of momentum of the body upon which it acts.
B
In a perfectly elastic collision, the relative momentum of the bodies before impact is equal to
their relative momentum after impact.
C
The momentum of a body is the product of the mass of the body and its velocity.
D
The total momentum of a system of interacting bodies remains constant, providing no
resultant external force acts on the system.
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10 A charged particle is placed in a uniform field of force. The direction of the force on the particle is
opposite to the direction of the field.
What is the field and what is the charge on the particle?
field
charge on particle
A
electric
negative
B
electric
positive
C
gravitational
negative
D
gravitational
positive
11 A uniform rod of length 200 cm is freely pivoted at point P. The rod is held horizontally in
equilibrium by a 60 N weight that is attached to the rod by a string passing over a frictionless
pulley.
frictionless
pulley
uniform rod
40 cm
30°
P
200 cm
weight
60 N
What is the weight of the rod?
A
30 N
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B
60 N
C
80 N
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D
140 N
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12 A ladder rests in equilibrium on rough ground against a rough wall.
P
G
rough
wall
Q
rough ground
The weight W of the ladder acts through the centre of gravity G. Forces also act on the ladder at
P and at Q. These forces are P and Q respectively.
Which vector triangle represents the forces on the ladder?
A
P
W
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C
B
P
Q
Q
D
P
W
W
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P
Q
W
Q
9
13 A vertical tube, closed at one end, is immersed in water. A column of air is trapped inside the
tube.
water surface
20.0 cm
water
30.0 cm
air
30.0 cm
vertical tube
The density of water is 1000 kg m–3.
What is the difference between the pressure of the air in the tube and the atmospheric pressure?
A
1960 Pa
B
2940 Pa
C
4910 Pa
D
7850 Pa
14 A rocket is fired upwards.
As it accelerates upwards after leaving the launch pad, which forms of energy are changing?
A
chemical energy, gravitational potential energy and kinetic energy
B
chemical energy and gravitational potential energy only
C
chemical energy and kinetic energy only
D
gravitational potential energy and kinetic energy only
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15 A mass m is on top of a platform that is supported by gas in a cylinder of cross-sectional area A,
as shown.
mass m
platform
h
gas
The platform has negligible mass and can move freely up and down.
The gas is heated and expands so that the mass is raised through a height h. Atmospheric
pressure is p.
What is the ratio
A
mg
pA
© UCLES 2018
gain in gravitatio nal potential energy of the mass
?
work done by the gas
B
mg
mg + pA
C
pA
mg
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D
mg − pA
mg
11
16 An 8.00 N weight is attached to the lower end of a spring which is fixed at its upper end. The
weight is initially held at rest at position X and the spring is unstretched. The weight is then
released and falls to position Y, which is 4.00 cm below X. The weight oscillates and then
eventually comes to rest at O, which is 2.00 cm below X.
X
2.00 cm
8.00 N
O
4.00 cm
Y
8.00 N
8.00 N
spring
unstretched
position after
initial drop
final position after
many oscillations
How much energy is lost from the system?
A
0.04 J
B
0.08 J
C
0.16 J
D
0.32 J
17 The force resisting the motion of a car is proportional to the square of the car’s speed. The
magnitude of the force at a speed of 20.0 m s–1 is 800 N.
What useful output power is required from the car’s engine to maintain a steady speed of
40.0 m s–1?
A
32 kW
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B
64 kW
C
128 kW
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D
512 kW
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18 Two wires X and Y are made from the same material. Wire Y has twice the diameter and
experiences twice the tension of wire X. The wires obey Hooke’s law and have the same original
length.
wire X
diameter d
wire Y
diameter 2d
tension T
tension 2T
Wire X has extension e.
What is the extension of wire Y?
A
e
4
B
e
2
C
e
D
2e
19 What is represented by the gradient of a graph of force (vertical axis) against extension
(horizontal axis) for a wire obeying Hooke’s law?
A
elastic limit
B
spring constant
C
stress
D
Young modulus
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20 Forces are applied to the ends of a rod so that its length increases. The variation with load L of
the extension e of the rod is shown.
e
P
0
L
0
The point P is the elastic limit.
Which shaded area represents the work done during the plastic deformation of the rod?
A
B
e
e
P
P
0
0
L
0
C
D
e
e
P
P
0
0
0
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L
0
L
0
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L
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21 The graph shows the variation of a quantity P with a quantity Q for a sound wave travelling in air.
P
0
Q
0
What could P and Q be?
P
Q
A
amplitude
intensity
B
frequency
wavelength
C
speed
frequency
D
wavelength
period
22 A vibration generator produces a progressive wave on a rope. The diagram shows the rope at
one instant. The wave travels at a speed of 4.0 m s–1.
4.0 m s–1
rope
length / m
0
0.2
0.4
0.6
What are the wavelength and the frequency of the wave?
wavelength
/m
frequency
/ Hz
A
0.13
15
B
0.13
30
C
0.27
15
D
0.27
30
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0.8
15
23 The diagram shows the waveform of a signal displayed on a cathode-ray oscilloscope.
The time-base is set at 5.0 ms per division.
The Y-gain is set at 5.0 mV per division.
What are the amplitude and the frequency of the signal?
amplitude
/ mV
frequency
/ Hz
A
10
50
B
10
100
C
20
50
D
20
100
24 A jet aircraft travels at a speed of 0.8v where v is the speed of sound. The aircraft approaches a
stationary observer. The frequency of sound emitted by the aircraft is 100 Hz.
Which frequency does the observer hear?
A
56 Hz
B
180 Hz
C
400 Hz
D
500 Hz
25 A telescope detects and analyses some electromagnetic radiation of wavelength 2 cm.
Which type of telescope is it?
A
microwave telescope
B
optical telescope
C
radio telescope
D
X-ray telescope
26 What may be used to produce stationary waves?
A
blowing air over the top of an empty bottle
B
making a loud sound near a mountain
C
passing monochromatic light through a double slit
D
passing water waves through a narrow slit
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27 What is an example of the diffraction of a wave?
A
laser light travelling along an optic fibre
B
light waves forming images on a cinema screen
C
microwaves passing the edge of a metal plate
D
sound waves diverging as they pass through air
28 When the light from two lamps falls on a screen, no interference pattern can be obtained.
Why is this?
A
The lamps are not point sources.
B
The lamps emit light of different amplitudes.
C
The light from the lamps is not coherent.
D
The light from the lamps is white.
29 A beam of light consists of two wavelengths of 436 nm and 654 nm. A diffraction grating of
5.00 × 105 lines m–1 produces a diffraction pattern in which the second order of one of these
wavelengths occurs at the same angle θ as the third order of the other wavelength.
overlapping orders
θ
θ
436 nm
654 nm
zero order
What is the angle θ ?
A
19.1°
B
25.8°
C
40.8°
D
78.8°
30 Which diagram shows the electric field lines surrounding an isolated negative point charge?
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A
B
C
D
–
–
–
–
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17
31 A beam of electrons is directed into an electric field and is deflected by it.
Diagram 1 represents an electric field in the plane of the paper.
Diagram 2 represents an electric field directed perpendicular to the plane of the paper.
The lines A, B, C and D represent possible paths of the electron beam. All paths are in the plane
of the paper.
Which line best represents the path of the electrons inside the field?
diagram 1
A
diagram 2
B
C
D
electric field
in the plane
of the paper
electrons
electrons
electric field into the paper
and perpendicular to the
plane of the paper
32 A charged particle of charge q and mass m is initially at rest in a uniform electric field. The field is
produced by parallel metal plates separated by a distance d and having a potential difference V
between them.
What is an expression for the acceleration of the charged particle?
A
md
qV
B
mV
qd
C
qd
mV
D
qV
md
33 When there is a current of 5.0 A in a copper wire, the average drift velocity of the free electrons is
8.0 × 10–4 m s–1.
What is the average drift velocity in a different copper wire that has twice the diameter and a
current of 10.0 A?
A
4.0 × 10–4 m s–1
B
8.0 × 10–4 m s–1
C
1.6 × 10–3 m s–1
D
3.2 × 10–3 m s–1
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34 What is equivalent to one volt?
A
one coulomb per second
B
one joule per coulomb
C
one joule per second
D
one joule second per coulomb squared
35 The diagram shows a rectangular block with dimensions x, 2x and 3x.
top face P
2x
3x
Q
R
x
R
Q
bottom face P
Electrical contact can be made to the block between opposite pairs of faces (for example,
between the faces labelled R).
Which statement describing the electrical resistance of the block is correct?
A
It is maximum between the faces labelled P.
B
It is maximum between the faces labelled Q.
C
It is maximum between the faces labelled R.
D
It is the same, whichever pair of faces is used.
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36 A battery, with internal resistance, is connected to a parallel arrangement of two resistors and a
switch S, as shown.
V
A
switch
S
Initially switch S is open.
What happens to the voltmeter and ammeter readings when switch S is closed?
voltmeter reading
ammeter reading
A
decreases
increases
B
decreases
decreases
C
increases
increases
D
increases
decreases
37 A battery is connected to a network of six resistors, as shown.
1.2 V
2.2 V
4.1 V
1.2 V
3.7 V
R
The potential differences across five of the resistors are labelled on the diagram.
What is the potential difference across resistor R?
A
4.4 V
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B
4.6 V
C
6.6 V
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D
11.2 V
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38 The diagram shows a battery of electromotive force (e.m.f.) 6 V, connected in series with a
resistor and a uniform resistance wire RQ of length 60 cm.
The resistance of RQ is equal to the resistance of the resistor.
6V
R
Q
L
P
X
Y
Terminal X is connected to fixed point R. Terminal Y is connected to point P, a connection that
may be made at any position along the wire. L is the distance between R and P.
Which graph shows the variation with L of the potential difference (p.d.) V across XY?
A
B
6
6
V/V
V/V
0
0
0
L / cm
60
0
C
60
D
6
6
V/V
V/V
0
0
0
© UCLES 2018
L / cm
L / cm
60
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0
L / cm
60
21
39 A nucleus emits a β– particle.
What is the change to the proton number and to the nucleon number of the nucleus?
proton number
nucleon number
A
–1
+1
B
0
–1
C
+1
–1
D
+1
0
40 How many up quarks and how many down quarks are in a nucleus of the nuclide
up quarks
down quarks
A
51
60
B
54
57
C
57
54
D
60
51
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17 Cl
?
22
BLANK PAGE
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BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/11/O/N/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
October/November 2018
1 hour 15 minutes
Additional Materials:
*3374435795*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 19 printed pages and 1 blank page.
IB18 11_9702_12/RP
© UCLES 2018
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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1
A car is travelling at a speed of 20 m s–1. The table contains values for the kinetic energy and the
momentum of the car.
Which values are reasonable estimates?
2
3
kinetic energy
/J
momentum
/ kg m s–1
A
3 × 105
3 × 104
B
3 × 105
5 × 106
C
2 × 107
3 × 104
D
2 × 107
5 × 106
What is the unit of resistance when expressed in SI base units?
A
kg m2 s–2 A–1
B
kg m2 s–3 A–2
C
kg m s–2 A–1
D
kg m s–3 A–1
Which list contains both scalar and vector quantities?
A
acceleration, momentum, velocity, weight
B
area, current, force, work
C
distance, kinetic energy, power, pressure
D
mass, temperature, time, speed
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4
Vectors P and Q are drawn to scale.
P
Q
Which diagram represents the vector (P + Q)?
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A
B
C
D
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5
Students take readings of the volume of a liquid using three different pieces of measuring
equipment X, Y and Z.
The true value of the volume of the liquid is V.
The students’ results are shown.
X
Y
number of
readings
Z
number of
readings
0
0
V
0
number of
readings
volume
0
V volume
0
0
V
volume
How many pieces of equipment are precise and how many are accurate?
6
number of precise
pieces of equipment
number of accurate
pieces of equipment
A
1
1
B
1
2
C
2
1
D
2
2
A sprinter runs a 100 m race. The sprinter has a constant acceleration from rest of 2.5 m s–2 until
reaching a speed of 10 m s–1. The speed then remains constant until the end of the race.
Which time does it take the sprinter to run the race?
A
8.9 s
© UCLES 2018
B
10 s
C
12 s
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D
14 s
7
7
A resultant force of 10 N acts on a body for a time of 2.0 s.
Which graph could show the variation with time t of the momentum p of the body?
20
p / kg m s
–1
15
A
10
B
5
D
C
0
0
8
1.0
t/s
2.0
The acceleration of free fall on the surface of planet P is one tenth of that on the surface of
planet Q.
On the surface of P, a body has a mass of 1.0 kg and a weight of 1.0 N.
What are the mass and the weight of the same body on the surface of planet Q?
mass on Q / kg
9
A
1.0
B
1.0
weight on Q / N
0.1
10
C
10
10
D
10
100
Two bodies travelling along the same straight line collide in a perfectly elastic collision.
Which statement must be correct?
A
The initial speed of one body will be the same as the final speed of the other body.
B
The relative speed of approach between the two bodies equals their relative speed of
separation.
C
The total momentum is conserved but the total kinetic energy will be reduced.
D
One of the bodies will be stationary at one instant.
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10 The diagram shows two identical spheres X and Y.
v
X
Y
Initially, X moves with speed v directly towards Y. Y is stationary. The spheres collide elastically.
What happens?
X
A
B
moves with speed
Y
1
2
v to the right
moves with speed
moves with speed v to the left
C
moves with speed
D
stops
1
2
v to the left
1
2
v to the right
remains stationary
moves with speed
1
2
v to the right
moves with speed v to the right
11 A positively-charged particle of negligible mass, moving at constant velocity v in a vacuum, enters
a uniform electric field between two parallel plates, as shown.
positive plate
+
v
negative plate
A short time later, the particle is at the position shown.
positive plate
negative plate
Which diagram represents the force or forces acting on the particle?
A
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B
C
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D
9
12 A uniform rectangular board is supported by a frictionless pivot at its centre point P.
R
2.5F
20 cm
P
Q
F
Two forces act in the plane of the board. Force F acts at corner Q and force 2.5F acts at
corner R. The perpendicular distance between the line of action of force F and point P is 20 cm.
The board is in equilibrium.
What is the area of the board?
A
160 cm2
B
320 cm2
C
640 cm2
D
1600 cm2
13 A kite is in equilibrium at the end of a string, as shown.
kite
string
W
The kite has three forces acting on it: the weight W, the tension T in the string, and the force F
from the wind.
Which vector diagram represents the forces acting on the kite?
W
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A
B
T
T
F
W
D
C
T
F
F
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W
F
W
T
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14 The density of the air in the atmosphere decreases as the height h above the surface of the Earth
increases.
Which graph best shows the variation with height h of the pressure p of the air?
A
B
p
C
p
0
p
0
h
0
D
0
h
p
0
h
0
0
0
h
15 A bungee jumper on a platform over a river is attached to an elastic rope that is 20 m long when
unstretched. He falls towards the river and his lowest point is 30 m below the platform.
The initial gravitational potential energy of the jumper is transferred to other forms during the
jump.
Which other forms of energy do the jumper and rope have when the jumper has fallen half-way
and when he is at the lowest point of his jump?
half-way
lowest point
A
kinetic energy and elastic potential energy
kinetic energy and elastic potential energy
B
kinetic energy and elastic potential energy
elastic potential energy only
C
kinetic energy only
kinetic energy and elastic potential energy
D
kinetic energy only
elastic potential energy only
16 A cylinder contains a fixed mass of gas. The gas, at a constant pressure of 1.3 × 105 Pa, expands
from a volume of 900 cm3 to a volume of 1100 cm3.
What is the work done by the gas during this expansion?
A
26 J
© UCLES 2018
B
130 J
C
2600 J
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D
13 000 J
11
17 An object is thrown into the air.
Which graph shows how the gravitational potential energy Ep of the object varies with height h
above the ground?
A
B
Ep
C
Ep
h
0
D
Ep
h
0
Ep
h
0
h
0
18 A car of mass 1800 kg accelerates along a horizontal road so that its speed increases from
20 m s–1 to 25 m s–1 in a time of 5.4 s.
What is the average useful power output of the car’s engine?
A
4.2 kW
B
38 kW
C
120 kW
D
1100 kW
19 A variable force is applied to ensure that a constant power is supplied to a train.
Which graph best shows the variation of the force F applied with the velocity v of the train?
A
B
F
C
F
0
0
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v
D
F
0
0
v
F
0
0
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v
0
0
v
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20 A metal cylinder is able to withstand a compressive force of 4.0 kN without deforming plastically.
4.0 kN
4.0 kN
The cylinder has cross-sectional area A and would be at its elastic limit when a stress σ is
applied.
What is a possible pair of values for A and σ ?
A / m2
σ / MPa
A
1.5 × 10–5
50
B
1.5 × 10–5
80
C
7.5 × 10–5
50
D
7.5 × 10–5
80
21 A wire has both elastic and plastic properties. When it is slowly loaded, its extension varies with
load as shown by line OXY. The removal of the load is represented by line YZ. This creates areas
P, Q and R on the graph.
Y
X
load
P
Q
R
O
0
0
Z
extension
Which area represents the maximum elastic potential energy stored in the wire?
A
P
B
Q
C
Q+R
D
R
22 A progressive wave on a wire has a frequency of 10 Hz. Two points on the wire, separated by a
distance of 0.25 m, have a phase difference of 22.5°.
What is the maximum speed of the wave?
A
2.5 m s–1
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B
10 m s–1
C
20 m s–1
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D
40 m s–1
13
23 When a guitar string is plucked, it causes a longitudinal sound wave in the air, as shown.
0.0
0.2
0.4
0.6
0.8
distance / m
The speed of sound in the air is 340 m s–1.
What is the approximate frequency of the sound wave shown?
A
430 Hz
B
680 Hz
C
1100 Hz
D
1400 Hz
24 The sound from a loudspeaker placed above a tube causes resonance of the air in the tube.
A stationary wave is formed with two nodes and two antinodes as shown.
loudspeaker
60 cm
The speed of sound in the air is 340 m s–1.
What is the frequency of the sound?
A
430 Hz
B
570 Hz
C
850 Hz
D
1700 Hz
25 A police car has a two-tone siren emitting sound of frequencies of 700 Hz and 1000 Hz.
The police car is travelling at a speed of 40.0 m s–1 towards a stationary observer. The speed of
sound in the air is 340 m s–1.
What is the difference between the two frequencies of the sound that is heard by the observer?
A
268 Hz
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B
300 Hz
C
335 Hz
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D
340 Hz
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26 A surveyor’s device emits a pulse of light. The light is reflected from a wall 150 m away.
What is the time taken for the pulse to travel from the device to the wall and then back to the
device?
A
0.05 ns
B
0.10 ns
C
0.50 µs
D
1.0 µs
27 Progressive sound waves of wavelength 20 cm enter the air columns in a closed pipe P and an
open pipe Q. The lengths of the pipes are shown.
P
Q
35 cm
50 cm
In which pipe or pipes are stationary waves formed?
A
P and Q
B
P only
C
Q only
D
neither P nor Q
28 What happens when waves pass through a gap equal to their wavelength?
A
There is diffraction and the wavelength decreases.
B
There is diffraction and the wavelength stays the same.
C
There is no diffraction and the wavelength decreases.
D
There is no diffraction and the wavelength stays the same.
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15
29 Two sources of microwaves P and Q produce coherent waves with a phase difference of 180°.
The waves have the same wavelength λ.
S
P
Q
At the point S there is a minimum in the interference pattern produced by waves from the two
sources. The distance (QS – PS) is called the path difference.
In the expressions shown, n is an integer.
Which expression represents the path difference?
A
nλ
B
1
2
nλ
C
(n +
1
2
)λ
D
(2n +
1
2
)λ
30 A parallel beam of monochromatic light of wavelength λ is incident normally on a diffraction
grating G. The angle between the directions of the two second-order diffracted beams at P1 and
at P2 is α, as shown.
P1
G
α
light
P2
What is the spacing of the lines on the grating?
A
2λ
sin α
© UCLES 2018
B
λ
sin α
C
2λ
sin(α / 2)
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D
λ
sin(α / 2)
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31 A flat plate is positively charged and a curved plate is negatively charged.
Which diagram shows the electric field lines between the two plates?
A
+
B
+
–
–
+
+
–
–
+
D
+
–
–
–
C
+
+
–
+
+
–
–
+
+
–
–
32 Two parallel metal plates are connected to a d.c. supply, as shown.
P
The two plates are moved towards each other at constant speed.
It may be assumed that the electric field between the plates is uniform.
Point P is mid-way between the two plates.
Which graph shows the variation with time t of the electric field strength E at point P?
A
B
E
C
E
0
0
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t
D
E
0
0
t
E
0
0
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t
0
0
t
17
33 Which two units are used to define the coulomb?
A
ampere and second
B
ampere and volt
C
volt and ohm
D
volt and second
34 An electrical device of fixed resistance 20 Ω is connected in series with a variable resistor and a
battery of electromotive force (e.m.f.) 16 V and negligible internal resistance.
16 V
20 Ω
device
What is the resistance of the variable resistor when the power dissipated in the electrical device
is 4.0 W?
16 Ω
A
36 Ω
B
C
44 Ω
D
60 Ω
35 A wire of length L has resistance R. The cross-section of the wire is circular with radius r.
A second wire, also of circular cross-section, and of the same material, has resistance
1
2
R.
What could be the radius and the length of the second wire?
radius
length
A
r
2
L
2
B
r
2
L
2
C
r 2
2L
D
2r
2L
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36 A battery of negligible internal resistance may be connected between any two points P, Q, R and
S of the network of resistors shown.
3.0 Ω
P
Q
6.0 Ω
5.0 Ω
S
4.0 Ω
R
Which connections will give the largest current and the smallest current in the battery?
largest current
smallest current
A
PQ
PR
B
PQ
QS
C
RS
PR
D
RS
QS
37 Kirchhoff’s second law is a consequence of a basic principle.
What is this principle?
A
The charge flowing in an electric circuit is conserved.
B
The energy in an electric circuit is conserved.
C
The sum of the electric currents entering a point in an electrical circuit is equal to the sum of
the electric currents leaving that point.
D
The sum of the potential differences in a circuit is equal to the sum of the products of the
current and resistance.
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19
38 Two cells are investigated using a potentiometer. At the balance point, cell X gives a reading of
44 cm and cell Y gives a reading of 70 cm.
6V
6V
R
44 cm
R
70 cm
cell X
cell Y
galvanometer
galvanometer
Which statement is not correct?
A
A potentiometer balance point results in zero current through the galvanometer.
B
At the balance point, the current through resistor R in both circuits is the same.
C
The electromotive force (e.m.f.) of cell X is larger than that of cell Y.
D
The value of the e.m.f. of each of the cells X and Y is less than 6 V.
39 A proton in a nucleus undergoes β+ decay. One of the products is a neutron.
What are the other products?
A
an electron and a neutrino
B
an electron and an antineutrino
C
a positron and a neutrino
D
a positron and an antineutrino
40 A certain type of hadron has zero charge. It is composed of a down quark, a strange quark and
one other quark.
What could be the other quark?
A
up
B
down
C
strange
D
anti-strange
© UCLES 2018
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20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/12/O/N/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
9702/13
PHYSICS
Paper 1 Multiple Choice
October/November 2018
1 hour 15 minutes
Additional Materials:
*4302523063*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 19 printed pages and 1 blank page.
IB18 11_9702_13/RP
© UCLES 2018
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2018
9702/13/O/N/18
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2018
9702/13/O/N/18
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4
1
2
Which statement is not a reasonable estimate?
A
Atmospheric pressure at sea level is about 1 × 105 Pa.
B
Light takes 5 × 102 s to reach us from the Sun.
C
The frequency of ultraviolet light is 3 × 1012 Hz.
D
The lifespan of a man is about 2 × 109 s.
Three of these quantities have the same unit.
Which quantity has a different unit?
3
4
A
energy
distance
B
force
C
power × time
D
rate of change of momentum
Which group of quantities contains only vectors?
A
acceleration, displacement, speed
B
acceleration, work, electric field strength
C
displacement, force, velocity
D
power, electric field strength, force
An ammeter is calibrated so that it shows a full-scale deflection when it measures a current of
2.0 A.
The diagram shows the display of this ammeter when it is measuring a current.
2
0
1
4
6
2
3
8
10
4
5
0
Which current is the ammeter measuring?
A
0.75 A
© UCLES 2018
B
1.5 A
C
3.8 A
9702/13/O/N/18
D
7.5 A
5
5
The width of a table is measured as (50.3 ± 0.1) cm. Its length is measured as (1.40 ± 0.01) m.
What is the area of the table and its absolute uncertainty?
6
A
(0.7 ± 0.1) m2
B
(0.704 ± 0.006) m2
C
(0.704 ± 0.011) m2
D
(70.4 ± 0.6) m2
A stone is projected horizontally at time t = 0 and falls. Air resistance is negligible. The stone has
a horizontal component of velocity vH and a vertical component of velocity vV.
Which graph shows how vH and vV vary with time t ?
A
B
velocity
vV
velocity
vH
vH
0
0
t
0
C
D
vH
0
velocity
vH
vV
0
t
0
t
0
vV
velocity
7
vV
t
0
Two isolated spheres have masses 2.0 kg and 4.0 kg. The spheres collide and then move apart.
During the collision, the 2.0 kg mass has an average acceleration of 8.0 m s–2.
What is the average acceleration of the 4.0 kg mass?
A
2.0 m s–2
© UCLES 2018
B
4.0 m s–2
C
8.0 m s–2
9702/13/O/N/18
D
16 m s–2
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6
8
A mass is placed on a frictionless slope inclined at 30° to the horizontal. The mass is then
released.
What is its acceleration down the slope?
4.9 m s–2
A
9
B
5.7 m s–2
C
8.5 m s–2
D
9.8 m s–2
A parachutist falls vertically from rest at time t = 0 from a hot-air balloon. She falls for some
distance before opening her parachute.
Which graph best shows the variation with time t of the speed v of the parachutist?
A
B
v
v
0
0
t
0
t
0
C
D
v
v
0
0
0
t
0
t
10 A ship of mass 8.4 × 107 kg is approaching a harbour with speed 16.4 m s–1. By using reverse
thrust it can maintain a constant total stopping force of 920 000 N.
How long will it take to stop?
A
15 seconds
B
150 seconds
C
25 minutes
D
250 minutes
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7
11 A rigid, hollow sphere is immersed deep in water and released from rest. It experiences an
upthrust which propels it towards the surface of the water.
Which graph best shows the variation with time t of its upward velocity v?
A
B
v
v
0
0
t
0
t
0
C
D
v
v
0
0
t
0
t
0
12 A flat metal disc has radius R.
Forces of magnitude F are applied tangentially at the edge of the disc. The forces are in the plane
of the disc.
Which arrangement of forces produces only a torque of magnitude 2FR ?
B
A
F
F
R
F
© UCLES 2018
D
C
2F
R
2F
R
F
2F
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R
2F
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13 The diagram shows the jib of a crane at an angle of 35° to the vertical. A cable passes over a
frictionless pulley and carries a load of 1830 N.
R
pulley
cable
35°
35°
jib
cable
1830 N
The force R that the pulley exerts on the cable is in line with the jib. The cable and the pulley are
in equilibrium.
What is the value of R ?
A
1000 N
B
1500 N
C
2100 N
D
3000 N
C
kg cm–2
D
µg mm–3
14 What is a unit for density?
A
N m–3
B
g mm–1
15 Which statement about energy is not correct?
A
Energy is never lost but it may be transferred between different forms.
B
In an inelastic collision, the total energy is constant.
C
The efficiency of a system is the ratio of the useful energy output to the total energy input.
D
When a machine does work, friction reduces the total energy.
16 An electric kettle is rated as having an input power of 1.50 kW and an efficiency of 65.0%.
The kettle is switched on for 2.00 minutes.
How much energy is transferred to the water in the kettle?
A
0.975 kJ
© UCLES 2018
B
117 kJ
C
180 kJ
9702/13/O/N/18
D
277 kJ
9
17 On a planet, a gravitational force F acts on a mass of 6.0 kg. The mass is moved by force F a
distance of 30 m in the direction of the gravitational field. The work done by the field is 450 J.
What is the force F on the mass and what is the acceleration of free fall g on the planet?
g / m s–2
F/N
A
0.067
0.011
B
0.067
0.40
C
15
D
15
2.5
90
18 A girl of mass 50 kg runs up a flight of 20 steps in 7.0 seconds. Each step is 25 cm high.
What is the useful average output power provided by the girl to climb the flight of steps?
A
18 W
© UCLES 2018
B
36 W
C
350 W
9702/13/O/N/18
D
2500 W
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19 In an experiment to measure the Young modulus of a metal, a wire of the metal of diameter
0.25 mm is clamped, as shown.
wire
clamp
pulley
pulley
marker
F
scale
The wire passes from a clamp, around a frictionless pulley, and then to a second frictionless
pulley where loads F are applied to it. A marker is attached to the wire so that the total length of
wire between the clamp and the marker is initially 3.70 m. A scale is fixed near to this marker.
The graph shows how the reading on the scale varies with F.
8.0
marker position 7.0
on scale / mm 6.0
5.0
4.0
3.0
2.0
1.0
0
0
2
4
6
8
F/N
What is the Young modulus of the metal?
A
5.5 × 1010 Pa
B
9.4 × 1010 Pa
C
1.6 × 1011 Pa
D
2.2 × 1011 Pa
© UCLES 2018
9702/13/O/N/18
10
11
20 A scientist is investigating the properties of a new material. She plots a force-extension graph for
the material up to its breaking point.
R
force
Q
P
0
0
extension
Which statement must be correct?
A
The area under the graph from P to R is the strain energy stored in the material.
B
The area under the graph from P to R is the work done in stretching the material.
C
The material stretches elastically from Q to R.
D
The material stretches plastically from P to Q.
21 A progressive sound wave in air has amplitude x0 and intensity I.
The amplitude of the wave increases to 3x0.
What is the new intensity of the wave?
A
I
9
© UCLES 2018
B
I
3
C
3I
9702/13/O/N/18
D
9I
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22 The variation with distance x of the displacement y of a transverse wave on a rope is shown at
time t = 0.
The wave has a frequency of 0.5 Hz.
A point X on the rope is marked. The diagram shows the original position of X and four new
positions.
What is the position of X at time t = 1 s?
C
X
y
direction of
propagation
D
A
0
0
x
B
23 A sound wave is detected by a microphone. The output from the microphone is connected to the
Y-input of a cathode-ray oscilloscope (c.r.o.). The trace on the c.r.o. is shown.
The time-base is set at 0.20 ms per division.
What is the frequency of the sound wave?
A
1000 Hz
B
1250 Hz
C
2000 Hz
D
2500 Hz
24 A bat flies directly towards a fixed ultrasound detector at a speed of 25.0 m s–1 emitting pulses of
ultrasound of frequency 40.0 kHz.
The speed of sound in air is 330 m s–1.
Which frequency does the ultrasound detector record?
A
37.0 kHz
© UCLES 2018
B
37.2 kHz
C
43.0 kHz
9702/13/O/N/18
D
43.3 kHz
13
25 An electromagnetic wave has a wavelength of 1.0 × 10–7 m.
To which region of the electromagnetic spectrum does this wave belong?
A
infra-red
B
ultraviolet
C
visible
D
X-ray
26 The diagram shows a stationary wave on a string. The stationary wave has three nodes N1, N2
and N3.
N1
N2
N3
Which statement is correct?
A
All points on the string vibrate in phase.
B
All points on the string vibrate with the same amplitude.
C
Points equidistant from N2 vibrate with the same frequency and in phase.
D
Points equidistant from N2 vibrate with the same frequency and the same amplitude.
27 In which situation does diffraction occur?
A
A wave bounces back from a surface.
B
A wave passes from one medium into another.
C
A wave passes through an aperture.
D
Waves from two identical sources are superposed.
© UCLES 2018
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28 A student connects two loudspeakers to a signal generator.
Q
signal
generator
P
As the student walks from P to Q, he notices that the loudness of the sound rises and falls
repeatedly.
What causes the loudness of the sound to vary?
A
diffraction of the sound waves
B
Doppler shift of the sound waves
C
interference of the sound waves
D
reflection of the sound waves
29 A parallel beam of white light is incident normally on a diffraction grating. The second-order and
third-order spectra partially overlap.
Which wavelength in the third-order spectrum appears at the same angle as the wavelength of
600 nm in the second-order spectrum?
A
300 nm
© UCLES 2018
B
400 nm
C
600 nm
9702/13/O/N/18
D
900 nm
15
30 Two parallel metal plates are at electric potentials of +800 V and +1300 V.
Which diagram best represents the electric field between the metal plates?
A
+800 V
B
+1300 V
+800 V
C
+800 V
© UCLES 2018
+1300 V
D
+1300 V
+800 V
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+1300 V
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31 The diagram shows two metal plates P and Q. There is a potential difference of 700 V between
the plates. Plate Q is earthed.
–700 V
plate P
R
5.0 mm
plate Q
0V
What is the magnitude and direction of the electric field at point R?
A
1.4 × 102 N C–1 from P towards Q
B
1.4 × 102 N C–1 from Q towards P
C
1.4 × 105 N C–1 from P towards Q
D
1.4 × 105 N C–1 from Q towards P
32 The current I in a copper wire can be calculated using the equation shown.
I = Anvq
What does the symbol v represent?
A
the average drift velocity of the charge carriers
B
the instantaneous velocity of the charge carriers
C
the voltage applied across the wire
D
the volume of the wire
33 Three resistors are to be connected into a circuit with the arrangement shown.
X
100 Ω
100 Ω
Y
100 Ω
The power in any resistor must not be greater than 4.0 W.
What is the maximum voltage across XY?
A
24 V
© UCLES 2018
B
30 V
C
40 V
9702/13/O/N/18
D
60 V
17
34 Gold is sometimes used to make very small connecting wires in electronic circuits.
A particular gold wire has length 2.50 × 10–3 m and cross-sectional area 6.25 × 10–8 m2. Gold has
resistivity 2.30 × 10–8 Ω m.
What is the resistance of the wire?
A
3.6 × 10–18 Ω
B
5.8 × 10–13 Ω
C
9.2 × 10–4 Ω
D
6.8 × 10–3 Ω
35 A resistor X of resistance 40 Ω and a variable resistor are connected to a battery of electromotive
force (e.m.f.) 12 V and internal resistance 2.0 Ω, as shown.
12 V
2.0 Ω
0 – 40 Ω
40 Ω
X
The resistance of the variable resistor is changed from 0 to 40 Ω.
What is the change in power dissipated in resistor X?
A
2.4 W
© UCLES 2018
B
2.7 W
C
3.6 W
9702/13/O/N/18
D
5.6 W
[Turn over
18
36 All the resistors shown in the resistor networks W, X, Y and Z have the same resistance.
W
X
Y
Z
Which list gives the networks in order of increasing total resistance?
A
W→Z→Y→X
B
X→W→Y→Z
C
X→Y→W→Z
D
X→Y→Z→W
37 In the circuit shown, the ammeter reading is zero.
50 Ω
R
12 V
24 V
100 Ω
200 Ω
A
What is the resistance of resistor R?
A
100 Ω
© UCLES 2018
B
200 Ω
C
400 Ω
9702/13/O/N/18
D
600 Ω
19
38 A neutron collides with a nucleus of uranium-235. One possible nuclear reaction that results is
represented by the equation
235
92 U
+
1
0n
→
154
60 Nd
+
80
32 Ge
+ x
where x represents one or more particles.
What does x represent?
A
one neutron
B
two electrons
C
two neutrons
D
two protons
39 A nucleus Q has the notation yx Q .
Which of the following is an isotope of Q?
A
y −1
xQ
B
y
x −1 Q
C
y
x +1Q
D
y −1
x +1Q
40 In β– decay, a neutron inside a nucleus changes to a proton.
Which statement describes the quark composition of the nucleus during the decay?
A
The number of down quarks decreases by one.
B
The number of down quarks increases by one.
C
The number of down quarks stays the same.
D
The number of up quarks stays the same.
© UCLES 2018
9702/13/O/N/18
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at
www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/13/O/N/18
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/11
PHYSICS
Paper 1 Multiple Choice
May/June 2019
1 hour 15 minutes
Additional Materials:
*7108167400*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 19 printed pages and 1 blank page.
IB19 06_9702_11/4RP
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
9702/11/M/J/19
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
9702/11/M/J/19
[Turn over
4
1
2
Which unit can be expressed in base units as kg m2 s–2?
A
joule
B
newton
C
pascal
D
watt
The luminosity L of a star is given by
L = 4πr 2σT 4
where
r is the radius of the star,
T is the temperature of the star and
σ is a constant with units W m–2 K–4.
What are the SI base units of L ?
kg m2 s–1
A
3
B
kg m2 s–2
C
kg m2 s–3
D
kg m2 s–4
A particle has velocity V at an angle θ to the horizontal.
The components of the particle’s velocity are Vv upwards in the vertical direction and Vh to the
right in the horizontal direction, as shown.
V
Vv
θ
Vh
What are expressions for the magnitude of V and for the angle θ ?
θ
A
(Vv2 + Vh2 )
V 
tan–1  
V 
B
(Vv2 + Vh2 )
V 
tan–1  v 
 Vh 
C
(Vv 2 − Vh2)
V 
tan–1  
V 
D
(Vv 2 − Vh2)
V 
tan–1  v 
 Vh 
h
magnitude of V
v
h
v
© UCLES 2019
9702/11/M/J/19
5
4
A whale produces sound waves of frequency 5 Hz. The waves are detected by a microphone and
displayed on an oscilloscope.
What is the time-base setting on the oscilloscope?
A
5
0.1 ms div–1
B
1 ms div–1
C
10 ms div–1
D
100 ms div–1
The speed shown on a car’s speedometer is proportional to the rate of rotation of the tyres.
The variation of the diameter of a tyre as it wears introduces an error in the speed shown on the
speedometer.
A car has new tyres of diameter 600 mm. The speedometer is accurately calibrated for this
diameter.
The tyres wear as shown, with 6 mm of material being removed from the outer surface.
not to scale
6 mm
new tyre
worn tyre
What is the error in the speed shown on the speedometer after this wear has taken place?
A
The speed shown is too high by 1%.
B
The speed shown is too high by 2%.
C
The speed shown is too low by 1%.
D
The speed shown is too low by 2%.
© UCLES 2019
9702/11/M/J/19
[Turn over
6
6
A car travels along a straight horizontal road. The graph shows the variation of the velocity v of
the car with time t for 6.0 s of its journey.
30
v / m s–1
20
10
0
0
1.0
2.0
3.0
4.0
5.0
6.0
t/s
The brakes of the car are applied from t = 1.0 s to t = 4.0 s.
How far does the car travel while the brakes are applied?
A
7
21 m
B
45 m
C
67 m
D
83 m
A stone is thrown horizontally from the top of a cliff and falls into the sea some time later. Air
resistance is negligible.
Which graph shows how the vertical component vv of velocity of this stone varies with its
horizontal component vh of velocity as it moves through the air?
A
B
vv
vv
0
vh
0
8
C
D
vv
0
0
vh
vv
0
0
vh
0
0
vh
A positive charge of 2.6 × 10–8 C is in a uniform electric field of field strength 300 000 V m–1.
How much work must be done on the charge in order to move it a distance of 4.0 mm in the
opposite direction to the direction of the field?
A
3.1 × 10–5 J
B
2.0 × 10–3 J
C
3.1 × 10–2 J
D
2.0 J
© UCLES 2019
9702/11/M/J/19
7
9
Each diagram illustrates a pair of forces of equal magnitude.
Which diagram gives an example of a pair of forces that is described by Newton’s third law of
motion?
A
B
total
resistive
forces
gravitational
attraction
Earth
driving
force
gravitational
Moon
attraction
C
D
support force
lift
weight
weight
10 A stone is dropped from a tall building. Air resistance is significant. The variation of distance
fallen with time is shown by the dashed line.
A second stone with the same dimensions but a smaller mass is dropped from the same building.
Which line represents the motion of the second stone?
A
B
distance
path of first stone
C
D
0
0
© UCLES 2019
time
9702/11/M/J/19
[Turn over
8
11 A helium atom of mass m collides normally with a wall. The atom arrives at the wall with speed v
and then rebounds along its original path. Assume that the collision is perfectly elastic.
What is the change in the momentum of the atom during its collision?
A
zero
B
0.5 mv
C
mv
D
2mv
12 A cylindrical iceberg of height H floats in sea water. The top of the iceberg is at height h above
the surface of the water.
iceberg
h
H
sea water
The density of ice is ρ i and the density of sea water is ρ w.
What is the height h of the iceberg above the sea water?
A

ρ 
1 − i  H
ρw 

B
 ρi


− 1 H
 ρw 
C
ρw
H
ρi
D
ρi
H
ρw
13 A couple is applied to a tap as shown.
F
pivot
tap
d
d
F
What is the torque of the couple?
A
Fd
2
© UCLES 2019
B
Fd
C
2Fd
9702/11/M/J/19
D
4Fd
9
14 A crane uses a counterweight to stop it from toppling over when lifting a load, as shown.
pivot
counterweight
5000 kg
17.0 m
12.0 kN
not to
scale
crane
The counterweight has a mass of 5000 kg. The crane is required to lift a load of 12.0 kN and the
horizontal distance from the pivot to the load is 17.0 m.
How far from the pivot should the centre of gravity of the counterweight be positioned in order to
keep the crane in equilibrium?
A
0.0408 m
B
0.240 m
C
4.16 m
D
40.8 m
15 Three parallel forces act on an object. As a result of these forces, the object is in equilibrium.
What must be correct for these forces?
A
They all act along the same line.
B
They all have the same magnitude.
C
They do not all act along the same line.
D
They do not all have the same magnitude.
16 An empty glass beaker has a mass of 103 g. When filled with water, it has a total mass of 361 g.
When filled with cooking oil, it has a total mass of 351 g.
The density of water is 1.00 g cm–3.
What is the density of the cooking oil?
A
0.961 g cm–3
© UCLES 2019
B
0.972 g cm–3
C
1.03 g cm–3
9702/11/M/J/19
D
1.04 g cm–3
[Turn over
10
17 A rope is attached to a sledge and a boy uses the rope to pull the sledge along a horizontal
surface with a constant velocity. The tension in the rope is 100 N and the rope is held at 30° to
the horizontal.
100 N
rope
sledge
30°
horizontal
surface
How much work does the boy do on the sledge when he pulls it a distance of 5.0 m along the
surface?
A
250 J
B
290 J
C
430 J
D
500 J
18 The kinetic energy Ek of an object of mass m moving at speed v is given by the equation shown.
Ek =
1
2
mv2
Which equation is not used in the derivation of this equation?
A
F = ma
B
s = vt
C
v2 = u2 + 2as
D
W = Fs
19 A grasshopper of mass 0.12 g jumps vertically. It uses its back legs over a time of 0.020 s to jump,
leaving the ground with a velocity of 3.0 m s–1.
What is the average power developed by the legs of the grasshopper?
A
9.0 × 10–3 W
B
1.8 × 10–2 W
C
2.7 × 10–2 W
D
37 W
20 A spring of original length 100 mm is compressed by a force. The graph shows the variation of the
compressing force F with the length L of the spring.
12
F / N 10
8
6
4
2
0
40
50
60
70
80
90
100
L / mm
What is the energy stored in the spring when the length is 70 mm?
A
0.090 J
© UCLES 2019
B
0.21 J
C
0.27 J
9702/11/M/J/19
D
0.63 J
11
21 A 0.80 m length of steel wire and a 1.4 m length of brass wire are joined together. The combined
wires are suspended from a fixed support and a force of 40 N is applied, as shown.
steel
brass
40 N
The Young modulus of steel is 2.0 × 1011 Pa.
The Young modulus of brass is 1.0 × 1011 Pa.
Each wire has a cross-sectional area of 2.4 × 10–6 m2.
The wires obey Hooke’s law.
What is the total extension? Ignore the weights of the wires.
A
1.7 × 10–4 m
© UCLES 2019
B
3.0 × 10–4 m
C
3.9 × 10–4 m
9702/11/M/J/19
D
9.0 × 10–4 m
[Turn over
12
22 A transverse wave in a medium has the waveform shown, where
y = vertical displacement and x = horizontal distance.
The speed of the wave is 20.0 cm s–1.
+1.0
y / mm
x / cm
0
0
2.0
4.0
6.0
8.0
–1.0
A particle of the medium oscillates vertically.
Which graph of vertical displacement y against time t best represents the motion of this particle?
A
B
+1.0
+1.0
y / mm
y / mm
0
0
0.10
t/s
0.20
t/s
0
0
–1.0
2.0
4.0
–1.0
C
D
+2.0
+2.0
y / mm
y / mm
0
0
0
4.0
8.0
0
t/s
© UCLES 2019
9702/11/M/J/19
5.0
10.0
t/s
13
23 The graph shows the variation of the displacement of particles with distance along a transverse
wave at an instant in time. The wave is moving to the right.
Which position along the wave corresponds to a point where particles in the wave are travelling
the fastest upwards?
D
displacement
0
A
0
direction of
travel of wave
C
distance
B
24 A long tube, filled with water, has a tap fitted at its base, as shown.
A tuning fork is sounded above the tube and the water is allowed to run gradually out of the tube.
tuning fork
tube
water
tap
A louder sound is heard at intervals as the water runs out of the tube. The change in water level
between louder sounds is 32 cm.
What is the wavelength of the sound in the tube?
A
16 cm
© UCLES 2019
B
32 cm
C
64 cm
9702/11/M/J/19
D
128 cm
[Turn over
14
25 A stationary insect on the surface of water creates circular waves with its legs, as shown in
diagram 1. The insect begins to travel to the right as shown in diagram 2.
insect
X
X
diagram 1
diagram 2
Which row describes the change to the waves at X caused by the movement of the insect?
frequency
wave speed
A
decreases
increases
B
decreases
stays the same
C
increases
increases
D
increases
stays the same
26 A toy motorboat moving with constant velocity v vibrates up and down on the surface of a pond.
This causes the boat to act as a source of circular water waves of frequency 2.0 Hz. The speed of
the waves is 1.5 m s–1.
A man, standing at the edge of the pond, observes that the waves from the boat approach him
with a frequency of 3.0 Hz.
The formula for Doppler effect calculations with sound waves may also be used for water waves.
What is a possible value of v?
speed / m s–1
direction
A
0.50
directly away from the man
B
0.50
directly towards the man
C
0.75
directly away from the man
D
0.75
directly towards the man
27 Two progressive waves of frequency 300 Hz superpose to produce a stationary wave in which
adjacent nodes are 1.5 m apart.
What is the speed of the progressive waves?
