F
GENERAL CERTIFICATE OF SECONDARY EDUCATION
B281A
MATHEMATICS C (GRADUATED ASSESSMENT)
Terminal Paper – Section A
(Foundation Tier)
*OCE/T68120*
Monday 1 June 2009
Morning
Candidates answer on the question paper
OCR Supplied Materials:
None
Duration: 1 hour
Other Materials Required:
•
Geometrical instruments
•
Pie chart scale (optional)
•
Tracing paper (optional)
*
B
2
8
1
A
*
INSTRUCTIONS TO CANDIDATES
•
•
•
•
•
•
•
Write your name clearly in capital letters, your Centre Number and Candidate Number in the boxes above.
Use black ink. Pencil may be used for graphs and diagrams only.
Read each question carefully and make sure that you know what you have to do before starting your answer.
Show your working. Marks may be given for a correct method even if the answer is incorrect.
Answer all the questions.
Do not write in the bar codes.
Write your answer to each question in the space provided, however additional paper may be used if
necessary.
INFORMATION FOR CANDIDATES
•
•
•
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this Section is 50.
This document consists of 12 pages. Any blank pages are indicated.
WARNING
No calculator can be
used for Section A of
this paper
© OCR 2009 [100/1142/0]
SPA (KN) T68120/5
OCR is an exempt Charity
Turn over
2
Formulae Sheet
a
Area of trapezium =
1
2
h
(a + b)h
b
Volume of prism = (area of cross-section)
length
crosssection
h
lengt
PLEASE DO NOT WRITE ON THIS PAGE
© OCR 2009
3
1
Work out.
(a) 300 – 139
(a) .................................... [2]
(b) 65 ÷ 5
(b) ................................... [1]
2
At 9 am each day Andy records the temperature in his garden.
The table shows the temperatures for 5 days in January.
Day
Temperature (°C)
Monday
2
Tuesday
–4
Wednesday
–2
Thursday
5
Friday
1
(a) On which day was the temperature lowest?
(a) .................................... [1]
(b) How many degrees warmer was Thursday than Wednesday?
(b) ................................... [1]
(c) On Saturday the temperature was 4 degrees lower than on Friday.
What was the temperature on Saturday?
(c) ............................... °C [1]
© OCR 2009
Turn over
4
3
Work out the value of 5a + 3b when a = 4 and b = 2.
......................................... [2]
(a) This bar chart shows the number of newspapers a shop sells on some days during one week.
500
450
400
350
Number of newspapers sold
4
300
250
200
150
100
50
0
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
(i) How many newspapers did the shop sell on Monday?
(a)(i) ................................ [1]
(ii) On Friday the shop sold 440 newspapers.
Show this on the bar chart.
[1]
(iii) How many more newspapers did the shop sell on Saturday than on Sunday?
(iii) ................................ [1]
© OCR 2009
5
(b) This table shows the average daily sales of newspapers in the UK in July 2007.
Newspaper
Average daily sales
Daily Express
735 307
Daily Mirror
1 496 572
Daily Star
811 988
Financial Times
130 007
The Daily Mail
2 205 172
The Daily Telegraph
833 430
The Guardian
311 768
The Independent
189 797
The Sun
2 916 821
The Times
595 172
(i) Which newspaper had the lowest average daily sales?
(b)(i) .................................................... [1]
(ii) Write 2 916 821 correct to the nearest million.
(ii) .................................................... [1]
(iii) Write 833 430 correct to the nearest thousand.
(iii) .................................................... [1]
(c) These were the weekday prices, in pence, of the newspapers.
40
40
35
130
45
70
70
70
35
65
(i) Find the mode and the median of these prices.
(c)(i) mode ................... p
median ................. p [3]
(ii) Give a reason why the median is a better average to use than the
mode for these newspaper prices.
....................................................................................................................................................
............................................................................................................................................... [1]
© OCR 2009
Turn over
6
5
The cash price of this TV is £600.
Phony
The shop offers a ʻcredit dealʼ.
Pay 25% deposit and then 12 payments of £49
(a) Work out 25% of £600.
(a) £ ................................. [2]
(b) John chooses the credit deal.
How much more does John pay than the cash price?
(b) £ ................................ [4]
© OCR 2009
7
6
This is a sketch of Maryʼs rectangular garden.
House
12 m
Not to scale
9m
(a) Mary is buying new fence panels for the two long sides and one short side of the garden.
