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MATHEMATICS (SYLLABUS D)
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Ordinary Level
4024/21
May/June 2012
Paper 2
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials:
Geometrical instruments
Electronic calculator
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 a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Section A
Answer all questions.
Section B
Answer any four questions.
If working is needed for any question it must be shown in the space below that question.
Omission of essential working will result in loss of marks.
You are expected to use an electronic calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 100.
For Examiner’s Use
This document consists of 24 printed pages.
DC (LEO/SW) 49518/3
© UCLES 2012
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2
ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.
1
(a) Express 72% as a fraction in its lowest terms.
Answer
..................................... [1]
(b) Write down two fractions that are equivalent to 0.4 .
Answer ............... and ............... [1]
2
The temperature in a freezer is –18 °C.
The outside temperature is 24 °C.
(a) Find the difference between the outside temperature and the freezer temperature.
Answer
................................°C [1]
(b) The temperature in a fridge is 22 °C warmer than the freezer temperature.
Find the temperature in the fridge.
Answer
© UCLES 2012
4024/12/M/J/12
................................°C [1]
For
Examiner’s
Use
3
3
(a) On the grid below, draw a quadrilateral with
For
Examiner’s
Use
no rotational symmetry
and just 1 line of symmetry.
[1]
(b) Complete this description.
A parallelogram has rotational symmetry of order ...........................
and ........................... lines of symmetry.
4
[1]
(a) A bag contains red and blue counters in the ratio 3 : 8.
There are 24 blue counters in the bag.
How many red counters are there?
Answer
..................................... [1]
(b) Amy and Ben share $360 in the ratio 3 : 2.
How much is Ben’s share?
Answer $ ................................... [1]
© UCLES 2012
4024/12/M/J/12
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4
5
y is inversely proportional to the square of x.
For
Examiner’s
Use
Given that y = 2 when x = 6, find the value of y when x = 2.
Answer y = ............................... [2]
6
A circle of diameter 6 cm is cut from a square of side 8 cm.
Find an expression, in the form a – bπ , for the shaded area.
6
Answer
© UCLES 2012
4024/12/M/J/12
8
..............................cm2 [2]
5
7
(a) Solve
x+2
2.
3
For
Examiner’s
Use
Answer
..................................... [1]
Answer
..................................... [1]
(b) Write down all the integers that satisfy this inequality.
–1 4y + 3 11
8
The length of a rectangular rug is given as 0.9 m, correct to the nearest ten centimetres.
The width of the rug is given as 0.6 m, correct to the nearest ten centimetres.
(a) Write down the upper bound, in metres, of the length of the rug.
Answer
................................. m [1]
(b) Find the lower bound, in metres, of the perimeter of the rug.
Answer
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4024/12/M/J/12
................................. m [1]
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6
9
(a) Evaluate
2 3.
+
5 8
For
Examiner’s
Use
Answer
..................................... [1]
2
1
(b) Evaluate 1 × 2 , giving your answer as a mixed number in its lowest terms.
3
4
Answer
..................................... [2]
Answer
..................................... [1]
10 (a) Evaluate 6 × 3 + 8 ÷ 2 .
(b) By writing each number correct to 1 significant figure, estimate the value of
19.2 × 9.09 .
0.583
Answer
© UCLES 2012
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..................................... [2]
7
11
c=
b(a – b)
a
For
Examiner’s
Use
(a) Find c when a = 4 and b = –2.
Answer c = ............................... [1]
(b) Rearrange the formula to make a the subject.
Answer a = .............................. [2]
© UCLES 2012
4024/12/M/J/12
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8
12
m=
冢 –23冣
n=
冢 –14冣
For
Examiner’s
Use
(a) Calculate m – 2n .
Answer
(b) Given that sm + 3n =
冢 12t 冣 , calculate s and t .
冢 冣
[1]
Answer s = ...............................
t = ............................... [2]
© UCLES 2012
4024/12/M/J/12
9
13 The diagram shows two triangles, A and B.
For
Examiner’s
Use
y
7
6
5
4
3
2
A
1
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7 x
–1
–2
B
–3
–4
–5
–6
–7
(a) Write down the vector that represents the translation that maps triangle A onto triangle B.
Answer
[1]
(b) Triangle C is an enlargement of triangle A with centre (5, 3) and scale factor 3.
Draw and label triangle C.
© UCLES 2012
[2]
4024/12/M/J/12
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10
14 A is the point (0, 4) and B is the point (–6, 1).
For
Examiner’s
Use
(a) M is the midpoint of the line AB.
Find the coordinates of M.
Answer
(............, ............)
[1]
(b) Find the equation of the line AB.
Answer
..................................... [2]
15
A
4
B
65
D
C
ABCD is a rectangle with AC = 65 cm and AD = 4 cm.
Calculate the area of ABCD.
Answer
© UCLES 2012
4024/12/M/J/12
..............................cm2 [3]
11
16
For
Examiner’s
Use
A
C
B
D
The diagram shows parts of two identical regular 12-sided polygons.
(a) Calculate angle ABC.