A
100 m s–1
© UCLES 2019
B
200 m s–1
C
450 m s–1
9702/11/M/J/19
D
900 m s–1
15
28 The diagrams show the diffraction of water waves in a ripple tank as they pass through a gap
between two barriers.
Which diagram is correct?
A
B
C
D
29 A double-slit interference experiment is set up as shown.
*
red
light
source
single
slit
double
slit
screen
not to scale
Fringes are formed on the screen. The distance between successive bright fringes is found to be
4 mm.
Two changes are then made to the experimental arrangement. The double slit is replaced by
another double slit which has half the spacing. The screen is moved so that its distance from the
double slit is twice as great.
What is now the distance between successive bright fringes?
A
1 mm
© UCLES 2019
B
4 mm
C
8 mm
9702/11/M/J/19
D
16 mm
[Turn over
16
30 The interference patterns from a diffraction grating and a double slit are compared.
Using the diffraction grating, yellow light of the first order is seen at 30° to the normal to the
grating.
The same light produces interference fringes on a screen 1.0 m from the double slit. The slit
separation is 500 times greater than the line spacing of the grating.
What is the fringe separation on the screen?
A
2.5 × 10–7 m
B
1.0 × 10–5 m
C
1.0 × 10–3 m
D
1.0 × 10–1 m
31 Which diagram shows the pattern of the electric field lines due to a negative point charge?
A
B
C
D
32 In an electrolyte, the electric current is carried by charged particles (ions) in solution.
What is not a possible value for the charge on an ion in solution?
A
– 4.8 × 10–19 C
B
+1.6 × 10–19 C
C
+3.2 × 10–19 C
D
+4.0 × 10–19 C
© UCLES 2019
9702/11/M/J/19
17
33 A voltmeter connected between two points P and Q in an electrical circuit shows a reading of 1 V.
V
+
–
P
Q
Which statement is correct?
A
The energy needed to move +1 C of charge from P to Q is 1 J.
B
The energy needed to move +1 C of charge from Q to P is 1 J.
C
The energy needed to move one electron from P to Q is 1 J.
D
The energy needed to move one electron from Q to P is 1 J.
34 Which graph best represents the variation with current I of potential difference V for a filament
lamp?
A
B
V
V
0
0
0
I
0
C
D
V
V
0
0
© UCLES 2019
I
0
I
0
9702/11/M/J/19
I
[Turn over
18
35 When a battery is connected to a resistor, the battery gradually becomes warm. This causes the
internal resistance of the battery to increase whilst its electromotive force (e.m.f.) stays
unchanged.
As the internal resistance of the battery increases, how do the terminal potential difference and
the output power change, if at all?
terminal potential
difference
output power
A
decreases
decreases
B
decreases
unchanged
C
unchanged
decreases
D
unchanged
unchanged
36 A cell is connected to a resistor of resistance 3.00 Ω. The current in the resistor is 1.00 A.
A second identical resistor is added in parallel. The current becomes 1.93 A.
What are the e.m.f. E and internal resistance r of the cell?
E/V
r/Ω
A
0.113
3.11
B
3.04
0.0358
C
3.11
0.113
D
9.34
6.34
37 A battery with negligible internal resistance is connected to three resistors, as shown.
0.30 A
X
All three resistors have the same resistance.
The current in the battery is 0.30 A.
What is the current in resistor X?
A
0.10 A
© UCLES 2019
B
0.15 A
C
0.20 A
9702/11/M/J/19
D
0.30 A
19
38 The diagram shows a potentiometer and a fixed resistor connected across a 12 V battery of
negligible internal resistance.
fixed resistor
20 Ω
12 V
20 Ω
output
The fixed resistor and the potentiometer each have resistance 20 Ω. The circuit is designed to
provide a variable output voltage.
What is the range of output voltages?
A
0–6V
B
0 – 12 V
C
6 – 12 V
D
12 – 20 V
39 Which statement about the alpha-particle scattering experiment provides evidence for the
existence of the nucleus?
A
A tiny proportion of the alpha-particles are deflected through large angles.
B
Slower alpha-particles are deflected through larger angles.
C
The kinetic energies of the deflected alpha-particles are unchanged.
D
The number of alpha-particles deflected depends on the thickness of the foil.
40 Some particles are a combination of three quarks.
Which combination of quarks would not result in a particle with a charge of either +1.6 × 10–19 C
or zero?
A
up, down, down
B
up, strange, strange
C
up, up, down
D
up, up, up
© UCLES 2019
9702/11/M/J/19
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/11/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
May/June 2019
1 hour 15 minutes
Additional Materials:
*2852605020*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages and 4 blank pages.
IB19 06_9702_12/3RP
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
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4
1
What is equivalent to 2000 microvolts?
2 µJ C–1
A
2
3
B
2 mV
C
2 pV
D
2000 mV
What is the number of SI base units required to express electric field strength and power?
electric field
strength
power
A
3
3
B
3
2
C
4
2
D
4
3
The Planck constant h has SI units J s.
Which equation could be used to calculate the Planck constant?
A
h=
B
h=
C
h=
D
h=
© UCLES 2019
DE
where D is distance, E is energy and v is velocity
v
v
D
where v is velocity and D is distance
1
4πE
Fr 2
m
where E is electric field strength
where F is force, r is radius and m is mass
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5
4
Two cables are attached to a bracket and exert forces as shown.
bracket
15.0 N
20.0°
horizontal
6.00 N
40.0°
vertical
What are the magnitudes of the horizontal and vertical components of the resultant of the two
forces?
5
horizontal
component / N
vertical
component / N
A
9.73
0.534
B
9.73
C
18.0
D
18.0
10.2
0.534
10.2
A student wishes to determine the density ρ of lead. She measures the mass and diameter of a
small sphere of lead:
mass = (0.506 ± 0.005) g
diameter = (2.20 ± 0.02) mm.
What is the best estimate of the percentage uncertainty in her calculated value of ρ ?
A
1.7%
© UCLES 2019
B
1.9%
C
2.8%
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D
3.7%
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6
6
Two quantities p and q are directly proportional to each other.
Experimental results are taken and plotted in a graph of q against p.
Which graph shows there were random errors in the measurements of p and q?
A
B
q
q
0
p
0
7
C
D
q
0
0
p
q
0
0
p
0
0
p
A man of mass 75.2 kg uses a set of weighing scales to measure his mass three times. He
obtains the following readings.
mass / kg
reading 1
80.2
reading 2
80.1
reading 3
80.2
Which statement best describes the precision and accuracy of the weighing scales?
A
not precise to ± 0.1 kg and accurate to ± 0.1 kg
B
not precise to ± 0.1 kg and not accurate to ± 0.1 kg
C
precise to ± 0.1 kg and accurate to ± 0.1 kg
D
precise to ± 0.1 kg and not accurate to ± 0.1 kg
© UCLES 2019
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7
8
The graph shows how a physical quantity varies with time.
quantity
0
0
time
Which event could best be represented by the graph?
9
A
the acceleration of a firework rising to a maximum height and falling to the ground
B
the acceleration of a skydiver leaving an aircraft, falling, opening a parachute and falling to
the ground
C
the speed of a javelin as it leaves an athlete’s hand, falls and sinks into the ground
D
the speed of a high jump athlete leaving the ground, jumping over a bar and descending to
the ground
What describes the mass of an object?
A
the force the object experiences due to gravity
B
the momentum of the object before a collision
C
the resistance of the object to changes in motion
D
the weight of the object as measured by a balance
10 A car has mass m. A person needs to push the car with force F in order to give the car
acceleration a. The person needs to push the car with force 2F in order to give the car
acceleration 3a.
Which expression gives the constant resistive force opposing the motion of the car?
A
ma
© UCLES 2019
B
2ma
C
3ma
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D
4ma
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8
11 Two bar magnets P and Q are mounted on floats which can slide without friction along an air
track.
P
S
Q
N
N
S
air track
floats
The two magnets slide towards each other along the air track and interact, without making
contact.
The relative speed of approach of the magnets is equal to their relative speed of separation.
Which statement about P and Q must be correct?
A
During the interaction between P and Q some of the total kinetic energy is lost.
B
During the interaction between P and Q some of the total momentum is lost.
C
The momentum of Q after the interaction is equal to the momentum of P before the
interaction.
D
The values of (kinetic energy of P + kinetic energy of Q) before and after the interaction are
equal.
12 A submarine descends vertically at constant velocity. The three forces acting on the submarine
are viscous drag, upthrust and weight.
Which relationship between their magnitudes is correct?
A
weight < drag
B
weight = drag
C
weight < upthrust
D
weight > upthrust
© UCLES 2019
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9
13 A small positive charge can move inside a uniform electric field.
P
Q
uniform
electric
field
S
R
The charge moves along different straight paths between points P, Q, R and S.
Which row gives two paths that result in the same total work done on the charge?
path 1
path 2
A
P to R
Q to S
B
P to R
P to S
C
S to Q
S to R
D
S to Q
R to P
14 A car of mass m travels at constant speed up a slope at an angle θ to the horizontal, as shown in
the diagram. Air resistance and friction provide a resistive force F. The acceleration of free fall
is g.
resistive force F
θ
What is the force needed to propel the car at this constant speed?
A
mg cos θ
B
mg sin θ
C
mg cos θ + F
D
mg sin θ + F
© UCLES 2019
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10
15 A volume of 1.5 m3 of water is mixed with 0.50 m3 of alcohol. The density of water is 1000 kg m–3
and the density of alcohol is 800 kg m–3.
The volume of the mixture is 2.0 m3.
What is the density of the mixture?
A
850 kg m–3
B
900 kg m–3
C
940 kg m–3
D
950 kg m–3
16 A parachutist is falling at constant (terminal) velocity.
Which statement is not correct?
A
Gravitational potential energy is converted into kinetic energy of the air.
B
Gravitational potential energy is converted into kinetic energy of the parachutist.
C
Gravitational potential energy is converted into thermal energy of the air.
D
Gravitational potential energy is converted into thermal energy of the parachutist.
17 A combined heat and power (CHP) station generates electrical power and useful heat. The
diagram shows the input and output powers for a CHP station.
wasted power
60 MW
useful heating power
160 MW
input power
from fuel
useful electrical power
100 MW
What is the efficiency of the CHP station for producing useful power?
A
31%
© UCLES 2019
B
38%
C
50%
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D
81%
11
18 A bungee jumper jumps off a high bridge, when attached to it by a long elastic rope which obeys
Hooke’s law.
The gravitational potential energy of the jumper is measured relative to the lowest point reached
by the jumper.
Which graph shows the variation of the gravitational potential energy of the jumper, and the
elastic potential energy in the rope, with the vertical distance fallen from the top of the bridge?
A
B
energy
energy
key
0
0
elastic potential
energy in rope
0
vertical
distance fallen
vertical
distance fallen
0
C
gravitational potential
energy of jumper
D
energy
energy
0
0
vertical
distance fallen
0
vertical
distance fallen
0
19 A train on a mountain railway is carrying 200 people of average mass 70 kg up a slope at an
angle of 30° to the horizontal and at a speed of 6.0 m s–1. The train itself has a mass of 80 000 kg.
The percentage of the power from the engine which is used to raise the passengers and the train
is 40%.
What is the power of the engine?
A
1.1 MW
B
2.8 MW
C
6.9 MW
D
14 MW
20 A wire X is stretched by a force and gains elastic potential energy E.
The same force is applied to wire Y of the same material, with the same initial length but twice the
diameter of wire X. Both wires obey Hooke’s law.
What is the gain in elastic potential energy of wire Y?
A
0.25E
© UCLES 2019
B
0.5E
C
2E
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D
4E
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12
21 The diagram shows the arrangement of atoms in a particular crystal.
Each atom is at the corner of a cube.
The mass of each atom is 3.5 × 10–25 kg. The density of the crystal is 9.2 × 103 kg m–3.
What is the shortest distance between the centres of two adjacent atoms?
A
3.8 × 10–29 m
B
6.2 × 10–15 m
C
3.4 × 10–10 m
D
3.0 × 10–9 m
22 The stress-strain graphs for loading and unloading four different materials are shown.
Which material exhibits purely elastic behaviour?
A
stress
B
stress
loading
loading
unloading
unloading
0
0
0
0
strain
C
D
loading
stress
strain
stress
loading
unloading
unloading
0
0
0
© UCLES 2019
0
strain
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strain
13
23 The diagram illustrates the position of particles in a progressive sound wave at one instant in
time.
P
Q
L
The speed of the wave is v. P and Q are two points in the wave a distance L apart.
What is an expression for the frequency of the wave?
A
v
2L
© UCLES 2019
B
v
L
C
2v
L
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D
L
v
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14
24 A wave moves along the surface of water.
The diagram shows the variation of displacement s with distance along the wave at time t = 0.
direction of travel
s
P
distance
along wave
0
0
Which graph best shows the variation with time t of the displacement s of the point P on the
wave?
s
A
t
0
0
s
B
t
0
0
s
C
t
0
0
s
D
t
0
0
25 In an experiment to determine the wavelength of sound in air, a stationary wave is set up in an air
column.
The distance between a node and an adjacent antinode is L.
What is the wavelength of the sound?
A
1
2
L
© UCLES 2019
B
L
C
2L
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D
4L
15
26 In one of the first experiments to demonstrate the Doppler effect, a train was filled with trumpeters
all playing a note of frequency 440 Hz. The difference in observed frequency of the note as the
train directly approached a stationary observer was 22 Hz. The speed of sound was 340 m s–1.
At which speed was the train moving?
15.4 m s–1
A
B
16.2 m s–1
C
17.0 m s–1
D
17.9 m s–1
27 The electromagnetic spectrum consists of waves with different wavelengths.
Which row correctly identifies regions of the electromagnetic spectrum?
10–10 m
10–8 m
10–5 m
10–2 m
A
microwaves
X-rays
ultraviolet
infrared
B
infrared
microwaves
X-rays
ultraviolet
C
microwaves
infrared
ultraviolet
X-rays
D
X-rays
ultraviolet
infrared
microwaves
28 A cathode-ray oscilloscope (CRO) is used to display the trace from a sound wave. The time-base
is set at 5 µs mm–1.
1 cm
1 cm
What is the frequency of the sound wave?
A
6.7 Hz
© UCLES 2019
B
67 Hz
C
6.7 kHz
9702/12/M/J/19
D
67 kHz
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16
29 Monochromatic light is directed at a diffraction grating, as shown.
Which diagram could show all the possible directions of the light, after passing through the
grating, that give maximum intensity?
A
B
C
D
30 Why can an observable interference pattern never be obtained between two monochromatic
beams of light from different lamps?
A
The frequency of the light from the two lamps can never be the same.
B
The light from the two lamps can never be coherent.
C
The temperature of the filaments of the two lamps used can never be the same.
D
The wavelength of the light from the two lamps must always be different.
© UCLES 2019
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17
31 A student sets up apparatus to observe the double-slit interference of monochromatic light, as
shown.
monochromatic
light
double slit
screen
Interference fringes are formed on the screen.
Which change would increase the distance between adjacent fringes?
A
Decrease the distance between the two slits.
B
Decrease the width of each slit.
C
Move the screen closer to the double slit.
D
Use light of a higher frequency.
32 An electron is situated in a vacuum between two charged plates, as shown.
–
–
–
–
–
–
–
–
+
+
electron
+
+
+
+
+
+
Which statement describes the motion of the electron due to the uniform electric field?
A
It moves downwards with a constant acceleration.
B
It moves downwards with zero acceleration.
C
It moves upwards with a constant acceleration.
D
It moves upwards with a decreasing acceleration.
© UCLES 2019
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18
33 A length of wire is connected into a circuit.
area A
area 12 A
S
R
The area of the cross-section of the wire changes from A at R to
1
2
A at S.
There is a constant current in the wire. Charge Q passes R in time t.
What is the charge passing point S in the same time t ?
A
1
2
Q
B
Q
C
Q 2
D
2Q
34 Four wires are made of the same metal. The cross-sectional areas, lengths and thermodynamic
temperatures of the wires are shown.
Which wire has the largest resistance?
cross-sectional
area
length
temperature
A
A
2L
2T
B
A
L
T
C
2A
2L
2T
D
2A
L
T
© UCLES 2019
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19
35 A cell with internal resistance is connected to a variable resistor R as shown.
cell
I
R
The resistance of R is gradually decreased.
How do the current I and the terminal potential difference across the cell change?
current I
terminal potential
difference across cell
A
decreases
decreases
B
decreases
increases
C
increases
decreases
D
increases
increases
36 Kirchhoff’s first law states that the sum of the currents entering a junction in a circuit is equal to
the sum of the currents leaving it.
The law is based on the conservation of a physical quantity.
What is this physical quantity?
A
charge
B
energy
C
mass
D
momentum
© UCLES 2019
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20
37 A circuit contains two batteries, each of negligible internal resistance, and two resistors as shown.
9.0 Ω
galvanometer
24 V
3.0 Ω
X
The galvanometer has a current reading of zero.
What is the electromotive force (e.m.f.) of battery X?
A
6.0 V
B
8.0 V
C
16.0 V
D
18.0 V
209
38 A nucleus of francium-221 ( 221
87 Fr) decays into a nucleus of bismuth-209 ( 83 Bi) in several steps.
Which particles could be emitted?
A
2 α-particles and 4 β– particles
B
2 α-particles and 4 β+ particles
C
3 α-particles and 2 β– particles
D
3 α-particles and 2 β+ particles
39 Which equation describes the changes to the quark composition of a nucleus and the lepton
emission during the process of β+ decay?
A
down → up + positron + electron neutrino
B
down → up + positron + electron antineutrino
C
up → down + positron + electron neutrino
D
up → down + positron + electron antineutrino
40 There are protons, neutrons and electrons in the simple model of an atom.
To which class (group), hadron or lepton, do these particles belong?
hadron
lepton
A
electron
proton and neutron
B
neutron
proton and electron
C
proton and electron
neutron
D
proton and neutron
electron
© UCLES 2019
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21
BLANK PAGE
© UCLES 2019
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22
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© UCLES 2019
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23
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© UCLES 2019
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24
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/12/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/13
PHYSICS
Paper 1 Multiple Choice
May/June 2019
1 hour 15 minutes
Additional Materials:
*3457171416*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 17 printed pages and 3 blank pages.
IB19 06_9702_13/4RP
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
9702/13/M/J/19
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
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[Turn over
4
1
2
Which is an SI base unit?
A
current
B
gram
C
kelvin
D
volt
Osmium, a naturally occurring element, has a density of 23 000 kg m–3.
What is also a value of the density of osmium?
3
A
2.3 × 104 µg cm–3
B
2.3 × 104 g cm–3
C
2.3 kg cm–3
D
2.3 × 10–2 kg cm–3
Two tugs are towing an oil rig as shown.
tug
4.0 kN
20°
oil rig
east
50°
5.0 kN
tug
The tensions in the towing cables are 4.0 kN and 5.0 kN.
What is the total force acting on the rig due to the cables, in the direction to the east?
A
4
3.1 kN
B
5.2 kN
C
7.0 kN
D
7.3 kN
What is the approximate kinetic energy of an Olympic athlete when running at maximum speed
during a 100 m race?
A
400 J
© UCLES 2019
B
4000 J
C
40 000 J
9702/13/M/J/19
D
400 000 J
5
5
The diagram shows the reading on an analogue ammeter.
5
10
milliamperes (mA)
0
15
Which digital ammeter reading is the same as the reading on the analogue ammeter?
display units
6
display reading
A
µA
1600
B
µA
160
C
mA
D
A
16.0
1.60
A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The
micrometer reading is 5.00 mm ± 0.01 mm.
What will be the percentage uncertainty in a calculation of the volume of the sphere, using these
values?
A
0.2%
© UCLES 2019
B
0.4%
C
0.6%
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D
1.2%
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6
7
The graph shows the variation of velocity v with time t for an object.
24.0
v / m s–1
20.0
16.0
12.0
8.0
4.0
0
0
1.0 2.0 3.0 4.0 5.0
t/s
The object passes a fixed point at time t = 0.
What is the displacement of the object from the fixed point at time t = 5.0 s and what is the
acceleration of the object?
8
displacement
/m
acceleration
/ m s–2
A
60
4.0
B
70
4.0
C
60
4.8
D
70
4.8
A skydiver jumps from an aeroplane and falls vertically through the air.
Which graph shows the variation with time t of the skydiver’s vertical velocity v?
A
B
v
C
v
0
0
© UCLES 2019
t
D
v
0
0
t
v
0
0
9702/13/M/J/19
t
0
0
t
7
9
A nucleus collides with a stationary nucleus in a vacuum. The diagrams show the paths of the
nuclei before and after the collision.
No other particles are involved in the collision.
Which diagram is not possible?
A
B
C
D
10 A uniform electric field is created by two parallel vertical plates. A positively charged particle is in
the vacuum between the plates, as shown.
+
–
–
–
positively
charged
particle
+
+
–
+
–
+
–
+
–
+
–
+
Which statement is correct?
A
The electric field makes the particle move towards the negative plate with a constant speed.
B
The electric field makes the particle move towards the negative plate with a constant
acceleration.
C
The electric field produces a uniform rate of decrease in the particle’s acceleration.
D
The electric field produces a uniform rate of increase in the particle’s acceleration.
© UCLES 2019
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8
11 A picture is suspended from a nail by a single cord connected to two points X and Y on the
picture. There is negligible friction between the cord and the nail so that the tension in both sides
of the cord is the same. The picture hangs symmetrically, as shown.
nail
cord
θ
picture
θ
X
Y
The tension in the cord is T. The angle between the cord and the vertical is θ on both sides.
Which statement is correct?
A
Increasing the length of the cord, with points X and Y in the same place on the picture, would
reduce the tension in the cord.
B
Moving points X and Y further apart on the picture while keeping the length of the cord
constant would reduce the tension in the cord.
C
Moving points X and Y to the top edge of the picture while keeping their distance apart
constant and the length of the cord constant would reduce the tension in the cord.
D
The weight of the picture is equal to T cosθ.
12 A shop sign weighing 75 N hangs from a frame attached to a vertical wall.
Z
30°
X
Y
0.50 m
wall
sign
weight 75 N
The frame consists of a horizontal rod XY and a rod YZ that is at an angle of 30° to the horizontal.
Rod XY is attached to the wall by a hinge at X and has length 0.50 m. Assume that the weights of
the rods are negligible.
What is the horizontal force exerted by the wall on rod XY?
A
0N
© UCLES 2019
B
43 N
C
130 N
9702/13/M/J/19
D
150 N
9
13 What is the torque of the couple shown?
15 N
15.0 cm
5.0 cm
15 N
A
0.75 N m
B
1.50 N m
C
3.00 N m
D
5.25 N m
14 Water has a density of 1.0 g cm–3.
Glycerine has a density of 1.3 g cm–3.
A student measures out a volume of 40 cm3 of glycerine into a container.
The student adds water to the container to make a mixture of water and glycerine. Assume that
the total volume of water and glycerine does not change when the two liquids are mixed.
Which volume of water needs to be added to make a mixture of density 1.1 g cm–3?
A
4.0 cm3
B
8.0 cm3
C
34 cm3
D
80 cm3
15 Which statement about the principle of conservation of energy is correct?
A
Energy conversion helps to conserve energy sources.
B
Energy is conserved only in systems with an efficiency of 100%.
C
The supply of energy is limited so energy should be conserved.
D
The total amount of energy in a closed system is constant.
16 A student can run or walk up the stairs to her classroom.
Which statement describes the power required and the gravitational potential energy gained while
running up the stairs compared to walking up them?
A
Running provides more gravitational potential energy and uses more power.
B
Running provides more gravitational potential energy and uses the same power.
C
Running provides the same gravitational potential energy and uses more power.
D
Running provides the same gravitational potential energy and uses the same power.
© UCLES 2019
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10
17 A lead pellet is shot vertically upwards into a clay block that is stationary at the moment of impact
but is able to rise freely after impact.
stationary clay
block
mass 95 g
impact velocity
200 m s–1
lead pellet
mass 5.0 g
The mass of the pellet is 5.0 g and the mass of the clay block is 95 g.
The pellet hits the block with an initial vertical velocity of 200 m s–1. It embeds itself in the block
and does not emerge.
How high above its initial position will the block rise?
A
5.1 m
B
5.6 m
C
10 m
D
100 m
18 On the surface of a planet, 30 J of work is done against gravity to raise a mass of 1.0 kg through a
height of 10 m.
How much work must be done to raise a mass of 4.0 kg through a height of 5.0 m on this planet?
A
15 J
B
60 J
C
120 J
D
200 J
19 Four solid steel rods, each of length 2.0 m and cross-sectional area 250 mm2, equally support an
object weighing 10 kN. The weight of the object causes the rods to contract by 0.10 mm. The rods
obey Hooke’s law.
What is the Young modulus of steel?
A
2.0 × 108 N m–2
B
2.0 × 1011 N m–2
C
8.0 × 108 N m–2
D
8.0 × 1011 N m–2
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11
20 A wire is attached at one end to a fixed point. A tensile force F is applied to the other end of the
wire, causing it to extend. This is shown on the graph by the line OSP.
The force F is then gradually reduced to zero and the wire contracts. This is shown on the graph
by the line PQ.
P
F
S
O Q
T
R
extension
Which area on the graph represents the work done by the wire as it contracts?
A
OSTO
B
OSPRO
C
QPRQ
D
OSPQO
21 The graph shows the variation of displacement y with distance x along a progressive wave at one
instant in time.
y
Q
0
0
x
P
What is the phase difference between points P and Q on the wave?
A
90°
B
270°
C
540°
D
630°
22 Wave-power generators take advantage of the energy that is transferred by the motion of waves
across the surface of the oceans. The energy of a wave depends on its amplitude.
What is the correct definition of amplitude?
A
the average amount of energy possessed by a wave
B
the difference in displacement between a peak and a trough
C
the maximum displacement of a point on the wave from equilibrium
D
the number of oscillations of a wave that occur per second
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12
23 A sound wave of frequency 270 Hz is recorded by a cathode-ray oscilloscope (CRO).
The waveform on the CRO is shown.
1 cm
What is the time-base setting on the CRO?
A
0.1 ms cm–1
B
1 ms cm–1
C
10 ms cm–1
D
100 ms cm–1
24 A motor boat vibrates in the water so that it produces water waves of frequency 0.20 Hz. The
speed of these waves in the water is 20 m s–1. The motor boat moves with a speed of 5.0 m s–1
directly towards a stationary sailing boat.
The Doppler effect equation for sound waves also applies to water waves.
What is the frequency with which the waves hit the stationary sailing boat?
A
0.15 Hz
B
0.16 Hz
C
0.25 Hz
D
0.27 Hz
25 Infrared laser light is used for the transmission of data along optic fibres.
What is a typical wavelength of infrared radiation?
A
5 × 10–5 m
B
5 × 10–7 m
C
2 × 10–9 m
D
2 × 10–11 m
26 An elastic string is attached to an oscillator at one end and clamped at the other end so that the
string is horizontal and in tension.
The oscillator is made to oscillate vertically. The frequency of oscillation is gradually increased
from zero until a stationary wave is set up in the string. The frequency is then increased further to
frequency f, when a second stationary wave is set up in the string.
The frequency is then increased further.
At which frequency does a third stationary wave occur?
A
1.2f
© UCLES 2019
B
1.5f
C
2.0f
9702/13/M/J/19
D
3.0f
13
27 In an experiment, water waves in a ripple tank are incident on a gap, as shown.
Some diffraction of the water waves is observed.
Which change to the experiment would provide a better demonstration of diffraction?
A
Increase the amplitude of the waves.
B
Increase the frequency of the waves.
C
Increase the wavelength of the waves.
D
Increase the width of the gap.
28 Light of wavelength λ is emitted from two point sources R and S and falls onto a distant screen.
screen
R
P
S
(not to scale)
At point P on the screen, the light intensity is zero.
What could explain the zero intensity at P?
A
Light from the two sources is emitted 180° out of phase and the path difference to P is 21 λ .
B
Light from the two sources is emitted in phase and the path difference to P is λ.
C
Light from the two sources is emitted 90° out of phase and the path difference to P is λ.
D
Light from the two sources is emitted in phase and the path difference to P is
1
2
λ.
29 Apparatus is arranged to show double-slit interference using monochromatic light. The slit
separation is 0.10 mm. The distance from the double slit to the screen where the interference
pattern is observed is 2.4 m and the fringe width is 12 mm.
The distance to the screen is now changed to 1.8 m and the slit separation is doubled.
What is the new fringe width?
A
1.5 mm
© UCLES 2019
B
4.5 mm
C
6.0 mm
9702/13/M/J/19
D
9.0 mm
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14
30 Monochromatic light of wavelength 690 nm passes through a diffraction grating with
300 lines per mm, producing a series of maxima (bright spots) on a screen.
screen
diffraction
grating
What is the greatest number of maxima that can be observed?
A
4
B
5
C
8
D
9
31 Which diagram represents the electric field line pattern due to a combination of two positive
charges?
A
B
C
D
32 Which two units are used to define the volt?
A
ampere and ohm
B
coulomb and joule
C
coulomb and ohm
D
coulomb and second
© UCLES 2019
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15
33 The graph shows the variation with length of the resistance of a uniform metal wire.
resistance
0
0
length
The gradient of the graph is G.
The wire has cross-sectional area A.
Which expression could be used to calculate the resistivity of the metal of the wire?
G×A
A
B
G
A
C
A
G
D
G × A2
34 Diagram 1 shows a lamp connected to a supply through two switches.
During repairs, an electrician mistakenly reverses the connections X1 and Z1, so that Z1 is
connected to the supply and X1 to the other switch at Z2, as shown in diagram 2.
X1
diagram 1
supply
X1
diagram 2
Y1
Y2
Z1
Z2
Y1
Y2
Z1
supply
X2
X2
Z2
Which switch positions will now light the lamp?
A
X1 to Y1
X2 to Y2
B
X1 to Y1
X2 to Z2
C
X1 to Z1
X2 to Y2
D
X1 to Z1
X2 to Z2
© UCLES 2019
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16
35 A wire supplying a shower heater with a current of 35 A has a resistance of 25 mΩ.
What is the power dissipated in the wire?
A
31 W
B
49 W
C
31 kW
D
49 kW
36 A student has a set of identical cells and identical lamps. The cells have negligible internal
resistance.
A lamp connected to a cell lights with normal brightness.
What happens when the student connects the lamps and the cells as shown?
2
1
3
A
All three lamps light with normal brightness.
B
Only lamp 2 lights with normal brightness.
C
Only lamps 1 and 3 light with normal brightness.
D
None of the lamps light with normal brightness.
37 A potential divider circuit is shown.
150 Ω
12.0 V
R
5.00 V
What is the resistance of resistor R in the potential divider circuit?
A
62.5 Ω
© UCLES 2019
B
107 Ω
C
210 Ω
9702/13/M/J/19
D
360 Ω
17
38 Two cells of electromotive force (e.m.f.) 3.0 V and 1.2 V and negligible internal resistance are
connected to resistors of resistance 9.0 Ω and 18 Ω as shown.
3.0 V
1.2 V
9.0 Ω
I
18 Ω
What is the current I in the 9.0 Ω resistor?
A
0.10 A
B
0.20 A
C
0.30 A
D
0.47 A
39 What is a correct estimate of the order of magnitude of the diameter of a typical atomic nucleus?
A
10–14 m
B
10–18 m
C
10–22 m
D
10–26 m
40 Which statement describes β– decay in terms of a simple quark model?
A
A down quark changes to an up quark, and an electron and an electron antineutrino
are emitted.
B
A down quark changes to an up quark, and a positron and an electron neutrino are emitted.
C
An up quark changes to a down quark, and an electron and an electron antineutrino
are emitted.
D
An up quark changes to a down quark, and a positron and an electron neutrino are emitted.
© UCLES 2019
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18
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© UCLES 2019
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19
BLANK PAGE
© UCLES 2019
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20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/13/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
February/March 2019
1 hour 15 minutes
Additional Materials:
*5008401313*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages.
IB19 03_9702_12/4RP
© UCLES 2019
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
9702/12/F/M/19
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
9702/12/F/M/19
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4
1
A wave has a frequency of 5 GHz.
What is the period of the wave?
2
A
200 ps
B
2 ns
C
20 ns
D
20 000 µs
At temperatures close to 0 K, the specific heat capacity c of a particular solid is given by c = bT 3,
where T is the temperature and b is a constant, characteristic of the solid.
The SI unit of specific heat capacity is J kg–1 K–1.
What is the unit of constant b, expressed in SI base units?
3
A
m2 s–2 K–3
B
m2 s–2 K–4
C
kg m2 s–2 K–3
D
kg m2 s–2 K–4
The speed of an aircraft in still air is 200 km h–1. The wind blows from the west at a speed of
85.0 km h–1.
In which direction must the pilot steer the aircraft in order to fly due north?
A
23.0° east of north
B
23.0° west of north
C
25.2° east of north
D
25.2° west of north
© UCLES 2019
9702/12/F/M/19
5
4
A digital balance is used to weigh ingredients in a laboratory. When a weight is applied to the
digital balance, an electronic circuit generates a current which is then converted into a digital
readout on the display.
The electronic circuit gives a current of 2.0 mA when a weight of 30 N is applied, and a current of
0.5 mA when a weight of 5 N is applied.
Which calibration curve could represent this circuit?
A
B
2
2
current / mA
current / mA
0
0
0
30
weight / N
0
C
D
2
2
current / mA
current / mA
0
0
0
5
30
weight / N
30
weight / N
0
30
weight / N
Four students measure a time interval that is known to be 1.734 s.
The measurement recorded by each student is shown.
Which measurement is the most accurate?
A
1s
© UCLES 2019
B
1.7 s
C
1.83 s
9702/12/F/M/19
D
1.604 s
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6
6
A mass on the end of a spring bounces up and down as shown, after being released at time t = 0.
distance up
0
0
time t
distance down
Which graph shows how the velocity varies with time?
velocity up
A
0
0
time t
velocity up
B
0
0
time t
velocity up
C
0
0
time t
velocity up
D
7
0
0
time t
A stone is thrown vertically upwards from a point that is 12 m above the sea. It then falls into the
sea below after 3.4 s.
Air resistance is negligible.
At which speed was the stone released when it was thrown?
A
3.5 m s–1
© UCLES 2019
B
6.6 m s–1
C
13 m s–1
9702/12/F/M/19
D
20 m s–1
7
8
Two balls X and Y are moving towards each other with speeds of 5 m s–1 and 15 m s–1
respectively.
5 m s–1
15 m s–1
X
Y
They make a perfectly elastic head-on collision and ball Y moves to the right with a speed
of 7 m s–1.
What is the speed and direction of ball X after the collision?
9
A
3 m s–1 to the left
B
13 m s–1 to the left
C
3 m s–1 to the right
D
13 m s–1 to the right
In the absence of air resistance, a ball thrown horizontally from a tower with velocity v, will land
after time T seconds.
If, however, air resistance is taken into account, which statement is correct?
A
The ball lands with a horizontal velocity less than v after more than T seconds.
B
The ball lands with a horizontal velocity less than v after T seconds.
C
The ball lands with a horizontal velocity v after more than T seconds.
D
The ball lands with a horizontal velocity v after T seconds.
10 Two balls, of masses m and 2m, travelling in a vacuum with initial velocities 2v and v
respectively, collide with each other head-on, as shown.
m
v
2v
2m
After the collision, the ball of mass m rebounds to the left with velocity v.
What is the loss of kinetic energy in the collision?
A
3
4
mv2
© UCLES 2019
B
3
2
mv2
C
9
4
mv2
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D
9
2
mv2
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8
11 A ball falls through a liquid at a constant speed. It is acted upon by three forces: an upthrust, a
drag-force and its weight.
Which statement is correct?
A
The drag-force increases with increasing depth.
B
The drag-force is equal to the sum of the upthrust and weight.
C
The upthrust is constant with increasing depth.
D
The weight is greater than the sum of the drag-force and the upthrust.
12 A fairground ride consists of four carriages connected to a central vertical pole, as shown in the
following view from above.
direction
of rotation
vertical
central pole
not to
scale
carriages
A motor rotates the central pole about its axis. This results in the four carriages each moving
along a circular path.
The distance from the middle of each carriage to the centre of the pole is 3.20 m. When they are
moving, each carriage experiences an air resistance force of 85.0 N. Assume that there are no
other significant resistive forces.
Which torque does the motor need to apply to the pole to keep the system rotating at constant
maximum speed?
A
5.44 N m
© UCLES 2019
B
272 N m
C
544 N m
9702/12/F/M/19
D
1090 N m
9
13 A uniform horizontal beam OX, 4.0 m long and weighing 100 N, is hinged at a wall at point O. It is
supported by a cord XY which is attached to the wall at Y.
Y
cord
O
30°
X
4.0 m
What is the tension in the cord?
A
50 N
B
58 N
C
86 N
D
100 N
14 An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r
and density ρ.
r
table
The volume of a sphere is
4
3
πr 3.
Which average pressure does the object exert on the table?
A
1
3
ρr 2
B
1
3
ρr 2g
C
2
3
ρr
D
2
3
ρrg
15 Which statement best represents the principle of conservation of energy?
A
Energy cannot be used faster than it is created.
B
The supply of energy is limited, so energy must be conserved.
C
The total energy in a closed system is constant.
D
The total energy input to a system is equal to the useful energy output.
16 A crane is being used to lift containers off a ship. One container has a mass of 14 000 kg and is
being lifted vertically with a speed of 3.2 m s–1.
The electric motor being used to supply the power to lift the container is using a current of 240 A
at a potential difference of 2200 V.
What is the efficiency of the system?
A
8.1%
© UCLES 2019
B
8.5%
C
48%
9702/12/F/M/19
D
83%
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10
17 The data below are taken from a test of a petrol engine for a motor car.
power output
150 kW
fuel consumption
20 litres per hour
energy content of fuel
40 MJ per litre
What is the ratio
power output
power input
A
150 × 103
40 × 10 6 × 20 × 60 × 60
B
150 × 103 × 60 × 60
20 × 40 × 10 6
C
150 × 10 3 × 40 × 10 × 20
60 × 60
D
150 × 10 3 × 20
40 × 10 3 × 60 × 60
?
6
18 Leonardo da Vinci proposed a flying machine that would work like a screw to lift the pilot into the
air. The ‘screw’ is rotated by the pilot.
The machine and the pilot together have a total mass of 120 kg.
Which useful output power must the pilot provide to move vertically upwards at a constant speed
of 2.5 m s–1?
A
48 W
B
300 W
C
470 W
D
2900 W
19 A metal wire, fixed at one end, has length l and cross-sectional area A. The wire extends a
distance e when mass m is hung from the other end of the wire.
What is an expression for the Young Modulus E of the metal?
A
E=
© UCLES 2019
ml
Ae
B
E=
mgl
Ae
C
E=
me
Al
9702/12/F/M/19
D
E=
mge
Al
11
20 A spring has a spring constant of 6.0 N cm –1. It is joined to another spring whose spring constant
is 4.0 N cm–1. A load of 80 N is suspended from this composite spring.
6.0 N cm–1
4.0 N cm–1
load
80 N
What is the extension of this composite spring?
A
8.0 cm
B
16 cm
C
17 cm
D
33 cm
21 The graph shows the extension of a sample of a type of rubber as different loads F are applied
and then gradually removed.
100
F/N
80
60
40
20
0
0
4
8
12
16
extension / mm
What is the best estimate of the strain energy in the rubber when a load of 80 N is applied?
A
0.40 J
© UCLES 2019
B
0.64 J
C
0.88 J
9702/12/F/M/19
D
1.3 J
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12
22 A sound wave passes through air.
The diagram shows the positions of the molecules of the air at one instant.
P
Q
R
S
Which distance is equal to the wavelength of the wave?
A
PQ
B
PS
C
QR
D
QS
23 The top row of bars represents a set of particles inside the Earth and at rest.
The lower row represents the same particles at one instant as a longitudinal wave passes from
left to right through the Earth.
What should be measured to determine the amplitude of the oscillations of the particles in the
lower row as the wave passes?
A
half the maximum displacement of the particles from their position at rest
B
half the maximum distance apart of the particles
C
the maximum displacement of the particles from their position at rest
D
the maximum distance apart of the particles
24 A straight tube is closed at one end and has a loudspeaker positioned at the open end. The
frequency of the loudspeaker is initially very low and is increased slowly. A series of loudness
maxima are heard. The stationary wave which gives the first maximum has a node at the closed
end and an antinode at the open end. The frequency of the loudspeaker is f1 when the first
maximum is heard.
What is the frequency of the loudspeaker when the fourth maximum is heard?
A
7f 1
4
© UCLES 2019
B
2f1
C
4f1
9702/12/F/M/19
D
7f1
13
25 A buzzer emitting sound of frequency 846 Hz is attached to a string and rotated in a horizontal
circle. The linear speed of the buzzer is 25.0 m s–1.
buzzer
observer
The speed of sound is 340 m s–1.
What is the maximum frequency heard by the observer?
A
783 Hz
B
788 Hz
C
908 Hz
D
913 Hz
26 The diagram shows the principal regions of the electromagnetic spectrum, with some details
labelled. The diagram is not to scale.
Q
10–10 m
wavelength increasing
What is a typical order of magnitude of the wavelength of the radiation in region Q?
A
10–7 m
B
10–5 m
C
10–2 m
D
100 m
27 P and Q are fixed points at the end of a string. A transverse stationary wave of constant
maximum amplitude is formed on the string.
x
P
S
x
R
T
Q
P, R and Q are the only points on the string where nodes are formed. S and T are two points on
the string at a distance x from R.
What is the relationship between points S and T?
A
the same amplitude and in phase
B
different amplitudes and in phase
C
the same amplitude and a phase difference of 180°
D
different amplitudes and a phase difference of 180°
© UCLES 2019
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28 Two identical loudspeakers are connected in series to an a.c. supply, as shown.
P
speaker
a.c. supply
speaker
Q
A microphone is moved along the line PQ.
Which graph best shows the variation with distance from P of the intensity of the sound detected
by the microphone?
A
B
intensity
intensity
0
0
P
Q
P
Q
distance
distance
C
D
intensity
intensity
0
0
P
Q
P
distance
© UCLES 2019
Q
distance
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15
29 A diffraction grating experiment is set up using orange light of wavelength 600 nm. The grating
has a slit separation of 2.00 µm.
2nd order orange
1st order orange
θ2
θ1
light of
wavelength
600 nm
grating
What is the angular separation (θ2 – θ1) between the first and second order maxima of the orange
light?
A
17.5°
B
19.4°
C
36.9°
D
54.3°
30 Two horizontal parallel plate conductors are separated by a distance of 5.0 mm in air. The lower
plate is earthed and the potential of the upper plate is +50 V.
What is the electric field strength E at a point midway between the plates?
A
1.0 × 104 V m–1 downwards
B
1.0 × 104 V m–1 upwards
C
2.0 × 104 V m–1 downwards
D
2.0 × 104 V m–1 upwards
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31 The diagram shows the electric field near a point charge and two electrons X and Y.
Y
X
Which row describes the forces acting on X and on Y?
direction of force
magnitude of force on X
A
radially inwards
less than force on Y
B
radially inwards
greater than force on Y
C
radially outwards
less than force on Y
D
radially outwards
greater than force on Y
32 The electric current in a wire may be calculated using the equation I = Anvq.
Which statement is not correct?
A
n is the number of charge carriers per unit volume of the wire.
B
nA is the number of charge carriers per unit length of the wire.
C
q is the charge of each charge carrier.
D
v is the velocity of each charge carrier.
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17
33 Three resistors are connected in parallel across a power supply, as shown.
+
–
2Ω
3Ω
4Ω
The power dissipated in each of the resistors of resistance 2 Ω, 3 Ω and 4 Ω is P2, P3 and P4
respectively.
What is the ratio P2 : P3 : P4?
A
2:3:4
B
4:3:2
C
6:4:3
D
36 : 16 : 9
34 Which graph shows the variation with current I of the potential difference V of a filament lamp?
A
B
V
C
V
0
V
0
I
0
D
0
I
V
0
I
0
0
I
0
35 A wire of cross-sectional area 5.0 × 10–6 m2 is made of a metal of resistivity 50 × 10–8 Ω m.
The potential difference across the wire is 6.0 V and the current is 3.0 A.
What is the length of the wire?
A
0.050 m
© UCLES 2019
B
0.20 m
C
5.0 m
9702/12/F/M/19
D
20 m
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36 A cell of internal resistance r and electromotive force (e.m.f.) E is connected in series with a
resistor of resistance R.
E
r
I
R
The resistance R and the e.m.f. E remain fixed. The internal resistance r of the cell changes over
time.
Which graph best shows the variation of the current I in the circuit with the internal resistance r ?
A
B
I
I
0
0
r
0
C
D
I
I
0
0
© UCLES 2019
r
0
0
r
0
9702/12/F/M/19
r
19
37 Identical resistors are connected in four combinations P, Q, R and S between terminals X and Y.
P
Q
X
Y
X
Y
R
S
X
Y
Y
X
What is the order of decreasing combined resistance between X and Y (largest first)?
A
P→S→Q→R
B
P→S→R→Q
C
Q→R→S→P
D
S→P→Q→R
38 The circuit shown consists of two resistors of resistances 10 kΩ and 50 kΩ and a component Y.
A 6.0 V supply is provided. The electric potential of the bottom wire is 0 V.
6.0 V
10 kΩ
X
component Y
50 kΩ
0V
The current in component Y is negligible.
What is the electric potential at junction X?
A
1.0 V
© UCLES 2019
B
1.2 V
C
4.8 V
9702/12/F/M/19
D
5.0 V
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20
39 A neutron 10 n is fired at a
to form nuclei of
141
56 Ba
235
92 U nucleus.
92
and 36
Kr .
The neutron is absorbed by the nucleus which then splits
What is the number of neutrons emitted when the
A
0
B
1
C
235
92 U
nucleus splits?
2
D
3
40 Which word equation represents β+ decay?
A
proton → neutron + electron + electron antineutrino
B
proton → neutron + electron + electron neutrino
C
proton → neutron + positron + electron antineutrino
D
proton → neutron + positron + electron neutrino
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/12/F/M/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/11
PHYSICS
Paper 1 Multiple Choice
October/November 2019
1 hour 15 minutes
Additional Materials:
*8952989673*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 20 printed pages.
IB19 11_9702_11/3RP
© UCLES 2019
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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4
1
2
For which quantity is the magnitude a reasonable estimate?
A
frequency of a radio wave
500 pHz
B
mass of an atom
500 µg
C
the Young modulus of a metal 500 kPa
D
wavelength of green light
500 nm
The speed of a wave in deep water depends on its wavelength L and the acceleration of free
fall g.