Each fence panel is 1·5 m wide.
Work out how many panels Mary needs to buy.
(a) .................................... [2]
(b) Mary decides to use 1–3 of the garden for growing vegetables.
Work out the area for growing vegetables.
(b) ..............................m2 [3]
© OCR 2009
Turn over
8
7
Solve these equations.
x
(a) – = 5
4
(a) .................................... [1]
(b) 2x – 5 = 21
(b) ................................... [2]
8
Here are three consecutive integers.
n
n+1
n+2
(a) Find an expression for the sum of these three integers.
Write your answer as simply as possible.
(a) .................................... [1]
(b) Explain how you can tell from the answer to part (a) that the sum of
three consecutive integers is always divisible by 3.
............................................................................................................................................................
....................................................................................................................................................... [1]
© OCR 2009
9
9
For a drink, Meera mixes lime cordial and lemonade in the ratio 1 : 4.
(a) How much lemonade does she need to use with 100 ml of lime cordial?
(a) ............................... ml [1]
(b) Meera wants to make 800 ml of this drink.
Calculate how much lime cordial she needs.
(b) .............................. ml [2]
(c) Meera drinks 480 ml of the 800 ml.
Write the ratio 480 : 800 as simply as possible.
(c) ................. : ................ [2]
© OCR 2009
Turn over
10
10 (a) Insert brackets in each of the following calculations so that they are correct.
2 + 5 ×
—4
= —28
2 × 5 +
—4 2
= 2
2 × 5 +
—4 2
= 36
[3]
(b) Expand.
5(3x − 4)
(b) ................................... [1]
(c) Factorise fully.
6x + 3x2
(c) .................................... [2]
© OCR 2009
11
11
(a) Complete the table for y = 3 + 3x − x2.
x
–1
0
y
–1
3
1
2
3
4
3
–1
[1]
(b) Draw the graph of y = 3 + 3x − x2.
y
6
5
4
3
2
1
–1
0
–1
1
2
3
4
x
–2
[2]
(c) Use your graph to find the values of x for which 3 + 3x − x2 = 0.
(c) .................................... [2]
© OCR 2009
12
PLEASE DO NOT WRITE ON THIS PAGE
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, is given to all schools that receive assessment material 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 1PB.
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 2009
F
GENERAL CERTIFICATE OF SECONDARY EDUCATION
B281B
MATHEMATICS C (GRADUATED ASSESSMENT)
Terminal Paper – Section B
(Foundation Tier)
*OCE/T68122*
Monday 1 June 2009
Morning
Candidates answer on the question paper
OCR Supplied Materials:
None
Duration: 1 hour
Other Materials Required:
•
Geometrical instruments
•
Pie chart scale (optional)
•
Tracing paper (optional)
•
Scientific or graphical calculator
*
B
2
8
1
B
*
INSTRUCTIONS TO CANDIDATES
•
•
•
•
•
•
•
Write your name clearly in capital letters, your Centre Number and Candidate Number in the boxes above.
Use black ink. Pencil may be used for graphs and diagrams only.
Read each question carefully and make sure that you know what you have to do before starting your answer.
Show all your working. Marks may be given for a correct method even if the answer is incorrect.
Answer all the questions.
Do not write in the bar codes.
Write your answer to each question in the space provided, however additional paper may be used if
necessary.
INFORMATION FOR CANDIDATES
•
•
•
•
•
•
The number of marks is given in brackets [ ] at the end of each question or part question.
Section B starts with question 12.
You are expected to use a calculator in Section B of this paper.
Use the π button on your calculator or take π to be 3·142 unless the question says otherwise.
The total number of marks for this Section is 50.
This document consists of 12 pages. Any blank pages are indicated.
© OCR 2009 [100/1142/0]
SPA (KN) T68122/5
OCR is an exempt Charity
Turn over
2
Formulae Sheet
a
Area of trapezium =
1
2
h
(a + b)h
b
Volume of prism = (area of cross-section)
length
crosssection
h
lengt
PLEASE DO NOT WRITE ON THIS PAGE
© OCR 2009
3
12
y
6
5
4
3
2
1
–2
–1
0
1
2
3
4
5
6
7
x
–1
–2
(a) Plot the points A (–1, 2) and B (5, 4).
[2]
(b) Mark the midpoint of the line AB with a cross. Label it M.