Answer
..................................... [2]
(b) A different regular shape will fit exactly into the space at B.
Name this shape.
Answer
© UCLES 2012
4024/12/M/J/12
........................................................ [1]
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12
17 (a) A carton contains 2.5 litres of juice.
Carlos drinks 650 ml of the juice.
For
Examiner’s
Use
How much juice is left in the carton?
Give your answer in litres.
Answer
........................... litres [1]
(b) The time in Chennai is 4 12 hours ahead of the time in London.
(i) What time is it in London when it is 14 45 in Chennai?
Answer
..................................... [1]
(ii) A flight leaves London at 13 25 local time.
It arrives in Chennai at 04 00 local time the next day.
Work out, in hours and minutes, the length of the flight.
Answer
© UCLES 2012
4024/12/M/J/12
............... hours ............... minutes [2]
13
18 (a) Find the value of
121,
(i)
(ii)
For
Examiner’s
Use
3
Answer
..................................... [1]
Answer
..................................... [1]
–27.
(b) Write the following numbers in order of size, starting with the smallest.
23
32
Answer
40
................
smallest
5–1
................
................
................ [1]
3
(c) Evaluate 16 2.
Answer
© UCLES 2012
4024/12/M/J/12
..................................... [1]
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14
f(x) = x3 – 4
19 (a)
For
Examiner’s
Use
Find
(i) f(–2),
Answer f(–2) = ......................... [1]
(ii) f –1(x).
Answer f –1(x) = ................................. [1]
g(y) = y2 – 3y + 1
(b)
Write down and simplify an expression for g(a – 2).
Answer g(a – 2) = ........................................ [2]
© UCLES 2012
4024/12/M/J/12
15
20 The table below shows the populations of some countries in 2010.
Country
Indonesia
For
Examiner’s
Use
Population
2.4 × 108
Mexico
Russia
1.4 × 108
Senegal
1.4 × 107
South Korea
4.8 × 107
(a) The population of Mexico was 111 210 000.
In the table above, complete the row for Mexico.
Give your answer in standard form, correct to two significant figures.
[1]
(b) Complete the following sentences.
The population of Russia is ten times the population of .....................................
The population of ..................................... is one fifth of the population of Indonesia.
[2]
(c) Calculate the difference in population between South Korea and Senegal.
Give your answer in standard form.
Answer
© UCLES 2012
4024/12/M/J/12
..................................... [1]
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16
21 In class A there are 10 boys and 15 girls.
In class B there are 20 boys and 10 girls.
One student is picked from each class at random.
For
Examiner’s
Use
(a) Complete the tree diagram to show the probabilities of the possible outcomes.
&ODVV$
&ODVV%
%R\
*LUO
%R\
*LUO
%R\
*LUO
[2]
(b) Find the probability that one student is a boy and one is a girl.
Express your answer as a fraction in its lowest terms.
Answer
© UCLES 2012
4024/12/M/J/12
..................................... [2]
17
22 The diagrams below show the first three patterns in a sequence.
Pattern 1
For
Examiner’s
Use
Pattern 2
Pattern 3
(a) Complete the table.
Pattern number
1
2
Number of dots
5
8
3
4
5
[1]
(b) Find an expression, in terms of n, for the number of dots in Pattern n.
Answer
..................................... [1]
(c) In this sequence, Pattern p has 83 dots.
Find the value of p.
Answer p = .............................. [2]
© UCLES 2012
4024/12/M/J/12
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18
23 The table summarises the times, in minutes, taken by a group of people to complete a puzzle.
Time (t minutes)
Frequency
0<t4
4<t8
8 < t 12
12 < t 16
16 < t 20
4
8
7
4
2
For
Examiner’s
Use
(a) On the grid draw a frequency polygon to represent this information.
Frequency
0
2
4
6
8
10
12
14
Time (t minutes)
16
18
20
[2]
(b) Write down the modal class.
Answer
..................................... [1]
(c) How many people took more than 8 minutes to complete the puzzle?
Answer
..................................... [1]
(d) Imran says:
‘The longest time to complete the puzzle was 20 minutes.’
Explain why he may not be correct.
...................................................................................................................................................
.............................................................................................................................................. [1]
© UCLES 2012
4024/12/M/J/12
19
24 (a) The price of a television is $350.
In a sale, its price is reduced by 30%.
For
Examiner’s
Use
Calculate the sale price of the television.
Answer $ ................................... [1]
(b) The exchange rate between dollars and euros is $1 = €0.80 .
Ben changes $275 into euros.
Calculate the number of euros Ben receives.
Answer € ................................... [1]
(c) Aisha buys a new car.
Cash price
Credit terms
$4500
Deposit: 25% of cash price
+
12 monthly payments of $320
She buys the car using the credit terms.
How much more than the cash price will she pay overall for the car?
Answer $ ................................... [3]
Question 25 is printed on the following page.
© UCLES 2012
4024/12/M/J/12
[Turn over
20
25 (a) Factorise
For
Examiner’s
Use
(i) x2 + x – 12 ,
Answer
............................................... [1]
Answer
............................................... [1]
(ii) 25x2 – 4y2 .