What is a possible equation for the speed v of the wave?
A
3
v=
 gL 


 2π 
B
v=
gL
4π2
C
g 
v = 2π  
L
D
v=
2πg
L
The diagram shows two vectors X and Y, drawn to scale.
Y
X
If X = Y – Z, which diagram best represents the vector Z?
A
© UCLES 2019
B
9702/11/O/N/19
C
D
5
4
A student intends to measure accurately the diameter of a wire (known to be approximately
1 mm) and the internal diameter of a pipe (known to be approximately 2 cm).
What are the most appropriate instruments for the student to use to make these measurements?
5
wire
pipe
A
calipers
calipers
B
calipers
micrometer
C
micrometer
calipers
D
micrometer
micrometer
The power P dissipated in a resistor of resistance R is calculated using the expression
2
P= V
R
where V is the potential difference (p.d.) across the resistor. The percentage uncertainty in V is
5% and in R is 2%.
What is the percentage uncertainty in P ?
A
6
3%
B
7%
C
8%
D
12%
The velocity-time graph for an object of mass 2.5 kg is shown.
12.0
velocity
10.0
/ m s–1
8.0
6.0
4.0
2.0
0
0
5.0
10.0
15.0
time / s
What is the resultant force acting on the object?
A
0.60 N
© UCLES 2019
B
0.80 N
C
1.5 N
9702/11/O/N/19
D
2.0 N
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6
7
8
Which statement follows directly from Newton’s first law?
A
A body remains at constant velocity unless acted upon by a resultant force.
B
A satellite in circular motion about the Earth has a constant velocity.
C
A water drop leaving a spinning umbrella travels at a constant velocity.
D
The force acting on an object is equal to its change in momentum.
A resultant force causes an object to accelerate.
What is equal to the resultant force?
9
A
the acceleration of the object per unit mass
B
the change in kinetic energy of the object per unit time
C
the change in momentum of the object per unit time
D
the change in velocity of the object per unit time
A skydiver falls from an aircraft that is moving horizontally.
The vertical component of the velocity of the skydiver is v.
The vertical component of the acceleration of the skydiver is a.
Which row describes v and a during the first few seconds after the skydiver leaves the aircraft?
v
a
A
constant
constant
B
constant
decreasing
C
increasing
constant
D
increasing
decreasing
© UCLES 2019
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7
10 Two gliders are travelling towards each other on a horizontal air track. Glider P has mass 0.30 kg
and is moving with a constant speed of 1.2 m s–1. Glider Q has mass 0.60 kg and is moving with a
constant speed of 1.8 m s–1.
1.2 m s–1
1.8 m s–1
air
air
track
glider P
mass 0.30 kg
glider Q
mass 0.60 kg
The gliders have a perfectly elastic collision.
What are the speeds of the two gliders after the collision?
speed of P
/ m s–1
speed of Q
/ m s–1
A
1.2
0.6
B
2.0
1.4
C
2.8
0.2
D
3.6
0.6
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11 An object of weight W is suspended from a newton meter. When the object is completely
immersed in water, the newton meter reads P. When the object is completely immersed in oil, the
newton meter reads Q.
N
N
P
Q
water
What is the ratio
W −P
Q−P
A
density of oil
density of water
?
Q−P
W −P
B
oil
C
W −P
W −Q
D
W −Q
W −P
12 Which diagram shows a couple?
F
A
F
B
F
C
F
F
F
© UCLES 2019
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D
F
9
13 An object of weight 120 N is supported in equilibrium by two strings as shown.
T1
70°
20°
120 N
What is the tension T1 in the left-hand string?
A
41 N
B
77 N
C
113 N
D
128 N
14 In a large container in an oil refinery, three oils of different densities are mixed. No chemical
activity occurs.
The mixture consists of:
1200 kg of oil of density 1100 kg m–3
1500 kg of oil of density 860 kg m–3
4000 kg of oil of density 910 kg m–3.
What is the density of the mixture?
927 kg m–3
A
B
933 kg m–3
C
957 kg m–3
D
1045 kg m–3
15 An electric motor produces 120 W of useful mechanical output power. The efficiency of the motor
is 60%.
Which row is correct?
electrical power
input / W
waste heat power
output / W
A
72
48
B
192
72
C
200
72
D
200
80
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16 A fixed amount of a gas undergoes a series of changes to its pressure and volume.
In two of the changes, no work is done by or on the gas. In one change work is done by the gas
on its surroundings. In another change work is done on the gas by its surroundings.
2.0
pressure
/ 105 Pa 1.5
1.0
0.5
0
0
1
2
5
3
4
–4
3
volume / 10 m
During the change when work is done on the gas by its surroundings, how much work is done on
the gas?
A
15 J
B
25 J
C
30 J
D
45 J
17 An object travelling with a speed of 10 m s–1 has kinetic energy 1500 J.
The speed of the object is increased to 40 m s–1.
What is the new kinetic energy of the object?
A
4500 J
B
6000 J
C
24 000 J
D
1 350 000 J
18 The engine of a car exerts a force of 600 N in moving the car 1.0 km in 150 seconds.
What is the average useful output power of the engine?
A
4.0 W
© UCLES 2019
B
4.0 kW
C
90 kW
9702/11/O/N/19
D
90 MW
11
19 An extension–force graph for a spring is shown.
15
extension / cm
0
0
6.0
force / N
What is the spring constant of the spring?
A
0.025 N m–1
B
0.40 N m–1
2.5 N m–1
C
D
40 N m–1
20 A wire is extended by a force. The graph shows how the extension of the wire varies with the
force applied.
S
2d
R
extension
T
d
M
O
0
0
P
W
Q
2W
force
Initially a force W gives an extension d. The force is then increased to 2W. This increases the
extension to 2d.
Which area of the graph represents the work done by the force when the force increases from W
to 2W ?
A
ORQ
© UCLES 2019
B
OQRS
C
ORS
9702/11/O/N/19
D
TMRS
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21 A transverse wave on a rope has wavelength λ and period T.
The graph shows the variation of the displacement of the particles of the rope with distance in the
direction of travel of the wave at time t = 0.
direction
of travel
displacement
X
0
λ
0
distance
A particle X is labelled.
Which graph shows the variation of the displacement of particle X with time t ?
A
B
displacement
displacement
0
0
0
T
0
t
C
T
t
T
t
D
displacement
displacement
0
0
0
T
t
0
22 Which statement about all types of transverse waves is correct?
A
They all have the same speed.
B
They all have vibrations that are parallel to the direction of propagation of energy.
C
They can all form stationary waves.
D
They can all travel through a vacuum.
© UCLES 2019
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13
23 Source S emits microwaves with a constant amplitude. The microwaves hit a metal screen P and
are reflected. A stationary wave is formed between S and P. The wavelength of the microwaves
is much smaller than the distance between S and P.
S
P
Q
A detector Q is moved at a slow, constant speed from S to P.
What happens to the amplitude of the signal detected by Q?
A
decreases steadily
B
increases and decreases regularly
C
increases steadily
D
remains constant
24 The siren of a moving police car emits a sound wave with a frequency of 440 Hz. A stationary
observer hears sound of frequency 494 Hz. The speed of sound in the air is 340 m s–1.
What could be the speed and the direction of movement of the car?
A
37 m s–1 directly towards the observer
B
37 m s–1 directly away from the observer
C
42 m s–1 directly towards the observer
D
42 m s–1 directly away from the observer
25 An electromagnetic wave has a wavelength of 138 pm in a vacuum.
To which region of the electromagnetic spectrum does this wave belong?
A
radio wave
B
microwave
C
visible light
D
X-ray
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26 Two wave pulses are travelling towards each other on a long rope. The pulses have the same
amplitude and wavelength and are travelling at a speed of 0.50 m s–1. The diagram shows the
rope at time t ꞊ 0.
0.50 m s–1
4.0
4.5
0.50 m s–1
5.0
5.5
6.0
6.5
7.0
7.5
8.0
distance / m
Which diagram shows the rope at time t ꞊ 3.0 s?
A
5.0
5.5
6.0
B
6.5
7.0
7.5
5.0
5.5
6.0
6.5
distance / m
5.5
6.0
D
6.5
7.0
7.5
5.0
distance / m
© UCLES 2019
7.5
distance / m
C
5.0
7.0
5.5
6.0
6.5
7.0
7.5
distance / m
9702/11/O/N/19
15
27 Water waves of wavelength λ are incident normally on an obstacle with a narrow gap. The width
of the gap is equal to λ. The waves from the gap emerge over an angle θ as shown.
λ
λ
incident
water waves
diffracted
water waves
θ
The gap is slowly widened.
Which changes, if any, occur to θ and to the wavelength of the emerging waves?
θ
wavelength
A
decreases
remains the same
B
increases
remains the same
C
remains the same
decreases
D
remains the same
increases
28 Light of wavelength 720 nm from a laser X is incident normally on a diffraction grating and a
diffraction pattern is observed. Light from a laser Y is then also incident normally on the same
grating. The third-order maximum due to laser Y is seen at the same place as the second-order
maximum due to laser X.
What is the wavelength of the light from laser Y?
A
480 nm
B
540 nm
C
720 nm
D
1080 nm
29 Monochromatic light of frequency f is incident on a diffraction grating of line spacing d. The speed
of light is c.
Which expression can be used to determine the highest order of intensity maximum produced by
the grating?
A
n= d
cf
© UCLES 2019
B
n = df
c
C
n = dc
f
9702/11/O/N/19
D
n= c
df
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16
30 A metal plate of uniform thickness is connected to a cell as shown.
metal plate
viewed from
above
electron
flow
Electrons move clockwise around the circuit.
Which statement about the metal plate is correct?
A
The average drift speed of the conduction electrons decreases as they move from right to left
through the plate.
B
The average drift speed of the conduction electrons increases as they move from right to left
through the plate.
C
The number density of the conduction electrons decreases from right to left through the
plate.
D
The number density of the conduction electrons increases from right to left through the plate.
31 The diagram shows the direction of the current in a metal block. The charge carriers enter the
block through the face PQRS and leave the block through the opposite face.
P
Q
S
x
y
current
R
x
The number density of charge carriers is n. Each charge carrier has charge e. The average drift
speed of the charge carriers is v.
Which expression gives the current in the block?
A
envx2
© UCLES 2019
B
envxy
C
envx3y2
9702/11/O/N/19
D
envx4y
17
32 What could not be used as a unit of potential difference?
AΩ
A
N m–1 C–1
B
C
1
W A–1
D
(Ω W ) 2
33 Which graph could show how the resistance R of a filament lamp varies with the applied potential
difference (p.d.) V, as V is increased to the normal operating p.d.?
A
B
R
C
R
0
V
0
D
R
0
V
0
R
0
0
V
0
0
V
34 Kirchhoff’s two laws for electric circuits can be derived by using conservation laws.
On which conservation laws do Kirchhoff’s laws depend?
Kirchhoff’s
first law
Kirchhoff’s
second law
A
charge
current
B
charge
energy
C
current
mass
D
energy
current
© UCLES 2019
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35 The diagram shows a circuit.
V
Which statement about the circuit is not correct?
A
Electromotive force is the energy transferred per unit charge.
B
Energy is transferred from chemical potential energy in the cell to other forms when the
switch is closed.
C
The electromotive force of the cell is greater than the terminal potential difference when the
switch is closed.
D
When the switch is open, the voltmeter measures the electromotive force of the cell.
36 The diagram shows a circuit containing four voltmeters. The readings on the voltmeters are V1,
V2, V3 and V4. All the readings are positive.
V1 V
V1 = V2 + V4
B
V1 = V2 + V3 + V4
C
V2 + V3 = V4
D
V3 + V4 – V2 = 0
© UCLES 2019
V3
V
V4
V V2
Which equation relating the voltmeter readings is correct?
A
V
9702/11/O/N/19
19
37 A network consists of a 3.0 Ω resistor and two 6.0 Ω resistors, as shown.
4.0 V
+
–
6.0 Ω
3.0 Ω
6.0 Ω
The potential difference (p.d.) across the network is 4.0 V.
What is the current through the 3.0 Ω resistor?
A
0.17 A
B
0.25 A
C
0.33 A
D
1.3 A
38 In the circuit shown, all the resistors are identical and all the ammeters have negligible
resistance.
A1
A2
A
A3
A
A4
A
A
The reading A1 is 0.6 A.
What are the readings on the other ammeters?
A2 / A
A3 / A
A4 / A
A
1.0
0.3
0.1
B
1.4
0.6
0.2
C
1.8
0.9
0.3
D
2.2
1.2
0.4
39 An unstable nucleus of an element decays by emitting an α-particle or a β– particle to become a
nucleus of a different element. This nucleus is also unstable and also emits an α-particle or a
β– particle. The process continues until an isotope of the original element is produced.
What is the minimum possible number of these particles emitted?
A
2
© UCLES 2019
B
3
C
4
9702/11/O/N/19
D
5
[Turn over
20
40 The diagrams show the quark composition of four different hadrons. One of the hadrons is a Σ+
particle. It has a charge of +e, where e is the elementary charge.
Which hadron could be the Σ+ particle?
A
s
d
C
B
d
s
d
s
D
s
u
s
s
u
u
key
u = up quark
d = down quark
s = strange quark
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/11/O/N/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/12
PHYSICS
Paper 1 Multiple Choice
October/November 2019
1 hour 15 minutes
Additional Materials:
*0358068952*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 18 printed pages and 2 blank pages.
IB19 11_9702_12/3RP
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
9702/12/O/N/19
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
9702/12/O/N/19
[Turn over
4
1
A cyclist has a speed of 5 m s–1 and a small car has a speed of 12 m s–1.
Which statement does not give a reasonable estimate?
2
3
4
A
The kinetic energy of the cyclist is 1 × 103 J.
B
The kinetic energy of the car is 7 × 104 J.
C
The momentum of the cyclist is 4 × 102 kg m s–1.
D
The momentum of the car is 2 × 105 kg m s–1.
Which expression gives an SI base quantity?
A
charge per unit time
B
force per unit area
C
mass per unit volume
D
work done per unit distance
Which list contains only scalar quantities?
A
area, length, displacement
B
kinetic energy, speed, power
C
potential energy, momentum, time
D
velocity, distance, temperature
A micrometer is used to measure the 28.50 mm width of a plastic ruler. The micrometer reads to
the nearest 0.01 mm.
What is the correct way to record this reading?
A
0.02850 ± 0.01 m
B
0.0285 ± 0.001 m
C
(2.850 ± 0.001) × 10–2 m
D
(2.850 ± 0.001) × 10–3 m
© UCLES 2019
9702/12/O/N/19
5
5
The sides of a wooden block are measured with calipers. The lengths of the sides are measured
as 20.0 mm, 40.0 mm and 10.0 mm.
20.0 mm
10.0 mm
40.0 mm
The calipers can measure with an absolute uncertainty of ± 0.1 mm.
What is the percentage uncertainty in the calculated volume of the block?
A
6
0.3%
B
1.8%
C
3.8%
D
30%
A ball is thrown vertically upwards from ground level and reaches a maximum height of 12.7 m
before falling back to ground level.
Assume air resistance is negligible.
What is the total time for which the ball is in the air?
A
7
1.61 s
B
3.22 s
C
3.88 s
D
5.18 s
A snooker ball has a mass of 200 g. It hits the cushion of a snooker table and rebounds along its
original path.
The ball arrives at the cushion with a speed of 14.0 m s–1 and then leaves it with a speed of
7.0 m s–1. The ball and the cushion are in contact for a time of 0.60 s.
What is the average force exerted on the ball by the cushion?
A
8
1.4 N
B
2.3 N
C
4.2 N
D
7.0 N
A tennis ball is released from rest at time t = 0 and falls through air for a long time.
Which graph of its displacement s against time t best represents the motion of the ball?
A
B
s
0
C
s
0
© UCLES 2019
0
t
D
s
0
0
t
s
0
9702/12/O/N/19
0
t
0
t
[Turn over
6
9
The space probe Rosetta was designed to investigate a comet. The probe consisted of an orbiter
and a lander. The orbiter had a mass of 170 kg and the lander had a mass of 100 kg. When the
two parts separated, the lander was pushed towards the surface of the comet so that its change
in velocity towards the comet was 3.0 m s–1.
orbiter
mass 170 kg
lander
mass 100 kg
3.0 m s–1
Assume that the orbiter and lander were an isolated system.
The orbiter moved away from the comet during the separation.
What was the change in the speed of the orbiter?
A
1.8 m s–1
2.3 m s–1
B
3.0 m s–1
C
D
5.1 m s–1
10 A positively charged oil droplet falls in air in a uniform electric field that is vertically upwards. The
droplet has a constant terminal speed v0 and the electric field strength is E.
The magnitude of the force due to air resistance acting on the droplet is proportional to the speed
of the droplet.
Which graph shows the variation with E of v0?
A
B
v0
C
v0
0
v0
0
0
© UCLES 2019
E
D
v0
0
0
E
0
0
9702/12/O/N/19
E
0
E
7
11 A rigid uniform bar of length 2.4 m is pivoted horizontally at its midpoint.
0.8 m
0.8 m
200 N
300 N
Weights are hung from two points on the bar as shown in the diagram. To maintain equilibrium, a
couple is applied to the bar.
What is the torque and direction of this couple?
A
40 N m clockwise
B
40 N m anticlockwise
C
80 N m clockwise
D
80 N m anticlockwise
12 Two coplanar forces act on an object as shown.
object
Which diagram shows the resultant F of these two forces?
A
B
F
F
C
D
F
F
© UCLES 2019
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8
13 Four measuring cylinders are filled with the same liquid to the heights shown.
At which position is the pressure the greatest?
A
30 cm
30 cm
B
C
10 cm
D
10 cm
14 The gas in an engine does work on a piston of cross-sectional area 80 cm2. The pressure on the
piston has a constant value of 4.6 × 105 Pa.
25 cm
force of gas
pushing piston
final position
of piston
initial position
of piston
How much work is done by the gas on the piston when it moves through a distance of 25 cm?
A
9.2 × 102 J
B
9.2 × 104 J
C
9.2 × 106 J
D
9.2 × 108 J
15 A power station using coal as fuel has an average power output of 3000 MW. Coal is supplied by
20 trains each day. The efficiency of the station in converting the thermal energy released from
the coal to electrical energy is 26%.
A mass of 1.0 kg of coal will release 33 MJ of thermal energy when burnt.
Which mass of coal does each train bring?
A
2.5 × 104 kg
© UCLES 2019
B
6.3 × 104 kg
C
1.5 × 106 kg
9702/12/O/N/19
D
3.0 × 107 kg
9
16 A wooden cylinder floats partially submerged in a bath of water. A force F is applied to the
cylinder until it is just fully submerged.
wooden cylinder
water
F
Which statement is not correct?
A
Some of the water gains gravitational potential energy.
B
The cylinder loses gravitational potential energy.
C
Work is done by force F on the cylinder.
D
Work is done by the upthrust on the cylinder.
17 The motor of a crane lifts a load of mass 600 kg. The load rises vertically at a constant speed of
12 m per minute.
What is the useful power output of the motor?
A
0.12 kW
B
1.2 kW
C
7.2 kW
D
71 kW
18 The graph shows the effect of applying a force of up to 5.0 N to a spring.
14
spring length / cm
11
10
0
5.0
force / N
The spring obeys Hooke’s law for forces up to 7.0 N.
What is the total extension of the spring produced by a 7.0 N force?
A
4.2 cm
© UCLES 2019
B
5.6 cm
C
15 cm
9702/12/O/N/19
D
20 cm
[Turn over
10
19 A rubber cord hangs from a rigid support. A weight attached to its lower end is gradually
increased from zero, and then gradually reduced to zero.
force
stretching
rubber
cord
contraction
weight
0
0
extension
The force–extension curve for contraction is below the force–extension curve for stretching.
What does the shaded area between the curves represent?
A
the elastic potential energy stored in the rubber cord
B
the thermal energy dissipated in the rubber cord
C
the work done on the rubber cord during stretching
D
the work done by the rubber cord during contraction
© UCLES 2019
9702/12/O/N/19
11
20 A transverse wave is travelling along a rope. The frequency of the wave is 2.0 Hz. The graph
shows the variation with distance of the displacement of the wave at time t ꞊ 0.
direction of wave travel
displacement
0
2
4
6
8
10 distance / m
Which diagram shows the position of the wave at time t = 0.5 s?
displacement
A
0
2
4
6
8
10 distance / m
0
2
4
6
8
10 distance / m
0
2
4
6
8
10 distance / m
0
2
4
6
8
10 distance / m
displacement
B
displacement
C
displacement
D
© UCLES 2019
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12
21 The two graphs represent the same wave.
Graph 1 shows the variation with time of the displacement at a particular distance. Graph 2
shows the variation with distance of the displacement at one instant.
displacement
0
displacement
0
0.5
1.0
0
time / s
0
30
60
distance
90 / cm
graph 2
graph 1
What is the speed of the wave?
A
22.5 cm s–1
B
30.0 cm s–1
C
90.0 cm s–1
D
120 cm s–1
22 A microphone is connected to a cathode-ray oscilloscope (CRO). When a tuning fork is struck
and then held next to the microphone, the following waveform is shown on the display of the
CRO.
The time-base setting on the CRO is 2.00 ms per division.
What is the best estimate of the frequency of the sound produced by the tuning fork?
A
63 Hz
B
170 Hz
C
250 Hz
D
500 Hz
23 A loudspeaker emitting a constant frequency of 2000 Hz is swung in a horizontal circle with a
speed of 15.0 m s–1.
A stationary observer is level with the loudspeaker and situated a long distance from the
loudspeaker. The observer hears a sound of varying frequency. The maximum frequency heard
is 2097 Hz.
What is the speed of the sound in the air?
A
294 m s–1
© UCLES 2019
B
309 m s–1
C
324 m s–1
9702/12/O/N/19
D
330 m s–1
13
24 Two electromagnetic waves have wavelengths of 5.0 × 10–7 m and 5.0 × 10–2 m.
Which row identifies the regions of the electromagnetic spectrum to which the waves belong?
wavelength
5.0 × 10–7 m
wavelength
5.0 × 10–2 m
A
ultraviolet
infrared
B
visible
microwave
C
ultraviolet
microwave
D
visible
infrared
25 A transmitter of electromagnetic waves is placed 45 cm from a reflective surface.
reflective surface
transmitter
45 cm
The emitted waves have a frequency of 1.00 GHz. A stationary wave is produced with a node at
the transmitter and a node at the surface.
How many antinodes are in the space between the transmitter and the surface?
A
1
B
2
C
3
D
4
26 Which statement about a light wave and a sound wave is correct?
A
Both can travel through free space.
B
Both have a frequency inversely proportional to their wavelength.
C
Both have an intensity proportional to their amplitude.
D
Both have oscillations perpendicular to the direction of energy transfer.
© UCLES 2019
9702/12/O/N/19
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14
27 An outdoor concert has two large speakers beside the stage for broadcasting music.
In order to test the speakers, they are made to emit sound of the same wavelength and the same
amplitude.
The curved lines in the diagram represent wavefronts.
Where is the loudest sound heard?
C
A
D
B
speakers
stage
28 An electromagnetic wave is incident normally on a diffraction grating.
A second-order maximum is produced at an angle of 30° to a normal to the grating.
The grating has 5000 lines per cm.
What is the wavelength of the wave?
A
2.5 × 10–7 m
B
5.0 × 10–7 m
C
1.0 × 10–6 m
D
5.0 × 10–5 m
29 P is a point near to charge X as shown.
X
P
When a negatively charged test charge is placed at point P, it is found to experience a force of
repulsion from X that is radially away from X.
Which arrow correctly shows the direction of the electric field at point P due to the charge X?
A
© UCLES 2019
B
C
9702/12/O/N/19
D
15
30 A charged oil drop of mass m, with n excess electrons, is held stationary in the uniform electric
field between two horizontal plates separated by a distance d.
V
m
d
The voltage between the plates is V, the elementary charge is e and the acceleration of free fall
is g.
What is the value of n ?
eV
mgd
A
B
mgd
eV
C
meV
gd
D
gd
meV
31 When the current in a wire is 5.0 A, the average drift speed of the conduction electrons in the wire
is 7.4 × 10–4 m s–1.
Which row gives a possible cross-sectional area and number of conduction electrons per unit
volume for this wire?
cross-sectional
area / m2
number of conduction
electrons per unit
volume / m–3
A
7.2 × 10–7
1.2 × 1028
B
7.2 × 10–7
5.9 × 1028
C
2.3 × 10–6
7.3 × 1026
D
2.3 × 10–6
3.7 × 1027
32 A fixed resistor of resistance 12 Ω is connected to a battery. There is a current of 0.20 A in the
resistor. The current is now doubled.
What is the new power dissipated in the resistor?
A
0.48 W
B
0.96 W
C
1.9 W
D
4.8 W
33 There is a current in a resistor for an unknown time.
Which two quantities can be used to calculate the energy dissipated by the resistor?
A
the current in the resistor and the potential difference across the resistor
B
the resistance of the resistor and the current in the resistor
C
the total charge passing through the resistor and the potential difference across the resistor
D
the total charge passing through the resistor and the resistance of the resistor
© UCLES 2019
9702/12/O/N/19
[Turn over
16
34 Two cells with electromotive forces E1 and E2 and internal resistances r1 and r2 are connected to
a resistor R as shown.
cell 2
cell 1
E1
E2
r1
r2
current
R
The terminal potential difference across cell 1 is zero.
Which expression gives the resistance of resistor R?
A
E 2r 1 − E 1r 2
E1
B
E 2r 1 − E 1r 2
E2
C
E 1r 2 − E 2r 1
E1
D
E 1r 2 − E 2r 1
E2
35 A battery has an electromotive force (e.m.f.) E and internal resistance r. The battery delivers a
current I to a variable resistor and the potential difference (p.d.) across its terminals is V.
E
I
r
V
The variable resistor is adjusted so that I increases.
Why does V decrease?
A
The e.m.f. E decreases.
B
The internal resistance r increases.
C
The p.d. across r increases.
D
The resistance of the variable resistor increases.
© UCLES 2019
9702/12/O/N/19
17
36 Three identical resistors are connected between terminals P and Q in different networks X, Y and
Z as shown.
X
Y
P
Q
P
Z
Q
P
Q
What is the order of increasing combined resistance between P and Q (lowest first)?
A
X→Y→Z
B
X→Z→Y
C
Y→X→Z
D
Y→Z→X
37 The diagram shows a variable resistor R and two fixed resistors connected in series in a circuit to
act as a potential divider.
6.0 V
2.0 Ω
R
10 Ω
2.0 V
The cell of electromotive force (e.m.f.) 6.0 V has negligible internal resistance. A cell of e.m.f.
2.0 V and a galvanometer are connected into the potential divider. The resistance of R is varied
until the galvanometer reads zero.
What is the resistance of resistor R?
A
3.0 Ω
© UCLES 2019
B
5.0 Ω
C
8.0 Ω
9702/12/O/N/19
D
18 Ω
[Turn over
18
38 The table gives some data relating to four neutral (uncharged) atoms W, X, Y and Z.
W
X
Y
Z
nucleon (mass) number
16
17
17
18
total number of particles (protons,
neutrons and electrons) in the atom
24
26
25
28
Two of the atoms are isotopes of the same element.
What is the proton number of this element?
A
7
B
8
C
9
D
10
39 What is not a fundamental particle?
A
electron
B
neutrino
C
neutron
D
positron
40 An unstable nucleus decays and emits a β– particle.
Which changes, if any, occur to the quark composition of the nucleus?
quark changes
up quarks
down quarks
A
+1
0
B
+1
–1
C
–1
+1
D
0
+1
© UCLES 2019
9702/12/O/N/19
19
BLANK PAGE
© UCLES 2019
9702/12/O/N/19
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/12/O/N/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
9702/13
PHYSICS
Paper 1 Multiple Choice
October/November 2019
1 hour 15 minutes
Additional Materials:
*2329761207*
Multiple Choice Answer Sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.
Do not use staples, paper clips, glue or correction fluid.
Write your name, centre number and candidate number on the Answer Sheet in the spaces provided
unless this has been done for you.
DO NOT WRITE IN ANY BARCODES.
There are forty questions on this paper. Answer all questions. For each question there are four possible
answers A, B, C and D.
Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.
Read the instructions on the Answer Sheet very carefully.
Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
Any working should be done in this booklet.
Electronic calculators may be used.
This document consists of 19 printed pages and 1 blank page.
IB19 11_9702_13/3RP
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2019
9702/13/O/N/19
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2019
9702/13/O/N/19
[Turn over
4
1
2
3
Which quantity with its unit is correct?
A
acceleration of a bicycle = 1.4 m s–1
B
electric current in a lamp = 0.25 A s–1
C
electric potential difference across a battery = 8.0 J C–1
D
kinetic energy of a car = 4500 N m–1
Which two units are not equivalent to each other?
A
N m and kg m2 s–2
B
N s and kg m s–1
C
J s–1 and kg m2 s–3
D
Pa and kg m s–2
The arrow represents a vector R.
Which diagram does not represent R as two perpendicular components?
© UCLES 2019
A
B
C
D
9702/13/O/N/19
5
4
5
What could reduce systematic errors?
A
averaging a large number of measurements
B
careful calibration of measuring instruments
C
reducing the sample size
D
repeating measurements
2
The power loss P in a resistor is calculated using the formula P = V .
R
The percentage uncertainty in the potential difference V is 3% and the percentage uncertainty in
the resistance R is 2%.
What is the percentage uncertainty in P ?
A
6
4%
B
7%
C
8%
D
11%
A lead sphere is released from rest at point X, a long way above the surface of a planet. The
sphere falls in a vacuum. After a time of 4.0 s, it has fallen through a vertical distance of 3.0 m.
Assume the acceleration of free fall is constant.
How far will the sphere have fallen from point X at a time of 20 s after its release?
A
7
15 m
B
75 m
C
80 m
D
2000 m
A box rests on the Earth, as shown.
Newton’s third law describes how forces of the same type act in pairs. One of the forces of a pair
is the weight W of the box.
Which arrow represents the other force of this pair?
B
box
D
C
W
not to
scale
A
Earth
© UCLES 2019
9702/13/O/N/19
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6
8
A snowflake is falling from the sky on a still day. Its weight acts vertically downwards and air
resistance acts vertically upwards. As the snowflake falls, air resistance increases until it is equal
to the weight and there is no resultant force acting on the snowflake.
air resistance
weight
When the forces become equal, which statement is correct?
9
A
The snowflake accelerates.
B
The snowflake decelerates.
C
The snowflake is stationary.
D
The snowflake moves at a constant velocity.
Two objects X and Y in an isolated system undergo a perfectly elastic collision. The velocities of
the objects before and after the collision are shown.
20 m s–1
12 m s–1
10 m s–1
v
X
Y
X
Y
before
collision
after
collision
What is the speed v of Y after the collision?
A
2.0 m s–1
© UCLES 2019
B
18 m s–1
C
22 m s–1
9702/13/O/N/19
D
24 m s–1
7
10 A solid sphere, which is less dense than water, is held completely immersed in water a few
metres below the surface. The density of the water is uniform.
The sphere is released. Immediately after release, the sphere rises.
Which row correctly describes the changes in the upthrust on the sphere and the resultant force
on the sphere?
upthrust on
the sphere
resultant force
on the sphere
A
constant
increasing
B
constant
decreasing
C
decreasing
increasing
D
decreasing
decreasing
11 The diagram shows two pairs X and Y of parallel forces.
X
Y
20 N
40 N
50 cm
50 cm
40 N
20 N
Which statement is correct?
A
X is equivalent to a clockwise torque of 10 N m and a force of 20 N to the left.
B
X is equivalent to a clockwise torque of 20 N m only.
C
Y is equivalent to an anticlockwise torque of 30 N m and a force of 20 N to the left.
D
Y is equivalent to an anticlockwise torque of 30 N m only.
© UCLES 2019
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8
12 A heavy ball hanging from a cable is held in equilibrium by a chain, as shown.
point of
suspension
cable
chain
heavy ball
Which vector diagram shows the three forces acting on the ball?
B
A
tension
in cable
tension
in cable
weight
of ball
weight
of ball
tension
in chain
tension
in chain
C
tension
in cable
D
tension
in cable
weight
of ball
tension
in chain
© UCLES 2019
tension
in chain
9702/13/O/N/19
weight
of ball
9
13 At sea level, atmospheric pressure is 100 kPa and the density of air is 1.3 kg m–3.
Assume that the density of air decreases linearly with height above sea level.
What is an estimate of the total height of the atmosphere based on this information?
A
7.8 km
B
16 km
C
77 km
D
150 km
14 Trains supply coal to a power station. The table shows quantities describing the operation of the
power station.
symbol
unit
power station average output
P
W
number of trains per day
N
mass of coal on a train
M
kg
energy from 1 kg of coal
E
J
number of seconds in one day
S
Which expression gives the efficiency of the power station?
A
PS
NME
B
PSN
ME
C
NME
PS
D
NM
PSE
15 A piston in a gas supply pump has an area of 500 cm2 and it moves a distance of 30 cm.
The pump moves the gas against a fixed pressure of 4000 Pa.
How much work is done by the piston?
A
60 J
© UCLES 2019
B
6.0 × 103 J
C
6.0 × 105 J
9702/13/O/N/19
D
6.0 × 107 J
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10
16 A steel ball is falling at constant speed in oil.
Which graph shows the variation with time of the gravitational potential energy Ep and the kinetic
energy Ek of the ball?
A
B
energy
energy
0
Ek
Ek
Ep
Ep
0
time
time
C
D
Ek
energy
Ek
energy
Ep
0
Ep
0
time
time
17 The maximum useful output power of a car travelling on a horizontal road is P. The total resistive
force acting on the car is kv2, where v is the speed of the car and k is a constant.
Which equation is correct when the car is travelling at maximum speed?
A
v3 = P
k
B
v2 = P
k
C
 
v = P 
k
2
 
v = P 
k
D
3
18 Initially, four identical uniform blocks, each of mass m and thickness h, are spread on a table.
h
h
The acceleration of free fall is g.
How much work is done on the blocks in stacking them on top of one another?
A
3 mgh
© UCLES 2019
B
6 mgh
C
8 mgh
9702/13/O/N/19
D
10 mgh
11
19 The stress–strain graph for a wire is shown.
stress / 108 Pa
2.1
0
0
1.4
strain / 10–3
What is the Young modulus of the material of the wire?
A
6.7 × 10–12 Pa
B
6.7 × 10–9 Pa
C
1.5 × 108 Pa
D
1.5 × 1011 Pa
20 The diagram shows a force–extension graph for a rubber band as the band is extended and then
the stretching force is decreased to zero.
force
rubber
band
extends
rubber
band
contracts
0
0
extension
What can be deduced from the graph?
A
The rubber band does not return to its original length when the force is decreased to zero.
B
The rubber band obeys Hooke’s law for the extensions shown.
C
The rubber band remains elastic for the extensions shown.
D
The shaded area represents the work done in extending the rubber band.
© UCLES 2019
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21 Which statement about light waves and sound waves is not correct?
A
Light waves and sound waves can both demonstrate the Doppler effect.
B
Light waves are transverse waves and sound waves are longitudinal waves.
C
Light waves can be diffracted but sound waves cannot.
D
Light waves can travel in a vacuum but sound waves cannot.
22 The graph represents a sound wave.
3
displacement
/ µm
0
0
5
10
15
20
25
30
35
40
45
50
55
time / ms
–3
Which statement is correct?
A
The wave is longitudinal and has a period of 25 ms.
B
The wave is longitudinal and has a frequency of 50 Hz.
C
The wave is transverse and has an amplitude of 3 µm.
D
The wave is transverse and has a wavelength of 20 ms.
23 A cathode-ray oscilloscope (CRO) is used to display a wave of frequency 5.0 kHz. The display is
shown.
1 cm
1 cm
What is the time-base setting of the CRO?
A
10 µs cm–1
© UCLES 2019
B
100 µs cm–1
C
10 ms cm–1
9702/13/O/N/19
D
100 ms cm–1
13
24 A siren emits sound of frequency 1000 Hz. The siren moves at 20 m s–1 towards an observer who
is standing still.
The speed of sound in the air is 330 m s–1.
Which expression would correctly give the frequency heard by the observer?
A
B
C
D
1000 × 330
330 + 20
1000 × 330
330 − 20
1000 (330 + 20)
330
1000 (330 − 20)
330
25 A source of sound of constant power P is situated in an open space. The intensity I of sound at
distance r from this source is given by
I=
P .
4πr 2
How does the amplitude a of the vibrating air molecules vary with the distance r from the source?
A
a∝ 1
r
© UCLES 2019
B
a ∝ 12
r
C
a∝r
9702/13/O/N/19
D
a ∝ r2
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14
26 In an experiment to demonstrate a stationary wave, two microwave transmitters, emitting waves
of wavelength 4 cm, are set facing each other, as shown.
transmitter
transmitter
d
detector
A detector is moved along a straight line between the transmitters. It detects positions of
maximum and minimum signal. The detector is a distance d from the left-hand transmitter.
Assume that both transmitters are at antinodes of the stationary wave.
Which row gives a value of d for a maximum and for a minimum?
value of d for
a maximum / cm
value of d for
a minimum / cm
A
46
48
B
47
48
C
48
47
D
49
47
27 The graph shows how the height of the water surface at a point in a harbour varies with time t as
waves pass the point.
height
mean height
p
t
q
What are p and q?
p
q
A
displacement
period
B
displacement
wavelength
C
amplitude
period
D
amplitude
wavelength
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15
28 The diagram shows a sketch of a wave pattern over a short period of time.
1.0 m
Which description of this wave is correct?
A
The wave is longitudinal, has a wavelength of 20 cm and is stationary.
B
The wave is transverse, has a wavelength of 20 cm and is stationary.
C
The wave is transverse, has a wavelength of 40 cm and is progressive.
D
The wave is transverse, has a wavelength of 40 cm and is stationary.
29 The double-slit experiment demonstrates interference between two coherent sources of light
waves. In the diagram, the curved lines represent wavefronts.
At which point does complete destructive interference (a minimum) occur?
A
C
B
D
single slit
double slit
30 Light of wavelength 567 nm is incident normally on a diffraction grating. The grating has 400 lines
per mm. A number of diffraction maxima are observed on the far side of the grating.
What is the angle between the second-order maximum and the third-order maximum?
A
13.1°
© UCLES 2019
B
13.9°
C
15.9°
9702/13/O/N/19
D
27.0°
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16
31 The diagram shows the electric field pattern between two opposite and unequal point charges
P and Q.
P
Q
Which statement about the charges is correct?
A
P is negatively charged and has a smaller charge than Q.
B
P is negatively charged and has a greater charge than Q.
C
P is positively charged and has a smaller charge than Q.
D
P is positively charged and has a greater charge than Q.
32 A uniform electric field is represented by five horizontal field lines.
P
Q
P and Q are two points in the field. The field causes a positively charged particle in a vacuum to
move from P to Q.
Which statement must be correct?
A
The acceleration of the particle between P and Q is increasing.
B
The kinetic energy of the particle at P is the same as the kinetic energy of the particle at Q.
C
The force on the particle at Q is greater than the force on the particle at P.
D
Work is done on the particle as it moves from P to Q.
33 A metal electrical conductor has a resistance of 5.6 kΩ. A potential difference (p.d.) of 9.0 V is
applied across its ends.
How many electrons pass a point in the conductor in one minute?
A
6.0 × 1020
© UCLES 2019
B
1.0 × 1019
C
6.0 × 1017
9702/13/O/N/19
D
1.0 × 1016
17
34 A battery of electromotive force (e.m.f.) 12 V and negligible internal resistance is connected to
three resistors, each of resistance 6.0 Ω, as shown.
6.0 Ω
6.0 Ω
6.0 Ω
R
12 V
What is the power dissipated in resistor R?
A
2.7 W
B
6.0 W
C
11 W
D
24 W
35 A box containing two electrical components is connected into a circuit.
V
box
A
The variable resistor is adjusted and measurements are taken to determine the I–V characteristic
for the box, as shown.
I
0
0
V
Which arrangement of two electrical components in the box would create the best fit to the
measured I–V characteristic?
A
a filament lamp and a fixed resistor in parallel
B
a filament lamp and a fixed resistor in series
C
a semiconductor diode and a filament lamp in parallel
D
a semiconductor diode and a filament lamp in series
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36 A cell of internal resistance 0.5 Ω is connected to a fixed resistor of resistance 10 Ω.
The resistance of the resistor is changed to 20 Ω.
Which statement is not correct?
A
The current in the circuit will halve.
B
The e.m.f. of the cell will remain constant.
C
The power dissipated by the fixed resistor will decrease.
D
The terminal p.d. of the cell will increase.
37 Which row correctly describes Kirchhoff’s laws?
Kirchhoff’s first law
physics principle
applied for first
law
Kirchhoff’s second law
physics principle
applied for
second law
A
The sum of the
currents entering a
junction equals the
sum of the currents
leaving the junction.
conservation
of charge
The sum of the e.m.f.s
around any closed loop
in a circuit equals the
sum of the p.d.s around
the same loop.
conservation
of energy
B
The sum of the
currents entering a
junction equals the
sum of the currents
leaving the junction.
conservation
of energy
The sum of the e.m.f.s
around any closed loop
in a circuit equals the
sum of the p.d.s around
the same loop.
conservation
of charge
C
The sum of the e.m.f.s
around any closed
loop in a circuit equals
the sum of the p.d.s
around the same loop.
conservation
of energy
The sum of the currents
entering a junction
equals the sum of the
currents leaving the
junction.
conservation
of charge
D
The sum of the e.m.f.s
around any closed
loop in a circuit equals
the sum of the p.d.s
around the same loop.
conservation
of charge
The sum of the currents
entering a junction
equals the sum of the
currents leaving the
junction.
conservation
of energy
© UCLES 2019
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19
38 In the circuit shown, all the resistors are identical.
V4
V
V
V1
V2
V
V
V3
The reading V1 is 8.0 V and the reading V2 is 1.0 V.
What are the readings on the other voltmeters?
V3 / V
V4 / V
A
1.5
1.0
B
3.0
2.0
C
4.5
3.0
D
6.0
4.0
39 A radioactive nucleus emits an α-particle or a β– particle, creating a product nucleus.
Which decay could create the product nucleus stated?
radioactive nucleus
decay
product nucleus
A
226
88 Ra
α
224
86 Rn
B
238
92 U
α
242
94 Pu
C
228
88 Ra
β–
228
87 Fr
D
231
90Th
β–
231
91Pa
40 Which statement is correct?
A
Electrons and neutrinos are fundamental particles.
B
Electrons and neutrinos are hadrons.
C
Protons and neutrons are leptons.
D
Protons and neutrons are quarks.
© UCLES 2019
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20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/13/O/N/19
Cambridge International AS & A Level
PHYSICS
9702/11
Paper 1 Multiple Choice
May/June 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*2410119342*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
• There are forty questions on this paper. Answer all questions.
• For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
• Follow the instructions on the multiple choice answer sheet.
• Write in soft pencil.
• Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
• Do not use correction fluid.
• Do not write on any bar codes.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 40.
• Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
• Any rough working should be done on this question paper.
This document has 20 pages. Blank pages are indicated.
IB20 06_9702_11/2RP
© UCLES 2020
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
9702/11/M/J/20
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2020
9702/11/M/J/20
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1
What is a reasonable estimate of the kinetic energy of a car travelling at a speed of 30 m s–1?
102 J
A
2
104 J
B
C
106 J
D
108 J
The frequency f of vibration of a mass m supported by a spring with spring constant k is given by
the equation
f = Cm pk q
where C is a constant with no units.
What are the values of p and q?
3
p
q
A
– 21
– 21
B
– 21
1
2
C
1
2
– 21
D
1
2
1
2
The power produced by a force moving an object is given by the equation shown.
power =
work
force × displacement
=
time
time
Which quantities are scalars and which are vectors?
scalars
vectors
A
displacement, time
force, power
B
power, work
displacement, force
C
power, force
displacement, work
D
work, time
power, displacement
© UCLES 2020
9702/11/M/J/20
5
4
A cathode-ray oscilloscope displays a square wave, as shown.
The time-base setting is 0.20 ms per division.
What is the frequency of the square wave?
A
5
0.83 Hz
B
830 Hz
C
1300 Hz
D
1700 Hz
A measurement is taken correctly but with a ruler at a significantly higher temperature than that at
which the ruler was calibrated. The higher temperature causes the ruler to expand.
What describes the effect on the measurement caused by the higher temperature and how the
measurement may be improved?
A
The measurement will be subject to a random error. The measurement can be made more
accurate by taking the average of several repeated measurements.
B
The measurement will be subject to a random error. The measurement can be made more
precise by taking the average of several repeated measurements.
C
The measurement will be subject to a systematic error. The measurement can be made more
accurate by taking the average of several repeated measurements.
D
The measurement will be subject to a systematic error. The measurement can be made more
precise by taking the average of several repeated measurements.
© UCLES 2020
9702/11/M/J/20
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6
6
The velocity of an electric car changes as shown.
150
velocity
/ km h–1
100
50
0
0
1
2
3
4
time / s
What is the acceleration of the car?
A
7
210 m s–2
58 m s–2
B
C
26 m s–2
D
7.3 m s–2
A projectile is fired from point P with velocity V at an angle θ to the horizontal. It lands at point Q,
a horizontal distance R from P, after time T.
path of projectile
V
P
θ
Q
R
The acceleration of free fall is g. Air resistance is negligible.
Which equation is correct?
A
R = VT cos θ
B
R = VT sin θ
C
R = VT cos θ – 21 gT 2
D
R = VT sin θ – 21 gT 2
© UCLES 2020
9702/11/M/J/20
horizontal
7
8
A car accelerates from rest in a straight line with constant acceleration.
Which graph best represents the variation of the momentum p of the car with the distance s
travelled by the car?
A
B
p
p
0
D
p
0
s
0
9
C
0
p
0
s
s
0
0
s
0
The resultant force F on a raindrop of mass m falling with velocity v is given by the equation
F = mg – kv2
where k is a constant and g is the acceleration of free fall.
What is the velocity of the raindrop when it reaches a constant (terminal) velocity?
A
k
mg
B
k
mg
C
mg
k
D
mg
k
10 A stationary toy gun fires a bullet.
Which statement about the bullet and the gun, immediately after firing, is not correct?
A
The force exerted on the bullet by the gun has the same magnitude as the force exerted on
the gun by the bullet.
B
The force exerted on the bullet by the gun is in the opposite direction to the force exerted on
the gun by the bullet.
C
The gun and the bullet have the same magnitude of momentum.