[1]
(c) Write down the coordinates of M.
(c) (............... , ...............) [1]
13 (a) Here are the first four terms of a sequence.
5
9
13
17
(i) Write down the next term in the sequence.
(a)(i) ................................ [1]
(ii) Describe the rule you used to work out the next term.
............................................................................................................................................... [1]
(b) Here are the first four terms of another sequence.
1280
640
320
160
(i) Write down the next term in the sequence.
(b)(i) ................................ [1]
(ii) Describe the rule you used to work out the next term.
............................................................................................................................................... [1]
© OCR 2009
Turn over
4
14 This is a map of the Isle of Portland.
Key
Area
1 km2
Scale: 2 cm to 1 km
R
N
Fortuneswell
× Easton
E
Weston
Southwell
ISLE OF
PORTLAND
L
Portland Bill
(a) Estimate the area of the Isle of Portland.
(a) .............................km2 [2]
© OCR 2009
5
(b) Jenny walks from the roundabout (marked R) to Easton (marked E).
In which compass direction does she start walking?
(b) ................................... [1]
(c) She meets some friends at Easton and they walk along the road to the
lighthouse at Portland Bill (marked L).
Estimate the distance from Easton to the lighthouse.
Give the units of your answer.
(c) .................................... [3]
(d) Jenny buys 3 coffees and 3 biscuits at the café near the lighthouse.
The coffees cost 80p each and the biscuits cost 27p each.
Jenny pays with a £5 note.
How much change should she receive?
(d) £ ................................ [3]
(e) After visiting the café they travel home by bus.
The bus leaves Portland Bill at 11 39 and they arrive home at 12 06.
How long does this journey take?
(e) .......................minutes [1]
© OCR 2009
Turn over
6
15 Each of these two statements is false.
For each statement, give an example to show that it is false.
Statement
Example
odd number + odd number = odd number
odd number × odd number = even number
[2]
16 (a) Shade three more squares so that the dashed line is a line of symmetry.
[2]
(b) Write down the order of rotation symmetry for each of these shapes.
....................................
....................................
....................................
[2]
© OCR 2009
7
17 (a) Move-it estate agency sells 5 properties during one week.
These are the selling prices.
£145 000
£210 000
£165 000
£95 000
£180 000
Work out the mean selling price.
(a) £.................................. [3]
(b) During the year Move-it sells 180 properties.
• 18 bungalows
• 45 flats
• 117 houses
Draw and label a pie chart to illustrate the data.
[3]
© OCR 2009
Turn over
8
18 ABCD is a quadrilateral.
AD is extended to E.
B
110°
C
y
A
55°
Not to scale
x 130°
D
E
Work out angles x and y.
Give a reason for each answer.
x = ....................° because .........................................................................................................................
............................................................................................................................................................... [2]
y = ....................° because .........................................................................................................................
............................................................................................................................................................... [2]
© OCR 2009
9
19 The two cuboids, P and Q, each have the same volume.
Q
h cm
P
15 cm
4 cm
5 cm
10 cm
5 cm
(a) Work out the volume of cuboid P.
(a) ............................. cm3 [2]
(b) Work out the height, h cm, of cuboid Q.
(b) ..............................cm [2]
© OCR 2009
Turn over
10
20
y
9
8
7
6
5
4
B
3
2
A
1
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
x
–1
–2
–3
(a) Enlarge triangle A with centre (0, 2) and scale factor 3.
[3]
(b) Write down the column vector of the translation which maps triangle A onto triangle B.
(b)
冢 冣
.......
.......
© OCR 2009
[1]
11
21 Ana did a survey for the local optician.
She asked 100 people whether or not they wore glasses.
This table shows her results.
Wear glasses
Male
Not wear
glasses
Total
32
60
Female
15
40
Total
43
100
(a) Complete the table.
[1]
(b) One of the 100 people is chosen at random.
What is the probability that this person does not wear glasses?
(b) ................................... [1]
(c) One of the females is chosen at random.
What is the probability that she wears glasses?
(c) .................................... [1]
(d) In the survey, Ana wanted to find out how long each day people wore their glasses.
Write a suitable question she could ask, with response boxes for people to tick.
TURN OVER FOR QUESTION 22
© OCR 2009
[2]
12
22 The equation x3 − 8x + 6 = 0 has a solution between x = 2 and x = 3.
Use trial and improvement to find this solution correct to 1 decimal place.