(b) Write as a single fraction
4
1 .
+
3p 6p
Answer
..................................... [1]
(c) Solve the simultaneous equations.
3x + 5y = 2
2x – 3y = 14
Answer x = ...............................
y = ............................... [3]
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.
University of 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 2012
4024/12/M/J/12
Page 2
Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012
Syllabus
4024
Abbreviations
cao
correct answer only
cso
correct solution only
dep
dependent
ft
follow through after error
isw
ignore subsequent working
oe
or equivalent
SC
Special Case
www
without wrong working
soi
seen or implied
Qu
Answers
Mark
(a)
18
cao
25
1
(b)
2 k1
2k 2
and
5k 1
5k 2
1
(a)
42
1
(b)
4
1
(a)
Drawing of kite or isosceles
trapezium
1
(b)
2
0
1
(a)
9
1
(b)
144
1
5
18
2
B1 for x2y = k soi or
for 2 × 62 = y × 22 soi
6
64 – 9π cao isw
2
B1 for π × 32 or for 64 – πr 2
(a)
(x) Y 4
1
(b)
–1, 0, 1
1
(a)
0.95
1
(b)
2.8(0)
1
(a)
31
oe
40
1
(b)
3
1
2
3
4
7
8
9
3
cao
4
2
Part marks
SC1 for both 95 and 280
B1 for
5 9
× oe
3 4
© University of Cambridge International Examinations 2012
Paper
12
Page 3
10 (a)
(b)
11 (a)
Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012
22
1
300
2
–3 cao
1
a=
(b)
b2
b−c
2
 5 
 oe

 −10 
12 (a)
13 (a)
(b)
14 (a)
2
 2 
  oe
 − 4
1
Correct triangle
2
(–3, 2.5) oe
1
y=
(b)
Paper
12
B1 for two of 20, 9, 0.6 seen
B1 for ac = b(a – b) or c = b −
b2
a
1
(s =) 5
(t =) 2
(b)
Syllabus
4024
1
x + 4 isw
2
C1 for one correct or
 3s   − 3  12 
 +   =   oe
M1 for 
 − 2 s   12   t 
B1 for two vertices correct or
triangle correct size and orientation
2
B1 for m =
1
or c = 4 soi
2
15
28
3
M1 for CD2 = their ( 65 ) 2 – 42 oe and
A1 for CD = 7 or
B1 for theirCD × 4
After 0 SC1 for ( 65 )2 = 65
16 (a)
150°
2
B1 for
Equilateral triangle
1
1.85
1
10 15 oe
1
10 hours 5 minutes
2
18 (a) (i)
11
1
(ii)
–3
1
(b)
5–1, 40, 23, 32 oe
1
(c)
64
1
(b)
17 (a)
(b) (i)
(ii)
360
soi or (12 – 2) × 180 soi
12
B1 for 17 55 or 23 30 seen or
M1 for 24 00 – (13 25 + 4 30) + 4 oe
© University of Cambridge International Examinations 2012
Page 4
Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012
Syllabus
4024
Paper
12
–12
1
3
x + 4 oe
1
a2 – 7a + 11
2
1.1 × 108
1
Senegal
South Korea
2
3.4 × 107
1
Tree diagram correct
2
B1 for both
8
cao
15
2
M1 for
11, 14, 17
1
(b)
3n + 2
1
(c)
27 cao
2
M1 for 3p + 2 = 83 ft
Correct frequency polygon
2
Frequency axis scaled to show 4, 8, 7, 4, 2
Plots at midpoints 2, 6, 10, 14, 18
and joined by straight lines
19 (a) (i)
(ii)
(b)
20 (a)
(b)
(c)
21 (a)
(b)
22 (a)
23 (a)
B1 for (a – 2)2 – 3(a – 2) + 1
C1 for one correct in the correct place
10 15
,
oe correct or
25 25
20 10
,
oe correct
both
30 30
10 10 15 20
× + ×
oe
25 30 25 30
B1 for 1 mis plot , everything else correct
or
if plots not joined, everything else correct
or
if there is no vertical scale, everything else
correct
or
for 5 correct frequencies not at midpoints but
correctly spaced, everything else correct.
or
SC1 for a completely accurate frequency polygon
seen alongside other graphs on the same diagram.
(b)
4<tY8
1
(c)
13
1
(d)
Convincing explanation
1
e.g. longest time is in the group 16 < t Y 20, but
may not be 20
© University of Cambridge International Examinations 2012
Page 5
Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012
24 (a)
245
1
(b)
220
1
(c)
465
3
(x + 4)(x – 3)
1
(5x + 2y)(5x – 2y)
1
(b)
3
oe
2p
1
(c)
x = 4 y = –2
3
25 (a) (i)
(ii)
Syllabus
4024
Paper
12
B2 for 4965 or
25
M2 for
× 4500 + 320 × 12 – 4500 or
100
B1 for 1125 or
3840 seen
C2 for one correct or
M1 for correct method to eliminate one variable
© University of Cambridge International Examinations 2012