D
The kinetic energy of the gun must equal the kinetic energy of the bullet.
© UCLES 2020
9702/11/M/J/20
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8
11 A wooden block rests on the rough surface of a board. One end of the board is then raised until
the block slides down the board at constant velocity v.
block
v
board
What describes the forces acting on the block when it is sliding with constant velocity?
frictional force on block
resultant force on block
A
down the board
down the board
B
down the board
zero
C
up the board
down the board
D
up the board
zero
12 Which statement best describes a couple?
A
a pair of forces of equal magnitude acting in opposite directions which produce rotational
motion but not translational motion
B
a pair of forces of equal magnitude acting in opposite directions which produce translational
motion but not rotational motion
C
a pair of forces of equal magnitude acting in the same direction which produce rotational
motion but not translational motion
D
a pair of forces of equal magnitude acting in the same direction which produce translational
motion but not rotational motion
© UCLES 2020
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9
13 A uniform rod XY of weight 10.0 N is freely hinged to a wall at X. It is held horizontal by a force F
acting from Y at an angle of 30° to the horizontal, as shown.
F
wall
60°
30°
X
Y
10.0 N
What is the value of F ?
A
5.0 N
© UCLES 2020
B
8.7 N
C
10.0 N
9702/11/M/J/20
D
20.0 N
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10
14 Four combinations of vectors are shown, each representing all the forces acting on an object.
The forces all act in the same plane.
The object is in equilibrium.
Which combination of vectors could represent the forces acting on the object?
A
B
C
D
15 A rectangular metal bar exerts a pressure of 15 200 Pa on the horizontal surface on which it rests.
The height of the metal bar is 80 cm.
What is the density of the metal?
A
190 kg m–3
B
1900 kg m–3
C
19 000 kg m–3
D
190 000 kg m–3
© UCLES 2020
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11
16 A mass attached to the lower end of a spring bounces up and down.
At which points in the path of the mass do the gravitational potential energy of the mass (GPE),
the elastic potential energy in the spring (EPE) and the kinetic energy of the mass (KE) have their
highest values?
GPE
EPE
KE
A
bottom
middle
top
B
bottom
top
middle
C
top
bottom
middle
D
top
bottom
top
17 A block of weight 80 N is pushed a distance of 60 cm up a slope inclined at 30° to the horizontal.
There is a frictional force of 25 N between the block and the surface of the slope.
60 cm
30°
80 N
weight
horizontal
What is the work Wg done against the gravitational force and the work Wf done against the
frictional force?
Wg / J
Wf / J
A
24
7.5
B
24
C
48
D
48
© UCLES 2020
15
7.5
15
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18 A ball is dropped from rest and falls towards the ground. Air resistance is negligible.
Which graph shows the variation with speed of the height of the ball above the ground?
A
B
height
above
ground
height
above
ground
0
0
speed
0
speed
0
C
D
height
above
ground
height
above
ground
0
0
speed
0
speed
0
19 Power is transferred through a machine as shown.
power input PI
machine
power output PO
power loss PL
What is the efficiency of the machine?
A
PI
PO + PL
© UCLES 2020
B
PL
PI
C
PL
PO
9702/11/M/J/20
D
PO
PI
13
20 A tensile force is used to extend a sample of a material. The force is then removed.
The variation with strain of the applied stress is shown on the graph.
Which point on the graph could represent the elastic limit for the material?
C
B
stress
A
D
0
strain
0
21 A tensile force is applied to an unstretched rubber band, causing it to stretch. The tensile force is
then removed.
Which statement about the rubber band must be correct?
A
If the rubber band stretches elastically and plastically, all the work done by the force is
converted to thermal energy in the rubber.
B
If the rubber band stretches elastically, it obeys Hooke’s law.
C
If the rubber band stretches elastically, the gradient of the force–extension graph represents
the work done by the force.
D
If the rubber band stretches plastically, the rubber band will be longer after the force is
removed than it was before the force is applied.
22 A sound wave reduces in intensity but maintains a constant frequency as it travels through air.
Which statement is correct?
A
The maximum displacement of the particles changes between one particle and the next
particle.
B
The phase difference between adjacent particles is zero.
C
The wavelength is the distance between two particles that have a phase difference of 180°.
D
Two particles that have a phase difference of 360° have the same maximum displacement.
© UCLES 2020
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23 The graph shows the variation with time of the displacement of an electromagnetic wave at a
point.
displacement 3.0
arbitrary units
0
0
5
10
15
20
25
30
35
40
45
50
55
time / µs
–3.0
The wave is travelling in a vacuum.
What is the amplitude and what is the wavelength of the wave?
amplitude
/ arbitrary units
wavelength
/m
A
3.0
6000
B
6.0
6000
C
3.0
7500
D
6.0
7500
24 A long glass tube is almost completely immersed in a large tank of water. A tuning fork is struck
and held just above the open end of the tube as it is slowly raised.
A louder sound is first heard when the height h of the end of the tube above the water is 18.8 cm.
A louder sound is next heard when h is 56.4 cm. The speed of sound in air is 330 m s–1.
tuning fork
glass tube
h
water
What is the frequency of the sound produced by the tuning fork?
A
220 Hz
© UCLES 2020
B
440 Hz
C
660 Hz
9702/11/M/J/20
D
880 Hz
15
25 A source emitting sound of a single frequency fs travels at constant speed directly towards an
observer. The source then passes the observer and continues to move directly away from the
observer. The velocity of the source remains constant.
Which graph represents the variation with time of the frequency fo of the sound heard by the
observer?
A
B
fo
fo
fs
fs
time
time
C
D
fo
fo
fs
fs
time
time
26 What are the names of the electromagnetic waves that have wavelengths in a vacuum of 100 pm
and of 100 µm?
wavelength
100 pm
wavelength
100 µm
A
γ-rays
infrared
B
γ-rays
red light
C
X-rays
infrared
D
X-rays
red light
© UCLES 2020
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27 The diagram shows a string stretched between fixed points X and Y. There is a stationary wave
on the string.
S
X
Q
R
Y
P
T
The solid curve shows the string at a position of maximum displacement. The dashed curve
shows the other position of maximum displacement. The straight central dashed line shows the
mean position of the string. Point S on the string is directly above point P. Point T on the string is
directly below Q.
Which statement is correct?
A
A short time later, point R on the string will be displaced.
B
Points S and T on the string move in opposite directions.
C
The distance between P and Q is one wavelength.
D
Two points on the string that are equal distances from point R vibrate in phase.
28 Which statement must be true for diffraction to occur when a wave passes through a gap?
A
The wave is able to travel in a vacuum.
B
The wave is progressive.
C
The wave has a large amplitude.
D
The wave has a long wavelength.
29 Light of a single wavelength is incident normally on two slits that are 0.20 mm apart. Interference
fringes are observed on a screen that is 5.4 m away from the slits. The distance between
successive bright fringes is 12 mm.
What is the wavelength of the light?
A
440 nm
© UCLES 2020
B
540 nm
C
650 nm
9702/11/M/J/20
D
900 nm
17
30 A diffraction grating and a screen are used to determine the single wavelength λ of the light from
a source.
What is an essential feature of this experiment?
A
A curved screen must be used.
B
The diffraction angle θ must be measured for at least two interference maxima.
C
The light waves incident on the grating must be coherent.
D
The third order intensity maximum must be produced.
31 A small charge q is placed in the electric field of a large charge Q.
Both charges experience a force F.
What is the electric field strength of the charge Q at the position of the charge q?
A
F
Qq
B
F
Q
C
FqQ
D
F
q
32 A charged particle is in a vacuum between two horizontal metal plates as shown.
horizontal plate
charged particle
+300 V
2.0 cm
horizontal plate
0V
The acceleration of the particle is 7.15 × 1011 m s–2 downwards. The particle has a mass of
3.34 × 10–27 kg.
What is the charge on the particle?
A
+1.6 × 10–19 C
B
–1.6 × 10–19 C
C
+1.6 × 10–17 C
D
–1.6 × 10–17 C
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33 The current in the circuit shown is 3.2 mA.
R
Y
X
What are the direction of flow and the rate of flow of electrons through the resistor R?
direction of flow
rate of flow / s–1
A
X to Y
2.0 × 1016
B
X to Y
5.1 × 10–22
C
Y to X
2.0 × 1016
D
Y to X
5.1 × 10–22
34 Which graph best represents the way the current I through a filament lamp varies with the
potential difference V across it?
A
B
I
C
I
0
0
I
0
0
V
D
I
0
0
V
V
0
0
V
35 A cylindrical metal wire X has resistance R. The same volume of the same metal is made into a
cylindrical wire Y of double the length.
What is the resistance of wire Y?
A
R
© UCLES 2020
B
2R
C
4R
9702/11/M/J/20
D
8R
19
36 A cell of electromotive force (e.m.f.) E and internal resistance r is connected to a resistor of
resistance R.
A maximum power P can be dissipated by the resistor without overheating.
E
r
R
What is the maximum value of E if the resistor does not overheat?
A
R
P
(R − r )
B
R
P
(R + r )
C
(R − r )
P
R
D
(R + r )
P
R
37 Three identical resistors can be connected together in four different ways.
The resistances of two of these combinations are 4.0 Ω and 9.0 Ω.
What is the resistance of each individual resistor?
A
3.0 Ω
© UCLES 2020
B
6.0 Ω
C
12 Ω
9702/11/M/J/20
D
18 Ω
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38 In the circuit shown, a battery of negligible internal resistance is connected in series with a pair of
fixed resistors R1 and R2.
R1
60 Ω
6.0 V
X
R2
20 Ω
Y
The circuit is to be used to test whether the electromotive force (e.m.f.) of a particular cell is 1.5 V.
The cell is connected between terminals X and Y in parallel with R2 and in series with a
galvanometer.
Which statement about the test is correct?
A
Any non-zero reading on the galvanometer means the cell has an e.m.f. of 1.5 V.
B
The battery does not need to have an e.m.f. of 6.0 V.
C
The cell may be connected either way round between X and Y.
D
The galvanometer does not need a scale calibrated in amperes.
39 An element has two isotopic forms.
What are the nuclear arrangements of these two isotopes?
A
They have different nucleon numbers and different proton numbers.
B
They have different nucleon numbers but the same proton number.
C
They have the same nucleon number and the same proton number.
D
They have the same nucleon number but different proton numbers.
40 A hadron has a charge +e, where e is the elementary charge.
Which combination of up (u) and down (d) quarks could form this hadron?
A
ddd
B
udd
C
uud
D
uuu
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/11/M/J/20
Cambridge International AS & A Level
PHYSICS
9702/12
Paper 1 Multiple Choice
May/June 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*2458956383*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
• There are forty questions on this paper. Answer all questions.
• For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
• Follow the instructions on the multiple choice answer sheet.
• Write in soft pencil.
• Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
• Do not use correction fluid.
• Do not write on any bar codes.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 40.
• Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
• Any rough working should be done on this question paper.
This document has 24 pages. Blank pages are indicated.
IB20 06_9702_12/3RP
© UCLES 2020
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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1
What is a reasonable estimate of the mass of a raindrop?
A
2
3
101 kg
B
10–1 kg
C
10–3 kg
D
10–5 kg
Which quantity is a scalar?
A
acceleration
B
force
C
kinetic energy
D
momentum
A galvanometer of resistance 5 Ω is to be used in a null method.
In order to protect the galvanometer from damage due to an excessive initial current, resistors of
resistance 0.5 Ω and 1 kΩ are available.
Which arrangement would provide this protection?
4
A
the 0.5 Ω resistor in series with the galvanometer
B
the 0.5 Ω resistor in parallel with the galvanometer and this combination placed in series with
the 1 kΩ resistor
C
the 1 kΩ resistor in parallel with the galvanometer
D
the 1 kΩ resistor in parallel with the galvanometer and this combination placed in series with
the 0.5 Ω resistor
Readings are made of the current I for different voltages V across a fixed resistor. The results are
plotted on a graph to show the variation of I with V.
I
0
0
V
What is the best description of the errors in the readings?
A
both systematic and random
B
neither systematic nor random
C
random only
D
systematic only
© UCLES 2020
9702/12/M/J/20
5
5
A stone is dropped from a height of 20 m above water. The graph shows the variation with time of
the velocity of the stone.
20
velocity / m s–1
5
0
0
2
4
time / s
Which statement describes the approximate position of the stone four seconds after it is
dropped?
A
It is at a distance of 10 m above the surface of the water.
B
It is at a distance of 10 m below the surface of the water.
C
It is at a distance of 20 m below the surface of the water.
D
It is at a distance of 30 m below the surface of the water.
© UCLES 2020
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6
A car X is travelling at a constant speed u along a straight road. At time t = 0 a second car Y is a
distance d0 behind car X and travelling at a speed v in the same direction. Speed v is less than
speed u.
v
u
car Y
car X
d0
At time t = 0 car Y begins to accelerate with a constant acceleration.
Car Y overtakes car X at time t = T.
Which graph could best show the variation with time t of the distance d between the cars?
A
B
d0
d0
0
t T
d0
d
0
0
D
d0
d
d
7
C
d
0
t T
0
0
t T
0
0
The resultant force acting on an object is slowly increased.
Which graph could show the variation with time t of the momentum p of the object?
A
B
p
p
0
0
t
0
C
D
p
p
0
0
0
© UCLES 2020
t
0
t
0
9702/12/M/J/20
t
t T
7
8
An astronaut has a weight of 660 N when she is standing on the Earth’s surface.
The acceleration of free fall on the surface of Mars is 3.71 m s–2.
What would be the weight of the astronaut if she stood on the surface of Mars?
A
9
67.3 N
B
178 N
C
250 N
D
660 N
A mass m1 travelling with speed u1 collides with a mass m2 travelling with speed u2 in the same
direction. After the collision, mass m1 has speed v1 and mass m2 has speed v2 in the same
direction. The collision is perfectly elastic.
m1
u1
m2
u2
m1
before the collision
v1
m2
v2
after the collision
Which equation is not correct?
A
m1u12 – m1v12 = m2v22 – m2u22
B
v 2 + u2 = v 1 + u1
C
m1(u1 – v1) = m2(v2 – u2)
D
m1(u1 – v1)2 = m2(u2 – v2)2
© UCLES 2020
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10 The diagrams show a negative electric charge situated in a uniform electric field and a mass
situated in a uniform gravitational field.
mass
– charge
uniform gravitational field
uniform electric field
Which row shows the directions of the forces acting on the charge and on the mass?
charge
A
–
B
–
C
–
D
–
mass
11 A bicycle pedal is connected to a pivot by a metal bar, as shown.
force 60 N
pedal
bar
12 cm
20 cm
pivot
16 cm
The force on the pedal is 60 N downwards.
What is the moment of this force about the pivot?
A
7.2 N m
© UCLES 2020
B
9.6 N m
C
12 N m
9702/12/M/J/20
D
1200 N m
9
12 A thin horizontal beam XY is freely hinged at point Y to a vertical wall. The beam is held
stationary by a cable XZ which is attached to the wall at point Z.
Z
wall
cable
Y
hinge
X
beam
W
The beam supports a weight W at point X. The forces in the cable and the beam are FC and FB
respectively.
Which vector triangle represents the forces acting on point X?
W
A
B
C
D
FB
FB
FB
FB
W
FC
W
FC
FC
W
FC
13 A pipe, open at one end, floats in a liquid as shown.
0.40 m
0.30 m
area 0.012 m2
The cross-sectional area of the pipe is 0.012 m2. The weight of the pipe is 32 N.
What is the density of the liquid?
A
680 kg m–3
© UCLES 2020
B
910 kg m–3
C
6700 kg m–3
9702/12/M/J/20
D
8900 kg m–3
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14 During an interval of time, fuel supplies energy X to a car.
Some of this energy is converted into kinetic energy as the car accelerates.
The rest of the energy Y is lost as thermal energy.
What is the efficiency of the car?
A
X
X −Y
B
Y
X −Y
X −Y
X
C
D
X −Y
Y
15 In which situation is work done on an object?
A
The object slides with a constant velocity along a horizontal frictionless surface in a vacuum.
B
A person holds the object at arm’s length and at a fixed height above the ground.
C
A person pushes the object up a frictionless ramp.
D
The stationary object floats partially submerged in water.
16 A spring is attached at one end to a fixed point. A mass is then hung from the other end of the
spring. The spring has extension x when the system is in equilibrium.
P
Q
tension
spring
S
R
0
0
x
x
extension
The variation of the tension in the spring with its extension is shown on the graph.
Which statement is correct?
A
Area SPR represents the energy stored in the spring which cannot be recovered.
B
Area SPQR represents the energy stored in the spring which can be recovered.
C
Area SPQ represents the loss of gravitational potential energy of the mass due to the
extension of the spring.
D
Area SQR represents the elastic potential energy stored in the spring.
© UCLES 2020
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11
17 An escalator in an underground station has 25 people standing on it and is moving with a speed
of 4.3 m s–1. The average mass of a person is 78 kg and the angle of the escalator to the
horizontal is 40°.
What is the minimum power required to lift these people?
A
5.4 kW
B
6.4 kW
C
53 kW
D
63 kW
18 An elastic cord of unstretched total length 16.0 cm and cross-sectional area 2.0 × 10–6 m2 is held
horizontally by two smooth pins a distance 8.0 cm apart.
The cord obeys Hooke’s law. A load of mass 0.40 kg is suspended centrally on the cord. The
angle between the two sides of the cord supporting the load is 60°.
pin
unstretched cord
pin
pin
pin
8.0 cm
8.0 cm
cord
8.0 cm
60°
mass 0.40 kg
What is the Young modulus of the cord material?
A
5.7 × 105 Pa
© UCLES 2020
B
1.1 × 106 Pa
C
2.3 × 106 Pa
9702/12/M/J/20
D
3.9 × 106 Pa
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12
19 A student is investigating the mechanical properties of a metal. He applies different loads to a
long thin wire up to its breaking point, and measures the extension of the wire for each load. He
then plots a graph of stress against strain.
stress
/ 106 Pa
4
3
2
1
0
0
10
20
30
40
strain / 10–3
The student repeats the experiment with a wire made from the same metal, with twice the original
length and half the diameter.
Which graph is obtained?
A
stress
/ 106 Pa
B
4
stress
/ 106 Pa
3
4
3
2
2
1
1
0
0
0
20
40
60
80
0
10
20
strain / 10–3
40
strain / 10–3
C
D
stress 16
/ 106 Pa 12
stress 16
/ 106 Pa 12
8
8
4
4
0
0
0
20
40
60
80
strain / 10–3
© UCLES 2020
30
9702/12/M/J/20
0
10
20
30
strain / 10–3
40
13
20 Which statement describes what is meant by the plastic deformation of a material?
A
It always obeys Hooke’s law.
B
It does not return to its original length when the extending force is removed.
C
It never obeys Hooke’s law.
D
It returns to its original length when the extending force is removed.
21 A transverse wave is moving along a rope. Two points X and Y on the rope are a quarter of a
wavelength apart from each other.
Which statement is not possible for the two points X and Y at any instant?
A
They are both stationary.
B
They are displaced in opposite directions from their equilibrium position.
C
They are moving in opposite directions.
D
They both have displacements of the same magnitude from their equilibrium positions.
22 Two progressive waves meet at a fixed point P. The variation with time of the displacement of
each wave at point P is shown in the graph.
displacement
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1 1.2
time / s
What is the phase difference between the two waves at point P?
A
45°
© UCLES 2020
B
90°
C
135°
9702/12/M/J/20
D
180°
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23 A microphone connected to the Y-plates of a cathode-ray oscilloscope (CRO) is placed in front of
a loudspeaker. The trace on the screen of the CRO is shown.
1 cm
1 cm
The time-base setting is 0.5 ms cm–1 and the Y-plate sensitivity is 0.2 mV cm–1.
What is the frequency of the sound from the loudspeaker and what is the amplitude of the trace
on the CRO?
frequency
/ Hz
amplitude
/ mV
A
330
0.6
B
330
1.2
C
670
0.6
D
670
1.2
© UCLES 2020
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15
24 The diagram shows an experiment to produce a stationary wave in an air column. A tuning fork,
placed above the column, vibrates and produces a sound wave. The length of the air column can
be varied by altering the volume of the water in the tube.
tuning fork
air column
water
tap
The tube is filled and then water is allowed to run out of it. The first two stationary waves occur
when the air column lengths are 0.14 m and 0.42 m.
What is the wavelength of the sound wave?
A
0.14 m
B
0.28 m
C
0.42 m
D
0.56 m
25 A stationary person measures the speed and wavelength of the sound from a horn on a
stationary vehicle. The person then repeats the measurements when the vehicle is approaching
at a constant speed.
Which row describes the measured wavelength and the measured speed of the sound wave from
the moving vehicle when compared with the sound wave from the stationary vehicle?
wavelength of
the sound wave
speed of
the sound wave
A
longer
greater
B
shorter
greater
C
longer
same
D
shorter
same
© UCLES 2020
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26 The table shows the wavelengths of five electromagnetic waves.
Which row correctly identifies the principal radiation for each of these wavelengths?
10–14 m
10–10 m
10–6 m
10–2 m
102 m
A
gamma-ray
X-ray
infrared
microwave
radio wave
B
radio wave
microwave
infrared
X-ray
gamma-ray
C
radio wave
microwave
ultraviolet
infrared
X-ray
D
X-ray
infrared
ultraviolet
microwave
radio wave
27 Two progressive waves meet at a point.
Which condition must be met for superposition of the waves to occur?
A
The waves must be coherent.
B
The waves must be of the same type.
C
The waves must be travelling in opposite directions.
D
The waves must meet in phase.
28 A hill separates a television (TV) transmitter from a house. The transmitter cannot be seen from
the house. However, the house has good TV reception.
hill
TV transmitter
house
By which wave effect at the hill could the TV signal reach the house?
A
coherence
B
diffraction
C
interference
D
reflection
© UCLES 2020
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17
29 The diagram shows an arrangement for demonstrating two-source interference using coherent
light of a single wavelength λ.
P
second bright fringe
first bright fringe
central bright fringe
X
Q
Y
light of
wavelength λ
3.0 m
NOT TO
SCALE
slits
screen
An interference pattern is observed on a screen 3.0 m away from the slits X and Y, which have a
separation of 1.0 mm.
The central bright fringe is at Q, and the second bright fringe from the centre is at P.
What is the distance between Q and P?
A
6.0 × 103 λ
B
3.0 × 103 λ
C
6.7 × 10–4 λ
D
3.3 × 10–4 λ
30 Light of wavelength λ is incident normally on a diffraction grating. The angle between the
second-order maximum and the normal to the grating is θ. The variation with sin θ of λ is shown
on the graph.
750
λ / 10–9 m
500
250
0
0
0.2
0.4
0.6
sin θ
How many lines per millimetre are on the diffraction grating?
A
400 mm–1
© UCLES 2020
B
625 mm–1
C
800 mm–1
9702/12/M/J/20
D
1250 mm–1
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18
31 A dipole is a pair of charges of equal magnitude, one negative and one positive. The electric field
of a dipole is shown below.
In which direction does the force act on an electron when at point X?
X
A
D
B C
–
+
32 A charged oil droplet of mass m is falling, initially freely, in a vacuum between two horizontal
metal plates that are separated by a distance x.
A potential difference (p.d.) V is then applied across the plates. This results in the oil droplet
continuing to accelerate downwards but with a reduced acceleration a.
The polarity of the applied p.d. is then reversed so that the direction of the electric force on the
droplet is reversed. This results in the downwards acceleration of the oil droplet increasing to 3a.
What is the magnitude of the charge on the oil droplet?
A
max
V
B
2 max
V
C
3 max
V
D
4 max
V
33 The number density of free electrons in copper is 8.0 × 1028 m–3.
A copper wire has diameter 0.42 mm.
What is the average drift speed of the free electrons in the wire when the current in the wire is
0.57 A?
A
8.0 × 10–11 m s–1
B
3.2 × 10–10 m s–1
C
8.0 × 10–5 m s–1
D
3.2 × 10–4 m s–1
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19
34 An electric kettle is rated at 2.0 kW, which describes the power supplied to the heating coil in the
kettle.
The coil has a resistance of 5.0 kΩ.
What is the current in the coil?
A
0.40 A
B
0.63 A
C
1.6 A
D
2.5 A
35 A conductor consists of three wires connected in series. The wires are all made of the same
metal but have different cross-sectional areas. There is a current I in the conductor.
I
X
conductor
Y
I
Point Y on the conductor is at zero potential.
Which graph best shows the variation of potential V with distance along the conductor?
V
A
0
X
distance
Y
V
B
0
X
distance
Y
V
C
0
X
distance
Y
V
D
0
X
© UCLES 2020
distance
Y
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20
36 A cell of electromotive force (e.m.f.) E and internal resistance 0.50 Ω is connected to a resistor of
resistance 4.7 Ω.
E
0.50 Ω
4.7 Ω
The maximum power that can be dissipated by the resistor without overheating is 0.50 W.
What is the maximum value of E for the resistor not to overheat?
A
1.4 V
B
1.5 V
C
1.7 V
D
2.9 V
37 Kirchhoff’s first and second laws link to the conservation of physical quantities.
Which quantities do they link to?
first law
second law
A
charge
energy
B
charge
momentum
C
energy
charge
D
energy
momentum
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21
38 In the circuit shown, X is a variable resistor whose resistance can be changed from 5.0 Ω to
500 Ω. The electromotive force (e.m.f.) of the battery is 12.0 V. It has negligible internal
resistance.
40 Ω
12.0 V
X
output
What is the maximum range of values of potential difference across the output?
A
1.3 V to 11.1 V
B
1.3 V to 12.0 V
C
1.5 V to 11.1 V
D
1.5 V to 12.0 V
39 An unstable nucleus goes through successive decays to become a final, stable nucleus.
The initial nucleus and the final nucleus are isotopes of each other.
How many α and β– particles could have been emitted during the decay sequence?
particle
α
β–
A
1
0
B
1
2
C
2
0
D
2
1
40 A hadron has a charge of –e and is composed of three quarks.
What could be the quark composition of the hadron?
A
B
C
D
key
s
s
s
© UCLES 2020
u
s
s
u
s
u
9702/12/M/J/20
u
u
u
u = up quark
s = strange quark
22
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© UCLES 2020
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23
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© UCLES 2020
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24
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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/12/M/J/20
Cambridge International AS & A Level
PHYSICS
9702/13
Paper 1 Multiple Choice
May/June 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*9562105662*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
• There are forty questions on this paper. Answer all questions.
• For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
• Follow the instructions on the multiple choice answer sheet.
• Write in soft pencil.
• Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
• Do not use correction fluid.
• Do not write on any bar codes.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 40.
• Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
• Any rough working should be done on this question paper.
This document has 24 pages. Blank pages are indicated.
IB20 06_9702_13/3RP
© UCLES 2020
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2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
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3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
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1
A man is running a race in a straight line.
What is an approximate value of his kinetic energy?
A
2
10 J
B
100 J
C
1000 J
D
10 000 J
A sample of gas has a mass of 4.8 µg and occupies a volume of 1.2 dm3.
What is the density of the sample of gas?
3
4
A
4.0 × 10–3 kg m–3
B
4.0 × 10–5 kg m–3
C
4.0 × 10–6 kg m–3
D
4.0 × 10–8 kg m–3
Which characteristics are possessed by a vector quantity but not by a scalar quantity?
A
direction only
B
magnitude and direction
C
magnitude and unit
D
unit only
A circuit is set up in order to determine the resistance of a 12 V, 1.2 W lamp when operating
normally. An analogue ammeter and an analogue voltmeter are used.
Which ranges for the meters would be most suitable?
5
ammeter range
/A
voltmeter range
/V
A
0–0.5
0–20
B
0–0.5
0–100
C
0–10
0–20
D
0–10
0–100
Two liquid-in-glass thermometers in a well-mixed liquid are individually observed by 10 different
students. All agree that one thermometer reads 21 °C and the other thermometer reads 23 °C.
What is a possible explanation for the difference?
A
The liquid is not all at the same temperature.
B
The readings are not precise.
C
There is a random error affecting the readings.
D
There is a systematic error affecting the readings.
© UCLES 2020
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5
6
The graph shows how the velocity of a ball varies with time from the moment it is hit vertically
upwards from the ground.
20
velocity
15
/ m s–1
10
5
0
0
1
2
3
time / s
–5
–10
What is the displacement of the ball from the ground after a time of 3.0 s?
A
7
15 m
B
25 m
C
30 m
D
45 m
Two students each throw a ball horizontally from the top of a tower. The two balls are released at
the same time.
The first student throws her ball with a speed of 20 m s–1 and the second student throws his ball
with a speed of 10 m s–1.
Assume air resistance is negligible and that the balls land on horizontal ground.
Which row describes the horizontal distances travelled and the landing times of the two balls on
the ground?
horizontal
distances
landing times
A
same
same
B
same
different
C
different
same
D
different
different
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8
A ball of mass m travels vertically downwards and then hits a horizontal floor at speed u.
It rebounds vertically upwards with speed v.
The collision lasts a time ∆t.
What is the average resultant force exerted on the ball during the collision?
9
A
mv – mu
downwards
∆t
B
mv – mu
upwards
∆t
C
mv + mu
downwards
∆t
D
mv + mu
upwards
∆t
The resultant force F on a raindrop of mass m falling vertically with velocity v is given by the
equation
F = mg – kv 2
where k is a constant and g is the acceleration of free fall.
The falling raindrop eventually reaches a constant (terminal) velocity.
Which graph shows the variation of the terminal velocity of the raindrop with mass m?
A
B
terminal
velocity
terminal
velocity
0
0
m
0
C
D
terminal
velocity
terminal
velocity
0
0
0
© UCLES 2020
m
0
m
0
9702/13/M/J/20
m
7
10 A ball of mass m, moving at a velocity v, collides with a stationary ball of mass 2m.
The two balls stick together.
Which fraction of the initial kinetic energy is lost on impact?
A
1
9
B
1
3
C
2
3
D
8
9
11 A submarine is in equilibrium in a fully submerged position.
sea
water
steel
air
What causes the upthrust on the submarine?
A
The air in the submarine is less dense than sea water.
B
There is a difference in water pressure acting on the top and on the bottom of the submarine.
C
The sea water exerts a greater upward force on the submarine than the weight of the steel.
D
The submarine displaces its own volume of sea water.
12 Two forces, each of magnitude F, act along the edges of a rectangular metal plate, as shown.
a
F
b
P
F
The plate has length a and width b.
What is the torque about point P?
A
Fa
© UCLES 2020
B
Fb
C
2Fa
9702/13/M/J/20
D
2Fb
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13 A non-uniform rod has a mass of 100 g and a length of 50 cm. It is supported by a chain at its
midpoint. The rod is held in equilibrium by having a mass of 60 g suspended from its right-hand
end, as shown.
non-uniform rod
of mass 100 g
centre
of gravity
of rod
chain supporting the
rod at its midpoint
50 cm
d
mass 60 g
The centre of gravity of the rod is a distance d from its left-hand end.
What is the value of d ?
A
10 cm
B
15 cm
C
25 cm
D
40 cm
14 A light rigid rod XY has an object of weight W fixed at one end. The rod is in equilibrium, resting
on a support at Z and a vertical wall at X. The support exerts a force R on the rod as shown. The
diagram shows the directions, but not the magnitudes, of the forces R and W.
Y
wall
W
R
Z
X
What is the direction of the force on the rod at X?
A
B
C
D
15 Liquid Q has twice the density of liquid R.
At depth x in liquid R, the pressure due to the liquid is 4 kPa.
At which depth in liquid Q is the pressure due to the liquid 7 kPa?
A
2x
7
© UCLES 2020
B
7x
8
C
8x
7
9702/13/M/J/20
D
7x
2
9
16 A trolley starts from rest at X. It rolls down to Y and eventually comes to rest at Z.
X
Z
Y
Which row is a possible summary of the energy changes during this process?
X to Y
Y to Z
A
PE → KE
KE → PE
B
PE → KE
KE → PE + heat
C
PE → KE + heat
KE → PE
D
PE → KE + heat
KE → PE + heat
key
PE = potential energy
KE = kinetic energy
17 A cylinder is heated, causing the air inside to expand at a constant pressure of 2.2 × 105 Pa.
piston raised
0.50 m
piston
cylinder
air pressure
2.2 × 105 Pa
The expansion of the air causes the piston to rise through a vertical distance of 0.50 m, doing
11 kJ of work. Frictional forces are negligible.
What is the cross-sectional area of the piston?
A
1.0 × 10–4 m2
B
2.5 × 10–2 m2
C
5.0 × 10–2 m2
D
1.0 × 10–1 m2
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18 A ball slides down a curved track, as shown.
X
0.40 m
Y
Point X is at a height of 0.40 m above point Y. The speed of the ball at point X is 2.5 m s–1.
Frictional forces are negligible.
What is the speed of the ball at point Y?
A
2.8 m s–1
B
3.2 m s–1
3.8 m s–1
C
D
14 m s–1
19 The force diagram shows an aircraft accelerating. At the instant shown, the velocity of the aircraft
is 40 m s–1.
velocity 40 m s–1
600 kN lift
500 kN
engine thrust
200 kN
air resistance
600 kN weight
At which rate is its kinetic energy increasing?
A
2.4 MW
© UCLES 2020
B
8.0 MW
C
12 MW
9702/13/M/J/20
D
20 MW
11
20 The diagram shows a simplified model of a building with four identical heavy floors.
top rods
floors
middle rods
bottom rods
The spacing of the bottom floor from the ground is twice that of the spacing between the floors.
Between each floor are equal numbers of vertical steel supporting rods of negligible mass
compared with the floors. The rods are of different diameters so that the stress in each rod is the
same.
What is the ratio diameter of bottom rods ?
diameter of top rods
A
2
B
4
C
8
D
16
21 The Achilles tendon in a rabbit’s leg is stretched when the rabbit jumps.
The graph shows the variation with tension of the length of the tendon.
40
length / mm
38
36
34
32
30
0
100 200 300 400 500
tension / N
What is the strain energy in the tendon when the tension is 400 N?
A
0.40 J
© UCLES 2020
B
0.80 J
C
2.4 J
9702/13/M/J/20
D
7.4 J
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22 A wave of amplitude A has an intensity I.
After passing through a certain medium, the wave has a new intensity of I .
4
What is the new amplitude of the wave?
A
2A
B
A
2
C
A
4
D
A
16
23 A wave travels along a coiled spring.
The graph shows the variation with time of the displacement of a point on the spring.
displacement
0
0
0.1
0.2
0.3
0.4
0.5
time / s
What is the frequency of the wave?
A
0.13 Hz
B
0.20 Hz
C
5.0 Hz
D
7.5 Hz
24 A loudspeaker is set up at the open end of a closed tube containing powder.
When the loudspeaker produces sound of frequency 1200 Hz, a stationary wave is produced in
the tube. The powder gathers at the nodes of the stationary wave as shown.
loudspeaker
closed end
x
powder
The speed of sound in the air is 336 m s–1.
What is the value of distance x?
A
28 cm
© UCLES 2020
B
42 cm
C
84 cm
9702/13/M/J/20
D
112 cm
13
25 A stationary source S emits a sound wave of frequency f.
The source now moves away from a stationary observer.
Which statement is correct?
A
The frequency of the source S and the observed frequency are now both higher than f.
B
The frequency of the source S and the observed frequency are now both lower than f.
C
The frequency of the source S is now lower than f.
D
The observed frequency is now lower than f.
26 The table lists possible wavelengths of four different electromagnetic waves.
Which row is correct?
type of wave
approximate
wavelength / m
A
infrared
10–5
B
radio
10–3
C
ultraviolet
10–12
D
X-rays
10–7
© UCLES 2020
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27 A vertical tube is partially filled with water. A sound wave moves down the tube and is reflected
by the surface of the water. The frequency of the sound wave is gradually increased from zero
until a much louder sound is heard.
sound
tube
water
Water is then removed from the tube until a second louder sound is heard.
Which diagram shows the new pattern of the stationary wave that is formed?
A
© UCLES 2020
B
C
9702/13/M/J/20
D
15
28 Water waves in a ripple tank are made to pass through a small gap as shown.
Which diagram shows the waves after they have passed through the gap?
A
B
C
D
29 A double-slit interference experiment is set up using green light.
A pattern of interference fringes is formed on a screen.
Which single change will increase the separation of the fringes?
A
increase the width of each slit
B
move the screen nearer to the double slit
C
use slits that are further apart
D
use red light instead of green light
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30 Light of a single wavelength from a distant point source falls normally onto a diffraction grating
positioned with its lines vertical.
diffraction
grating
light from
distant
point source
eye of
student
NOT TO SCALE
The plane of the diffraction grating is at right angles to the incident light. A student looks at the
grating from a position near to the grating.
What could the student see?
A
a central point source with a series of point source images on either side
B
a central vertical line with a series of spectra on either side
C
a series of fine vertical lines
D
a single point source
31 Which diagram best represents the electric field between two point charges of equal magnitude
and opposite sign?
© UCLES 2020
A
B
C
D
+
+
+
+
–
–
–
–
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17
32 A negatively charged oil drop of mass m is between two horizontal parallel metal plates a
distance d apart.
oil drop
mass m
horizontal
metal plates
+
d
–
When the potential difference (p.d.) between the plates is V1 the oil drop rises at a constant
speed. When the p.d. is decreased to a value V2 the oil drop falls at the same constant speed.
Air resistance acts on the drop when it is moving. The upthrust on the drop is negligible.
The acceleration of free fall is g.
What is the charge on the oil drop?
A
mdg
B
V1 – V 2
mdg
V1 + V 2
C
2mdg
V1 – V 2
D
2mdg
V1 + V 2
33 The unit of electric charge is the coulomb.
What is meant by 1 coulomb?
A
the charge passing a point in 1 second when a current produces 1 joule of work
B
the charge passing a point in 1 second when a current produces 1 watt of power
C
the charge passing a point in 1 second when there is a current of 1 ampere
D
the charge passing a point in 1 second when there is 1 ohm of resistance
34 Two copper wires are joined together and carry a current, as shown.
current
current
wire P
diameter d
wire Q
diameter 2d
Wire P has diameter d and wire Q has diameter 2d.
What is the ratio
A
1
4
© UCLES 2020
average drift speed of the free electrons in wire P
?
average drift speed of the free electrons in wire Q
B
1
2
C
2
9702/13/M/J/20
D
4
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18
35 A power supply of electromotive force (e.m.f.) V and negligible internal resistance is connected in
the circuit shown. There is a current of 3.0 A in the 4.0 Ω resistor.
+
3.0 Ω
V
–
4.0 Ω
3.0 A
2.0 Ω
What is the value of V ?
A
15 V
B
29 V
C
39 V
D
51 V
36 The wire of a heating element has resistance R. The wire breaks and is replaced by a different
wire.
Data for the original wire and for the replacement wire are shown in the table.
length
diameter
resistivity
of metal
original wire
l
d
ρ
replacement wire
l
2d
2ρ
What is the resistance of the replacement wire?
A
R
4
© UCLES 2020
B
R
2
C
R
9702/13/M/J/20
D
2R
19
37 A fixed resistor and a variable resistor are connected in series with a cell that has an internal
resistance, as shown.
R
The graph shows the variation of a quantity X with the resistance R of the variable resistor as R is
increased from zero to its maximum value.
X
0
0
R
What could X represent?
A
the current in the circuit
B
the electromotive force of the cell
C
the potential difference across the internal resistance
D
the terminal potential difference across the cell
© UCLES 2020
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38 A cell of electromotive force (e.m.f.) 4.0 V and negligible internal resistance is connected to a
fixed resistor of resistance 1.0 Ω and a potentiometer of maximum resistance 3.0 Ω, as shown.
4.0 V
3.0 Ω
Y
1.0 Ω
X
Which range of potential differences can be obtained between the terminals X and Y?
A
0 V to 3.0 V
B
0 V to 4.0 V
C
1.0 V to 3.0 V
D
1.0 V to 4.0 V
39 Radiation from a radioactive source has a range of a few millimetres in air and can be deflected
by an electric field.
Which type of radiation is being emitted?
A
α-radiation
B
β– radiation
C
β+ radiation
D
γ-rays
40 Which equation describes the process of β+ decay?
key:
u = up quark
d = down quark
ν = (electron) neutrino
ν = (electron) antineutrino
A
ddu → uud + β+ + ν
B
ddu → uud + β+ + ν
C
uud → ddu + β+ + ν
D
uud → ddu + β+ + ν
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23
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© UCLES 2020
9702/13/M/J/20
24
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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/13/M/J/20
Cambridge International AS & A Level
PHYSICS
9702/12
Paper 1 Multiple Choice
February/March 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*3195679825*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
• There are forty questions on this paper. Answer all questions.
• For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
• Follow the instructions on the multiple choice answer sheet.
• Write in soft pencil.
• Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
• Do not use correction fluid.
• Do not write on any bar codes.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 40.
• Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
• Any rough working should be done on this question paper.
This document has 20 pages. Blank pages are indicated.
IB20 03_9702_12/3RP
© UCLES 2020
[Turn over
2
Data
c = 3.00 × 108 m s–1
speed of light in free space
permeability of free space
µ0 = 4π × 10–7 H m–1
permittivity of free space
ε0 = 8.85 × 10–12 F m–1
(
1
= 8.99 × 109 m F–1)
4πε 0
elementary charge
e = 1.60 × 10–19 C
the Planck constant
h = 6.63 × 10–34 J s
unified atomic mass unit
1 u = 1.66 × 10–27 kg
rest mass of electron
me = 9.11 × 10–31 kg
rest mass of proton
mp = 1.67 × 10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02 × 1023 mol–1
the Boltzmann constant
k = 1.38 × 10–23 J K–1
gravitational constant
G = 6.67 × 10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
9702/12/F/M/20
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = p∆V
gravitational potential
φ = – Gm
r
hydrostatic pressure
p = ρ gh
pressure of an ideal gas
p=
simple harmonic motion
a = – ω 2x
velocity of particle in s.h.m.
v = v0 cos ω t
1
3
Nm <c 2>
V
v = ±ω
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02 − x 2 )
fsv
v ± vs
Q
4 πε 0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(–λt)
decay constant
λ = 0.693
t1
2
© UCLES 2020
9702/12/F/M/20
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4
1
The table shows some measurable quantities.
Which row gives the correct order of magnitude of the measurable quantity in the stated unit?
2
measurable quantity
order of
magnitude
unit
A
mass of a coin
10–4
kg
B
thickness of a sheet of paper
10–2
m
C
weight of an apple
100
N
D
temperature of a person’s body
101
K
A byte (b) comprises 8 bits.
How many bits are there in 1 terabyte (1Tb)?
A
3
4
1 × 109
B
8 × 109
C
1 × 1012
D
8 × 1012
Which pair of quantities contains both a scalar and a vector?
A
acceleration and momentum
B
charge and resistance
C
kinetic energy and mass
D
temperature and velocity
A transmitter emits a pulse of electromagnetic waves towards a reflector. The pulse is reflected
and returns to the transmitter.
A detector is located at the transmitter. The emitted pulse and the reflected pulse are displayed
on a cathode-ray oscilloscope (CRO) as shown.
1 cm
1 cm
The pulse takes 6.3 µs to travel from the transmitter to the reflector.
What is the time-base setting of the CRO?
A
2.1 µs cm–1
© UCLES 2020
B
3.2 µs cm–1
C
4.2 µs cm–1
9702/12/F/M/20
D
6.3 µs cm–1
5
5
A micrometer is used to measure the diameters of two cylinders.
diameter of first cylinder = (12.78 ± 0.02) mm
diameter of second cylinder = (16.24 ± 0.03) mm
The difference in the diameters is calculated.
What is the uncertainty in this difference?
A
6
0.01 mm
B
0.02 mm
C
0.03 mm
D
0.05 mm
A stone is thrown horizontally from the top of a cliff and falls into the sea below. Air resistance is
negligible. The path of the stone is shown.
stone
cliff
sea
In which direction does the resultant force on the stone act during its fall?
7
A
horizontally to the right
B
parallel to its velocity
C
perpendicular to its velocity
D
vertically downwards
A car moves with uniform acceleration along a straight road. Oil leaks from the car at the rate of
one drop every two seconds. The diagram shows the distances between three successive oil
drops on the road.
9.0 m
12.0 m
What is the acceleration of the car?
A
0.75 m s–2
© UCLES 2020
B
1.5 m s–2
C
3.0 m s–2
9702/12/F/M/20
D
6.0 m s–2
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8
A person of mass 60 kg stands on accurate bathroom scales, placed on the floor of an
elevator (lift) which operates in a tall building.
At a certain instant the bathroom scales read 58 kg.
Which row could give the person’s direction of movement and type of motion?
9
direction
motion
A
downwards
constant speed
B
downwards
slowing down
C
upwards
constant speed
D
upwards
slowing down
The diagram shows graphs of various quantities plotted against time for an object dropped from a
stationary balloon high in the atmosphere.
graph 1
graph 2
0
0
time
0
time
0
graph 3
graph 4
0
0
0
time
0
time
Which statement could be correct?
A
Graph 1 is acceleration against time and graph 3 is resultant force against time.
B
Graph 1 is acceleration against time and graph 4 is resultant force against time.
C
Graph 3 is acceleration against time and graph 1 is velocity against time.
D
Graph 3 is acceleration against time and graph 2 is velocity against time.
© UCLES 2020
9702/12/F/M/20
7
10 The diagram shows a particle P, travelling at speed v, about to collide with a stationary particle Q
of the same mass. The collision is perfectly elastic.
v
P
Q
Which statement describes the motion of P and of Q immediately after the collision?
A
P and Q both travel in the same direction with speed
B
P comes to rest and Q acquires speed v.
C
P rebounds with speed
D
P rebounds with speed v and Q remains stationary.
1
v
2
and Q acquires speed
1
v
2
1
v
2
.
.
11 A particle is in a uniform field. The particle experiences a force in the opposite direction to the
field.
In which type of field is the particle, and on which property of the particle is the field acting?
type of field
property of particle
on which the field acts
A
electric
charge
B
electric
current
C
gravitational
mass
D
gravitational
weight
© UCLES 2020
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12 A uniform rod of weight 20 N and length 2.0 m is acted upon by two vertical forces, as shown.
15 N
5.0 N
What are the resultant force acting on the rod and the resultant moment about the centre of
gravity of the rod?
resultant force
/N
resultant moment
/Nm
A
0
10
B
0
20
C
20
10
D
20
20
13 Three coplanar forces act on a block.
Which diagram shows the directions of the forces such that the block could be in equilibrium?