Show all your trials and the values of their outcomes.
......................................... [3]
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, is given to all schools that receive assessment material 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 1PB.
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 2009
H
GENERAL CERTIFICATE OF SECONDARY EDUCATION
B282A
MATHEMATICS C (GRADUATED ASSESSMENT)
Terminal Paper – Section A
(Higher Tier)
Monday 1 June 2009
Morning
*OCE/T68124*
Candidatesansweronthequestionpaper
OCR Supplied Materials:
None
Duration:1hour
Other Materials Required:
• Geometricalinstruments
• Tracingpaper(optional)
*
B
2
8
2
A
*
INSTRUCTIONS TO CANDIDATES
•
•
•
•
•
•
•
Writeyournameclearlyincapitalletters,yourCentreNumberandCandidateNumberintheboxesabove.
Useblackink.Pencilmaybeusedforgraphsanddiagramsonly.
Readeachquestioncarefullyandmakesurethatyouknowwhatyouhavetodobeforestartingyouranswer.
Showyourworking.Marksmaybegivenforacorrectmethodeveniftheanswerisincorrect.
Answerallthequestions.
Donotwriteinthebarcodes.
Writeyouranswertoeachquestioninthespaceprovided,howeveradditionalpapermaybeusedif
necessary.
INFORMATION FOR CANDIDATES
•
•
•
Thenumberofmarksisgiveninbrackets[ ]attheendofeachquestionorpartquestion.
ThetotalnumberofmarksforthisSectionis50.
Thisdocumentconsistsof12pages.Anyblankpagesareindicated.
WARNING
No calculator can be
used for Section A of
this paper
©OCR2009 [100/1142/0]
SPA(KN)T68124/5
OCRisanexemptCharity
Turn over
2
Formulae Sheet
Formulae Sheet
a
Area of trapezium =
1
2
h
(a + b)h
b
Volume of prism = (area of cross-section) × length
crosssection
h
lengt
In any triangle ABC
a = b = c
Sine rule
sin A sin B sin C
C
a
b
Cosine rule a 2 = b 2 + c 2 – 2bc cos A
A
Area of triangle =
1
2 ab
Volume of sphere =
B
c
sin C
4
3
3 πr
r
Surface area of sphere = 4πr 2
Volume of cone = 13 πr 2h
Curved surface area of cone = πrl
l
h
r
The Quadratic Equation
The solutions of ax 2 + bx + c = 0, where a ≠ 0, are given by
x=
– b ± (b 2 – 4ac)
2a
PLEASE DO NOT WRITE ON THIS PAGE
© OCR 2009
1
3
For a drink, Meera mixes lime cordial and lemonade in the ratio 1 : 4.
(a) How much lemonade does she need to use with 100 ml of lime cordial?
(a) ............................... ml [1]
(b) Meera wants to make 800 ml of this drink.
Calculate how much lime cordial she needs.
(b) .............................. ml [2]
(c) Meera drinks 480 ml of the 800 ml.
Write the ratio 480 : 800 as simply as possible.
(c) ................. : ................ [2]
© OCR 2009
Turn over
2
4
(a) Insert brackets in each of the following calculations so that they are correct.
2 + 5 ×
—4
= —28
2 × 5 +
—4 2
= 2
2 × 5 +
—4 2
= 36
[3]
(b) Expand.
5(3x − 4)
(b) ................................... [1]
(c) Factorise fully.
6x + 3x2
(c) .................................... [2]
© OCR 2009
3
Here are three consecutive integers.
n
5
n+1
n+2
(a) Find an expression for the sum of these three integers.
Write your answer as simply as possible.
(a) .................................... [1]
(b) Explain how you can tell from the answer to part (a) that the sum of
three consecutive integers is always divisible by 3.
............................................................................................................................................................
....................................................................................................................................................... [1]
4
A
C
B
(a) Using ruler and compasses only, construct the bisector of angle ABC.
Leave in all your construction lines.
[2]
(b) The bisector of angle ABC intersects AC at D.
Measure AD.
(b) ..............................cm [1]
© OCR 2009
Turn over
5
(a) Complete the table for y = 3 + 3x − x2.
x
–1
0
y
–1
3
6
1
2
3
4
3
–1
[1]
(b) Draw the graph of y = 3 + 3x − x2.
y
6
5
4
3
2
1
–1
0
1
2
3
4
x
–1
–2
[2]
(c) Use your graph to find the values of x for which 3 + 3x − x2 = 0.
(c) .................................... [2]
© OCR 2009
6
(a) Solve.
7
5x − 2 = x + 4
(a) .................................... [3]
(b) Simplify.
(i) 3a2b × 4a3b
(b)(i) ................................ [2]
(ii) (x3)4
(ii) ............................... [1]
© OCR 2009
Turn over
7
8
These box plots represent data for the distances jumped in a Long Jump competition by boys and girls
in the under-15 age group.
Boys
Girls
3
3·5
4
4·5
5
5·5
Distance (metres)
(a) Find the median for the girls.
(a) ................................ m [1]
(b) Find the interquartile range for the boys.
(b) ............................... m [2]
(c) Make two comparisons between the distributions of the distances jumped
by the boys and the girls.
1 .........................................................................................................................................................
............................................................................................................................................................
2 .........................................................................................................................................................
....................................................................................................................................................... [2]
© OCR 2009
8
9
(a) In this diagram, O is the centre of the circle.
53°
Not to scale
O
x
Find angle x, giving your reason.
x = .................° because ....................................................................................................................
....................................................................................................................................................... [2]
(b) In this diagram, the tangent STU meets the circle at T.
Q
56°
Not to scale
R
y
42°
U
T
S
Find angle y, giving your reasons.
y = .................° because ....................................................................................................................
............................................................................................................................................................
....................................................................................................................................................... [3]
© OCR 2009
Turn over
9
10
A bowl contains 10 fruits.
There are 3 pears, 5 apples and 2 oranges.
Sarah takes a fruit at random from the bowl to eat at lunchtime.
Peter then takes a fruit at random from the bowl.
(a) Complete this tree diagram to show the probabilities of the fruits taken.
Sarah’s fruit
Peter’s fruit
pear
............
............
pear
orange
............
............
pear
............
............
............
apple
apple
orange
............
............
pear
............
............
orange
apple
............
apple
orange
[3]
(b) Calculate the probability that both Sarah and Peter take a pear.
(b) ................................... [2]
© OCR 2009
11
(c) Calculate the probability that at least one of Sarah and Peter takes an apple.
(c) .................................... [3]
TURN OVER FOR QUESTION 10
© OCR 2009
12
10 Find algebraically the coordinates of the points of intersection of the curve y = x2 + 7x + 9
and the line y = x + 4.
(............ , ............) and (............ , ............) [5]
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
AcknowledgementsBooklet.Thisisproducedforeachseriesofexaminations,isgiventoallschoolsthatreceiveassessmentmaterialandisfreelyavailabletodownloadfromourpublic
website(www.ocr.org.uk)aftertheliveexaminationseries.
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.
ForqueriesorfurtherinformationpleasecontacttheCopyrightTeam,FirstFloor,9HillsRoad,CambridgeCB21PB.
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
departmentoftheUniversityofCambridge.
© OCR 2009
H
GENERAL CERTIFICATE OF SECONDARY EDUCATION
B282B
MATHEMATICS C (GRADUATED ASSESSMENT)
Terminal Paper – Section B
(Higher Tier)
*OCE/T68126*
Monday 1 June 2009
Morning
Candidates answer on the question paper
OCR Supplied Materials:
None
Duration: 1 hour
Other Materials Required:
•
Geometrical instruments
•
Tracing paper (optional)
•
Scientific or graphical calculator
*
B
2
8
2
B
*
INSTRUCTIONS TO CANDIDATES
•
•
•
•
•
•
•
Write your name clearly in capital letters, your Centre Number and Candidate Number in the boxes above.
Use black ink. Pencil may be used for graphs and diagrams only.
Read each question carefully and make sure that you know what you have to do before starting your answer.
Show all your working. Marks may be given for a correct method even if the answer is incorrect.
Answer all the questions.
Do not write in the bar codes.
Write your answer to each question in the space provided, however additional paper may be used if
necessary.
INFORMATION FOR CANDIDATES
•
•
•
•
•
•
The number of marks is given in brackets [ ] at the end of each question or part question.
Section B starts with question 11.
You are expected to use a calculator in Section B of this paper.
Use the π button on your calculator or take π to be 3·142 unless the question says otherwise.
The total number of marks for this Section is 50.
This document consists of 12 pages. Any blank pages are indicated.