© UCLES 2020
A
B
C
D
9702/12/F/M/20
9
14 A cylinder contains a volume of 0.012 m3 of gas at a pressure of 1.0 × 105 Pa.
400 J of work is done on this gas, with its pressure remaining constant throughout.
What is the final volume of the gas?
A
0.0040 m3
B
0.0080 m3
C
0.016 m3
D
0.020 m3
15 A ball is thrown vertically upwards from the surface of the Earth.
Which statement describes the energy of the ball as it rises through the air?
A
The kinetic energy of the ball decreases as the gravitational potential energy decreases.
B
The kinetic energy of the ball decreases as the gravitational potential energy increases.
C
The kinetic energy of the ball increases as the gravitational potential energy decreases.
D
The total energy of the ball increases.
16 A sledge of mass 50 kg sits on a snowy surface. It is pulled horizontally for 10 m against a
frictional force of 200 N, then it is pulled horizontally across ice for 10 m. There is no friction
between the ice and the sledge. It is lifted up vertically by 1 m and finally carried back at a
constant speed to where it started.
During which stage of its journey is most work done on the sledge?
A
being carried back 20 m at constant speed
B
being lifted up 1 m
C
being pulled 10 m across ice
D
being pulled 10 m across snow
© UCLES 2020
9702/12/F/M/20
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17 An object is moved in a vertical plane from X to Y, and then from Y to Z, as shown in the diagram.
Z
5m
3m
4m
X
4m
3m
V
5m
Y
The distances between various points are indicated on the diagram.
Lines XY and VZ are vertical.
The object weighs 20 N.
How much gravitational potential energy does the object gain by moving from X to Z?
A
60 J
B
120 J
C
140 J
D
260 J
18 A car travels at a constant speed of 25 m s–1 up a slope. The wheels driven by the engine exert a
forward force of 3000 N. The total force due to air resistance and friction is 2100 N. The weight of
the car has a component down the slope of 900 N.
What is the rate at which thermal energy is dissipated?
A
zero
B
2.3 × 104 W
C
5.3 × 104 W
D
7.5 × 104 W
19 A composite rod is made by attaching a glass-reinforced plastic rod and a nylon rod end to end,
as shown.
1.00 m
1.00 m
glass-reinforced plastic
Ep = 40 GPa
nylon
En = 2.0 GPa
The rods have the same cross-sectional area and each rod is 1.00 m in length. The Young
modulus Ep of the plastic is 40 GPa and the Young modulus En of the nylon is 2.0 GPa.
The composite rod will break when its total extension reaches 3.0 mm.
What is the greatest tensile stress that can be applied to the composite rod before it breaks?
A
2.9 × 106 Pa
B
5.7 × 106 Pa
C
2.9 × 109 Pa
D
5.7 × 109 Pa
© UCLES 2020
9702/12/F/M/20
11
20 The graph shows the non-linear force–extension curve for a wire made from a new composite
material.
F/N
P
100
0
0
1.0
2.0
x / mm
What is the best estimate of the work done in stretching the wire to point P?
0.09 J
A
B
0.10 J
C
0.11 J
D
0.20 J
21 A wave of frequency 15 Hz travels at 24 m s–1 through a medium.
What is the phase difference between two points 2.0 m apart?
A
There is no phase difference.
B
They are out of phase by a quarter of a cycle.
C
They are out of phase by half a cycle.
D
They are out of phase by 0.80 of a cycle.
22 Which row describes a longitudinal wave and a medium through which it can travel?
direction of oscillation of the
medium compared with the
direction of propagation
of wave energy
medium
A
parallel
air
B
parallel
vacuum
C
perpendicular
air
D
perpendicular
vacuum
© UCLES 2020
9702/12/F/M/20
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23 A sound wave is displayed on the screen of a cathode-ray oscilloscope, as shown.
The time-base setting is 0.50 ms per division.
What is the frequency of the sound wave?
A
500 Hz
B
670 Hz
C
1000 Hz
D
1300 Hz
24 An observer is situated at the top of a tall tower. An aeroplane emitting sound at a frequency of
1000 Hz approaches the observer at a speed of 165 m s–1.
The speed of sound is 330 m s–1.
What is the frequency of the sound received by the observer?
A
330 Hz
B
667 Hz
C
1000 Hz
D
2000 Hz
25 What is the order of magnitude of the wavelengths of microwaves and X-rays?
wavelength of
microwaves / m
wavelength of
X-rays / m
A
10–6
103
B
10–2
103
C
10–6
10–10
D
10–2
10–10
© UCLES 2020
9702/12/F/M/20
13
26 A musical instrument is made using a long tube with a mouthpiece at one end. The other end is
open and flared, as shown.
A musician maintains stationary sound waves with a node at the mouthpiece and an antinode at
the other end. The lowest frequency of sound that the instrument can produce is 92 Hz.
Which different frequencies of sound can be produced by the instrument?
A
92 Hz, 138 Hz, 184 Hz, 230 Hz
B
92 Hz, 184 Hz, 276 Hz, 368 Hz
C
92 Hz, 276 Hz, 460 Hz, 644 Hz
D
92 Hz, 276 Hz, 828 Hz, 1288 Hz
27 A water wave passes through a gap between two barriers. The wavefronts spread out as shown.
wavefronts
direction
of travel
of wave
barrier
What is the name of this phenomenon?
A
coherence
B
diffraction
C
interference
D
superposition
© UCLES 2020
9702/12/F/M/20
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28 The table shows four possible combinations of values for the laser wavelength, slit separation
and slit-screen distance in a two-slit interference experiment to show the interference of visible
light on a white screen.
Which combination will result in visible fringes being observed?
laser wavelength
/ nm
slit separation
/ mm
slit-screen
distance / m
A
200
0.10
5.0
B
200
100
1.0
C
600
0.10
5.0
D
600
100
1.0
29 Light of wavelength λ is incident normally on a diffraction grating, as shown.
second-order maximum
light of
wavelength λ
ϕ
second-order maximum
diffraction
grating
The angle between the two second-order maxima is ϕ.
Which expression gives the spacing of the lines on the diffraction grating?
A
λ
sinϕ
© UCLES 2020
B
λ
sin (ϕ / 2)
C
2λ
sinϕ
9702/12/F/M/20
D
2λ
sin (ϕ / 2)
15
30 Two positive charges and one negative charge, all of equal magnitude, are set at the corners of
an equilateral triangle.
Which diagram represents the electric field surrounding the charges?
A
B
–
–
+
+
+
+
+
C
D
–
–
+
+
+
31 A negatively charged oil drop is held stationary, equidistant between two plates connected to a
high voltage supply, as shown.
+
oil drop
–
Which change would not increase the upward electrical force on the drop?
A
decreasing the distance between the plates whilst keeping the drop equidistant from them
B
increasing the amount of negative charge on the drop
C
increasing the supply voltage
D
moving the drop closer to the positive plate
© UCLES 2020
9702/12/F/M/20
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16
32 Electrons move in a vacuum from one metal plate to another metal plate. As a result of this, there
is an electric current of 48 µA between the two plates.
How many electrons are emitted by the first plate in a time of 5.0 minutes?
A
1.4 × 104
B
1.5 × 1015
C
1.8 × 1016
D
9.0 × 1016
33 A battery is connected to three resistors of resistances 12 Ω, 6 Ω and 2 Ω, as shown.
3A
12 Ω
2Ω
6Ω
The current from the battery is 3 A.
What is the value of the ratio
A
1
3
B
4
3
power dissipated in the resistor of resistance 6 Ω
?
power dissipated in the resistor of resistance 2 Ω
C
2
1
D
3
1
34 A manufacturer recommends that the longer the extension cord you use with an electric drill, the
bigger the cross-sectional area of the cord should be.
What is a reason for this recommendation?
A
Resistance is inversely proportional to both the length and the cross-sectional area.
B
Resistance is inversely proportional to the length and directly proportional to the
cross-sectional area.
C
Resistance is proportional to both the length and the cross-sectional area.
D
Resistance is proportional to the length and inversely proportional to the cross-sectional
area.
© UCLES 2020
9702/12/F/M/20
17
35 Two batteries are connected together, as shown.
battery 1
12 V
battery 2
9V
0.3 Ω
0.1 Ω
Battery 1 has electromotive force (e.m.f.) 12 V and internal resistance 0.3 Ω.
Battery 2 has e.m.f. 9 V and internal resistance 0.1 Ω.
What are the e.m.f. and the internal resistance of a single battery that has the same effect as the
combination?
e.m.f. / V
internal
resistance / Ω
A
3
0.2
B
3
0.4
C
21
0.2
D
21
0.4
36 The diagram shows a circuit.
6.0 V
0.1 Ω
2.0 Ω
V
What is the reading on the voltmeter?
A
0.3 V
© UCLES 2020
B
5.7 V
C
6.0 V
9702/12/F/M/20
D
6.3 V
[Turn over
18
37 In the circuits shown, the cell has negligible internal resistance.
Which diagram shows a potential divider circuit that can vary the potential difference (p.d.) across
the lamp?
A
B
C
D
38 Two alpha-particles with the same kinetic energy are moving towards, and are then deflected by,
a gold nucleus.
gold nucleus
alpha-particles
Which diagram could show the paths of the two alpha-particles?
© UCLES 2020
A
B
C
D
9702/12/F/M/20
19
39 The equation represents the decay of a nucleus X to a nucleus Y.
A
Z
X →
A
Z −1
Y +p+q
What are particles p and q?
p
q
A
β– particle
neutron
B
β– particle
proton
C
β+ particle
antineutrino
D
β+ particle
neutrino
40 Which row gives the correct type and quark composition for the named particle?
particle
type
quark composition
A
neutron
hadron
uud
key
B
neutron
lepton
udd
u = up quark
C
proton
hadron
uud
d = down quark
D
proton
lepton
udd
© UCLES 2020
9702/12/F/M/20
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/12/F/M/20
Cambridge International AS & A Level
PHYSICS
9702/11
Paper 1 Multiple Choice
October/November 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*2899225506*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
 There are forty questions on this paper. Answer all questions.
 For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
 Follow the instructions on the multiple choice answer sheet.
 Write in soft pencil.
 Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
 Do not use correction fluid.
 Do not write on any bar codes.
 You may use a calculator.
INFORMATION
 The total mark for this paper is 40.
 Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
 Any rough working should be done on this question paper.
This document has 20 pages. Blank pages are indicated.
IB20 11_9702_11/2RP
© UCLES 2020
[Turn over
2
Data
c = 3.00  108 m s–1
speed of light in free space
permeability of free space
0 = 4  10–7 H m–1
permittivity of free space
0 = 8.85  10–12 F m–1
(
1
= 8.99  109 m F–1)
4 0
elementary charge
e = 1.60  10–19 C
the Planck constant
h = 6.63  10–34 J s
unified atomic mass unit
1 u = 1.66  10–27 kg
rest mass of electron
me = 9.11  10–31 kg
rest mass of proton
mp = 1.67  10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02  1023 mol–1
the Boltzmann constant
k = 1.38  10–23 J K–1
gravitational constant
G = 6.67  10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
9702/11/O/N/20
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = pV
gravitational potential
 = – Gm
r
hydrostatic pressure
p =  gh
pressure of an ideal gas
p=
simple harmonic motion
a = –  2x
velocity of particle in s.h.m.
v = v0 cos  t
1
3
Nm <c 2>
V
v = 
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02  x 2 )
fsv
v  vs
Q
4  0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin  t
radioactive decay
x = x0 exp(–t)
decay constant
 = 0.693
t1
2
© UCLES 2020
9702/11/O/N/20
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4
1
2
Which quantity is a physical quantity?
A
atomic number
B
efficiency
C
number density of charge carriers
D
strain
Which time interval is the shortest?
A
3
0.05 ms
B
50 ns
C
500 000 ps
D
0.5 s
P and R are coplanar vectors.
P
R
If X = P – R, which diagram best represents vector X?
A
B
R
R
X
X
P
P
D
C
P
P
X
X
R
© UCLES 2020
R
9702/11/O/N/20
5
4
A student uses a cathode-ray oscilloscope (CRO) to measure the period of a signal. She sets the
time-base of the CRO to 5 ms cm–1 and observes the trace illustrated below. The trace has a
length of 10.0 cm.
10.0 cm
What is the period of the signal?
A
5
7.1  10–6 s
B
1.4  10–5 s
C
7.1  10–3 s
D
1.4  10–2 s
The diameter of a spherical golf ball is measured with calipers and found to be (4.11 ± 0.01) cm.
The volume of a sphere is V =
1
6
d 3, where d is the diameter of the sphere.
What is the volume of the golf ball?
A
(36.35 ± 0.01) cm3
B
(36.35 ± 0.03) cm3
C
(36.35 ± 0.09) cm3
D
(36.4 ± 0.3) cm3
© UCLES 2020
9702/11/O/N/20
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6
6
A student cycles uphill from home to a shop, taking 10 minutes. The student then spends
5 minutes in the shop, before cycling home downhill at twice the initial speed.
Which graph could show the variation with time of the distance travelled by the cyclist?
A
B
2
2
distance
/ km
distance
/ km
1
1
0
0
0
5
10
15
20
time / minutes
0
5
C
D
2
2
distance
/ km
distance
/ km
1
1
0
0
0
7
10
15
20
time / minutes
5
10
15
20
time / minutes
0
5
10
15
20
time / minutes
Two cars X and Y are travelling along the same straight road. Car X is travelling at a constant
speed of 6.0 m s–1. Car Y has a constant acceleration of 0.50 m s–2.
At the instant shown, car X is a distance d ahead of car Y. Car Y is travelling at a speed of
4.0 m s–1.
4.0 m s–1
6.0 m s–1
car Y
car X
d
Car Y is level with car X after a time of 20 seconds.
What is the distance d ?
A
40 m
© UCLES 2020
B
60 m
C
180 m
9702/11/O/N/20
D
300 m
7
8
The graph shows how quantity P varies with quantity Q for an object falling in air for a long time in
a uniform gravitational field.
P
0
Q
0
What could be the identities of P and Q?
9
P
Q
A
force of air resistance
acceleration
B
kinetic energy
time
C
potential energy
height
D
work done against air resistance
speed
A rock R of mass 1.0  1027 kg is a large distance from a star S and is travelling at a speed of
1.0  104 m s–1. The star has mass 1.0  1030 kg. The rock travels around the star on the path
shown so that it reverses its direction of motion and, when finally again a large distance from the
star, has the same speed as initially.
R
speed 1.0 104 m s–1
mass 1.0 1027 kg
X
S
mass 1.0 1030 kg
speed 1.0 104 m s–1
Which statement is correct?
A
The change in the momentum of S is in the direction of arrow X.
B
The change in the velocity of S is approximately 20 m s–1.
C
The magnitude of the change of momentum of R is 103 times greater than the magnitude of
the change of momentum of S.
D
The momentum of R does not change.
© UCLES 2020
9702/11/O/N/20
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8
10 The diagram shows the masses and velocities of two trolleys that are about to collide.
4.0 m s–1
1.0 m s–1
2.0 kg
4.0 kg
After the impact they move off together.
What is the kinetic energy lost in the collision?
A
4J
B
6J
C
12 J
D
14 J
11 A particle is situated at rest between two metal plates X and Y.
A potential difference (p.d.) is then applied across the plates and produces the electric field
shown.
X
Y
particle
electric
field
The particle moves towards plate X when the p.d. is applied.
What could be the particle?
A
alpha-particle
B
electron
C
neutron
D
proton
© UCLES 2020
9702/11/O/N/20
9
12 Two people push a vertical gate to open it. The forces exerted by the people on the gate are
shown.
d2
d1
gate
2
1
hinge
F1
F2
One person is distance d1 from the gate’s hinge and pushes with horizontal force F1 at angle 1 to
the gate.
The other person is at distance d2 from the hinge and pushes with horizontal force F2 at an angle
2 to the gate.
What is the total moment about the hinge due to forces F1 and F2?
A
(d1  F1 cos 1) + (d2  F2 cos 2)
B
(d1  F1 sin 1) + (d2  F2 sin 2)
C
(d1  F1 cos 1) – (d2  F2 cos 2)
D
(d1  F1 sin 1) – (d2  F2 sin 2)
13 A ball is rolling down a slope at a constant speed. The three forces acting on the ball are its
weight, the contact force normal to the slope and friction.
ball
Which diagram could represent these three forces?
A
© UCLES 2020
B
C
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D
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10
14 One end of a U-shaped tube is attached to a gas tap, with its other end open to the atmosphere.
It contains water of density 1000 kg m–3 and the heights of both sides of the water column are
shown.
open to
atmosphere
tube
pressure
from gas tap
31.4 cm
10.2 cm
water,
density 1000 kg m–3
The atmospheric pressure is 101 kPa.
What is the pressure of the gas from the gas tap?
A
99 kPa
B
100 kPa
C
102 kPa
D
103 kPa
15 A trolley runs from P to Q along a track. At Q its potential energy is 50 kJ less than at P.
trolley
P
Q
At P, the kinetic energy of the trolley is 5 kJ. Between P and Q, the trolley does 10 kJ of work
against friction.
What is the kinetic energy of the trolley at Q?
A
35 kJ
© UCLES 2020
B
45 kJ
C
55 kJ
9702/11/O/N/20
D
65 kJ
11
16 A hydroelectric power station uses the gravitational potential energy of water to generate
electrical energy.
In one particular power station, the mass of water flowing per unit time is 1.5  105 kg s–1. The
water falls through a vertical height of 120 m.
The electrical power generated is 100 MW.
What is the efficiency of the power station?
A
5.6%
B
43%
C
57%
D
77%
17 Which amount of energy is not 2400 J?
A
the decrease in gravitational potential energy of a mass of 60 kg when it moves vertically
downwards through 40 m near the Earth’s surface
B
the energy transferred in 15 s by a machine of power 160 W
C
the kinetic energy of a mass of 12 kg moving at a speed of 20 m s–1
D
the work done by a gas expanding against a constant external pressure of 120 kPa when its
volume increases by 0.020 m3
18 A train of mass 300 000 kg is accelerating at 0.80 m s–2. At one instant, the speed of the train is
5.0 m s–1 and the resistive force to its motion is 15 kN.
At this instant, what is the rate of increase of kinetic energy of the train?
A
0.075 MW
B
1.2 MW
C
1.3 MW
D
3.8 MW
19 A wire of circular cross-section, which obeys Hooke’s law, is used to suspend a basket as shown.
wire
basket
The Young modulus for the material of the wire is 2.5  1011 Pa.
When a weight of 34 N is added to the basket, the strain in the wire increases by 6.0  10–5.
What is the radius of the wire?
A
7.2  10–7 m
© UCLES 2020
B
2.3  10–6 m
C
8.5  10–4 m
9702/11/O/N/20
D
1.7  10–3 m
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20 An unstretched rubber cord is stretched by a force. The force F is plotted against the extension x.
F is slowly increased from zero, causing the cord to extend along path P. F is then reduced back
to zero along path Q.
F
P
Q
0
x
0
What is represented by the shaded area?
A
the elastic energy stored in the rubber cord
B
the energy that causes plastic deformation
C
the energy dissipated as heat
D
the work done to extend the rubber cord
21 A guitar string vibrates to create a sound. The speed of the wave in the guitar string is always
440 m s–1. The vibrating string creates a sound wave that moves in the air with a speed of
330 m s–1.
Which graph shows the variation of frequency f with the wavelength  for the waves in the string
and in the air?
A
B
air
f
C
string
f
string
D
f
f
air
air
string
air
0
0
© UCLES 2020
λ
0
0
λ
0
0
9702/11/O/N/20
λ
string
0
0
λ
13
22 The graph shows the variation with time of displacement for two different waves X and Y.
displacement
0
wave Y
0
time
wave X
Wave X has frequency f and amplitude A.
What is the frequency and what is the amplitude of wave Y?
frequency
amplitude
A
1
2
f
1
2
B
1
2
f
2A
C
2f
1
2
D
2f
2A
A
A
23 A loudspeaker emits a sound wave into a tube initially full of water.
loudspeaker
x
tube
y
water
tap
A tap at the bottom of the tube is opened so that water slowly leaves the tube. For some lengths
of the air column in the tube, the sound heard is much louder.
The first loud sound is heard when the air column in the tube has length x.
The next time that a loud sound is heard is when the air column in the tube has length y.
What is the wavelength of the sound wave from the loudspeaker?
A
2x
© UCLES 2020
B
4y
C
2(y – x)
9702/11/O/N/20
D
4(y – x)
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24 A source of sound of frequency 1000 Hz directly approaches a stationary observer. The observer
measures the frequency of the received sound to be 1500 Hz. The speed of sound in still air is
330 m s–1.
What is the speed of the source of sound?
A
110 m s–1
165 m s–1
B
C
220 m s–1
D
330 m s–1
25 The graph shows how the intensity of electromagnetic radiation emitted from a distant star varies
with wavelength.
intensity
0
0
100 200 300 400 500 600 700 800 900 1000
wavelength / nm
In which region of the electromagnetic spectrum is the radiation of greatest intensity?
A
infrared
B
visible light
C
ultraviolet
D
X-ray
26 Which statement concerning a stationary wave is correct?
A
All the particles between two adjacent nodes oscillate in phase.
B
The amplitude of the stationary wave is equal to the amplitude of one of the waves creating it.
C
The wavelength of the stationary wave is equal to the separation of two adjacent nodes.
D
There is no displacement of a particle at an antinode at any time.
27 Which waves would best demonstrate diffraction through a doorway?
A
sound waves
B
ultraviolet waves
C
visible light waves
D
X-rays
© UCLES 2020
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15
28 Two loudspeakers are placed near to each other and facing in the same direction.
A microphone connected to an oscilloscope is moved along a line some distance away from the
loudspeakers, as shown.
path of
microphone
loudspeakers
microphone
Which statement about the waves emitted by the loudspeakers is not a necessary condition for
the microphone to detect a fixed point along the line where there is no sound?
A
The waves must be emitted in phase.
B
The waves must be emitted with a similar amplitude.
C
The waves must have the same frequency.
D
The waves must have the same wavelength.
29 A parallel beam of white light passes through a diffraction grating. Orange light of wavelength
600 nm in the fourth-order diffraction maximum coincides with blue light in the fifth-order
diffraction maximum.
What is the wavelength of the blue light?
A
450 nm
© UCLES 2020
B
480 nm
C
500 nm
9702/11/O/N/20
D
750 nm
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16
30 The diagram shows the electric field near a positively charged sphere and a negatively charged
sphere.
Four electrons A, B, C and D are shown at different positions in the field.
On which electron is the direction of the force on the electron shown correctly?
B
D
–
+
C
A
31 An oil drop has mass m and charge q. The drop is held stationary in an electric field between two
parallel horizontal plates, a distance d apart, as shown.
oil drop
V
d
The potential difference between the plates is V and the acceleration of free fall is g.
What is the charge-to-mass ratio
A
gd
V
© UCLES 2020
B
V
dg
q
of the oil drop?
m
gV
C
d
9702/11/O/N/20
D
d
Vg
17
32 Free electrons flow along a copper wire X of radius 5.0  10–5 m with an average drift speed of
2.8  10–2 m s–1. The current in the wire is 3.0 A.
There is a current of 2.0 A in a copper wire Y of radius 1.0  10–4 m.
What is the average drift speed of the free electrons in copper wire Y?
A
4.7  10–3 m s–1
B
9.3  10–3 m s–1
C
1.1  10–2 m s–1
D
1.9  10–2 m s–1
33 What is the definition of potential difference?
A
power per unit current
B
product of current and resistance
C
product of electric field strength and distance
D
work done per unit charge
34 A cable of length L consisting of two wires is used to connect a 12.0 V power supply of negligible
internal resistance to a lamp, as shown.
L
2.50 A
12.0 V
10.5 V
The potential difference across the lamp is 10.5 V. The current in the wire is 2.50 A.
Each wire is made of metal of resistivity 1.70  10–8  m and has a cross-sectional area of
6.00  10–7 m2.
What is the length L of the cable?
A
10.6 m
© UCLES 2020
B
21.2 m
C
29.4 m
9702/11/O/N/20
D
58.8 m
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18
35 In the circuits shown, the power supply has an electromotive force (e.m.f.) greater than the
normal operating voltage of the lamp. The internal resistance of the power supply is negligible.
The resistance of the variable resistor is adjusted from zero to its maximum value.
In which circuit could the voltage across the lamp change from zero to its normal operating
voltage and not exceed its normal operating voltage?
© UCLES 2020
A
B
C
D
9702/11/O/N/20
19
36 Three identical lamps L1, L2 and L3 are connected to a battery with negligible internal resistance,
as shown.
L1
S
L2
L3
What happens to the brightness of lamps L1 and L2 when the switch S is closed?
lamp L1
lamp L2
A
brighter
brighter
B
brighter
dimmer
C
dimmer
brighter
D
dimmer
dimmer
37 In the circuit shown, the 6.0 V battery has negligible internal resistance. Resistors R1 and R2 and
the voltmeter each have a resistance of 100 k.
6.0 V
R1
R2
100 kΩ
100 kΩ
V
100 kΩ
What is the current in the resistor R2?
A
20 A
B
30 A
C
40 A
D
60 A
38 Which statement about two nuclei that are isotopes of the same element is correct?
A
The nuclei each have the same acceleration when in the same uniform electric field.
B
The nuclei each have the same number of neutrons.
C
The nuclei each have the same number of nucleons.
D
Uncharged atoms containing the nuclei each have the same number of electrons.
© UCLES 2020
9702/11/O/N/20
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32
39 In a nuclear physics experiment, a nucleus of 16
S collides with a nucleus of
combine together and immediately emit a single alpha-particle.
94
42
Mo. The nuclei
The nuclear reaction is shown.
32
16
S +
94
42
Mo  X + 
What is nucleus X?
A
122
56
X
B
124
54
X
C
126
58
X
126
59
D
X
40 Which diagram represents the quark composition of an antineutron?
A
B
key
u
u
u
d
d
d
C
up quark
d
down quark
u
up antiquark
d
down antiquark
D
u
u
d
d
u
d
u
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/11/O/N/20
Cambridge International AS & A Level
PHYSICS
9702/12
Paper 1 Multiple Choice
October/November 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*0407237101*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
 There are forty questions on this paper. Answer all questions.
 For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
 Follow the instructions on the multiple choice answer sheet.
 Write in soft pencil.
 Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
 Do not use correction fluid.
 Do not write on any bar codes.
 You may use a calculator.
INFORMATION
 The total mark for this paper is 40.
 Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
 Any rough working should be done on this question paper.
This document has 24 pages. Blank pages are indicated.
IB20 11_9702_12/3RP
© UCLES 2020
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2
Data
c = 3.00  108 m s–1
speed of light in free space
permeability of free space
0 = 4  10–7 H m–1
permittivity of free space
0 = 8.85  10–12 F m–1
(
1
= 8.99  109 m F–1)
4 0
elementary charge
e = 1.60  10–19 C
the Planck constant
h = 6.63  10–34 J s
unified atomic mass unit
1 u = 1.66  10–27 kg
rest mass of electron
me = 9.11  10–31 kg
rest mass of proton
mp = 1.67  10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02  1023 mol–1
the Boltzmann constant
k = 1.38  10–23 J K–1
gravitational constant
G = 6.67  10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
9702/12/O/N/20
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = pV
gravitational potential
 = – Gm
r
hydrostatic pressure
p =  gh
pressure of an ideal gas
p=
simple harmonic motion
a = –  2x
velocity of particle in s.h.m.
v = v0 cos  t
1
3
Nm <c 2>
V
v = 
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02  x 2 )
fsv
v  vs
Q
4  0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin  t
radioactive decay
x = x0 exp(–t)
decay constant
 = 0.693
t1
2
© UCLES 2020
9702/12/O/N/20
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1
A student uses the volume of a metal coin in order to determine the density of the metal.
What is not needed in order to determine an estimate of the volume of the coin?
2
A
estimate of the diameter
B
estimate of the mass
C
estimate of the thickness
D
use of the formula for the volume of a cylinder
The speed v of waves on a stretched wire is given by the equation
v = T pq
where T is the tension in the wire and  is the mass per unit length of the wire.
What are the values of p and q?
p
q
A
1
2
1
2
B
1
2
1
2
C
1
2
1
2
D
1
2
1
2
© UCLES 2020
9702/12/O/N/20
5
3
The diagram shows a force F. P is the horizontal component of F, at an angle  to F.
F
θ
P
Which graph best shows the variation with  of the magnitude of P ?
A
B
P
P
0
0
0
θ /°
90
0
C
90
D
P
P
0
0
0
4
θ /°
θ /°
90
0
θ /°
90
A student wishes to measure a distance of about 10 cm to a precision of 0.01 cm.
Which measuring instrument should be used?
A
metre rule
B
micrometer
C
tape measure
D
vernier calipers
© UCLES 2020
9702/12/O/N/20
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5
A steel ball is dropped and falls through a vertical height h. The time t taken to fall is measured
using light gates.
The results are given in the table.
h
(4.05  0.01) m
t
(0.91  0.02) s
The acceleration of free fall g is calculated using the equation shown.
h=
1
2
gt 2
What is the percentage uncertainty in the value of g?
A
6
2.4%
B
4.6%
C
5.1%
D
9.3%
A stone is thrown vertically upwards from a point X at time t ꞊ 0.
The variation with time t of the velocity v of the stone is shown.
v / m s–1
20
10
0
0
1.0
2.0
3.0
–10
What is the displacement of the stone from point X at time t ꞊ 3.0 s?
A
15 m above X
B
15 m below X
C
25 m above X
D
25 m below X
© UCLES 2020
9702/12/O/N/20
t/s
7
7
A mass of 5.0 kg is released from rest on a frictionless surface inclined at 30 to the horizontal. Air
resistance is negligible.
mass 5.0 kg
frictionless
surface
30°
horizontal
How far does the mass travel in a time of 0.80 s?
A
8
1.6 m
B
2.0 m
C
2.7 m
D
3.1 m
What is not a statement of one of Newton’s laws of motion?
A
If body X exerts a force on body Y, body Y exerts an equal and opposite force on body X.
B
If no resultant force acts on a body it has constant velocity.
C
The rate of change of momentum of a body is proportional to the resultant force acting on it
and takes place in the direction of the force.
D
The total momentum of a system of interacting bodies is constant if there is no external force.
© UCLES 2020
9702/12/O/N/20
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8
9
An object falls from a tall building.
The graph shows how the velocity of the object changes with time t.
velocity
0
0
Y
Z
t
The acceleration of free fall is g.
What describes the acceleration of the object at times t = Y and t = Z?
acceleration
at t = Y
acceleration
at t = Z
A
decreasing
g
B
decreasing
0
C
constant
g
D
constant
0
10 Two balls, one of mass 2m and one of mass m, collide.
The diagrams show the initial and final velocities of the balls.
Which collision is not elastic?
before collision
2m
A
2m
B
2m
C
2m
D
© UCLES 2020
4.0 m s–1
6.0 m s–1
8.0 m s–1
10.0 m s–1
m
m
m
m
1.0 m s–1
3.0 m s–1
2.0 m s–1
4.0 m s–1
after collision
2m
2m
2m
2m
9702/12/O/N/20
2.0 m s–1
4.0 m s–1
5.0 m s–1
6.0 m s–1
m
m
m
m
5.0 m s–1
7.0 m s–1
8.0 m s–1
12.0 m s–1
9
11 The diagram shows a ‘ballistic pendulum’.
block
pellet
m
M
A pellet of mass m travelling at a speed u hits a stationary block of mass M. The pellet becomes
embedded in the block and causes the block to move at a speed v immediately after the impact.
When a pellet of mass 2m, travelling at a speed 2u, hits a block of mass 2M, what is the speed of
the block immediately after the impact? (Neglect the small increase in the mass of the block as
the pellet’s mass is added during the collision.)
A
v
B
v 2
C
2v
D
4v
12 A rigid circular disc of radius r has its centre at X. A number of forces of equal magnitude F act at
the edge of the disc. All the forces are in the plane of the disc.
Which arrangement of forces provides a total moment of magnitude 2Fr about X?
F
A
B
X
X
F
F
C
D
F
X
X
F
F
© UCLES 2020
F
F
9702/12/O/N/20
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10
13 The diagram shows a uniform beam PQ. The length of the beam is 3.0 m and its weight is 50 N.
The beam is supported on a pivot 1.0 m from end P. A load of weight W is hung from end P. The
beam is in equilibrium.
3.0 m
1.0 m
P
Q
W
pivot
What is the value of W ?
A
25 N
B
50 N
C
75 N
D
100 N
14 In a high-wire circus act, a man of mass 85 kg is standing at rest at the midpoint of the wire.
20°
20°
T
T
The wire on either side of the man is at an angle of 20 to the horizontal.
What is the tension T in the wire?
A
0.44 kN
B
0.89 kN
C
1.2 kN
D
2.4 kN
15 A cylindrical block of ice of cross-sectional area 12 m2 is floating, partially submerged, in the sea.
The density of the sea water is 1020 kg m–3. A polar bear of mass 400 kg steps onto the block of
ice.
bear,
mass 400 kg
cross-sectional
area 12 m2
sea water,
density 1020 kg m–3
The block of ice sinks a vertical distance d.
What is the value of d ?
A
3.3 mm
© UCLES 2020
B
3.3 cm
C
0.32 m
9702/12/O/N/20
D
3.1 m
11
16 A ball is thrown vertically upwards. Air resistance is negligible.
Which statement is correct?
A
By the principle of conservation of energy, the total energy of the ball is constant throughout
its motion.
B
By the principle of conservation of momentum, the momentum of the ball is constant
throughout its motion.
C
The kinetic energy of the ball is greatest at the greatest height attained.
D
The potential energy of the ball increases at a constant rate during its ascent.
17 A hammer with 10 J of kinetic energy hits a nail and pushes it 5.0 mm into a plank.
Both the hammer and nail come to rest after the collision.
What is the approximate average force that acts on the nail while it moves through 5.0 mm?
A
0.050 N
B
2.0 N
C
50 N
D
2000 N
18 The change in gravitational potential energy ∆E of an object of mass m when moving through
height ∆h near the surface of the Earth is given by the equation shown.
∆E = mg∆h
Which equation is needed as part of the derivation of this expression?
 mass  (speed)2
A
kinetic energy =
B
moment = force  distance
C
weight = mass  acceleration of free fall
D
work done = power  time
1
2
19 A racing car has an output power of 300 kW when travelling at a constant speed of 60 m s–1.
What is the total resistive force acting on the car?
A
5 kN
B
10 kN
C
50 kN
D
100 kN
20 A mass of 60.0 g is suspended from a spring and the distance from the bottom of the spring to the
floor is measured to be 16.4 cm.
The mass is replaced with a 100.0 g mass and the distance from the bottom of the spring to the
floor is now measured to be 12.6 cm. The spring obeys Hooke’s law.
What is the spring constant of the spring?
A
1.05 N m–1
© UCLES 2020
B
1.35 N m–1
C
10.3 N m–1
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D
103 N m–1
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12
21 The graph shows the force–extension graph for a wire.
100
force / N
80
60
40
20
0
0
1.0
2.0
3.0
4.0
5.0
extension / 10–3 m
The wire is already extended by a force of 60 N.
How much work is done to increase the extension of the wire by 2.0 mm?
A
0.040 J
B
0.090 J
C
0.16 J
D
0.25 J
22 The speed v of waves in deep water is given by the equation
v2 =
g
2
where  is the wavelength of the waves and g is the acceleration of free fall.
A student measures the wavelength  and the frequency f of a number of these waves.
Which graph should he plot to give a straight line through the origin?
A
f 2 against 
B
f against 2
C
f against 1
D
f 2 against 1

© UCLES 2020

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13
23 When sound travels through air, the air particles vibrate. A graph of displacement against time for
a single air particle is shown.
displacement
0
0
T
2T
time
Which graph shows how the kinetic energy of the air particle varies with time?
A
B
kinetic
energy
kinetic
energy
0
0
T
2T
0
0
time
T
C
time
D
kinetic
energy
kinetic
energy
0
0
© UCLES 2020
2T
T
2T
time
9702/12/O/N/20
0
0
T
2T
time
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24 A vibrating tuning fork is held above a glass cylinder filled to the top with water. The water level is
steadily lowered. A loud sound is first heard when the water level is 83.5 cm above the bench.
The next loud sound is heard when the water level is 17.1 cm above the bench.
tuning fork
NOT TO
SCALE
cylinder
water
83.5 cm
water
bench
17.1 cm
The speed of sound in air is 340 m s–1.
What is the frequency of the tuning fork?
A
128 Hz
© UCLES 2020
B
256 Hz
C
384 Hz
9702/12/O/N/20
D
512 Hz
15
25 An emergency vehicle sounds its siren as it accelerates along a straight road between two points
X and Y, as shown in the diagram.
direction of travel
X
Y
emergency
vehicle
road
The frequency of the sound emitted by the siren is 750 Hz.
A person stands at X and another person stands at Y.
What describes the sounds heard by the people at X and at Y as the vehicle accelerates?
sound heard by person at X
sound heard by person at Y
A
higher than 750 Hz,
increasing in frequency
lower than 750 Hz,
decreasing in frequency
B
higher than 750 Hz,
decreasing in frequency
lower than 750 Hz,
increasing in frequency
C
lower than 750 Hz,
decreasing in frequency
higher than 750 Hz,
increasing in frequency
D
lower than 750 Hz,
increasing in frequency
higher than 750 Hz,
decreasing in frequency
26 Part of the electromagnetic spectrum is shown.
increasing frequency
visible
light
What is the name of the shaded region and what is the order of magnitude of a wavelength of a
wave from this region?
name
wavelength
/m
A
infrared
10–5
B
infrared
10–8
C
ultraviolet
10–5
D
ultraviolet
10–8
© UCLES 2020
9702/12/O/N/20
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16
27 The three waves shown in each diagram have the same amplitude and frequency but different
phase.
They are added together to give a resultant wave.
In which case is the resultant wave zero at this instant?
A
B
C
D
28 A transmitting mast sends out microwaves of wavelength 1.5 cm and radio waves of wavelength
1.5 km.
mountain
receiving
aerial
transmitting
mast
NOT TO SCALE
A receiving aerial behind a mountain can detect the radio waves but not the microwaves.
What is the reason for this?
A
The radio waves are coherent but the microwaves are not.
B
The radio waves are diffracted around the mountain but the microwaves are not.
C
The radio waves are reflected by the mountain but the microwaves are not.
D
The radio waves travel at the speed of light but the microwaves do not.
© UCLES 2020
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17
29 An experiment is carried out to demonstrate double-slit interference using light of wavelength
500 nm. The distance between bright fringes in the interference pattern is 5 mm.
What are possible values for the distance between the slits and the screen, and the slit
separation?
slit–screen
distance
slit separation
A
50 cm
0.5 mm
B
50 cm
5 mm
C
5m
0.5 mm
D
5m
5 mm
30 Light of a single frequency is incident on a diffraction grating. Seven bright spots are observed on
a screen.
Which change will result in an increase in the number of bright spots observed?
A
Increase the distance between the grating and the screen.
B
Increase the frequency of the incident light.
C
Increase the intensity of the incident light.
D
Increase the number of lines per metre in the grating.
© UCLES 2020
9702/12/O/N/20
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31 A molecule behaves as an electric ‘dipole’ consisting of two equal point charges of opposite sign,
separated by a fixed distance. The molecule moves with constant horizontal velocity as it enters a
vertical uniform electric field, as shown.
–
+
molecule
electric field
The positive and negative charges of the molecule enter the field at the same time.
What describes the effect of the electric field on the velocity of the molecule?
horizontal component
of velocity
vertical component
of velocity
A
constant
increases
B
constant
zero
C
increases
increases
D
increases
zero
32 Two parallel metal plates are connected to a battery of negligible internal resistance.
metal plates
One of the plates is slowly moved towards the other.
Which row is correct?
electric field strength
between the plates
potential difference
between the plates
A
decreases
constant
B
increases
constant
C
decreases
increases
D
increases
increases
© UCLES 2020
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19
33 Four point charges, each of charge Q, are placed on the edge of an insulating disc of radius r.
The disc rotates at a rate of n revolutions per unit time.
Q
r
Q
Q
Q
What is the equivalent electric current at the edge of the disc?
A
4Qn
B
4Q
n
C
8rQn
D
2Qn
πr
34 In the circuit shown, a fixed resistor X is connected in series with a battery and a variable resistor.
X
The power dissipated in resistor X is 7.2 W when a current of 3.0 A passes through it.
The variable resistor is adjusted so that the power dissipated in X increases by 50%.
What is the new current in the circuit?
A
2.4 A
© UCLES 2020
B
3.7 A
C
4.5 A
9702/12/O/N/20
D
14 A
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20
35 A resistor and a filament lamp are connected in series with a power supply. The I–V
characteristics of the resistor and of the lamp are shown below.
resistor
filament lamp
0.4
0.4
I/A
I/A
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
1
2
3
4
5
0
1
V/V
2
3
4
5
V/V
The potential difference (p.d.) across the resistor is 3.3 V.
What is the resistance of the lamp?
A
0.071 
B
4.2 
C
11 
D
14 
36 A car battery has an electromotive force (e.m.f.) of 12 V and an internal resistance of 0.05 . The
battery is connected to the starter motor of a car. The current in the motor is 160 A.
12 V
0.05 Ω
160 A
M
What is the terminal p.d. across the battery?
A
0V
© UCLES 2020
B
4V
C
8V
9702/12/O/N/20
D
12 V
21
37 A cell of negligible internal resistance is connected to a network of resistors and a voltmeter, as
shown.
R
3.00 Ω
14.4 Ω
V
2.00 Ω
4.80 Ω
The reading on the voltmeter is zero.
What is the resistance of resistor R?
1.20 
A
B
1.80 
C
7.20 
D
14.4 
38 A voltmeter is connected into a circuit with the polarity shown in the diagram.
Q
+
3V
–
V
3V
P
The sliding contact is moved to end P of the potentiometer and then to end Q.
What are the two readings of the voltmeter?
sliding contact
at end P
sliding contact
at end Q
A
0V
3V
B
0V
6V
C
3V
3V
D
3V
6V
© UCLES 2020
9702/12/O/N/20
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39 What is a conclusion from the alpha-particle scattering experiment?
A
Protons and electrons have equal but opposite charges.
B
Protons have a much larger mass than electrons.
C
The nucleus contains most of the mass of the atom.
D
The nucleus of an atom contains protons and neutrons.
40 Which particle is a hadron?
A
electron
B
neutrino
C
positron
D
proton
© UCLES 2020
9702/12/O/N/20
23
BLANK PAGE
© UCLES 2020
9702/12/O/N/20
24
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/12/O/N/20
Cambridge International AS & A Level
PHYSICS
9702/13
Paper 1 Multiple Choice
October/November 2020
1 hour 15 minutes
You must answer on the multiple choice answer sheet.
*0089266406*
You will need: Multiple choice answer sheet
Soft clean eraser
Soft pencil (type B or HB is recommended)
INSTRUCTIONS
 There are forty questions on this paper. Answer all questions.
 For each question there are four possible answers A, B, C and D. Choose the one you consider correct
and record your choice in soft pencil on the multiple choice answer sheet.
 Follow the instructions on the multiple choice answer sheet.
 Write in soft pencil.
 Write your name, centre number and candidate number on the multiple choice answer sheet in the
spaces provided unless this has been done for you.
 Do not use correction fluid.
 Do not write on any bar codes.
 You may use a calculator.
INFORMATION
 The total mark for this paper is 40.
 Each correct answer will score one mark. A mark will not be deducted for a wrong answer.
 Any rough working should be done on this question paper.
This document has 20 pages. Blank pages are indicated.
IB20 11_9702_13/3RP
© UCLES 2020
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2
Data
c = 3.00  108 m s–1
speed of light in free space
permeability of free space
0 = 4  10–7 H m–1
permittivity of free space
0 = 8.85  10–12 F m–1
(
1
= 8.99  109 m F–1)
4 0
elementary charge
e = 1.60  10–19 C
the Planck constant
h = 6.63  10–34 J s
unified atomic mass unit
1 u = 1.66  10–27 kg
rest mass of electron
me = 9.11  10–31 kg
rest mass of proton
mp = 1.67  10–27 kg
molar gas constant
R = 8.31 J K–1 mol–1
the Avogadro constant
NA = 6.02  1023 mol–1
the Boltzmann constant
k = 1.38  10–23 J K–1
gravitational constant
G = 6.67  10–11 N m2 kg–2
acceleration of free fall
g = 9.81 m s–2
© UCLES 2020
9702/13/O/N/20
3
Formulae
uniformly accelerated motion
s = ut +
1
at 2
2
v 2 = u 2 + 2as
work done on/by a gas
W = pV
gravitational potential
 = – Gm
r
hydrostatic pressure
p =  gh
pressure of an ideal gas
p=
simple harmonic motion
a = –  2x
velocity of particle in s.h.m.
v = v0 cos  t
1
3
Nm <c 2>
V
v = 
Doppler effect
fo =
electric potential
V=
capacitors in series
( x 02  x 2 )
fsv
v  vs
Q
4  0r
1 / C = 1 / C1 + 1 / C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1 / R = 1 / R1 + 1 / R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin  t
radioactive decay
x = x0 exp(–t)
decay constant
 = 0.693
t1
2
© UCLES 2020
9702/13/O/N/20
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4
1
What is a reasonable estimate of the volume of a fully inflated standard football?
A
2
3
4
600 cm3
B
6000 cm3
C
60 000 cm3
D
600 000 cm3
What is not an SI base unit?
A
coulomb
B
kelvin
C
kilogram
D
second
Which two quantities are both vector quantities?
A
displacement and distance
B
force and momentum
C
torque and time
D
weight and pressure
A calibration curve is shown for an ammeter whose scale is inaccurate.
0.6
ammeter
reading
/ mA
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
current / mA
Two readings taken on the meter at different times during an experiment are 0.13 mA and
0.47 mA.
By how much did the current really increase between taking the two readings?
A
0.30 mA
© UCLES 2020
B
0.34 mA
C
0.40 mA
9702/13/O/N/20
D
0.44 mA
5
5
A student measures the length l and the period T of oscillation of a simple pendulum. He then
uses the equation shown to calculate the acceleration of free fall g.
T = 2
l
g
His measurements are shown.
l
(87.3  0.2) cm
T
(1.9  0.05) s
What is the percentage uncertainty in his calculated value of g ?
A
6
2.4%
B
2.9%
C
5.5%
D
7.2%
An object moves in a straight line. The graph shows the variation with time t of the velocity v of
the object.
8
v/ms
–1
6
4
2
0
0
0.2
0.4
0.6
–2
0.8 1.0
t/s
At time t = 0 the object is at point X.
What is the displacement of the object from point X at time t = 0.80 s?
A
7
1.6 m
B
1.8 m
C
2.0 m
D
3.2 m
An object accelerates uniformly from rest to speed v. It then moves at constant speed v for a time
of 8.0 s before decelerating uniformly to rest. The total time taken is 12.0 s, and the total distance
travelled is 60 m.
What is the speed v ?
A
3.0 m s–1
© UCLES 2020
B
5.0 m s–1
C
6.0 m s–1
9702/13/O/N/20
D
15 m s–1
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6
8
A device for spraying paint consists of a box with its axes horizontal and vertical. One of its
vertical faces contains small holes. Paint is fed into the box under pressure via a vertical tube and
exits through the holes as fine streams moving horizontally.
paint in
paint out through holes
(only a few holes are shown)
The paint is ejected at a speed of 2.5 m s–1 through 400 holes, each of area 0.4 mm2. The density
of the paint is 900 kg m–3.
What is the horizontal force required to hold the device stationary as it ejects the paint?
A
9
0.36 N
B
0.90 N
C
2.3 N
D
900 N
A party balloon is filled with air and held stationary at a height of several metres above the
ground. The balloon is then dropped in still air.
Which statement describes the motion of the balloon from the moment of release until just before
it hits the floor?
A
The balloon decelerates continuously.
B
The balloon falls at a constant speed and then decelerates.
C
The balloon falls at a constant speed.
D
The balloon initially accelerates and then reaches a constant speed.
10 An object of mass m travelling with speed 5u collides with, and sticks to, an object of mass 5m
travelling in the same direction with speed u.
5u
u
m
5m
What is the speed with which the two objects travel together in the original direction?
A
3 u
10
© UCLES 2020
B
u
C
6u
5
9702/13/O/N/20
D
10 u
6
7
11 An air bubble is rising through a liquid at a constant speed. The forces on it are the upthrust U,
the viscous drag V and its weight W.
Which diagram shows the directions and relative sizes of the forces?
A
B
U
C
U
D
U
U
V
W
W
V
V
V
W
W
12 A couple applies a clockwise torque of 9.0 N m to a circular disc.
Which diagram shows this couple?
A
B
9.0 N
45 N
50 cm
20 cm
9.0 N
45 N
D
C
45 N
9.0 N
10 cm
100 cm
45 N
© UCLES 2020
9.0 N
9702/13/O/N/20
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13 A shelf PQ is attached to a vertical wall at P and supports a book.
The shelf is held horizontal by a rigid bar XY, as shown.
book
wall
shelf
P
Y
Q
θ
F
bar
X
Ws
Wb
The weight of the shelf is Ws and the weight of the book is Wb.
The bar is at an angle  to the shelf and exerts a force F on the shelf.
The shelf is in equilibrium.
What are the magnitudes of the horizontal and the vertical components of the force of the wall on
the shelf at P?
horizontal component
vertical component
A
F cos 
(Ws + Wb – F cos  )
B
F cos 
(Ws + Wb – F sin  )
C
F sin 
(Ws + Wb – F cos  )
D
F sin 
(Ws + Wb – F sin  )
© UCLES 2020
9702/13/O/N/20
9
14 A glider is descending at constant speed at an angle of 15 to the horizontal. The diagram shows
the directions of the lift L, air resistance R and weight W acting on the glider.
L
R
15°
W
Which vector triangle could represent the forces acting on the glider?
A
B
C
D
15 A solid cylinder of density  C, cross-sectional area A and length X is submerged in a liquid of
density  L. The upper face of the cylinder is at a depth H below the surface of the liquid, as
shown.
surface of liquid
H
cross-sectional area A
X
cylinder
The acceleration of free fall is g.
Which expression gives the magnitude of the upthrust force acting on the cylinder?
A
 CAHg
© UCLES 2020
B
 CAXg
C
 LAHg
9702/13/O/N/20
D
 LAXg
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16 A ball drops onto a horizontal surface and bounces elastically.
What happens to the kinetic energy of the ball during the very short time that it is in contact with
the surface?
A
Most of the kinetic energy is lost as heat and sound.
B
The kinetic energy decreases to zero and then returns to its original value.
C
The kinetic energy remains constant because it is an elastic collision.
D
The kinetic energy remains constant in magnitude but changes direction.
17 Some gas in a cylinder is supplied with thermal energy q.
The gas does useful work in expanding at constant pressure p from volume V0 to volume VF, as
shown.
volume V0
gas
pressure p
volume VF
Which expression gives the efficiency of this process?
A
pV0
q
B
VF
V0 q
C
p(VF  V0 )
q
D
(VF  V0 )
V0 q
18 An object of mass 0.30 kg is thrown vertically upwards from the ground with an initial velocity of
8.0 m s–1. The object reaches a maximum height of 1.9 m.
How much work is done against air resistance as the object rises to its maximum height?
A
4.0 J
B
5.6 J
C
9.6 J
D
15 J
19 A water pump raises a mass of 27  103 kg of water through a vertical distance of 80 m in a time
of 1.0 hour.
What is the average useful output power of the pump?
A
0.60 kW
© UCLES 2020
B
5.9 kW
C
36 kW
9702/13/O/N/20
D
350 kW
11
20 A platform is suspended by four steel wires. Each wire is 5.0 m long and has a diameter of
3.0 mm. The Young modulus of steel is 2.1  1011 Pa.
steel wires
steel wires
200
kg
platform
The wires obey Hooke’s law when a load of mass 200 kg is placed on the platform.
How far will the platform descend because of the extension of the wires?
A
1.7  10–4 m
B
4.1  10–4 m
C
1.7  10–3 m
D
6.6  10–3 m
21 A tensile force of 7.00 MN is applied to a sample of steel. This causes the sample to extend by
5.00 mm in the direction of the force. The sample obeys Hooke’s law.
What is the work done to extend the sample?
A
17.5 J
B
35.0 J
C
17.5 kJ
D
35.0 kJ
22 Two waves X and Y have the same frequency. The amplitude of X is 1.5A0 and the amplitude of
Y is 2.5A0. The waves meet at a point and superpose to form a resultant wave.
For the resultant wave, what is the ratio
A
1.7
© UCLES 2020
B
2.8
maximum possible intensity
minimum possible intensity
C
4.0
9702/13/O/N/20
D
?
16
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23 The displacement–time graph for an air particle in the path of a sound wave is shown.
displacement
0
time
0
Which property of the sound wave must be increasing?
A
amplitude
B
frequency
C
period
D
speed
24 A sound wave is displayed on the screen of a cathode-ray oscilloscope (CRO) as shown.
1 cm
1 cm
The time-base of the CRO is set at 2.5 ms cm–1.
What is the frequency of the sound wave?
A
50 Hz
B
100 Hz
C
200 Hz
D
400 Hz
25 The horn of a train emits sound of frequency f1. While the horn is sounding, the train moves
directly towards a stationary person. The speed of the train is 0.20v, where v is the speed of
sound.
The frequency of the sound heard by the person is f2.
What is the ratio
A
0.80
1
© UCLES 2020
f1
?
f2
B
1
1.2
C
1.2
1
9702/13/O/N/20
D
1
0.80
13
26 Two satellites in orbit around the Earth are at a constant distance of 100 km apart from each
other.
Satellite X transmits a microwave pulse towards satellite Y. The pulse takes time T to reach Y.
Satellite Y then transmits a pulse of visible light towards satellite X.
What is the time taken for the pulse of light to reach X?
A
10–5 T
B
10–3 T
C
10–2 T
D
T
27 A stationary wave is formed on a stretched string. The diagram illustrates the string at an instant
of time when the displacement of the string is at its maximum.
string
fixed
point
fixed
point
P
The frequency of the wave is 250 Hz. Point P on the string has a vertical displacement of –1.0 mm.
What will be the vertical displacement of the point P after a time of 5.0 ms?
A
–1.0 mm
B
zero
C
+0.5 mm
D
+1.0 mm
28 What is meant by diffraction?
A
the change in observed frequency when a wave source moves relative to an observer
B
the formation of nodes and antinodes by two progressive waves travelling in opposite
directions
C
the spreading of a wave around the edge of an obstacle
D
the superposition of two waves when they meet
29 In a dark room, a small source of red light illuminates two slits that are 0.75 mm apart. A few
metres beyond the slits, the light falls on a screen producing a series of equally spaced bright
lines.
Which change would cause the distance between the bright lines on the screen to be reduced?
A
Change the source for one emitting blue light.
B
Reduce the distance between the light source and the slits.
C
Reduce the distance between the slits to 0.55 mm.
D
Reduce the intensity of the light source.
© UCLES 2020
9702/13/O/N/20
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14
30 Light of wavelength 5.30  10–7 m is incident normally on a diffraction grating. The first-order
maximum is observed at an angle of 15.4 to the direction of the incident light.
What is the angle between the first-order and second-order diffraction maxima?
A
7.7
B
15.4
C
16.7
D
32.1
31 A stationary particle is in an electric field.
The only force on the particle is that from the electric field.
In which case is the electric field strength 5.0  105 V m–1?
A
a force of 1.6  10–14 N acting on an electron
B
a force of 3.2  10–14 N acting on an alpha-particle
C
a force of 8.0  10–14 N acting on an alpha-particle
D
a force of 8.0  10–14 N acting on a proton
32 A constant potential difference is applied between two horizontal metal plates. A charged oil
droplet is held stationary by the electric field between the plates.
horizontal
metal plates
charged
oil droplet
As some of the oil evaporates, the droplet loses mass and starts to accelerate. Its charge
remains constant.
In which direction does the droplet accelerate, and which change needs to be made to the
separation of the plates in order to stop this acceleration?
direction of
acceleration
separation
of the plates
A
downwards
decrease
B
downwards
increase
C
upwards
decrease
D
upwards
increase
© UCLES 2020
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15
33 Two resistors R1 and R2 are made from wire of the same material.
They are connected in parallel to each other in a circuit, as shown.
R1
R2
The diameter of R2 is half the diameter of R1.
The resistance of R2 is three times the resistance of R1.
What is the value of the ratio
A
3
2
B
average drift speed of free electrons in R1
?
average drift speed of free electrons in R 2
3
4
1
6
C
D
1
12
34 A student describes potential difference as the energy transferred per unit charge.
Which statement about the energy transfer is correct?
A
It is from electrical energy into other forms.
B
It is from other forms into electrical energy.
C
It only takes place inside a power supply.
D
It only takes place inside resistors.
35 A metal cube has a resistance of 4.0  between opposite faces.
Ten of these cubes are put together to make a cuboid of 1  2  5 cubes.
X
Y
There is no extra resistance where the faces of the cubes touch each other.
What is the resistance of the cuboid when connected between faces X and Y?
A
1.6 
© UCLES 2020
B
2.0 
C
10 
9702/13/O/N/20
D
40 
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16
36 A cell is connected to a fixed resistor. Over a long period of time, the internal resistance of the
cell increases.
What is the effect of the increase in internal resistance on the electromotive force (e.m.f.) of the
cell and on the power dissipated by the fixed resistor?
e.m.f.
power dissipated
A
decreases
decreases
B
decreases
no change
C
no change
decreases
D
no change
no change
37 Four identical resistors are connected in a circuit, as shown.
30 V
X
Y
The battery has negligible internal resistance and an e.m.f. of 30 V.
What is the potential difference between the two points X and Y?
A
6.0 V
© UCLES 2020
B
15 V
C
20 V
9702/13/O/N/20
D
24 V
17
38 A power supply and a solar cell are compared using the potentiometer circuit shown.
power supply
2.000 V
–
+
P
R
S
Q
40.0 cm
galvanometer
solar cell
The potentiometer wire PQ is 100.0 cm long and has a resistance of 5.00 . The power supply
has an e.m.f. of 2.000 V and the solar cell has an e.m.f. of 5.00 mV.
Which resistance R must be used so that the galvanometer reads zero when PS = 40.0 cm?
A
395 
B
405 
C
795 
D
805 
39 The table contains data for four different nuclei P, Q, R and S.
nucleus
number
of neutrons
nucleon
number
P
5
10
Q
6
10
R
6
14
S
8
16
Which two nuclei are isotopes of the same element?
A
P and Q
B
P and S
C
Q and R
40 Which particle is a fundamental particle?
A
alpha-particle
B
electron
C
neutron
D
proton
© UCLES 2020
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D
R and S
18
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© UCLES 2020
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19
BLANK PAGE
© UCLES 2020
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20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/13/O/N/20
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
* 0 0 6 7 7 0 7 4 9 1 *
9702/22
PHYSICS
May/June 2018
Paper 2 AS Level Structured Questions
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 14 printed pages and 2 blank pages.
DC (NH/CGW) 143985/2
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
9702/22/M/J/18
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
⟨c ⟩
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/22/M/J/18
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4
Answer all the questions in the spaces provided.
1
(a) Define force.
...............................................................................................................................................[1]
(b) State the SI base units of force.
...............................................................................................................................................[1]
(c) The force F between two point charges is given by
F=
Q1Q2
4πr 2ε
where Q1 and Q2 are the charges,
r is the distance between the charges,
ε is a constant that depends on the medium between the charges.
Use the above expression to determine the base units of ε.
base units ...........................................................[2]
[Total: 4]
© UCLES 2018
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5
2
(a) State the principle of conservation of momentum.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) A stationary firework explodes into three different fragments that move in a horizontal plane,
as illustrated in Fig. 2.1.
7.0 m s–1
3.0M
A
2.0M
θ
θ
6.0 m s–1
B
1.5M
8.0 m s–1
Fig. 2.1
The fragment of mass 3.0M has a velocity of 7.0 m s–1 perpendicular to line AB.
The fragment of mass 2.0M has a velocity of 6.0 m s–1 at angle θ to line AB.
The fragment of mass 1.5M has a velocity of 8.0 m s–1 at angle θ to line AB.
(i)
Use the principle of conservation of momentum to determine θ.
θ = ........................................................ ° [3]
(ii)
Calculate the ratio
kinetic energy of fragment of mass 2.0M .
kinetic energy of fragment of mass 1.5M
ratio = ...........................................................[2]
[Total: 7]
© UCLES 2018
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6
3
A child on a sledge slides down a steep hill and then travels in a straight line up an ice-covered
slope, as illustrated in Fig. 3.1.
ice-covered
slope
child and sledge
total mass 70 kg
B
18 m s–1
A
Fig. 3.1 (not to scale)
The sledge passes point A with speed 18 m s–1 at time t = 0 and then comes to rest at point B. The
child applies a brake to the sledge at point B. The brake does not keep the sledge stationary and
it immediately slides back down the slope towards A.
The variation with time t of the velocity v of the sledge from t = 0 to t = 24 s is shown in Fig. 3.2.
20
v / m s–1
10
0
0
4
8
12
16
20
24 t / s
–10
Fig. 3.2
(a) State the time taken for the sledge to travel from A to B.
time = ........................................................ s [1]
© UCLES 2018
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7
(b) Determine the displacement of the sledge up the slope from point A at time t = 24 s.
displacement = .......................................................m [3]
(c) Show that the acceleration of the sledge as it moves from B back towards A is 0.50 m s–2.
[2]
(d) The child and sledge have a total mass of 70 kg. The component of the total weight of the
child and sledge that acts down the slope is 80 N.
Determine
(i)
the frictional force on the sledge as it moves from B towards A,
frictional force = ....................................................... N [2]
(ii)
the angle θ of the slope to the horizontal.
θ = ........................................................ ° [2]
© UCLES 2018
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8
(e) The child on the sledge blows a whistle between t = 4.0 s and t = 8.0 s. The whistle emits
sound of frequency 900 Hz. The speed of the sound in the air is 340 m s–1. A man standing at
point A hears the sound.
Use Fig. 3.2 to
(i)
determine the initial frequency of the sound heard by the man,
initial frequency = ..................................................... Hz [2]
(ii)
describe and explain qualitatively the variation, if any, in the frequency of the sound
heard by the man.
...........................................................................................................................................
.......................................................................................................................................[1]
[Total: 13]
© UCLES 2018
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4
(a) (i)
Define the wavelength of a progressive wave.
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
State what is meant by an antinode of a stationary wave.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) A loudspeaker producing sound of constant frequency is placed near the open end of a pipe,
as shown in Fig. 4.1.
pipe
piston
loudspeaker
speed 0.75 cm s–1
x
Fig. 4.1
A movable piston is at distance x from the open end of the pipe. Distance x is increased from
x = 0 by moving the piston to the left with a constant speed of 0.75 cm s–1.
The speed of the sound in the pipe is 340 m s–1.
(i)
A much louder sound is first heard when x = 4.5 cm. Assume that there is an antinode of
a stationary wave at the open end of the pipe.
Determine the frequency of the sound in the pipe.
frequency = ..................................................... Hz [3]
(ii)
After a time interval, a second much louder sound is heard. Calculate the time interval
between the first louder sound and the second louder sound being heard.
time interval = ........................................................ s [2]
[Total: 7]
© UCLES 2018
9702/22/M/J/18
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10
5
A solid cylinder is lifted out of oil by a wire attached to a motor. Fig. 5.1 shows two different
positions X and Y of the cylinder during the lifting process.
beam
motor
wire
surface of oil
cylinder at
position Y
velocity
0.020 m s–1
cylinder at
position X
oil
Fig. 5.1
The motor is fixed to an overhead beam.
The cylinder has cross-sectional area 0.018 m2, length 1.2 m and weight 560 N.
The density of the oil is 940 kg m–3.
Throughout the lifting process, the cylinder moves vertically upwards with a constant velocity of
0.020 m s–1. The viscous force of the oil acting on the cylinder is negligible.
(a) Calculate the density of the cylinder.
density = ............................................... kg m–3 [2]
(b) For the cylinder at position X, show that the upthrust due to the oil is 200 N.
[2]
© UCLES 2018
9702/22/M/J/18
11
(c) Calculate, for the moving cylinder at position X,
(i)
the tension in the wire,
tension = ....................................................... N [1]
(ii)
the power output of the motor.
power = ...................................................... W [2]
(d) The cylinder is raised with constant velocity from position X to position Y.
(i)
State and explain the variation, if any, of the power output of the motor as the cylinder is
raised. Numerical values are not required.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[3]
(ii)
The rate of energy output of the motor is less than the rate of increase of gravitational
potential energy of the cylinder. Without calculation, explain this difference.
...........................................................................................................................................
.......................................................................................................................................[1]
[Total: 11]
© UCLES 2018
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12
6
(a) (i)
State Kirchhoff’s first law.
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
Kirchhoff’s first law is linked to the conservation of a certain quantity. State this quantity.
.......................................................................................................................................[1]
(b) A battery of electromotive force (e.m.f.) 8.0 V and internal resistance 2.0 Ω is connected to a
resistor X and a wire Y, as shown in Fig. 6.1.
8.0 V
2.0 Ω
2.5 A
15 Ω
X
RY
wire Y
Fig. 6.1
The resistance of X is 15 Ω. The resistance of Y is RY. The current in the battery is 2.5 A.
(i)
Calculate
1.
the thermal energy dissipated in the battery in a time of 5.0 minutes,
energy = ........................................................ J [2]
2.
the terminal potential difference of the battery.
terminal potential difference = ....................................................... V [1]
© UCLES 2018
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13
(ii)
Determine the resistance RY.
RY = ....................................................... Ω [3]
(iii)
A new wire Z has the same length but less resistance than wire Y.
1.
State two possible differences between wire Z and wire Y that would separately
cause wire Z to have less resistance than wire Y.
first difference: ...........................................................................................................
....................................................................................................................................
second difference: ......................................................................................................
....................................................................................................................................
[2]
2.
Wire Y is replaced in the circuit by wire Z. By considering the current in the battery,
state and explain the effect of changing the wires on the total power produced by
the battery.
....................................................................................................................................
....................................................................................................................................
................................................................................................................................[2]
[Total: 12]
© UCLES 2018
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14
7
A stationary nucleus X decays to form nucleus Y, as shown by the equation
X
Y + β– + ν.
(a) In the above equation, draw a circle around all symbols that represent a lepton.
[1]
(b) State the name of the particle represented by the symbol ν.
...............................................................................................................................................[1]
(c) Energy is released during the decay process. State the form of the energy that is gained by
nucleus Y.
...............................................................................................................................................[1]
(d) By comparing the compositions of X and Y, state and explain whether they are isotopes.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(e) The quark composition of one nucleon in X is changed during the emission of a β– particle.
Describe this change to the quark composition.
...................................................................................................................................................
...............................................................................................................................................[1]
[Total: 6]
© UCLES 2018
9702/22/M/J/18
15
BLANK PAGE
© UCLES 2018
9702/22/M/J/18
16
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/22/M/J/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
* 8 0 6 4 0 7 6 8 7 5 *
9702/23
PHYSICS
May/June 2018
Paper 2 AS Level Structured Questions
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (ST/SG) 143984/3
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
9702/23/M/J/18
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/23/M/J/18
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4
BLANK PAGE
© UCLES 2018
9702/23/M/J/18
5
Answer all the questions in the spaces provided.
1
(a) An analogue voltmeter is used to take measurements of a constant potential difference across
a resistor.
For these measurements, describe one example of
(i)
a systematic error,
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
a random error.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) The potential difference across a resistor is measured as 5.0 V ± 0.1 V. The resistor is labelled
as having a resistance of 125 Ω ± 3%.
(i)
Calculate the power dissipated by the resistor.
power = ..................................................... W [2]
(ii)
Calculate the percentage uncertainty in the calculated power.
percentage uncertainty = ...................................................... % [2]
(iii)
Determine the value of the power, with its absolute uncertainty, to an appropriate number
of significant figures.
power = ..................................... ± ..................................... W [2]
[Total: 8]
© UCLES 2018
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6
2
(a) State what is meant by work done.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A diver releases a solid sphere of radius 16 cm from the sea bed. The sphere moves vertically
upwards towards the surface of the sea.
The weight of the sphere is 20 N. The upthrust acting on the sphere is 170 N. The upthrust
remains constant as the sphere moves upwards.
(i)
Calculate the density of the material of the sphere.
density = ............................................... kg m–3 [2]
(ii)
Briefly explain the origin of the upthrust acting on the sphere.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[1]
(iii)
Calculate the acceleration of the sphere as it is released from rest.
acceleration = ................................................. m s–2 [2]
© UCLES 2018
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(iv)
The viscous (drag) force D acting on the sphere is given by
D = kr 2v 2
where r is the radius of the sphere and v is its speed.
The constant k is equal to 810 kg m–3.
Determine the constant (terminal) speed reached by the sphere.
speed = ................................................. m s–1 [3]
(v)
The diver releases a different sphere that moves with a constant speed of 6.30 m s–1
directly towards a stationary ship. The sphere emits sound of frequency 4850 Hz. The
ship detects sound of frequency 4870 Hz as the sphere moves towards it.
Determine, to three significant figures, the speed of the sound in the water.
speed = ................................................. m s–1 [2]
[Total: 11]
© UCLES 2018
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8
3
A ball is thrown vertically upwards towards a ceiling and then rebounds, as illustrated in Fig. 3.1.
ceiling
speed 3.8 m s–1
ball thrown
upwards
ball leaving
ceiling
speed 9.6 m s–1
Fig. 3.1
The ball is thrown with speed 9.6 m s–1 and takes a time of 0.37 s to reach the ceiling. The ball is
then in contact with the ceiling for a further time of 0.085 s until leaving it with a speed of 3.8 m s–1.
The mass of the ball is 0.056 kg. Assume that air resistance is negligible.
(a) Show that the ball reaches the ceiling with a speed of 6.0 m s–1.
[1]
(b) Calculate the height of the ceiling above the point from which the ball was thrown.
height = ...................................................... m [2]
(c) Calculate
(i)
the increase in gravitational potential energy of the ball for its movement from its initial
position to the ceiling,
increase in gravitational potential energy = ....................................................... J [2]
© UCLES 2018
9702/23/M/J/18
9
(ii)
the decrease in kinetic energy of the ball while it is in contact with the ceiling.
decrease in kinetic energy = ....................................................... J [2]
(d) State how Newton’s third law applies to the collision between the ball and the ceiling.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(e) Calculate the change in momentum of the ball during the collision.
change in momentum = .................................................... N s [2]
(f)
Determine the magnitude of the average force exerted by the ceiling on the ball during the
collision.
average force = ...................................................... N [2]
[Total: 13]
© UCLES 2018
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4
(a) Define the Young modulus of a material.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A metal rod is compressed, as shown in Fig. 4.1.
rod
F
F
L
Fig. 4.1
The variation with compressive force F of the length L of the rod is shown in Fig. 4.2.
151
L / mm
150
149
148
147
146
145
0
10
20
30
40
50
60
70
80
90
F / kN
Fig. 4.2
Use Fig. 4.2 to
(i)
determine the spring constant k of the rod,
k = ................................................ N m–1 [2]
© UCLES 2018
9702/23/M/J/18
11
(ii)
determine the strain energy stored in the rod for F = 90 kN.
strain energy = ....................................................... J [3]
(c) The rod in (b) has cross-sectional area A and is made of metal of Young modulus E. It is now
replaced by a new rod of the same original length. The new rod has cross-sectional area A / 3
and is made of metal of Young modulus 2E. The compression of the new rod obeys Hooke’s
law.
On Fig. 4.2, sketch the variation with F of the length L for the new rod from F = 0 to F = 90 kN.
[2]
[Total: 8]
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5
(a) State the relationship between the intensity and the amplitude of a wave.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) Microwaves of the same amplitude and wavelength are emitted in phase from two sources P
and Q. The sources are arranged as shown in Fig. 5.1.
P
1.840 m
X
2.020 m
path of detector
Q
Fig. 5.1
A microwave detector is moved along a path that is parallel to the line joining P and Q. A series
of intensity maxima and intensity minima are detected.
When the detector is at a point X, the distance PX is 1.840 m and the distance QX is 2.020 m.
The microwaves have a wavelength of 6.0 cm.
(i)
Calculate the frequency of the microwaves.
frequency = .................................................... Hz [2]
(ii)
Describe and explain the intensity of the microwaves detected at X.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[3]
© UCLES 2018
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13
(iii)
Describe the effect on the interference pattern along the path of the detector due to each
of the following separate changes.
1.
The wavelength of the microwaves decreases.
....................................................................................................................................
....................................................................................................................................
2.
The phase difference between the microwaves emitted from the sources changes to
180°.
....................................................................................................................................
....................................................................................................................................
[2]
[Total: 8]
© UCLES 2018
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14
6
A wire X has a constant resistance per unit length of 3.0 Ω m–1 and a diameter of 0.48 mm.
(a) Calculate the resistivity of the metal of wire X.
resistivity = ................................................... Ω m [3]
(b) The wire X is connected into the circuit shown in Fig. 6.1.
5.0 V
1.6 A
2.0 Ω
wire X
4.5 Ω
R
Fig. 6.1
The battery has an electromotive force (e.m.f.) of 5.0 V and an internal resistance of 2.0 Ω.
The wire X and a resistor R of resistance 4.5 Ω are connected in parallel. The current in the
battery is 1.6 A.
(i)
Calculate the potential difference across resistor R.
potential difference = ...................................................... V [1]
© UCLES 2018
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15
(ii)
Determine, for wire X,
1.
its resistance,
resistance = ...................................................... Ω [3]
2.
its length.
length = ...................................................... m [1]
[Total: 8]
Please turn over for Question 7.
© UCLES 2018
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16
7
A graph of nucleon number A against proton number Z is shown in Fig. 7.1.
219
218
A
217
216
215
P
214
213
212
211
210
209
80 81 82 83 84 85 86 87 88
Z
Fig. 7.1
The graph shows a cross (labelled P) that represents a nucleus P.
Nucleus P decays by emitting an α particle to form a nucleus Q.
Nucleus Q then decays by emitting a β– particle to form a nucleus R.
(a) On Fig. 7.1, use a cross to represent
(i)
nucleus Q (label this cross Q),
[1]
(ii)
nucleus R (label this cross R).
[1]
(b) State the name of the class (group) of particles that includes the β– particle.
...............................................................................................................................................[1]
(c) The quark composition of one nucleon in Q is changed during the emission of the β– particle.
Describe this change to the quark composition.
...................................................................................................................................................
...............................................................................................................................................[1]
[Total: 4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/23/M/J/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
* 0 8 0 0 2 3 3 3 9 1 *
9702/22
PHYSICS
Paper 2 AS Level Structured Questions
February/March 2018
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 14 printed pages and 2 blank pages.
DC (ST/SW) 143359/4
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
9702/22/F/M/18
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/22/F/M/18
[Turn over
4
Answer all the questions in the spaces provided.
1
(a) Complete Fig. 1.1 to indicate whether each of the quantities is a vector or a scalar.
quantity
vector or scalar
acceleration
speed
power
Fig. 1.1
[2]
(b) A ball is projected with a horizontal velocity of 1.1 m s–1 from point A at the edge of a table, as
shown in Fig. 1.2.
table
ball
1.1 m s–1
A
path of ball
B
0.43 m
horizontal
ground
Fig. 1.2
The ball lands on horizontal ground at point B which is a distance of 0.43 m from the base of
the table. Air resistance is negligible.
(i)
Calculate the time taken for the ball to fall from A to B.
time = ....................................................... s [1]
(ii)
Use your answer in (b)(i) to determine the height of the table.
height = ...................................................... m [2]
© UCLES 2018
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5
(iii)
The ball leaves the table at time t = 0.
For the motion of the ball between A and B, sketch graphs on Fig. 1.3 to show the
variation with time t of
1.
the acceleration a of the ball,
2.
the vertical component sv of the displacement of the ball from A.
Numerical values are not required.
a
sv
0
0
0
t
Fig. 1.3
0
t
[2]
(c) A ball of greater mass is projected from the table with the same velocity as the ball in (b). Air
resistance is still negligible.
State and explain the effect, if any, of the increased mass on the time taken for the ball to fall
to the ground.
...................................................................................................................................................
...............................................................................................................................................[1]
[Total: 8]
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2
(a) Explain what is meant by
(i)
work done,
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
kinetic energy.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) A leisure-park ride consists of a carriage that moves along a railed track. Part of the track lies
in a vertical plane and follows an arc XY of a circle of radius 13 m, as shown in Fig. 2.1.
13 m
Y
13 m
carriage
mass 580 kg
22 m s–1
X
track
Fig. 2.1
The mass of the carriage is 580 kg. At point X, the carriage has velocity 22 m s–1 in a horizontal
direction. The velocity of the carriage then decreases to 12 m s–1 in a vertical direction at
point Y.
(i)
For the carriage moving from X to Y
1.
show that the decrease in kinetic energy is 9.9 × 104 J,
[2]
2.
calculate the gain in gravitational potential energy.
gain in gravitational potential energy = ....................................................... J [2]
© UCLES 2018
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7
(ii)
Show that the length of the track from X to Y is 20 m.
[1]
(iii)
Use your answers in (b)(i) and (b)(ii) to calculate the average resistive force acting on
the carriage as it moves from X to Y.
resistive force = ...................................................... N [2]
(iv)
Describe the change in the direction of the linear momentum of the carriage as it moves
from X to Y.
...........................................................................................................................................
.......................................................................................................................................[1]
(v)
Determine the magnitude of the change in linear momentum when the carriage moves
from X to Y.
change in momentum = .................................................... N s [3]
[Total: 13]
© UCLES 2018
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8
3
(a) For the deformation of a wire under tension, define
(i)
stress,
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
strain.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) A wire is fixed at one end so that it hangs vertically. The wire is given an extension x by
suspending a load F from its free end. The variation of F with x is shown in Fig. 3.1.
F /N
8
7
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x / mm
0.8
Fig. 3.1
The wire has cross-sectional area 9.4 × 10–8 m2 and original length 2.5 m.
(i)
Describe how measurements can be taken to determine accurately the cross-sectional
area of the wire.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[3]
© UCLES 2018
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9
(ii)
Determine the Young modulus E of the material of the wire.
E = .................................................... Pa [2]
(iii)
Use Fig. 3.1 to calculate the increase in the energy stored in the wire when the load is
increased from 2.0 N to 4.0 N.
increase in energy = ....................................................... J [2]
(c) The wire in (b) is replaced by a new wire of the same material. The new wire has twice the
length and twice the diameter of the old wire. The new wire also obeys Hooke’s law.
On Fig. 3.1, sketch the variation with extension x of the load F for the new wire from x = 0 to
x = 0.80 mm.
[2]
[Total: 11]
© UCLES 2018
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10
4
(a) State the conditions required for the formation of a stationary wave.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) The sound from a loudspeaker is detected by a microphone that is connected to a cathode-ray
oscilloscope (c.r.o.). Fig. 4.1 shows the trace on the screen of the c.r.o.
1 cm
1 cm
Fig. 4.1
In air, the sound wave has a speed of 330 m s–1 and a wavelength of 0.18 m.
(i)
Calculate the frequency of the sound wave.
frequency = .................................................... Hz [2]
(ii)
Determine the time-base setting, in s cm–1, of the c.r.o.
time-base setting = ............................................... s cm–1 [2]
© UCLES 2018
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11
(iii)
The intensity of the sound from the loudspeaker is now halved. The wavelength of
the sound is unchanged. Assume that the amplitude of the trace is proportional to the
amplitude of the sound wave.
On Fig. 4.1, sketch the new trace shown on the screen of the c.r.o.
[2]
(c) The loudspeaker in (b) is held above a vertical tube of liquid, as shown in Fig. 4.2.
loudspeaker
liquid
level A
level A
level B
level B
tube
liquid
tap
Fig. 4.2
Fig. 4.3
A tap at the bottom of the tube is opened so that liquid drains out at a constant rate. The
wavelength of the sound from the loudspeaker is 0.18 m. The sound that is heard first
becomes much louder when the liquid surface reaches level A. The next time that the sound
becomes much louder is when the liquid surface reaches level B, as shown in Fig. 4.3.
(i)
Calculate the vertical distance between level A and level B.
distance = ...................................................... m [1]
(ii)
On Fig. 4.3, label with the letter N the positions of the nodes of the stationary wave that
is formed in the air column when the liquid surface is at level B.
[1]
(iii)
The mass of liquid leaving the tube per unit time is 6.7 g s–1. The tube has an internal
cross-sectional area of 13 cm2. The density of the liquid is 0.79 g cm–3.
Calculate the time taken for the liquid to move from level A to level B.
time = ....................................................... s [2]
[Total: 12]
© UCLES 2018
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5
(a) State Kirchhoff’s second law.
...................................................................................................................................................
...............................................................................................................................................[2]
(b) Two batteries, each of electromotive force (e.m.f.) 6.0 V and negligible internal resistance, are
connected in series with three resistors, as shown in Fig. 5.1.
R
4.0 Ω
X
6.0 V
V
6.0 V
Y
1.5 Ω
I
Fig. 5.1
Resistor X has resistance 4.0 Ω and resistor Y has resistance 1.5 Ω.
(i)
The resistance R of the variable resistor is changed until the voltmeter in the circuit reads
zero.
Calculate
1.
the current I in the circuit,
I = ....................................................... A [1]
2.
the resistance R.
R = ...................................................... Ω [2]
© UCLES 2018
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13
(ii)
Resistors X and Y are wires made from the same material. The diameter of the wire of X
is twice the diameter of the wire of Y.
Determine the ratio
average drift speed of free electrons in X
.
average drift speed of free electrons in Y
ratio = .......................................................... [2]
(iii)
The resistance R of the variable resistor is now increased.
State and explain the effect of the increase in R on the power transformed by each of the
batteries.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[3]
[Total: 10]
© UCLES 2018
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14
6
A sample of a radioactive isotope emits a beam of β– radiation.
(a) State the change, if any, to the number of neutrons in a nucleus of the sample that emits a
β– particle.
...............................................................................................................................................[1]
(b) The number of β– particles passing a fixed point in the beam in a time of 2.0 minutes is
9.8 × 1010.
Calculate the current, in pA, produced by the beam of β– particles.
current = ..................................................... pA [3]
(c) Suggest why the β– particles are emitted with a range of kinetic energies.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
[Total: 6]
© UCLES 2018
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15
BLANK PAGE
© UCLES 2018
9702/22/F/M/18
16
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/22/F/M/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
CANDIDATE
NAME
CANDIDATE
NUMBER
CENTRE
NUMBER
* 2 1 1 3 9 8 3 6 0 4 *
9702/21
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2018
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 14 printed pages and 2 blank pages.
DC (SR/FC) 146708/4
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
9702/21/O/N/18
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt

v =±ω√
(x02 – x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/21/O/N/18
[Turn over
4
Answer all the questions in the spaces provided.
1
(a) Define
(i)
displacement,
...........................................................................................................................................
...................................................................................................................................... [1]
(ii)
acceleration.
...........................................................................................................................................
...................................................................................................................................... [1]
(b) A remote-controlled toy car moves up a ramp and travels across a gap to land on another
ramp, as illustrated in Fig. 1.1.
path of car
car
5.5 m s–1
ramp P
θ
ramp Q
d
ground
Fig. 1.1
The car leaves ramp P with a velocity of 5.5 m s–1 at an angle θ to the horizontal. The
horizontal component of the car’s velocity as it leaves the ramp is 4.6 m s–1. The car lands at
the top of ramp Q. The tops of both ramps are at the same height and are distance d apart.
Air resistance is negligible.
(i)
Show that the car leaves ramp P with a vertical component of velocity of 3.0 m s–1.
[1]
(ii)
Determine the time taken for the car to travel between the ramps.
time taken = ....................................................... s [2]
© UCLES 2018
9702/21/O/N/18
5
(iii)
Calculate the horizontal distance d between the tops of the ramps.
d = ...................................................... m [1]
(iv)
Calculate the ratio
kinetic energy of the car at its maximum height
kinetic energy of the car as it leaves ramp P
.
ratio = ........................................................... [3]
(c) Ramp Q is removed. The car again leaves ramp P as in (b) and now lands directly on the
ground. The car leaves ramp P at time t = 0 and lands on the ground at time t = T.
On Fig. 1.2, sketch the variation with time t of the vertical component vy of the car’s velocity
from t = 0 to t = T. Numerical values of vy and t are not required.
vy
0
T tt
0
Fig. 1.2
[2]
[Total: 11]
© UCLES 2018
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6
BLANK PAGE
© UCLES 2018
9702/21/O/N/18
7
2
A wooden block moves along a horizontal frictionless surface, as shown in Fig. 2.1.
steel ball
mass 4.0 g
45 m s –1
2.0 m s –1
block
mass 85 g
horizontal
surface
Fig. 2.1
The block has mass 85 g and moves to the left with a velocity of 2.0 m s –1. A steel ball of mass
4.0 g is fired to the right. The steel ball, moving horizontally with a speed of 45 m s –1, collides
with the block and remains embedded in it. After the collision the block and steel ball both have
speed v.
(a) Calculate v.
v = ................................................ m s –1 [2]
(b) (i)
For the block and ball, state
1. the relative speed of approach before collision,
relative speed of approach = ...................................................... m s–1
2. the relative speed of separation after collision.
relative speed of separation = ...................................................... m s–1
[1]
(ii)
Use your answers in (i) to state and explain whether the collision is elastic or inelastic.
...........................................................................................................................................
...................................................................................................................................... [1]
(c) Use Newton’s third law to explain the relationship between the rate of change of momentum
of the ball and the rate of change of momentum of the block during the collision.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [2]
© UCLES 2018
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[Total: 6]
[Turn over
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3
(a) (i)
Define power.
...........................................................................................................................................
...................................................................................................................................... [1]
(ii)
State what is meant by gravitational potential energy.
...........................................................................................................................................
...................................................................................................................................... [1]
(b) An aircraft of mass 1200 kg climbs upwards with a constant velocity of 45 m s–1, as shown in
Fig. 3.1.
velocity
45 m s–1
thrust force
2.0 × 103 N
path of aircraft
aircraft
mass 1200 kg
Fig. 3.1 (not to scale)
The aircraft’s engine produces a thrust force of 2.0 × 103 N to move the aircraft through the
air. The rate of increase in height of the aircraft is 3.3 m s–1.
(i)
Calculate the power produced by the thrust force.
power = ..................................................... W [2]
© UCLES 2018
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9
(ii)
Determine, for a time interval of 3.0 minutes,
1. the work done by the thrust force to move the aircraft,
work done = ....................................................... J [2]
2. the increase in gravitational potential energy of the aircraft,
increase in gravitational potential energy = ....................................................... J [2]
3. the work done against air resistance.
work done = ....................................................... J [1]
(iii)
Use your answer in (b)(ii) part 3 to calculate the force due to air resistance acting on the
aircraft.
force = ...................................................... N [1]
(iv)
With reference to the motion of the aircraft, state and explain whether the aircraft is in
equilibrium.
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [2]
[Total: 12]
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4
(a) State the principle of superposition.
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [2]
(b) An arrangement for demonstrating the interference of light is shown in Fig. 4.1.
B
P
D
Q
B
D
light
wavelength
610 nm
22 mm
a
B
D
central
bright
fringe
B
D
2.7 m
B
screen
double
slit
Fig. 4.1 (not to scale)
The wavelength of the light is 610 nm. The distance between the double slit and the screen
is 2.7 m.
An interference pattern of bright fringes and dark fringes is observed on the screen. The
centres of the bright fringes are labelled B and centres of the dark fringes are labelled D.
Point P is the centre of a particular dark fringe and point Q is the centre of a particular bright
fringe, as shown in Fig. 4.1. The distance across five bright fringes is 22 mm.
(i)
The light waves leaving the two slits are coherent.
State what is meant by coherent.
...........................................................................................................................................
...................................................................................................................................... [1]
© UCLES 2018
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(ii)
1. State the phase difference between the waves meeting at Q.
phase difference = .............................................................. °
2. Calculate the path difference, in nm, of the waves meeting at P.
path difference = ......................................................... nm
[2]
(iii)
Determine the distance a between the two slits.
a = ...................................................... m [3]
(iv)
A higher frequency of visible light is now used. State and explain the change to the
separation of the fringes.
...........................................................................................................................................
...................................................................................................................................... [1]
(v)
The intensity of the light incident on the double slit is now increased without altering
its frequency. Compare the appearance of the fringes after this change with their
appearance before this change.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [2]
[Total: 11]
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5
(a) State what is meant by an electric field.
...................................................................................................................................................
.............................................................................................................................................. [1]
(b) A particle of mass m and charge q is in a uniform electric field of strength E. The particle has
acceleration a due to the field.
Show that
a=
Eq
.
m
[2]
(c) A stationary nucleus X decays by emitting an α-particle to form a nucleus of plutonium, 240
94 Pu,
as shown.
X
(i)
240
94 Pu
+α
Determine the number of protons and the number of neutrons in nucleus X.
number of protons = ...............................................................
number of neutrons = ...............................................................
[2]
(ii)
The total mass of the plutonium nucleus and the α-particle is less than that of nucleus X.
Explain this difference in mass.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [2]
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(iii)
The plutonium nucleus and the α-particle are both accelerated by the same uniform
electric field.
Use the expression in (b) to determine the ratio
acceleration of the α-particle
acceleration of the plutonium nucleus
.
ratio = ........................................................... [2]
[Total: 9]
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6
(a) State Kirchhoff’s second law.
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [2]
(b) An electric heater containing two heating wires X and Y is connected to a power supply of
electromotive force (e.m.f.) 9.0 V and negligible internal resistance, as shown in Fig. 6.1.
9.0 V
2.4 Ω
wire X
V
1.2 Ω
wire Y
Fig. 6.1
Wire X has a resistance of 2.4 Ω and wire Y has a resistance of 1.2 Ω. A voltmeter is connected
in parallel with the wires. A variable resistor is used to adjust the power dissipated in wires X
and Y.
The variable resistor is adjusted so that the voltmeter reads 6.0 V.
(i)
Calculate the resistance of the variable resistor.
resistance = ...................................................... Ω [3]
(ii)
Calculate the power dissipated in wire X.
power = ..................................................... W [2]
© UCLES 2018
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15
(iii)
The cross-sectional area of wire X is three times the cross-sectional area of wire Y.
Assume that the resistivity and the number density of free electrons for the metal of both
wires are the same.
Determine the ratio
1.
length of wire X ,
length of wire Y
ratio = .......................................................... [2]
2.
average drift velocity of free electrons in wire X .
average drift velocity of free electrons in wire Y
ratio = .......................................................... [2]
[Total: 11]
© UCLES 2018
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16
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/21/O/N/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
* 9 3 3 7 1 0 8 9 4 0 *
9702/22
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2018
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (CE/FC) 146703/3
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
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3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt

v =±ω√
(x02 – x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/22/O/N/18
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4
Answer all the questions in the spaces provided.
1
A golfer strikes a ball so that it leaves horizontal ground with a velocity of 6.0 m s–1 at an angle θ to
the horizontal, as illustrated in Fig. 1.1.
vY
ball
ground
6.0 m s–1
4.8 m s–1
θ
vX
Fig. 1.1 (not to scale)
The magnitude of the initial vertical component vY of the velocity is 4.8 m s–1.
Assume that air resistance is negligible.
(a) Show that the magnitude of the initial horizontal component vX of the velocity is 3.6 m s–1.
[1]
© UCLES 2018
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(b) The ball leaves the ground at time t = 0 and reaches its maximum height at t = 0.49 s.
On Fig. 1.2, sketch separate lines to show the variation with time t, until the ball returns to the
ground, of
(i)
the vertical component vY of the velocity (label this line Y),
[2]
(ii)
the horizontal component vX of the velocity (label this line X).
[2]
5.0
velocity / m s–1
4.0
3.0
2.0
1.0
0
0
0.1
0.2
0.3
0.4
0.5
–1.0
0.6
0.7
0.8
0.9
1.0
t/s
–2.0
–3.0
–4.0
–5.0
Fig. 1.2
(c) Calculate the maximum height reached by the ball.
maximum height = ...................................................... m [2]
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(d) For the movement of the ball from the ground to its maximum height, determine the ratio
kinetic energy at maximum height
.
change in gravitational potential energy
ratio = ...........................................................[4]
(e) In practice, significant air resistance acts on the ball. Explain why the actual time taken for the
ball to reach maximum height is less than the time calculated when air resistance is assumed
to be negligible.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[1]
[Total: 12]
© UCLES 2018
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2
(a) The kilogram, metre and second are all SI base units.
State two other SI base units.
1. ...............................................................................................................................................
2. ...............................................................................................................................................
[2]
(b) A uniform beam AB of length 6.0 m is placed on a horizontal surface and then tilted at an
angle of 31° to the horizontal, as shown in Fig. 2.1.
90 N
A
6.0 m
Y
W
X 31°
B
Fig. 2.1 (not to scale)
The beam is held in equilibrium by four forces that all act in the same plane. A force of 90 N
acts perpendicular to the beam at end A. The weight W of the beam acts at its centre of
gravity. A vertical force Y and a horizontal force X both act at end B of the beam.