© OCR 2009 [100/1142/0]
SPA (KN) T68126/5
OCR is an exempt Charity
Turn over
2
Formulae Sheet
a
Area of trapezium =
1
2
h
(a + b)h
b
Volume of prism = (area of cross-section) × length
crosssection
h
lengt
In any triangle ABC
a = b = c
Sine rule
sin A sin B sin C
C
a
b
2
Cosine rule a =
b2
+
c2
– 2bc cos A
A
Area of triangle =
1
2 ab
B
c
sin C
Volume of sphere = 43 πr 3
r
Surface area of sphere = 4πr 2
Volume of cone = 13 πr 2h
Curved surface area of cone = πrl
l
h
r
The Quadratic Equation
The solutions of ax 2 + bx + c = 0, where a ≠ 0, are given by
x=
– b ± (b 2 – 4ac)
2a
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11
y
9
8
7
6
5
4
B
3
2
A
1
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
x
–1
–2
–3
(a) Enlarge triangle A with centre (0, 2) and scale factor 3.
[3]
(b) Write down the column vector of the translation which maps triangle A onto triangle B.
(b)
冢 冣
.......
.......
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[1]
4
12 Ana did a survey for the local optician.
She asked 100 people whether or not they wore glasses.
This table shows her results.
Wear glasses
Male
Not wear
glasses
Total
32
60
Female
15
40
Total
43
100
(a) Complete the table.
[1]
(b) One of the 100 people is chosen at random.
What is the probability that this person does not wear glasses?
(b) ................................... [1]
(c) One of the females is chosen at random.
What is the probability that she wears glasses?
(c) .................................... [1]
(d) In the survey, Ana wanted to find out how long each day people wore their glasses.
Write a suitable question she could ask, with response boxes for people to tick.
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[2]
5
13 Calculate.
17 × 89
–––––––––
5·16 × 0·72
Give your answer correct to 2 decimal places.
......................................... [2]
14 The equation x3 − 8x + 6 = 0 has a solution between x = 2 and x = 3.
Use trial and improvement to find this solution correct to 1 decimal place.
Show all your trials and the values of their outcomes.
......................................... [3]
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6
15 A childʼs wooden building block is a cylinder.
Its radius is 1·3 cm and its height is 11·4 cm.
Its mass is 45 g.
1·3
11·4
Calculate the density of the wood, in grams per cubic centimetre.
Give your answer to an appropriate degree of accuracy.
Show your method clearly.
...............................g/cm3 [6]
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16 (a) In a Bank Holiday Sale, a computer shop reduced its price for a printer by 12%.
The normal price was £70.
Calculate the sale price.
(a) £................................. [3]
(b) In the sale, the price of a computer was reduced by 20%.
Its sale price was £492.
Calculate its normal price.
(b) £ ................................ [3]
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8
17 (a) Peter investigated how many people were living in each house in his road.
This table summarises his results.
Number of people
in house
Frequency
1
3
2
7
3
4
4
6
5
6
6
3
7
1
Calculate the mean number of people living in a house in Peterʼs road.
(a) .................................... [3]
(b) The estimated populations of India and Russia in July 2007 are shown below.
• India
• Russia
1·13 × 109
1·41 × 108
Calculate the difference between these populations.
Give your answer in standard form.
(b) ................................... [2]
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18 Triangles ABC and PQR are similar, as shown.
Calculate AB.
P
Not to
scale
A
9·6 cm
4·0 cm
8·4 cm
R
C
B
Q
....................................cm [3]
–
19 Find the value of t for which 5 × 0·2t = 6·4 × 10 5.
......................................... [2]
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10
20 (a) Solve.
3y + 2 > 5y − 1
(a) .................................... [2]
(b) Make p the subject of this formula.
C = 2p2
(b) ................................... [2]
(c)
Express x2 − 8x + 5 in the form (x − a)2 + b.
(c) .................................... [3]
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21
V
17
D
C
O
A
M
16
B
VABCD is a pyramid.
Its base ABCD is a square of side 16 cm.
O is the centre of the base.
All the sloping edges are equal.
M is the midpoint of AB and VM is 17 cm.
(a) Show clearly that the perpendicular height, VO, of the pyramid is 15 cm.
[2]
(b) Calculate the volume of the pyramid.
(b) ............................ cm3 [2]
(c) Calculate the angle between VM and the base of the pyramid.
(c) ..................................° [3]
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