(i)
State the name of force X.
.......................................................................................................................................[1]
(ii)
By taking moments about end B, calculate the weight W of the beam.
W = ...................................................... N [2]
(iii)
Determine the magnitude of force X.
magnitude of force X = ...................................................... N [1]
[Total: 6]
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3
(a) State the principle of conservation of momentum.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) The propulsion system of a toy car consists of a propeller attached to an electric motor, as
illustrated in Fig. 3.1.
moving air
speed 1.8 m s–1
0.045 m
propeller
electric motor of car
body of car
0.045 m
ground
Fig. 3.1
The car is on horizontal ground and is initially held at rest by its brakes. When the motor is
switched on, it rotates the propeller so that air is propelled horizontally to the left. The density
of the air is 1.3 kg m–3.
Assume that the air moves with a speed of 1.8 m s–1 in a uniform cylinder of radius 0.045 m.
Also assume that the air to the right of the propeller is stationary.
(i)
Show that, in a time interval of 2.0 s, the mass of air propelled to the left is 0.030 kg.
[2]
© UCLES 2018
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9
(ii)
Calculate
1.
the increase in the momentum of the mass of air in (b)(i),
increase in momentum = ......................................................... N s
2.
the force exerted on this mass of air by the propeller.
force = ........................................................... N
[3]
(iii)
Explain how Newton’s third law applies to the movement of the air by the propeller.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(iv)
The total mass of the car is 0.20 kg. The brakes of the car are released and the car
begins to move with an initial acceleration of 0.075 m s–2.
Determine the initial frictional force acting on the car.
frictional force = ...................................................... N [2]
[Total: 11]
© UCLES 2018
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10
4
(a) Sound waves are longitudinal waves. By reference to the direction of propagation of energy,
state what is meant by a longitudinal wave.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A stationary sound wave in air has amplitude A. In an experiment, a detector is used to
determine A2. The variation of A2 with distance x along the wave is shown in Fig. 4.1.
4.0
A2 / arbitrary
units
3.0
2.0
1.0
0
0
10
20
30
40
50
x / cm
60
Fig. 4.1
(i)
State the phase difference between the vibrations of an air particle at x = 25 cm and the
vibrations of an air particle at x = 50 cm.
phase difference = ....................................................... ° [1]
(ii)
The speed of the sound in the air is 330 m s–1. Determine the frequency of the sound
wave.
frequency = .................................................... Hz [3]
(iii)
Determine the ratio
amplitude A of wave at x = 20 cm
.
amplitude A of wave at x = 25 cm
ratio = ...........................................................[2]
© UCLES 2018
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[Total: 7]
11
5
Red light of wavelength 640 nm is incident normally on a diffraction grating having a line spacing
of 1.7 × 10–6 m, as shown in Fig. 5.1.
second order
diffraction
grating
θ
incident light
wavelength 640 nm
first order
zero order
first order
second order
Fig. 5.1 (not to scale)
The second order diffraction maximum of the light is at an angle θ to the direction of the incident
light.
(a) Show that angle θ is 49°.
[3]
(b) Determine a different wavelength of visible light that will also produce a diffraction maximum
at an angle of 49°.
wavelength = ...................................................... m [2]
[Total: 5]
© UCLES 2018
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6
(a) Define the volt.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A battery of electromotive force (e.m.f.) 7.0 V and negligible internal resistance is connected
in series with three components, as shown in Fig. 6.1.
7.0 V
Z
X
Y
5.2 Ω
6.0 Ω
1.4 V
Fig. 6.1
Resistor X has a resistance of 5.2 Ω. The resistance of the filament wire of lamp Y is 6.0 Ω.
The potential difference across resistor Z is 1.4 V.
(i)
Calculate the current in the circuit.
current = ....................................................... A [2]
(ii)
Determine the resistance of resistor Z.
resistance = ...................................................... Ω [1]
(iii)
Calculate the percentage efficiency with which the battery supplies power to the lamp.
efficiency = ...................................................... % [3]
© UCLES 2018
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13
(iv)
The filament wire of the lamp is made of metal of resistivity 3.7 × 10–7 Ω m at its operating
temperature in the circuit.
Determine, for the filament wire, the value of α where
α=
cross-sectional area
.
length
α = ...................................................... m [2]
[Total: 9]
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7
(a) The current I in a metal wire is given by the expression
I = Anve.
State what is meant by the symbols A and n.
A: ..............................................................................................................................................
n: ...............................................................................................................................................
[2]
(b) The diameter of a wire XY varies linearly with distance along the wire as shown in Fig. 7.1.
X
current I
Y
d
drift speed vx
d
2
current I
Fig. 7.1
There is a current I in the wire. At end X of the wire, the diameter is d and the average drift
speed of the free electrons is vx. At end Y of the wire, the diameter is d .
2
On Fig. 7.2, sketch a graph to show the variation of the average drift speed with position
along the wire between X and Y.
5vx
4vx
average
drift
speed
3vx
2vx
vx
0
X
position along wire
Fig. 7.2
© UCLES 2018
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Y
[2]
[Total: 4]
15
8
(a) In the following list, underline all particles that are leptons.
antineutrino
positron
proton
quark
[1]
–
(b) A stationary nucleus of magnesium-27, 27
12Mg, decays by emitting a β particle and γ radiation.
An incomplete equation to represent this decay is
27Mg
12
(i)
X + β– + γ.
State the nucleon number and the proton number of nucleus X.
nucleon number = ...............................................................
proton number = ...............................................................
[2]
(ii)
State the name of the interaction that gives rise to this decay.
.......................................................................................................................................[1]
(iii)
State two possible reasons why the sum of the kinetic energy of the β– particle and the
energy of the γ radiation is less than the total energy released during the decay of the
magnesium nucleus.
1. .......................................................................................................................................
...........................................................................................................................................
2. .......................................................................................................................................
...........................................................................................................................................
[2]
[Total: 6]
© UCLES 2018
9702/22/O/N/18
16
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/22/O/N/18
Cambridge International Examinations
Cambridge International Advanced Subsidiary and Advanced Level
* 7 0 9 7 2 8 2 7 2 1 *
9702/23
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2018
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (SC/FC) 146702/2
© UCLES 2018
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2018
9702/23/O/N/18
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt

v =±ω√
(x02 – x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2018
0.693
t
1
2
9702/23/O/N/18
[Turn over
4
Answer all the questions in the spaces provided.
1
(a) Mass, length and time are all SI base quantities.
State two other SI base quantities.
1. ...............................................................................................................................................
2. ...............................................................................................................................................
[2]
(b) A wire hangs between two fixed points, as shown in Fig. 1.1.
fixed
point
17°
wire
horizontal
150 N
150 N
17°
fixed
point
hook
rope
tyre
Fig. 1.1 (not to scale)
A child’s swing is made by connecting a car tyre to the wire using a rope and a hook. The
system is in equilibrium with the wire hanging at an angle of 17° to the horizontal. The tension
in the wire is 150 N. Assume that the rope and hook have negligible weight.
(i)
Determine the weight of the tyre.
weight = ....................................................... N [2]
© UCLES 2018
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5
(ii)
The wire has a cross-sectional area of 7.5 mm2 and is made of metal of Young modulus
2.1 × 1011 Pa. The wire obeys Hooke’s law.
Calculate, for the wire,
1.
the stress,
stress = ..................................................... Pa [2]
2.
the strain.
strain = .......................................................... [2]
[Total: 8]
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2
(a) State what is meant by kinetic energy.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A cannon fires a shell vertically upwards. The shell leaves the cannon with a speed of 80 m s–1
and a kinetic energy of 480 J. The shell then rises to a maximum height of 210 m. The effect
of air resistance is significant.
(i)
Show that the mass of the shell is 0.15 kg.
[2]
(ii)
For the movement of the shell from the cannon to its maximum height, calculate
1.
the gain in gravitational potential energy,
gain in gravitational potential energy = ........................................................ J [2]
2.
the work done against air resistance.
work done = ........................................................ J [1]
(iii)
Determine the average force due to the air resistance acting on the shell as it moves
from the cannon to its maximum height.
force = ....................................................... N [2]
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(iv)
The shell leaves the cannon at time t = 0 and reaches maximum height at time t = T.
On Fig. 2.1, sketch the variation with time t of the velocity v of the shell from time t = 0 to
time t = T. Numerical values of v and t are not required.
v
0
0
T
t
Fig. 2.1
(v)
[2]
The force due to the air resistance is a vector quantity.
Compare the force due to the air resistance acting on the shell as it rises with the force
due to the air resistance as it falls.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
[Total: 12]
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3
(a) State Newton’s second law of motion.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A toy rocket consists of a container of water and compressed air, as shown in Fig. 3.1.
container
compressed
air
water
density 1000 kg m–3
nozzle
radius 7.5 mm
Fig. 3.1
Water is pushed vertically downwards through a nozzle by the compressed air. The rocket
moves vertically upwards.
The nozzle has a circular cross-section of radius 7.5 mm. The density of the water
is 1000 kg m–3. Assume that the water leaving the nozzle has the shape of a cylinder of radius
7.5 mm and has a constant speed of 13 m s–1 relative to the rocket.
(i)
Show that the mass of water leaving the nozzle in the first 0.20 s after the rocket launch
is 0.46 kg.
[2]
© UCLES 2018
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(ii)
Calculate
1.
the change in the momentum of the mass of water in (b)(i) due to leaving the nozzle,
change in momentum = .......................................................... N s
2.
the force exerted on this mass of water by the rocket.
force = ............................................................ N
[3]
(iii)
State and explain how Newton’s third law applies to the movement of the rocket by the
water.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(iv)
The container has a mass of 0.40 kg. The initial mass of water before the rocket is
launched is 0.70 kg. The mass of the compressed air in the rocket is negligible. Assume
that the resistive force on the rocket due to its motion is negligible.
For the rocket at a time of 0.20 s after launching,
1.
show that its total mass is 0.64 kg,
2.
calculate its acceleration.
acceleration = ...................................................... m s–2
[3]
[Total: 11]
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4
(a) On Fig. 4.1, complete the two graphs to illustrate what is meant by the amplitude A, the
wavelength λ and the period T of a progressive wave.
Ensure that you label the axes of each graph.
0
0
Fig. 4.1
[3]
(b) A horizontal string is stretched between two fixed points X and Y. A vibrator is used to oscillate
the string and produce a stationary wave. Fig. 4.2 shows the string at one instant in time.
string
X
Y
Fig. 4.2
The speed of a progressive wave along the string is 30 m s–1. The stationary wave has a
period of 40 ms.
(i)
Explain how the stationary wave is formed on the string.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
© UCLES 2018
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11
(ii)
A particle on the string oscillates with an amplitude of 13 mm. At time t, the particle has
zero displacement.
Calculate
1.
the displacement of the particle at time (t + 100 ms),
displacement = ........................................................ mm
2.
the total distance moved by the particle from time t to time (t + 100 ms).
distance = ........................................................ mm
[3]
(iii)
Determine
1.
the frequency of the wave,
frequency = ..................................................... Hz [1]
2.
the horizontal distance from X to Y.
distance = ...................................................... m [3]
[Total: 12]
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5
A particle of mass m and charge q is in a uniform electric field of strength E. The particle has
acceleration a due to the field.
(a) Show that
q a
= .
m E
[2]
(b) The particle has a charge of 4e where e is the elementary charge. The electric field strength
is 3.5 × 104 V m–1. The acceleration of the particle is 1.5 × 1012 m s–2.
Use the expression in (a) to show that the mass of the particle is 9.0 u.
[2]
(c) The particle is a nucleus. State the number of protons and the number of neutrons in the
nucleus.
number of protons = ...............................................................
number of neutrons = ...............................................................
[1]
(d) A second nucleus that is an isotope of the nucleus in (c) is in the same uniform electric field.
State and explain whether the electric field produces, for the two nuclei, the same
magnitudes of
(i)
force,
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
acceleration.
...........................................................................................................................................
.......................................................................................................................................[1]
© UCLES 2018
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[Total: 7]
13
6
(a) Define the coulomb.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) An electric current is a flow of charge carriers.
In the following list, underline the possible charges for a charge carrier.
8.0 × 10–19 C
4.0 × 10–19 C
1.6 × 10–19 C
1.6 × 10–20 C
[1]
(c) The diameter of a wire ST varies linearly with distance along the wire as shown in Fig. 6.1.
S
current I
drift speed vs
T
d
2d
current I
Fig. 6.1
There is a current I in the wire. At end S of the wire, the diameter is d and the average drift
speed of the free electrons is vs. At end T of the wire, the diameter is 2d.
On Fig. 6.2, sketch a graph to show the variation of the average drift speed with position
along the wire between S and T.
1.00vs
0.75vs
average
drift
0.50vs
speed
0.25vs
0
S
position along wire
Fig. 6.2
T
[2]
[Total: 4]
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7
(a) State Kirchhoff’s first law.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A potentiometer is connected to a battery of electromotive force (e.m.f.) 9.6 V and negligible
internal resistance, as shown in Fig. 7.1.
9.6 V
800 Ω
X
Y
slider
400Ω
R
Fig. 7.1
The maximum resistance of the potentiometer is 800 Ω. A resistor R of resistance 400 Ω is
connected between the slider and end X of the potentiometer.
(i)
State the potential difference across resistor R when the slider is positioned
1.
at end X of the potentiometer,
potential difference = ............................................................ V
2.
at end Y of the potentiometer.
potential difference = ............................................................ V
[2]
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(ii)
Calculate the potential difference across resistor R when the slider is positioned half-way
between X and Y.
potential difference = ....................................................... V [3]
[Total: 6]
© UCLES 2018
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BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2018
9702/23/O/N/18
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 0 6 2 2 0 5 8 9 7 0 *
9702/21
PHYSICS
May/June 2019
Paper 2 AS Level Structured Questions
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (ST/CB) 162072/2
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
9702/21/M/J/19
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2019
0.693
t
1
2
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BLANK PAGE
© UCLES 2019
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Answer all the questions in the spaces provided.
1
(a) Define velocity.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) The speed v of a sound wave through a gas of pressure P and density ρ is given by the
equation
v=
kP
ρ
where k is a constant that has no units.
An experiment is performed to determine the value of k. The data from the experiment are
shown in Fig. 1.1.
quantity
value
uncertainty
v
3.3 × 102 m s−1
± 3%
P
9.9 × 104 Pa
± 2%
ρ
1.29 kg m−3
± 4%
Fig. 1.1
(i)
Use data from Fig. 1.1 to calculate k.
k = .......................................................... [2]
(ii)
Use your answer in (b)(i) and data from Fig. 1.1 to determine the value of k, with its
absolute uncertainty, to an appropriate number of significant figures.
k = ....................................... ± ....................................... [3]
[Total: 6]
© UCLES 2019
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2
A block X slides along a horizontal frictionless surface towards a stationary block Y, as illustrated
in Fig. 2.1.
momentum
0.40 kg m s–1
X
Y
surface
Fig. 2.1
There are no resistive forces acting on block X as it moves towards block Y. At time t = 0, block X
has momentum 0.40 kg m s−1. A short time later, the blocks collide and then separate.
The variation with time t of the momentum of block Y is shown in Fig. 2.2.
0.60
momentum / kg m s–1
0.50
block Y
0.40
0.30
0.20
0.10
0
– 0.10
0
20
40
60
– 0.20
– 0.30
– 0.40
– 0.50
– 0.60
Fig. 2.2
© UCLES 2019
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80
100 120 140 160
t / ms
7
(a) Define linear momentum.
...............................................................................................................................................[1]
(b) Use Fig. 2.2 to:
(i)
determine the time interval over which the blocks are in contact with each other
time interval = .................................................... ms [1]
(ii)
describe, without calculation, the magnitude of the acceleration of block Y from:
1.
time t = 80 ms to t = 100 ms
....................................................................................................................................
2.
time t = 100 ms to t = 120 ms.
....................................................................................................................................
[2]
(c) Use Fig. 2.2 to determine the magnitude of the force exerted by block X on block Y.
force = ...................................................... N [2]
(d) On Fig. 2.2, sketch the variation of the momentum of block X with time t from t = 0 to
t = 160 ms.
[3]
[Total: 9]
© UCLES 2019
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3
The variation with extension x of the force F acting on a spring is shown in Fig. 3.1.
5.0
F/N
4.0
3.0
2.0
1.0
0
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35
x/m
Fig. 3.1
The spring of unstretched length 0.40 m has one end attached to a fixed point, as shown in Fig. 3.2.
unstretched
spring
0.40 m
0.72 m
block
moving
downwards
Fig. 3.2
block,
weight 2.5 N
Fig. 3.3
A block of weight 2.5 N is then attached to the spring. The block is then released and begins to
move downwards. At one instant, as the block is continuing to move downwards, the spring has a
length of 0.72 m, as shown in Fig. 3.3.
Assume that the air resistance and the mass of the spring are both negligible.
© UCLES 2019
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9
(a) For the change in length of the spring from 0.40 m to 0.72 m:
(i)
use Fig. 3.1 to show that the increase in elastic potential energy of the spring is 0.64 J
[2]
(ii)
calculate the decrease in gravitational potential energy of the block of weight 2.5 N.
decrease in potential energy = ....................................................... J [2]
(b) Use the information in (a)(i) and your answer in (a)(ii) to determine, for the instant when the
length of the spring is 0.72 m:
(i)
the kinetic energy of the block
kinetic energy = ....................................................... J [1]
(ii)
the speed of the block.
speed = ................................................ m s−1 [2]
[Total: 7]
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4
(a) A spherical oil drop has a radius of 1.2 × 10−6 m. The density of the oil is 940 kg m−3.
(i)
Show that the mass of the oil drop is 6.8 × 10−15 kg.
[2]
(ii)
The oil drop is charged. Explain why it is impossible for the magnitude of the charge to
be 8.0 × 10−20 C.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) The charged oil drop in (a) is in a vacuum between two horizontal metal plates, as illustrated
in Fig. 4.1.
metal plate
+V
oil drop,
mass 6.8 × 10 –15 kg
8.0 mm
uniform electric field,
field strength 2.1 × 105 V m–1
metal plate
Fig. 4.1
The plates are separated by a distance of 8.0 mm. The electric field between the plates is
uniform and has a field strength of 2.1 × 105 V m−1.
The oil drop moves vertically downwards with a constant speed.
(i)
Calculate the potential difference V between the plates.
V = ...................................................... V [2]
(ii)
Explain how the motion of the oil drop shows that it is in equilibrium.
...........................................................................................................................................
.......................................................................................................................................[1]
© UCLES 2019
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11
(iii)
Determine the charge on the oil drop.
charge = ........................................................... C
sign of charge ...............................................................
[3]
(c) The magnitude of the potential difference between the plates in (b) is decreased.
(i)
Explain why the oil drop accelerates downwards.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(ii)
Describe the change to the pattern of the field lines (lines of force) representing the
uniform electric field as the potential difference decreases.
...........................................................................................................................................
.......................................................................................................................................[1]
(d) Two types of force, X and Y, can act on an oil drop when it is in air, but cannot act on an oil
drop when it is in a vacuum. Force X can act on an oil drop when it is stationary or when it is
moving. Force Y can only act on an oil drop when it is moving.
State the name of:
(i)
force X
.......................................................................................................................................[1]
(ii)
force Y.
.......................................................................................................................................[1]
[Total: 14]
© UCLES 2019
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5
(a) A loudspeaker oscillates with frequency f to produce sound waves of wavelength λ. The
loudspeaker makes N oscillations in time t.
(i)
State expressions, in terms of some or all of the symbols f, λ and N, for:
1.
the distance moved by a wavefront in time t
distance = ...............................................................
2.
time t.
time t = ...............................................................
[2]
(ii)
Use your answers in (i) to deduce the equation relating the speed v of the sound wave to
f and λ.
[1]
(b) The waveform of a sound wave is displayed on the screen of a cathode-ray oscilloscope
(c.r.o.), as shown in Fig. 5.1.
1.0 cm
1.0 cm
Fig. 5.1
The time-base setting is 0.20 ms cm−1.
Determine the frequency of the sound wave.
frequency = .................................................... Hz [2]
© UCLES 2019
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13
(c) Two sources S1 and S2 of sound waves are positioned as shown in Fig. 5.2.
S1
X
L
Q
S2
L
Q
7.40 m
L
Y
Fig. 5.2 (not to scale)
The sources emit coherent sound waves of wavelength 0.85 m. A sound detector is moved
parallel to the line S1S2 from a point X to a point Y. Alternate positions of maximum loudness
L and minimum loudness Q are detected, as illustrated in Fig. 5.2.
Distance S1X is equal to distance S2X. Distance S2Y is 7.40 m.
(i)
Explain what is meant by coherent waves.
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
State the phase difference between the two waves arriving at the position of minimum
loudness Q that is closest to point X.
phase difference = ....................................................... ° [1]
(iii)
Determine the distance S1Y.
distance = ...................................................... m [2]
[Total: 9]
© UCLES 2019
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14
6
A battery of electromotive force (e.m.f.) E and internal resistance r is connected to a variable
resistor of resistance R, as shown in Fig. 6.1.
r
E
I
R
V
Fig. 6.1
The current in the circuit is I and the potential difference across the variable resistor is V.
(a) Explain, in terms of energy, why V is less than E.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) State an equation relating E, I, r and V.
...............................................................................................................................................[1]
(c) The resistance R of the variable resistor is varied. The variation with I of V is shown in
Fig. 6.2.
3.0
V /V
2.0
1.0
0
0
0.5
1.0
1.5
I /A
Fig. 6.2
© UCLES 2019
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2.0
15
Use Fig. 6.2 to:
(i)
explain how it may be deduced that the e.m.f. of the battery is 2.8 V
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
calculate the internal resistance r.
r = ...................................................... Ω [2]
(d) The battery stores 9.2 kJ of energy. The variable resistor is adjusted so that V = 2.1 V. Use
Fig. 6.2 to:
(i)
calculate resistance R
R = ...................................................... Ω [1]
(ii)
calculate the number of conduction electrons moving through the battery in a time of
1.0 s
number = .......................................................... [1]
(iii)
determine the time taken for the energy in the battery to become equal to 1.6 kJ.
(Assume that the e.m.f. of the battery and the current in the battery remain constant.)
time taken = ....................................................... s [3]
[Total: 10]
© UCLES 2019
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16
7
(a) One of the results of the α-particle scattering experiment is that a very small minority of the
α-particles are scattered through angles greater than 90°.
State what may be inferred about the structure of the atom from this result.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) A hadron has an overall charge of +e, where e is the elementary charge. The hadron contains
three quarks. One of the quarks is a strange (s) quark.
(i)
State the charge, in terms of e, of the strange (s) quark.
charge = .......................................................... [1]
(ii)
The other two quarks in the hadron have the same charge as each other.
By considering charge, determine a possible type (flavour) of the other two quarks.
Explain your working.
...........................................................................................................................................
.......................................................................................................................................[2]
[Total: 5]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/21/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 0 6 5 8 6 3 4 1 4 3 *
9702/22
PHYSICS
May/June 2019
Paper 2 AS Level Structured Questions
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 14 printed pages and 2 blank pages.
DC (ST/CB) 162130/3
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
9702/22/M/J/19
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2019
0.693
t
1
2
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5
Answer all the questions in the spaces provided.
1
(a) The diameter d of a cylinder is measured as 0.0125 m ± 1.6%.
Calculate the absolute uncertainty in this measurement.
absolute uncertainty = ...................................................... m [1]
(b) The cylinder in (a) stands on a horizontal surface. The pressure p exerted on the surface by
the cylinder is given by
p=
4W
.
πd 2
The measured weight W of the cylinder is 0.38 N ± 2.8%.
(i)
Calculate the pressure p.
p = ................................................ N m−2 [1]
(ii)
Determine the absolute uncertainty in the value of p.
absolute uncertainty = ................................................ N m−2 [2]
[Total: 4]
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2
(a) State Newton’s second law of motion.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A car of mass 850 kg tows a trailer in a straight line along a horizontal road, as shown in
Fig. 2.1.
trailer
car
mass 850 kg
tow-bar
horizontal road
Fig. 2.1
The car and the trailer are connected by a horizontal tow-bar.
The variation with time t of the velocity v of the car for a part of its journey is shown in Fig. 2.2.
15
v / m s –1
14
13
12
11
10
9
8
0
5
10
Fig. 2.2
© UCLES 2019
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15
t /s
20
25
7
(i)
Calculate the distance travelled by the car from time t = 0 to t = 10 s.
distance = ...................................................... m [2]
(ii)
At time t = 10 s, the resistive force acting on the car due to air resistance and friction is
510 N. The tension in the tow-bar is 440 N.
For the car at time t = 10 s:
1.
use Fig. 2.2 to calculate the acceleration
acceleration = ................................................ m s−2 [2]
2.
use your answer to calculate the resultant force acting on the car
resultant force = ...................................................... N [1]
3.
show that a horizontal force of 1300 N is exerted on the car by its engine
[1]
4.
determine the useful output power of the engine.
output power = ..................................................... W [2]
© UCLES 2019
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(c) A short time later, the car in (b) is travelling at a constant speed and the tension in the tow-bar
is 480 N.
The tow-bar is a solid metal rod that obeys Hooke’s law. Some data for the tow-bar are listed
below.
Young modulus of metal = 2.2 × 1011 Pa
original length of tow-bar = 0.48 m
cross-sectional area of tow-bar = 3.0 × 10−4 m2
Determine the extension of the tow-bar.
extension = ...................................................... m [3]
(d) The driver of the car in (b) sees a pedestrian standing directly ahead in the distance. The
driver operates the horn of the car from time t = 15 s to t = 17 s. The frequency of the sound
heard by the pedestrian is 480 Hz. The speed of the sound in the air is 340 m s−1.
Use Fig. 2.2 to calculate the frequency of the sound emitted by the horn.
frequency = .................................................... Hz [2]
[Total: 14]
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3
(a) State what is meant by the centre of gravity of a body.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) A uniform square sign with sides of length 0.68 m is fixed at its corner points A and B to a wall.
The sign is also supported by a wire CD, as shown in Fig. 3.1.
wire
D
54 N
B
35°
sign
C
E
wall
0.68 m
W
A
0.68 m
Fig. 3.1 (not to scale)
The sign has weight W and centre of gravity at point E. The sign is held in a vertical plane
with side BC horizontal. The wire is at an angle of 35° to side BC. The tension in the wire is
54 N.
The force exerted on the sign at B is only in the vertical direction.
(i)
Calculate the vertical component of the tension in the wire.
vertical component of tension = ...................................................... N [1]
(ii)
Explain why the force on the sign at B does not have a moment about point A.
...........................................................................................................................................
.......................................................................................................................................[1]
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(iii)
By taking moments about point A, show that the weight W of the sign is 150 N.
[2]
(iv)
Calculate the total vertical force exerted by the wall on the sign at points A and B.
total vertical force = ...................................................... N [1]
(c) The sign in (b) is held together by nuts and bolts. One of the nuts falls vertically from rest
through a distance of 4.8 m to the pavement below. The nut lands on the pavement with a
speed of 9.2 m s−1.
Determine, for the nut falling from the sign to the pavement, the ratio
change in gravitational potential energy
.
final kinetic energy
ratio = .......................................................... [4]
[Total: 10]
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4
(a) For a progressive water wave, state what is meant by:
(i)
displacement
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
amplitude.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) Two coherent waves X and Y meet at a point and superpose. The phase difference between
the waves at the point is 180°. Wave X has an amplitude of 1.2 cm and intensity I. Wave Y
has an amplitude of 3.6 cm.
Calculate, in terms of I, the resultant intensity at the meeting point.
intensity = .......................................................... [2]
(c) (i)
Monochromatic light is incident on a diffraction grating. Describe the diffraction of the
light waves as they pass through the grating.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
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13
(ii)
A parallel beam of light consists of two wavelengths 540 nm and 630 nm. The light is
incident normally on a diffraction grating. Third-order diffraction maxima are produced for
each of the two wavelengths. No higher orders are produced for either wavelength.
Determine the smallest possible line spacing d of the diffraction grating.
d = ...................................................... m [3]
(iii)
The beam of light in (c)(ii) is replaced by a beam of blue light incident on the same
diffraction grating.
State and explain whether a third-order diffraction maximum is produced for this blue
light.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
[Total: 11]
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5
(a) State Kirchhoff’s second law.
...................................................................................................................................................
...............................................................................................................................................[2]
(b) A battery of electromotive force (e.m.f.) 5.6 V and internal resistance r is connected to two
external resistors, as shown in Fig. 5.1.
r
5.6 V
V
90
18
Fig. 5.1
The reading on the voltmeter is 4.8 V.
(i)
Calculate:
1.
the combined resistance of the two resistors connected in parallel
combined resistance = ...................................................... Ω [2]
2.
the current in the battery.
current = ....................................................... A [2]
(ii)
Show that the internal resistance r is 2.5 Ω.
[2]
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15
(iii)
Determine the ratio
power dissipated by internal resistance r
.
total power produced by battery
ratio = .......................................................... [3]
(c) The battery in (b) is now connected to a battery of e.m.f. 7.2 V and internal resistance 3.5 Ω.
The new circuit is shown in Fig. 5.2.
5.6 V
2.5
7.2 V
3.5
Fig. 5.2
Determine the current in the circuit.
current = ....................................................... A [2]
[Total: 13]
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6
(a) State what is meant by a field line (line of force) in an electric field.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) An electric field has two different regions X and Y. The field strength in X is less than that in Y.
Describe a difference between the pattern of field lines (lines of force) in X and in Y.
...................................................................................................................................................
...............................................................................................................................................[1]
(c) A particle P has a mass of 0.15 u and a charge of −1e, where e is the elementary charge.
(i)
Particle P and an α-particle are in the same uniform electric field. Calculate the ratio
magnitude of acceleration of particle P
.
magnitude of acceleration of α-particle
ratio = .......................................................... [3]
(ii)
Particle P is a hadron composed of only two quarks. One of them is a down (d) quark.
By considering charge, determine a possible type (flavour) of the other quark.
Explain your working.
...........................................................................................................................................
.......................................................................................................................................[3]
[Total: 8]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/22/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 3 9 0 2 3 9 8 2 4 5 *
9702/23
PHYSICS
May/June 2019
Paper 2 AS Level Structured Questions
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 14 printed pages and 2 blank pages.
DC (ST/CB) 162172/3
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
9702/23/M/J/19
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2019
0.693
t
1
2
9702/23/M/J/19
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4
BLANK PAGE
© UCLES 2019
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5
Answer all the questions in the spaces provided.
1
(a) (i)
Define resistance.
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
A potential difference of 0.60 V is applied across a resistor of resistance 4.0 GΩ.
Calculate the current, in pA, in the resistor.
current = ..................................................... pA [2]
(b) The energy E transferred when charge Q moves through an electrical component is given by
the equation
E = QV
where V is the potential difference across the component.
Use the equation to determine the SI base units of potential difference.
SI base units .......................................................... [3]
[Total: 6]
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2
(a) A resultant force F moves an object of mass m through distance s in a straight line. The
force gives the object an acceleration a so that its speed changes from initial speed u to final
speed v.
(i)
State an expression for:
1.
the work W done by the force, in terms of a, m and s
W = .......................................................... [1]
2.
the distance s, in terms of a, u and v.
s = .......................................................... [1]
(ii)
Use your answers in (i) to show that the kinetic energy of the object is given by
kinetic energy =
1
× mass × (speed)2.
2
Explain your working.
[2]
(b) A ball of mass 0.040 kg is projected into the air from horizontal ground, as illustrated in
Fig. 2.1.
Y
path of
ball
h
ball,
mass 0.040 kg
X
ground
Fig. 2.1
The ball is launched from a point X with a kinetic energy of 4.5 J. At point Y, the ball has a
speed of 9.5 m s−1. Air resistance is negligible.
© UCLES 2019
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7
(i)
(ii)
For the movement of the ball from X to Y, draw a solid line on Fig. 2.1 to show:
1.
the distance moved (label this line D)
2.
the displacement (label this line S).
[2]
By consideration of energy transfer, determine the height h of point Y above the ground.
h = ...................................................... m [3]
(iii)
On Fig. 2.2, sketch the variation of the kinetic energy of the ball with its vertical height
above the ground for the movement of the ball from X to Y.
Numerical values are not required.
kinetic
energy
0
0
height
Fig. 2.2
h
[2]
[Total: 11]
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3
A cylindrical disc of mass 0.24 kg has a circular cross-sectional area A, as shown in Fig. 3.1.
force X
8.9 N
cross-sectional
area A
30°
disc,
mass 0.24 kg
Fig. 3.1
disc
constant
speed 0.60 m s–1
ground
Fig. 3.2
The disc is on horizontal ground, as shown in Fig. 3.2. A force X of magnitude 8.9 N acts on the
disc in a direction of 30° to the horizontal. The disc moves at a constant speed of 0.60 m s−1 along
the ground.
(a) Determine the rate of doing work on the disc by the force X.
rate of doing work = ..................................................... W [2]
(b) The force X and the weight of the disc exert a combined pressure on the ground of 3500 Pa.
Calculate the cross-sectional area A of the disc.
A = .................................................... m2 [3]
(c) Newton’s third law describes how forces exist in pairs. One such pair of forces is the weight of
the disc and another force Y. State:
(i)
the direction of force Y
.......................................................................................................................................[1]
(ii)
the name of the body on which force Y acts.
.......................................................................................................................................[1]
[Total: 7]
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4
Two vertical metal plates in a vacuum are separated by a distance of 0.12 m.
Fig. 4.1 shows a side view of this arrangement.
0.080 m
X
sand
particle
2.0 m
0V
+ 900 V
path of
particle
metal plate
Y
metal plate
0.12 m
Fig. 4.1 (not to scale)
Each plate has a length of 2.0 m. The potential difference between the plates is 900 V. The electric
field between the plates is uniform.
A negatively charged sand particle is released from rest at point X, which is a horizontal distance
of 0.080 m from the top of the positively charged plate. The particle then travels in a straight line
and collides with the positively charged plate at its lowest point Y, as illustrated in Fig. 4.1.
(a) Describe the pattern of the field lines (lines of force) between the plates.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) State the names of the two forces acting on the particle as it moves from X to Y.
...............................................................................................................................................[1]
(c) By considering the vertical motion of the sand particle, show that the time taken for the particle
to move from X to Y is 0.64 s.
[2]
© UCLES 2019
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11
(d) Calculate the horizontal component of the acceleration of the particle.
horizontal component of acceleration = ................................................ m s−2 [2]
(e) (i)
Calculate the magnitude of the electric field strength.
electric field strength = ................................................ N C−1 [2]
(ii)
The sand particle has mass m and charge q. Use your answers in (d) and (e)(i) to
q
determine the ratio .
m
ratio = ............................................... C kg−1 [2]
(f)
q
Another particle has a smaller magnitude of the ratio than the sand particle. This particle is
m
also released from point X.
For the movement of this particle, state the effect, if any, of the decreased magnitude of the
ratio on:
(i)
the vertical component of the acceleration
.......................................................................................................................................[1]
(ii)
the horizontal component of the acceleration.
.......................................................................................................................................[1]
[Total: 13]
© UCLES 2019
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12
5
A vertical tube of length 0.60 m is open at both ends, as shown in Fig. 5.1.
A
tube
0.60 m
N
A
direction of
incident
sound wave
Fig. 5.1
An incident sinusoidal sound wave of a single frequency travels up the tube. A stationary wave
is then formed in the air column in the tube with antinodes A at both ends and a node N at the
midpoint.
(a) Explain how the stationary wave is formed from the incident sound wave.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[2]
(b) On Fig. 5.2, sketch a graph to show the variation of the amplitude of the stationary wave with
height h above the bottom of the tube.
amplitude
0
0
0.20
Fig. 5.2
© UCLES 2019
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0.40
h/m
0.60
[2]
13
(c) For the stationary wave, state:
(i)
the direction of the oscillations of an air particle at a height of 0.15 m above the bottom of
the tube
.......................................................................................................................................[1]
(ii)
the phase difference between the oscillations of a particle at a height of 0.10 m and a
particle at a height of 0.20 m above the bottom of the tube.
phase difference = ........................................................ ° [1]
(d) The speed of the sound wave is 340 m s−1.
Calculate the frequency of the sound wave.
frequency = .................................................... Hz [2]
(e) The frequency of the sound wave is gradually increased.
Determine the frequency of the wave when a stationary wave is next formed.
frequency = .................................................... Hz [1]
[Total: 9]
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6
(a) Define the ohm.
...............................................................................................................................................[1]
(b) A battery of electromotive force (e.m.f.) E and internal resistance 1.5 Ω is connected to a
network of resistors, as shown in Fig. 6.1.
1.5
E
I
2.0
RZ
1.8 A
Y
Z
8.0
0.60 A
X
Fig. 6.1
Resistor X has a resistance of 8.0 Ω. Resistor Y has a resistance of 2.0 Ω. Resistor Z has a
resistance of RZ. The current in X is 0.60 A and the current in Y is 1.8 A.
(i)
Calculate:
1.
the current I in the battery
I = ....................................................... A [1]
2.
resistance RZ
RZ = ...................................................... Ω [2]
3.
e.m.f. E.
E = ...................................................... V [2]
© UCLES 2019
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15
(ii)
Resistors X and Y are each made of wire. The two wires have the same length and are
made of the same metal.
Determine the ratio:
1.
cross-sectional area of wire X
cross-sectional area of wire Y
ratio = .......................................................... [2]
2.
average drift speed of free electrons in X
average drift speed of free electrons in Y
.
ratio = .......................................................... [2]
[Total: 10]
Please turn over for Question 7.
© UCLES 2019
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16
7
A sample of a radioactive substance may decay by the emission of either α-radiation or β-radiation
and/or γ-radiation.
State the type of radiation, one in each case, that:
(a) consists of leptons
...............................................................................................................................................[1]
(b) contains quarks
...............................................................................................................................................[1]
(c) cannot be deflected by an electric field
...............................................................................................................................................[1]
(d) has a continuous range of energies, rather than discrete values of energy.
...............................................................................................................................................[1]
[Total: 4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/23/M/J/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 5 0 5 4 1 5 9 8 7 8 *
9702/22
PHYSICS
Paper 2 AS Level Structured Questions
February/March 2019
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (RW/SW) 162371/4
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
9702/22/F/M/19
3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2019
0.693
t
1
2
9702/22/F/M/19
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BLANK PAGE
© UCLES 2019
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5
Answer all the questions in the spaces provided.
1
(a) The ampere, metre and second are SI base units.
State two other SI base units.
1. ...............................................................................................................................................
2. ...............................................................................................................................................
[2]
(b) The average drift speed v of electrons moving through a metal conductor is given by the
equation:
v=
μF
e
where e is the charge on an electron
F is a force acting on the electron
and μ is a constant.
Determine the SI base units of μ.
SI base units ...........................................................[3]
[Total: 5]
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2
(a) Define:
(i)
displacement
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
acceleration.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) A man wearing a wingsuit glides through the air with a constant velocity of 47 m s–1 at an
angle of 24° to the horizontal. The path of the man is shown in Fig. 2.1.
47 m s–1
man in wingsuit
total mass 85 kg
A
glide path
h
24°
horizontal
B
Fig. 2.1 (not to scale)
The total mass of the man and the wingsuit is 85 kg. The man takes a time of 2.8 minutes to
glide from point A to point B.
(i)
With reference to the motion of the man, state and explain whether he is in equilibrium.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(ii)
Show that the difference in height h between points A and B is 3200 m.
[1]
© UCLES 2019
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7
(iii)
For the movement of the man from A to B, determine:
1.
the decrease in gravitational potential energy
decrease in gravitational potential energy = ....................................................... J [2]
2.
the magnitude of the force on the man due to air resistance.
force = ...................................................... N [2]
(iv)
The pressure of the still air at A is 63 kPa and at B is 92 kPa. Assume the density of the
air is constant between A and B.
Determine the density of the air between A and B.
density = ............................................... kg m–3 [2]
[Total: 11]
© UCLES 2019
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3
Two balls, X and Y, move along a horizontal frictionless surface, as illustrated in Fig. 3.1.
X
A
60°
3.0 m s–1
B
9.6 m s–1
Y 2.5 kg
Fig. 3.1 (not to scale)
Ball X has an initial velocity of 3.0 m s–1 in a direction along line AB. Ball Y has a mass of 2.5 kg
and an initial velocity of 9.6 m s–1 in a direction at an angle of 60° to line AB.
The two balls collide at point B. The balls stick together and then travel along the horizontal surface
in a direction at right-angles to the line AB, as shown in Fig. 3.2.
V
X
Y
A
B
Fig. 3.2
(a) By considering the components of momentum in the direction from A to B, show that ball X
has a mass of 4.0 kg.
[2]
© UCLES 2019
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9
(b) Calculate the common speed V of the two balls after the collision.
V = ................................................. m s–1 [2]
(c) Determine the difference between the initial kinetic energy of ball X and the initial kinetic
energy of ball Y.
difference in kinetic energy = ....................................................... J [2]
[Total: 6]
© UCLES 2019
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4
(a) Define electric field strength.
...................................................................................................................................................
...............................................................................................................................................[1]
(b) Two very small metal spheres X and Y are connected by an insulating rod of length 72 mm. A
side view of this arrangement is shown in Fig. 4.1.
+3e
X
uniform electric field,
field strength 5.0 × 104 V m–1
in vertically upwards direction
72 mm
θ
horizontal
SIDE
VIEW
Z
rod
θ
Y –3e
Fig. 4.1 (not to scale)
Sphere X has a charge of +3e and sphere Y has a charge of –3e, where e is the elementary
charge. The rod is held at its mid point Z at an angle θ to the horizontal. The rod and
spheres have negligible mass and are in a uniform electric field. The electric field strength is
5.0 × 104 V m–1. The direction of this field is vertically upwards.
(i)
The electric field is produced by applying a potential difference of 4.0 kV between two
charged parallel metal plates.
1.
Calculate the separation between the plates.
separation = ...................................................... m [2]
© UCLES 2019
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11
2.
Describe the arrangement of the two plates. Include in your answer a statement of
the sign of the charge on each plate. You may draw on Fig. 4.1.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
................................................................................................................................[2]
(ii)
Determine the magnitude and direction of the force on sphere Y.
magnitude = ........................................................... N
direction ...............................................................
[2]
(iii)
The electric forces acting on the two spheres form a couple. This couple acts on the rod
with a torque of 6.2 × 10–16 N m.
Calculate the angle θ of the rod to the horizontal.
θ = ........................................................ ° [2]
[Total: 9]
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5
(a) By reference to two waves, state:
(i)
the principle of superposition
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(ii)
what is meant by coherence.
...........................................................................................................................................
.......................................................................................................................................[1]
(b) Two coherent waves P and Q meet at a point in phase and superpose. Wave P has an
amplitude of 1.5 cm and intensity I. The resultant intensity at the point where the waves meet
is 3I.
Calculate the amplitude of wave Q.
amplitude = .................................................... cm [2]
(c) The apparatus shown in Fig. 5.1 is used to produce an interference pattern on a screen.
laser light
wavelength 680 nm
a
double-slit
D
screen
Fig. 5.1 (not to scale)
Light of wavelength 680 nm is incident on a double-slit. The slit separation is a. The
separation between adjacent fringes is x. Fringes are viewed on a screen at distance D from
the double-slit.
© UCLES 2019
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13
Distance D is varied from 2.0 m to 3.5 m. The variation with D of x is shown in Fig. 5.2.
10.0
x / mm
8.0
6.0
4.0
2.0
0
2.0
2.5
D/m
3.0
3.5
Fig. 5.2
(i)
Use Fig. 5.2 to determine the slit separation a.
a = ...................................................... m [3]
(ii)
The laser is now replaced by another laser that emits light of a shorter wavelength.
On Fig. 5.2, sketch a possible line to show the variation with D of x for the fringes that
are now produced.
[2]
[Total: 10]
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6
(a) Using energy transformations, describe the electromotive force (e.m.f.) of a battery and the
potential difference (p.d.) across a resistor.
e.m.f.: ........................................................................................................................................
...................................................................................................................................................
p.d.: ...........................................................................................................................................
...............................................................................................................................................[2]
(b) A battery of e.m.f. 6.0 V and negligible internal resistance is connected to a network of
resistors and a voltmeter, as shown in Fig. 6.1.
Z
32 Ω
V
6.0 V
X
Y
24 Ω
Fig. 6.1
Resistor Y has a resistance of 24 Ω and resistor Z has a resistance of 32 Ω.
(i)
The resistance RX of the variable resistor X is adjusted until the voltmeter reads 4.8 V.
Calculate:
1.
the current in resistor Z
current = ....................................................... A [1]
2.
the total power provided by the battery
power = ..................................................... W [2]
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15
3.
the number of conduction electrons that move through the battery in a time interval
of 25 s
number = .......................................................... [2]
4.
the total resistance of X and Y connected in parallel
total resistance = ...................................................... Ω [2]
5.
the resistance RX.
RX = ...................................................... Ω [2]
(ii)
The resistance RX is now decreased.
State and explain the change, if any, to the reading on the voltmeter.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
[Total: 13]
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7
(a) The names of four particles are listed below.
alpha
beta-plus
neutron
proton
State the name(s) of the particle(s) in this list that:
(i)
are not fundamental
.......................................................................................................................................[1]
(ii)
do not experience an electric force when situated in an electric field
.......................................................................................................................................[1]
(iii)
has the largest ratio of charge to mass.
.......................................................................................................................................[1]
(b) A hadron has a charge of +e where e is the elementary charge. The hadron is composed of
only two quarks. One of these quarks is an antidown ( d ) quark. By considering charge, state
and explain the name (flavour) of the other quark.
...................................................................................................................................................
...............................................................................................................................................[3]
[Total: 6]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/22/F/M/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 4 1 5 6 5 6 3 8 3 7 *
9702/21
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2019
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (LEG/SG) 163798/2
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
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3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt)
decay constant
λ =
© UCLES 2019
0.693
t
1
2
9702/21/O/N/19
[Turn over
4
BLANK PAGE
© UCLES 2019
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5
Answer all the questions in the spaces provided.
1
(a) Make estimates of:
(i)
the mass, in g, of a new pencil
mass = ...................................................... g [1]
(ii)
the wavelength of ultraviolet radiation.
wavelength = ..................................................... m [1]
(b) The period T of the oscillations of a mass m suspended from a spring is given by
T = 2π
m
k
where k is the spring constant of the spring.
The manufacturer of a spring states that it has a spring constant of 25 N m–1 ± 8%. A mass
of 200 × 10–3 kg ± 4 × 10–3 kg is suspended from the end of the spring and then made to
oscillate.
(i)
Calculate the period T of the oscillations.
T = ...................................................... s [1]
(ii)
Determine the value of T, with its absolute uncertainty, to an appropriate number of
significant figures.
T = ............................................. ± ............................................. s [3]
[Total: 6]
© UCLES 2019
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2
A small charged glass bead of weight 5.4 × 10–5 N is initially at rest at point A in a vacuum. The
bead then falls through a uniform horizontal electric field as it moves in a straight line to point B, as
illustrated in Fig. 2.1.
vertical
glass bead
weight 5.4 × 10–5 N
charge –3.7 × 10–9 C
horizontal
A
uniform horizontal
electric field,
field strength 1.3 × 104 V m–1
path of the
falling bead
B
side view
Fig. 2.1 (not to scale)
The electric field strength is 1.3 × 104 V m–1. The charge on the bead is –3.7 × 10–9 C.
(a) Describe how two metal plates could be used to produce the electric field. Numerical values
are not required.
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
(b) Determine the magnitude of the electric force acting on the bead.
electric force = ..................................................... N [2]
© UCLES 2019
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7
(c) Use your answer in (b) and the weight of the bead to show that the resultant force acting on it
is 7.2 × 10–5 N.
[1]
(d) Explain why the resultant force on the bead of 7.2 × 10–5 N is constant as the bead moves
along path AB.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
(e) (i)
Calculate the magnitude of the acceleration of the bead along the path AB.
acceleration = ................................................ m s–2 [2]
(ii)
The path AB has length 0.58 m.
Use your answer in (i) to determine the speed of the bead at point B.
speed = ................................................ m s–1 [2]
[Total: 11]
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3
A small remote-controlled model aircraft has two propellers, each of diameter 16 cm.
Fig. 3.1 is a side view of the aircraft when hovering.
16 cm
propeller
body of
aircraft
16 cm
propeller
air
speed
7.6 m s–1
air
speed
7.6 m s–1
Fig. 3.1
Air is propelled vertically downwards by each propeller so that the aircraft hovers at a fixed
position. The density of the air is 1.2 kg m–3. Assume that the air from each propeller moves with
a constant speed of 7.6 m s–1 in a uniform cylinder of diameter 16 cm. Also assume that the air
above each propeller is stationary.
(a) Show that, in a time interval of 3.0 s, the mass of air propelled downwards by one propeller is
0.55 kg.
[3]
(b) Calculate:
(i)
the increase in momentum of the mass of air in (a)
increase in momentum = ................................................... N s [1]
(ii)
the downward force exerted on this mass of air by the propeller.
force = ..................................................... N [1]
© UCLES 2019
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9
(c) State:
(i)
the upward force acting on one propeller
force = ..................................................... N [1]
(ii)
the name of the law that explains the relationship between the force in (b)(ii) and the
force in (c)(i).
..................................................................................................................................... [1]
(d) Determine the mass of the aircraft.
mass = .................................................... kg [1]
(e) In order for the aircraft to hover at a very high altitude (height), the propellers must propel the
air downwards with a greater speed than when the aircraft hovers at a low altitude. Suggest
the reason for this.
...................................................................................................................................................
............................................................................................................................................. [1]
(f)
When the aircraft is hovering at a high altitude, an electric fault causes the propellers to stop
rotating. The aircraft falls vertically downwards. When the aircraft reaches a constant speed
of 22 m s–1, it emits sound of frequency 3.0 kHz from an alarm. The speed of the sound in the
air is 340 m s–1.
Determine the frequency of the sound heard by a person standing vertically below the falling
aircraft.
frequency = .................................................... Hz [2]
[Total: 11]
© UCLES 2019
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4
The variation with extension x of the force F applied to a spring is shown in Fig. 4.1.
4.0
3.0
F/N
2.0
1.0
0
0
0.010
0.020
0.030
x/m
0.040
0.050
Fig. 4.1
The spring has an unstretched length of 0.080 m and is suspended vertically from a fixed point, as
shown in Fig. 4.2.
0.080 m
0.095 m
0.120 m
position X
block hangs in
equilibrium
Fig. 4.2
Fig. 4.3
position Y
block held before release
Fig. 4.4
A block is attached to the lower end of the spring. The block hangs in equilibrium at position X
when the length of the spring is 0.095 m, as shown in Fig. 4.3.
The block is then pulled vertically downwards and held at position Y so that the length of the
spring is 0.120 m, as shown in Fig. 4.4. The block is then released and moves vertically upwards
from position Y back towards position X.
© UCLES 2019
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11
(a) Use Fig. 4.1 to determine the spring constant of the spring.
spring constant = ............................................... N m–1 [2]
(b) Use Fig. 4.1 to show that the decrease in elastic potential energy of the spring is 0.055 J when
the block moves from position Y to position X.
[2]
(c) The block has a mass of 0.122 kg. Calculate the increase in gravitational potential energy of
the block for its movement from position Y to position X.
increase in gravitational potential energy = ...................................................... J [2]
(d) Use the decrease in elastic potential energy stated in (b) and your answer in (c) to determine,
for the block, as it moves through position X:
(i)
its kinetic energy
kinetic energy = ...................................................... J [1]
(ii)
its speed.
speed = ................................................ m s–1 [2]
[Total: 9]
© UCLES 2019
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5
A ripple tank is used to demonstrate the interference of water waves.
Two dippers D1 and D2 produce coherent waves that have circular wavefronts, as illustrated in
Fig. 5.1.
D1
D2
X
Fig. 5.1
The lines in the diagram represent crests. The waves have a wavelength of 6.0 cm.
(a) One condition that is required for an observable interference pattern is that the waves must
be coherent.
(i)
Describe how the apparatus is arranged to ensure that the waves from the dippers are
coherent.
...........................................................................................................................................
..................................................................................................................................... [1]
(ii)
State one other condition that must be satisfied by the waves in order for the interference
pattern to be observable.
...........................................................................................................................................
..................................................................................................................................... [1]
(b) Light from a lamp above the ripple tank shines through the water onto a screen below the
tank. Describe one way of seeing the illuminated pattern more clearly.
...................................................................................................................................................
............................................................................................................................................. [1]
© UCLES 2019
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13
(c) The speed of the waves is 0.40 m s–1. Calculate the period of the waves.
period = ...................................................... s [2]
(d) Fig. 5.1 shows a point X that lies on a crest of the wave from D1 and midway between two
adjacent crests of the wave from D2.
For the waves at point X, state:
(i)
the path difference, in cm
path difference = ................................................... cm [1]
(ii)
the phase difference.
phase difference = ....................................................... ° [1]
(e) On Fig. 5.1, draw one line, at least 4 cm long, which joins points where only maxima of the
interference pattern are observed.
[1]
[Total: 8]
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6
(a) Define electric potential difference (p.d.).
...................................................................................................................................................
............................................................................................................................................. [1]
(b) The variation with potential difference V of the current I in a semiconductor diode is shown in
Fig. 6.1.
30
I / mA
25
20
15
10
5
0
0
0.5
V/V
1.0
Fig. 6.1
Use Fig. 6.1 to describe qualitatively the variation of the resistance of the diode as V increases
from 0 to 1.0 V.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
© UCLES 2019
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15
(c) The diode in (b) is part of the circuit shown in Fig. 6.2.
2.0 V
15 mA
60 Ω
X
Y
Fig. 6.2
The cell of electromotive force (e.m.f.) 2.0 V and negligible internal resistance is connected in
series with the diode and resistors X and Y. The resistance of Y is 60 Ω. The current in the cell
is 15 mA.
(i)
Use Fig. 6.1 to determine the resistance of the diode.
resistance = ..................................................... Ω [3]
(ii)
Calculate:
1.
the resistance of X
resistance = ..................................................... Ω [3]
2.
the ratio
power dissipated in resistor Y
.
total power produced by the cell
ratio = ......................................................... [2]
© UCLES 2019
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[Total: 11]
[Turn over
16
7
35Ar by β+ emission is represented by
(a) The decay of a nucleus 18
35
18 Ar
X + β+ + Y.
A nucleus X and two particles, β+ and Y, are produced by the decay.
State:
(i)
the proton number and the nucleon number of nucleus X
proton number = ...............................................................
nucleon number = ...............................................................
[1]
(ii)
the name of the particle represented by the symbol Y.
..................................................................................................................................... [1]
(b) A hadron consists of two down quarks and one strange quark.
Determine, in terms of the elementary charge e, the charge of this hadron.
charge = ......................................................... [2]
[Total: 4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/21/O/N/19
Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 5 9 5 4 0 8 8 8 6 4 *
9702/22
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2019
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 15 printed pages and 1 blank page.
DC (KS/TP) 164216/3
© UCLES 2019
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
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Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ= −
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p=
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt

v =±ω√
(x02 – x 2)
Doppler effect
fo =
electric potential
V=
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ=
© UCLES 2019
0.693
t
1
2
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BLANK PAGE
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Answer all the questions in the spaces provided.
1
(a) Distinguish between vector and scalar quantities.
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
(b) The electric field strength E at a distance x from an isolated point charge Q is given by the
equation
E=
Q
x 2b
where b is a constant.
(i)
Use the definition of electric field strength to show that E has SI base units of kg m A–1 s–3.
[2]
(ii)
Use the units for E given in (b)(i) to determine the SI base units of b.
SI base units of b ......................................................... [2]
[Total: 6]
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2
(a) Define acceleration.
............................................................................................................................................. [1]
(b) A steel ball of diameter 0.080 m is released from rest and falls vertically in air, as illustrated in
Fig. 2.1.
position of ball
when released
steel ball of
diameter 0.080 m
0.280 m
position P
of ball
horizontal
beam of light of
negligible width
Fig. 2.1 (not to scale)
A horizontal beam of light of negligible width is a vertical distance of 0.280 m below the bottom
of the ball when it is released. The ball falls through and breaks the beam of light.
(i)
Explain why the force due to air resistance acting on the ball may be neglected when
calculating the time taken for the ball to reach the beam of light.
...........................................................................................................................................
..................................................................................................................................... [1]
(ii)
Calculate the time taken for the ball to fall from rest to position P where the bottom of the
ball touches the beam of light.
time taken = ....................................................... s [2]
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(iii)
Determine the time interval during which the beam of light is broken by the ball.
time interval = ....................................................... s [2]
(c) A different ball is released from the same position as the steel ball in (b). This ball has the
same diameter but a much lower density. For this ball, the force due to air resistance cannot
be neglected as the ball falls.
State and explain the change, if any, to the time interval during which the beam of light is
broken by the ball.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
[Total: 8]
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3
(a) State Newton’s third law of motion.
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
(b) A block X of mass mX slides in a straight line along a horizontal frictionless surface, as shown
in Fig. 3.1.
mass mX
speed 5v
speed v
mass mY
X
X
Y
Fig. 3.1
Y
Fig. 3.2
The block X, moving with speed 5v, collides head-on with a stationary block Y of mass mY.
The two blocks stick together and then move with common speed v, as shown in Fig. 3.2.
(i)
Use conservation of momentum to show that the ratio
mY
is equal to 4.
mx
[2]
(ii)
Calculate the ratio
total kinetic energy of X and Y after collision
total kinetic energy of X and Y before collision
.
ratio = ......................................................... [3]
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(iii)
State the value of the ratio in (ii) for a perfectly elastic collision.
ratio = ......................................................... [1]
(c) The variation with time t of the momentum of block X in (b) is shown in Fig. 3.3.
momentum
0
0
10
20
30
40
50 60
t / ms
Fig. 3.3
Block X makes contact with block Y at time t = 20 ms.
(i)
Describe, qualitatively, the magnitude and direction of the resultant force, if any, acting
on block X in the time interval:
1. t = 0 to t = 20 ms
...........................................................................................................................................
2. t = 20 ms to t = 40 ms.
...........................................................................................................................................
...........................................................................................................................................
[3]
(ii)
On Fig. 3.3, sketch the variation of the momentum of block Y with time t from
t = 0 to t = 60 ms.
[3]
[Total: 14]
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4
(a) A sphere in a liquid accelerates vertically downwards from rest. For the viscous force acting
on the moving sphere, state:
(i)
the direction
..................................................................................................................................... [1]
(ii)
the variation, if any, in the magnitude.
..................................................................................................................................... [1]
(b) A man of weight 750 N stands a distance of 3.6 m from end D of a horizontal uniform beam
AD, as shown in Fig. 4.1.
FC
FB
A
B
2.0 m
C
380 N
750 N
D
2.0 m
3.6 m
9.0 m
Fig. 4.1 (not to scale)
The beam has a weight of 380 N and a length of 9.0 m. The beam is supported by a vertical
force FB at pivot B and a vertical force FC at pivot C. Pivot B is a distance of 2.0 m from end A
and pivot C is a distance of 2.0 m from end D. The beam is in equilibrium.
(i)
State the principle of moments.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
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(ii)
By using moments about pivot C, calculate FB.
FB = ...................................................... N [2]
(iii)
The man walks towards end D. The beam is about to tip when FB becomes zero.
Determine the minimum distance x from end D that the man can stand without tipping
the beam.
x = ...................................................... m [2]
[Total: 8]
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5
(a) State what is meant by the wavelength of a progressive wave.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) A cathode-ray oscilloscope (CRO) is used to analyse a sound wave. The screen of the CRO
is shown in Fig. 5.1.
1 cm
1 cm
Fig. 5.1
The time-base setting of the CRO is 2.5 ms cm–1.
Determine the frequency of the sound wave.
frequency = .................................................... Hz [2]
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(c) The source emitting the sound in (b) is at point A. Waves travel from the source to point C
along two different paths, AC and ABC, as shown in Fig. 5.2.
20.8 m
C
A
8.0 m
reflecting
surface
B
Fig. 5.2 (not to scale)
Distance AB is 8.0 m and distance AC is 20.8 m. Angle ABC is 90°. Assume that there is no
phase change of the sound wave due to the reflection at point B. The wavelength of the
waves is 1.6 m.
(i)
Show that the waves meeting at C have a path difference of 6.4 m.
[1]
(ii)
Explain why an intensity maximum is detected at point C.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
(iii)
Determine the difference between the times taken for the sound to travel from the source
to point C along the two different paths.
time difference = ....................................................... s [2]
(iv)
The wavelength of the sound is gradually increased. Calculate the wavelength of the
sound when an intensity maximum is next detected at point C.
wavelength = ...................................................... m [1]
[Total: 9]
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6
(a) State Kirchhoff’s first law.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) The variations with potential difference V of the current I for a resistor X and for a
semiconductor diode are shown in Fig. 6.1.
15.0
I / mA
12.5
resistor X
10.0
7.5
diode
5.0
2.5
0
0
0.1
0.2
0.3
0.4
0.5 0.6
V/V
0.7
0.8
Fig. 6.1
(i)
Determine the resistance of the diode for a potential difference V of 0.60 V.
resistance = ...................................................... Ω [3]
(ii)
Describe, qualitatively, the variation of the resistance of the diode as V increases from
0.60 V to 0.75 V.
..................................................................................................................................... [1]
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(c) The diode and the resistor X in (b) are connected into the circuit shown in Fig. 6.2.
E
9.3 mA
X
7.5 mA
Y
Fig. 6.2
The cell has electromotive force (e.m.f.) E and negligible internal resistance. Resistor Y is
connected in parallel with resistor X and the diode. The current in the cell is 9.3 mA and the
current in the diode is 7.5 mA.
(i)
Use Fig. 6.1 to determine E.
E = .......................................................V [1]
(ii)
Determine the resistance of resistor Y.
resistance = ...................................................... Ω [2]
(iii)
Calculate the power dissipated in the diode.
power = ......................................................W [2]
(iv)
The cell is now replaced by a new cell of e.m.f. 0.50 V and negligible internal resistance.
Use Fig. 6.1 to determine the new current in the diode.
current = ....................................................mA [1]
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7
A nucleus of plutonium-238 ( 238
94Pu) decays by emitting an α-particle to produce a new nucleus X
and 5.6 MeV of energy. The decay is represented by
238
94Pu
X + α + 5.6 MeV.
(a) Determine the number of protons and the number of neutrons in nucleus X.
number of protons = ...............................................................
number of neutrons = ...............................................................
[2]
(b) Calculate the number of plutonium-238 nuclei that must decay in a time of 1.0 s to produce a
power of 0.15 W.
number = ......................................................... [2]
[Total: 4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
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Cambridge Assessment International Education
Cambridge International Advanced Subsidiary and Advanced Level
* 5 4 1 6 2 4 8 0 7 2 *
9702/23
PHYSICS
Paper 2 AS Level Structured Questions
October/November 2019
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Electronic calculators may be used.
You may lose marks if you do not show your working or if you do not use appropriate units.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
This document consists of 17 printed pages and 3 blank pages.
DC (NH/CB) 164215/2
© UCLES 2019
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Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2019
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3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ= −
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p=
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt

v =±ω√
(x02 – x 2)
Doppler effect
fo =
electric potential
V=
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ=
© UCLES 2019
0.693
t
1
2
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4
Answer all the questions in the spaces provided.
1
(a) Determine the SI base units of the moment of a force.
SI base units ......................................................... [1]
(b) A uniform square sheet of card ABCD is freely pivoted by a pin at a point P. The card is held
in a vertical plane by an external force in the position shown in Fig. 1.1.
B
17 cm
A
45°
4.0 cm
P
G
C
0.15 N
D
Fig. 1.1 (not to scale)
The card has weight 0.15 N which may be considered to act at the centre of gravity G. Each
side of the card has length 17 cm. Point P lies on the horizontal line AC and is 4.0 cm from
corner A. Line BD is vertical.
The card is released by removing the external force. The card then swings in a vertical plane
until it comes to rest.
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(i)
Calculate the magnitude of the resultant moment about point P acting on the card
immediately after it is released.
moment = .................................................. N m [2]
(ii)
Explain why, when the card has come to rest, its centre of gravity is vertically below
point P.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
[Total: 5]
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2
(a) State what is meant by work done.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) A lift (elevator) of weight 13.0 kN is connected by a cable to a motor, as shown in Fig. 2.1.
motor
cable
lift (elevator)
weight 13.0 kN
v
Fig. 2.1
The lift is pulled up a vertical shaft by the cable. A constant frictional force of 2.0 kN acts on
the lift when it is moving. The variation with time t of the speed v of the lift is shown in Fig. 2.2.
3.0
v / m s –1
2.0
1.0
0
0
1
2
3
4
Fig. 2.2
© UCLES 2019
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5
t/s
6
7
8
7
(i)
Use Fig. 2.2 to determine:
1.
the acceleration of the lift between time t = 0 and t = 3.0 s
acceleration = ................................................ m s–2 [2]
2.
the work done by the motor to raise the lift between time t = 3.0 s and t = 6.0 s.
work done = ...................................................... J [2]
(ii)
The motor has an efficiency of 67%. The tension in the cable is 1.6 × 104 N at time
t = 2.5 s.
Determine the input power to the motor at this time.
input power = ..................................................... W [3]
(iii)
State and explain whether the increase in gravitational potential energy of the lift from
time t = 0 to t = 7.0 s is less than, the same as, or greater than the work done by the
motor. A calculation is not required.
...........................................................................................................................................
..................................................................................................................................... [1]
[Total: 9]
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3
(a) State the property of an object that experiences a force when the object is placed in:
(i)
a gravitational field
..................................................................................................................................... [1]
(ii)
an electric field.
..................................................................................................................................... [1]
(b) A potential difference of 1.2 × 103 V is applied between a pair of horizontal metal plates in a
vacuum, as shown in Fig. 3.1.
p
particle
charge –4.2 × 10–9 C
mass 5.9 × 10–6 kg
velocity 0.75 m s–1
1.8 cm
top metal plate
Y
X 1.8 cm
+
1.2 × 103 V
–
bottom metal plate
Fig. 3.1 (not to scale)
The separation of the plates is 3.6 cm. The electric field between the plates is uniform.
A particle of mass 5.9 × 10–6 kg and charge –4.2 × 10–9 C enters the field at point X with a
horizontal velocity of 0.75 m s–1 along a line midway between the two plates.
The particle is deflected by the field and hits the top plate at point Y.
(i)
Calculate the magnitude of the electric force acting on the particle in the field.
electric force = ...................................................... N [3]
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(ii)
By considering the resultant vertical force acting on the particle, show that the
acceleration of the particle in the electric and gravitational fields is 14 m s–2.
[4]
(iii)
Determine:
1.
the time taken for the particle to move from X to Y
time taken = ....................................................... s [2]
2.
the distance p of point Y from the left-hand edge of the top plate.
p = ...................................................... m [1]
[Total: 12]
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BLANK PAGE
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4
A ball X moves along a horizontal frictionless surface and collides with another ball Y, as illustrated
in Fig. 4.1.
X
0.300 kg
vX
60.0°
A
B
60.0°
A
B
X Y
6.00 m s–1
Y
0.200 kg
BEFORE COLLISION
AFTER COLLISION
Fig. 4.1 (not to scale)
Fig. 4.2 (not to scale)
Ball X has mass 0.300 kg and initial velocity vX at an angle of 60.0° to line AB.
Ball Y has mass 0.200 kg and initial velocity 6.00 m s–1 at an angle of 60.0° to line AB.
The balls stick together during the collision and then travel along line AB, as illustrated in Fig. 4.2.
(a) (i)
Calculate, to three significant figures, the component of the initial momentum of ball Y
that is perpendicular to line AB.
component of momentum = ............................................ kg m s–1 [2]
(ii)
By considering the component of the initial momentum of each ball perpendicular to
line AB, calculate, to three significant figures, vX.
vX = .................................................m s–1 [1]
(iii)
Show that the speed of the two balls after the collision is 2.4 m s–1.
[2]
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(b) The two balls continue moving together along the horizontal frictionless surface towards a
spring, as illustrated in Fig. 4.3.
balls of total
mass 0.500 kg
horizontal
surface
2.4 m s–1
X
spring of spring constant 72 N m–1
Y
Fig. 4.3
The balls hit the spring and remain stuck together as they decelerate to rest. All the kinetic
energy of the balls is converted into elastic potential energy of the spring. The energy E
stored in the spring is given by
E = 1 kx 2
2
where k is the spring constant of the spring and x is its compression.
The spring obeys Hooke’s law and has a spring constant of 72 N m–1.
(i)
Determine the maximum compression of the spring caused by the two balls.
maximum compression = ...................................................... m [3]
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(ii)
On Fig. 4.4, sketch graphs to show the variation with compression x of the spring, from
zero to maximum compression, of:
1.
the magnitude of the deceleration a of the balls
2.
the kinetic energy Ek of the balls.
Numerical values are not required.
a
0
Ek
0
0
x
Fig. 4.4
0
x
[3]
[Total: 11]
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5
(a) Light waves emerging from the slits of a diffraction grating are coherent and produce an
interference pattern.
Explain what is meant by:
(i)
coherence
...........................................................................................................................................
..................................................................................................................................... [1]
(ii)
interference.
...........................................................................................................................................
..................................................................................................................................... [1]
(b) A narrow beam of light from a laser is incident normally on a diffraction grating, as shown in
Fig. 5.1.
second order
maximum spot
laser
light
zero order
maximum spot
51°
51°
diffraction
grating
second order
maximum spot
screen
Fig. 5.1 (not to scale)
Spots of light are seen on a screen positioned parallel to the grating. The angle corresponding
to each of the second order maxima is 51°. The number of lines per unit length on the
diffraction grating is 6.7 × 105 m–1.
(i)
Determine the wavelength of the light.
wavelength = ..................................................... m [2]
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(ii)
State and explain the change, if any, to the distance between the second order maximum
spots on the screen when the light from the laser is replaced by light of a shorter
wavelength.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[1]
[Total: 5]
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6
A battery of electromotive force (e.m.f.) 12 V and negligible internal resistance is connected to a
network of two lamps and two resistors, as shown in Fig. 6.1.
0.50 A
0.20 A
12 V
R
Y
X
28 Ω
Fig. 6.1
The two lamps in the circuit have equal resistances. The two resistors have resistances R and
28 Ω. The lamps are connected at junction X and the resistors are connected at junction Y. The
current in the battery is 0.50 A and the current in the lamps is 0.20 A.
(a) Calculate:
(i)
the resistance of each lamp
resistance = ...................................................... Ω [2]
(ii)
resistance R.
R = ...................................................... Ω [2]
(b) Determine the potential difference VXY between points X and Y.
© UCLES 2019
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(c) Calculate the ratio
total power dissipated by the lamps .
total power produced by the battery
ratio = ......................................................... [2]
(d) The resistor of resistance R is now replaced by another resistor of lower resistance.
State and explain the effect, if any, of this change on the ratio in (c).
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
[Total: 11]
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7
A stationary nucleus of a radioactive isotope X decays by emitting an α-particle to produce a
nucleus of neptunium-237 and 5.5 MeV of energy. The decay is represented by
X
23 7 Np
93
+ α + 5.5 MeV.
(a) Calculate the number of protons and the number of neutrons in a nucleus of X.
number of protons = ...............................................................
number of neutrons = ...............................................................
[2]
(b) Explain why the energy transferred to the α-particle as kinetic energy is less than the 5.5 MeV
of energy released in the decay process.
...................................................................................................................................................
............................................................................................................................................. [1]
(c) A sample of X is used to produce a beam of α-particles in a vacuum. The number of α-particles
passing a fixed point in the beam in a time of 30 s is 6.9 × 1011.
(i)
Calculate the average current produced by the beam of α-particles.
current = ...................................................... A [2]
(ii)
Determine the total power, in W, that is produced by the decay of 6.9 × 1011 nuclei of X in
a time of 30 s.
power = ..................................................... W [2]
[Total: 7]
© UCLES 2019
9702/23/O/N/19
19
BLANK PAGE
© UCLES 2019
9702/23/O/N/19
20
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2019
9702/23/O/N/19
Cambridge International AS & A Level
* 8 3 9 1 3 2 2 5 3 8 *
PHYSICS
9702/21
Paper 2 AS Level Structured Questions
May/June 2020
1 hour 15 minutes
You must answer on the question paper.
No additional materials are needed.
INSTRUCTIONS
●
Answer all questions.
●
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
●
Write your name, centre number and candidate number in the boxes at the top of the page.
●
Write your answer to each question in the space provided.
●
Do not use an erasable pen or correction fluid.
●
Do not write on any bar codes.
●
You may use a calculator.
●
You should show all your working and use appropriate units.
INFORMATION
●
The total mark for this paper is 60.
●
The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Blank pages are indicated.
DC (PQ) 181668/3
© UCLES 2020
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2020
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3
Formulae
1
uniformly accelerated motion
s = ut + 2 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = p ΔV
Gm
r
gravitational potential
φ =−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p =
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V =
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W = 2 QV
electric current
resistors in series
resistors in parallel
Hall voltage
1
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ω t
radioactive decay
x = x0 exp(−λt )
decay constant
λ =
© UCLES 2020
0.693
t
1
2
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5
Answer all the questions in the spaces provided.
1
(a) Use an expression for work done, in terms of force, to show that the SI base units of energy
are kg m2 s–2.
[2]
(b) (i)
The energy E stored in an electrical component is given by
E=
Q2
2C
where Q is charge and C is a constant.
Use this equation and the information in (a) to determine the SI base units of C.
SI base units ......................................................... [2]
(ii)
Measurements of a constant current in a wire are taken using an analogue ammeter.
For these measurements, describe one possible cause of:
1. a random error
...........................................................................................................................................
...........................................................................................................................................
2. a systematic error.
...........................................................................................................................................
...........................................................................................................................................
[2]
[Total: 6]
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2
(a) State Newton’s second law of motion.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) A delivery company suggests using a remote-controlled aircraft to drop a parcel into the
garden of a customer. When the aircraft is vertically above point P on the ground, it releases
the parcel with a velocity that is horizontal and of magnitude 5.4 m s–1. The path of the parcel
is shown in Fig. 2.1.
5.4 m s–1
X
parcel
path of parcel
h
P
Q
d
horizontal
ground
Fig. 2.1 (not to scale)
The parcel takes a time of 0.81 s after its release to reach point Q on the horizontal ground.
Assume air resistance is negligible.
(i)
On Fig. 2.1, draw an arrow from point X to show the direction of the acceleration of the
parcel when it is at that point.
[1]
(ii)
Determine the height h of the parcel above the ground when it is released.
h = ..................................................... m [2]
(iii)
Calculate the horizontal distance d between points P and Q.
d = ..................................................... m [1]
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(c) Another parcel is accidentally released from rest by a different aircraft when it is hovering at a
great height above the ground. Air resistance is now significant.
(i)
On Fig. 2.2, draw arrows to show the directions of the forces acting on the parcel as it
falls vertically downwards. Label each arrow with the name of the force.
parcel
velocity
Fig. 2.2
(ii)
[2]
By considering the forces acting on the parcel, state and explain the variation, if any,
of the acceleration of the parcel as it moves downwards before it reaches constant
(terminal) speed.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [3]
(iii)
Describe the energy conversion that occurs when the parcel is falling through the air at
constant (terminal) speed.
...........................................................................................................................................
..................................................................................................................................... [1]
[Total: 11]
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3
(a) State two conditions for an object to be in equilibrium.
1. ...............................................................................................................................................
...................................................................................................................................................
2. ...............................................................................................................................................
...................................................................................................................................................
[2]
(b) A sphere of weight 2.4 N is suspended by a wire from a fixed point P. A horizontal string is
used to hold the sphere in equilibrium with the wire at an angle of 53° to the horizontal, as
shown in Fig. 3.1.
P
string
wire
T
53°
horizontal
F
sphere
weight
2.4 N
Fig. 3.1 (not to scale)
(i)
Calculate:
1. the tension T in the wire
T = ............................................................ N
2. the force F exerted by the string on the sphere.
F = ............................................................ N
[2]
(ii)
© UCLES 2020
The wire has a circular cross-section of diameter 0.50 mm. Determine the stress σ in the
wire.
9702/21/M/J/20
σ = .................................................... Pa [3]
9
(c) The string is disconnected from the sphere in (b). The sphere then swings from its initial rest
position A, as illustrated in Fig. 3.2.
P
75 cm
53°
h
A
B
Fig. 3.2 (not to scale)
The sphere reaches maximum speed when it is at the bottom of the swing at position B. The
distance between P and the centre of the sphere is 75 cm.
Air resistance is negligible and energy losses at P are negligible.
(i)
Show that the vertical distance h between A and B is 15 cm.
[1]
(ii)
Calculate the change in gravitational potential energy of the sphere as it moves from A
to B.
change in gravitational potential energy = ...................................................... J [2]
(iii)
Use your answer in (c)(ii) to determine the speed of the sphere at B.
Show your working.
speed = ................................................ m s–1 [3]
[Total: 13]
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4
(a) (i)
By reference to the direction of propagation of energy, state what is meant by a
longitudinal wave.
...........................................................................................................................................
..................................................................................................................................... [1]
(ii)
State the principle of superposition.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
(b) The wavelength of light from a laser is determined using the apparatus shown in Fig. 4.1.
double
slit
screen
light
3.7 × 10 –4 m
2.3 m
Fig. 4.1 (not to scale)
The light from the laser is incident normally on the plane of the double slit.
The separation of the two slits is 3.7 × 10–4 m. The screen is parallel to the plane of the double
slit. The distance between the screen and the double slit is 2.3 m.
A pattern of bright fringes and dark fringes is seen on the screen. The separation of adjacent
bright fringes on the screen is 4.3 × 10–3 m.
(i)
Calculate the wavelength, in nm, of the light.
wavelength = ................................................... nm [3]
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(ii)
The intensity of the light passing through each slit was initially the same. The intensity of
the light through one of the slits is now reduced.
Compare the appearance of the fringes before and after the change of intensity.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
[Total: 8]
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5
(a) Metal wire is used to connect a power supply to a lamp. The wire has a total resistance of
3.4 Ω and the metal has a resistivity of 2.6 × 10–8 Ω m. The total length of the wire is 59 m.
(i)
Show that the wire has a cross-sectional area of 4.5 × 10–7 m2.
[2]
(ii)
The potential difference across the total length of wire is 1.8 V.
Calculate the current in the wire.
current = ...................................................... A [1]
(iii)
The number density of the free electrons in the wire is 6.1 × 1028 m–3.
Calculate the average drift speed of the free electrons in the wire.
average drift speed = ................................................ m s–1 [2]
(b) A different wire carries a current. This wire has a part that is thinner than the rest of the wire, as
shown in Fig. 5.1.
wire
thinner part
Fig. 5.1
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(i)
State and explain qualitatively how the average drift speed of the free electrons in the
thinner part compares with that in the rest of the wire.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
(ii)
State and explain whether the power dissipated in the thinner part is the same, less or
more than the power dissipated in an equal length of the rest of the wire.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
(c) Three resistors have resistances of 180 Ω, 90 Ω and 30 Ω.
(i)
Sketch a diagram showing how two of these three resistors may be connected together
to give a combined resistance of 60 Ω between the terminals shown.
Ensure you label the values of the resistances in your diagram.
[1]
(ii)
A potential divider circuit is produced by connecting the three resistors to a battery of
electromotive force (e.m.f.) 12 V and negligible internal resistance. The potential divider
circuit provides an output potential difference VOUT of 8.0 V.
Fig. 5.2 shows the circuit diagram.
12 V
Fig. 5.2
On Fig. 5.2, label the resistances of all three resistors and the potential
difference VOUT.
[2]
[Total: 12]
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6
(a) Two horizontal metal plates are separated by a distance of 2.0 cm in a vacuum, as shown in
Fig. 6.1.
horizontal
plate
+180 V
2.0 cm
–120 V
horizontal
plate
Fig. 6.1
The top plate has an electric potential of +180 V and the bottom plate has an electric potential
of –120 V.
(i)
Determine the magnitude of the electric field strength between the plates.
electric field strength = ............................................... N C–1 [2]
(ii)
State the direction of the electric field.
..................................................................................................................................... [1]
238
(b) An uncharged atom of uranium-238 ( 92U) has a change made to its number of orbital
electrons. This causes the atom to change into a new particle (ion) X that has an overall
charge of +2e, where e is the elementary charge.
(i)
Determine the number of protons, neutrons and electrons in the particle (ion) X.
number of protons = ...............................................................
number of neutrons = ................................................................
number of electrons = ................................................................
[3]
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(ii)
The particle (ion) X is in the electric field in (a) at a point midway between the plates.
Determine the magnitude of the electric force acting on X.
force = ..................................................... N [2]
(iii)
238
The nucleus of uranium-238 ( 92U) decays in stages, by emitting α-particles and
230
β– particles, to form a nucleus of thorium-230 ( 90Th).
Calculate the total number of α-particles and the total number of β– particles that are
emitted during the decay of uranium-238 to thorium-230.
number of α-particles = ...............................................................
number of β– particles = ...............................................................
[2]
[Total: 10]
© UCLES 2020
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16
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
© UCLES 2020
9702/21/M/J/20
Cambridge International AS & A Level
* 4 6 4 2 4 2 7 0 6 7 *
PHYSICS
9702/22
Paper 2 AS Level Structured Questions
May/June 2020
1 hour 15 minutes
You must answer on the question paper.
No additional materials are needed.
INSTRUCTIONS
●
Answer all questions.
●
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
●
Write your name, centre number and candidate number in the boxes at the top of the page.
●
Write your answer to each question in the space provided.
●
Do not use an erasable pen or correction fluid.
●
Do not write on any bar codes.
●
You may use a calculator.
●
You should show all your working and use appropriate units.
INFORMATION
●
The total mark for this paper is 60.
●
The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Blank pages are indicated.
DC (PQ/FC) 181784/2
© UCLES 2020
[Turn over
2
Data
c = 3.00 × 108 m s−1
speed of light in free space
permeability of free space
μ0 = 4π × 10−7 H m−1
permittivity of free space
ε0 = 8.85 × 10−12 F m−1
(
1
= 8.99 × 109 m F−1)
4πε0
elementary charge
e = 1.60 × 10−19 C
the Planck constant
h = 6.63 × 10−34 J s
unified atomic mass unit
1 u = 1.66 × 10−27 kg
rest mass of electron
me = 9.11 × 10−31 kg
rest mass of proton
mp = 1.67 × 10−27 kg
molar gas constant
R = 8.31 J K−1 mol−1
the Avogadro constant
NA = 6.02 × 1023 mol−1
the Boltzmann constant
k = 1.38 × 10−23 J K−1
gravitational constant
G = 6.67 × 10−11 N m2 kg−2
acceleration of free fall
g = 9.81 m s−2
© UCLES 2020
9702/22/M/J/20
3
Formulae
uniformly accelerated motion
s = ut + 12 at 2
v 2 = u 2 + 2as
work done on/by a gas
W = pΔV
Gm
r
gravitational potential
φ=−
hydrostatic pressure
p = ρgh
pressure of an ideal gas
p=
simple harmonic motion
a = − ω 2x
velocity of particle in s.h.m.
v = v0 cos ωt
v = ± ω (x 02 - x 2)
Doppler effect
fo =
electric potential
V=
capacitors in series
1
3
Nm 2
〈c 〉
V
fsv
v ± vs
Q
4πε0r
1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel
C = C1 + C2 + . . .
energy of charged capacitor
W=
electric current
resistors in series
resistors in parallel
Hall voltage
1
QV
2
I = Anvq
R = R1 + R2 + . . .
1/R = 1/R1 + 1/R2 + . . .
VH =
BI
ntq
alternating current/voltage
x = x0 sin ωt
radioactive decay
x = x0 exp(−λt)
decay constant
λ=
© UCLES 2020
0.693
t
1
2
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© UCLES 2020
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5
Answer all the questions in the spaces provided.
1
(a) Define velocity.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) The drag force FD acting on a car moving with speed v along a straight horizontal road is
given by
FD = v 2Ak
where k is a constant and A is the cross-sectional area of the car.
Determine the SI base units of k.
SI base units ......................................................... [2]
(c) The value of k, in SI base units, for the car in (b) is 0.24. The cross-sectional area A of the
car is 5.1 m2.
The car is travelling with a constant speed along a straight road and the output power of the
engine is 4.8 × 104 W. Assume that the output power of the engine is equal to the rate at which
the drag force FD is doing work against the car.
Determine the speed of the car.
speed = ................................................ m s–1 [3]
[Total: 6]
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2
(a) Fig. 2.1 shows the velocity–time graph for an object moving in a straight line.
velocity
v
u
0
0
t
time
Fig. 2.1
(i)
Determine an expression, in terms of u, v and t, for the area under the graph.
area = .......................................................... [1]
(ii)
State the name of the quantity represented by the area under the graph.
..................................................................................................................................... [1]
(b) A ball is kicked with a velocity of 15 m s–1 at an angle of 60° to horizontal ground. The ball
then strikes a vertical wall at the instant when the path of the ball becomes horizontal, as
shown in Fig. 2.2.
path of
ball
vertical
wall
velocity
15 m s–1
ball
60°
horizontal
ground
Fig. 2.2 (not to scale)
Assume that air resistance is negligible.
© UCLES 2020
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7
(i)
By considering the vertical motion of the ball, calculate the time it takes to reach the wall.
time = ...................................................... s [3]
(ii)
Explain why the horizontal component of the velocity of the ball remains constant as it
moves to the wall.
...........................................................................................................................................
..................................................................................................................................... [1]
(iii)
Show that the ball strikes the wall with a horizontal velocity of 7.5 m s–1.
[1]
(c) The mass of the ball in (b) is 0.40 kg. It is in contact with the wall for a time of 0.12 s and
rebounds horizontally with a speed of 4.3 m s–1.
(i)
Use the information from (b)(iii) to calculate the change in momentum of the ball due to
the collision.
change in momentum = ........................................... kg m s–1 [2]
(ii)
Calculate the magnitude of the average force exerted on the ball by the wall.
average force = ..................................................... N [1]
[Total: 10]
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3
(a) Explain what is meant by work done.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) A ball of mass 0.42 kg is dropped from the top of a building. The ball falls from rest through
a vertical distance of 78 m to the ground. Air resistance is significant so that the ball reaches
constant (terminal) velocity before hitting the ground. The ball hits the ground with a speed
of 23 m s–1.
(i)
Calculate, for the ball falling from the top of the building to the ground:
1.
the decrease in gravitational potential energy
decrease in gravitational potential energy = ...................................................... J [2]
2.
the increase in kinetic energy.
increase in kinetic energy = ...................................................... J [2]
(ii)
Use your answers in (b)(i) to determine the average resistive force acting on the ball as
it falls from the top of the building to the ground.
average resistive force = ..................................................... N [2]
© UCLES 2020
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9
(c) The ball in (b) is dropped at time t = 0 and hits the ground at time t = T. The acceleration of
free fall is g.
On Fig. 3.1, sketch a line to show the variation of the acceleration a of the ball with time t from
time t = 0 to t = T.
g
a
0
0
t
Fig. 3.1
T
[2]
[Total: 9]
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4
(a) State the difference between progressive waves and stationary waves in terms of the transfer
of energy along the wave.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) A progressive wave travels from left to right along a stretched string. Fig. 4.1 shows part of
the string at one instant.
R
Q
string
direction of
wave travel
P
0.48 m
Fig. 4.1
P, Q and R are three different points on the string. The distance between P and R is 0.48 m.
The wave has a period of 0.020 s.
(i)
Use Fig. 4.1 to determine the wavelength of the wave.
wavelength = ..................................................... m [1]
(ii) Calculate the speed of the wave.
speed = ................................................ m s–1 [2]
(iii)
Determine the phase difference between points Q and R.
phase difference = ........................................................ ° [1]
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(iv)
Fig. 4.1 shows the position of the string at time t = 0. Describe how the displacement of
point Q on the string varies with time from t = 0 to t = 0.010 s.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
(c) A stationary wave is formed on a different string that is stretched between two fixed points
X and Y. Fig. 4.2 shows the position of the string when each point is at its maximum
displacement.
W
X
Z
Y
Fig. 4.2
(i)
Explain what is meant by a node of a stationary wave.
..................................................................................................................................... [1]
(ii)
State the number of antinodes of the wave shown in Fig. 4.2.
number = ......................................................... [1]
(iii)
State the phase difference between points W and Z on the string.
phase difference = ........................................................° [1]
(iv)
A new stationary wave is now formed on the string. The new wave has a frequency
that is half of the frequency of the wave shown in Fig. 4.2. The speed of the wave is
unchanged.
On Fig. 4.3, draw a position of the string, for this new wave, when each point is at its
maximum displacement.
X
Y
Fig. 4.3
[1]
[Total: 11]
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5
One end of a wire is attached to a fixed point. A force F is applied to the wire to cause extension x.
The variation with F of x is shown in Fig. 5.1.
0.6
0.5
x / mm
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
30
35
40
45
F/N
Fig. 5.1
The wire has a cross-sectional area of 4.1 × 10–7 m2 and is made of metal of Young modulus
1.7 × 1011 Pa. Assume that the cross-sectional area of the wire remains constant as the wire
extends.
(a) State the name of the law that describes the relationship between F and x shown in Fig. 5.1.
............................................................................................................................................. [1]
(b) The wire has an extension of 0.48 mm.
Determine:
(i)
the stress
stress = .................................................... Pa [2]
(ii)
the strain.
strain = ......................................................... [2]
© UCLES 2020
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13
(c) The resistivity of the metal of the wire is 3.7 × 10–7 Ω m.
Determine the change in resistance of the wire when the extension x of the wire changes
from x = 0.48 mm to x = 0.60 mm.
change in resistance = ..................................................... Ω [3]
(d) A force of greater than 45 N is now applied to the wire.
Describe how it may be checked that the elastic limit of the wire has not been exceeded.
...................................................................................................................................................
............................................................................................................................................. [1]
[Total: 9]
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6
(a) A battery of electromotive force (e.m.f.) 7.8 V and internal resistance r is connected to a
filament lamp, as shown in Fig. 6.1.
7.8 V
r
Fig. 6.1
A total charge of 750 C moves through the battery in a time interval of 1500 s. During this time
the filament lamp dissipates 5.7 kJ of energy. The e.m.f. of the battery remains constant.
(i)
Explain, in terms of energy and without a calculation, why the potential difference across
the lamp must be less than the e.m.f. of the battery.
...........................................................................................................................................
..................................................................................................................................... [1]
(ii)
Calculate:
1.
the current in the circuit
current = ...................................................... A [2]
2.
the potential difference across the lamp
potential difference = ...................................................... V [2]
3.
the internal resistance of the battery.
internal resistance = ...................................................... Ω [2]
© UCLES 2020
9702/22/M/J/20
15
(b) A student is provided with three resistors of resistances 90 Ω, 45 Ω and 20 Ω.
(i)
Sketch a circuit diagram showing how two of these three resistors may be connected
together to give a combined resistance of 30 Ω between the terminals shown. Label the
values of the resistances on your diagram.
[1]
(ii)
A potential divider circuit is produced by connecting the three resistors to a battery of
e.m.f. 9.0 V and negligible internal resistance. The potential divider circuit provides an
output potential difference VOUT of 3.6 V. The circuit diagram is shown in Fig. 6.2.
9.0 V
Fig. 6.2
On Fig. 6.2, label the resistances of all three resistors and the potential difference VOUT.
[2]
[Total: 10]
© UCLES 2020
9702/22/M/J/20
[Turn over
16
7
(a) A nucleus of an element X decays by emitting a β+ particle to produce a nucleus of
39
potassium-39 (19K) and a neutrino. The decay is represented by
Q
SX
(i)
39
19K
+ RP β+ + 00ν.
State the number represented by each of the following letters.
P ..............................
Q ..............................
R ..............................
S ..............................
(ii)
[2]
State the name of the interaction (force) that gives rise to β+ decay.
..................................................................................................................................... [1]
(b) A hadron is composed of three identical quarks and has a charge of +2e, where e is the
elementary charge.
Determine a possible type (flavour) of the quarks.
Explain your working.
...................................................................................................................................................
............................................................................................................................................. [2]
[Total: 5]
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© UCLES 2020
9702/22/M/J/20
Cambridge International AS & A Level
* 1 1 0 0 0 9 6 8 3 7 *
PHYSICS
9702/23
Paper 2 AS Level Structured Questions
May/June 2020
1 hour 15 minutes
You must answer on the question paper.
No additional materials are needed.
INSTRUCTIONS
●
Answer all questions.
●
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
●
Write your name, centre number and candidate number in the boxes at the top of the page.
●
Write your answer to each question in the space provided.
●
Do not use an erasable pen or correction fluid.
●
Do not write on any bar codes.
●
You may use a calculator.
●
You should show all your working and use appropriate units.
INFORMATION
●
The total mark for this paper is 60.
●
The number of marks for each ques