Maths O'level S2010-2014 Paper 1 PDF
Maths O'level S2010-2014 Paper 1 PDF
Maths O'level S2010-2014 Paper 1 PDF
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.
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.
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 80.
DC (LEO/CGW) 15629/3
© UCLES 2010 [Turn over
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2
1 Evaluate
(a) 1 + 2 ,
2 9
(b) 2 ÷ 9 .
3 11
2 (a) Evaluate 10 – 8 ÷ 2 + 3.
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3
3 Sara carries out a survey of the colours of cars in a car park. For
She draws a pie chart to represent her results. Examiner’s
Use
Calculate his average speed, in kilometres per hour, for the whole journey.
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4
5 For
North Examiner’s
Use
D A
C B
(b) Write down the largest integer which satisfies the inequality
6x – 5 ⬍ 9 + 2x.
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5
7 Given that n is an integer and n ⬎ 1, decide whether each statement in the table is true or false. For
Examiner’s
For each statement write true or false in the table. Use
n3 > 1
1> 1
n n2
(n – 1)(n + 3)
is always odd
[2]
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6
9 For
Examiner’s
Use
(b) Find the smallest width of a box that can always hold 8 pencils side by side.
Give your answer in centimetres.
10 Evaluate
(b) 3 ÷ 0.01,
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7
11 For
Examiner’s
Use
A B
O
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...........................................................................................................................................................
...................................................................................................................................................... [3]
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8
12 For
Examiner’s
Use
y
8
B
6
A
5
R
4
D C
0 x
0 1 2 3 4 5 6
In the diagram, the region, R, is bounded by the lines AB, BC, CD and DA.
...........................................
..................................... [ 2]
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9
13 Two families ordered three basic food items from their local shop. For
The Jones family ordered 1 bag of sugar, 4 cartons of milk and 3 loaves of bread. Examiner’s
The Singh family ordered no sugar, 3 cartons of milk and 5 loaves of bread. Use
冢 冣
1 0
A= 4 3 .
3 5
The cost of a bag of sugar is 80 cents, the cost of a carton of milk is 50 cents and the cost of a
loaf of bread is 40 cents.
This information can be represented by the matrix B where
B = ( 80 50 40 ).
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [1]
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10
14 Ida keeps a record of time spent on the internet each day. For
Her results are summarised in the table. Examiner’s
Use
1.8
1.6
1.4
1.2
Frequency
1.0
density
0.8
0.6
0.4
0.2
0
0 20 40 60 80 100 120
Time (t minutes)
[3]
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11
(ii) The rate of exchange between pounds (£) and dollars ($) was £1 = $2.50.
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12
His highest score was 7 runs more than his lowest score.
(a) Find the number of runs he scored in each of the three games.
Find the number of runs that Dai scored in the fourth game.
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13
x 3 2 q
y 4 p 1
Find
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14
18 For
Examiner’s
A B Use
135°
65°
E D C
Find
(a) AÊD,
(b) DÂB,
(c) BĈD,
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15
19 Some data about two planets, Earth and Mars, is shown in the table. For
Examiner’s
Use
Average Mass Volume
Planet
temperature (°C) (tonnes) (km3)
Earth 15 5.98 × 1021 1.08 × 1012
Mars –63 6.58 × 1020 162 000 m illion
(a) How much greater is the average temperature on Earth than that on Mars?
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16
20 For
Examiner’s
3 Use
A B
2 X
D C
(a) Find the ratio of the area of triangle ABX to the area of triangle CDX.
(b) Find the ratio of the area of triangle ABX to the area of triangle BCX.
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17
21 (a) Write down, in terms of n, an expression for the nth term of the sequence For
Examiner’s
19 16 13 10 ........... . Use
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18
22 A walker leaves his house at 10 00 and walks towards a shopping centre at a constant For
speed of 5 km/h. Examiner’s
A cyclist leaves the same house 10 minutes later. Use
He travels along the same road at a constant speed of 20 km/h until he reaches the shopping
centre which is 6 km from the house.
The cyclist stops at the shopping centre for 14 minutes.
He then returns to the house along the same road at a constant speed of 20 km/h.
On the same axes, draw the distance-time graph for the cyclist.
4
Distance
from
house 3
(km)
2
0
10 00 10 10 10 20 10 30 10 40 10 50 11 00 11 10
Time of day
[3]
(i) the time when the cyclist, on his return journey, meets the walker,
(ii) the distance from the house when this meeting takes place.
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19
23 A stone is thrown vertically upwards from the ground so that its height above the ground after For
t seconds is (20t – 5t 2) metres. Examiner’s
Use
(a) (i) Show that the values of t when the stone is 15 metres above the ground satisfy the
equation
t2 – 4t + 3 = 0.
[1]
(ii) Find the values of t when the stone is 15 metres above the ground.
(b) Find the value of t when the stone hits the ground.
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20
(ii) 2 = 3.
5t 4
5x – 2y = 16,
2x – 3y = 13.
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.
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Ordinary Level
*0725052732*
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.
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.
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 80.
DC (LEO/SW) 24603/2
© UCLES 2010 [Turn over
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2
1 Evaluate
(a) 5–2,
7 5
(b) 1 1 ÷ 2 1 .
5 3
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3
3 (a) In a town, 11 000 people out of the total population of 50 000 are aged under 18. For
Examiner’s
What percentage of the population is aged under 18? Use
(b) A company employing 1200 workers increased the number of workers by 15%.
4 Evaluate
(a) 91 + 90,
(b) 冢冣
1 2.
9
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4
5 By writing each number correct to 1 significant figure, estimate the value of For
Examiner’s
48.9 × 0.2072 . Use
3.94
6 (a) Solve 3 = 2.
x–1
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5
7 (a) On the regular hexagon below, draw all the lines of symmetry. For
Examiner’s
Use
[1]
(b) On the grid below, draw a quadrilateral with rotational symmetry of order 2.
[1]
8 The table shows the record minimum monthly temperatures, in °C, in Vostok and London.
Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Vostok –36 – 47 – 64 –70 –71 –71 –74 –75 –72 – 61 – 45 –35
London –10 –9 –8 –2 –1 5 7 6 3 –4 –5 –7
Find
(a) the difference between the temperatures in Vostok and London in July,
(b) the difference between the temperatures in Vostok in February and June.
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6
(c) Find the smallest positive integer, n, such that 168n is a square number.
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7
(b) f –1(x).
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8
x – 3y = 17
Answer x = .....................................
y = ..................................... [3]
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9
14 A straight line passes through the points P (–8, 10) and Q (4, 1). For
Examiner’s
Find Use
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10
15 For
Examiner’s
C Use
D
O Q
38° B
A
Find
(a) DÂC,
(b) DB̂ C,
(c) CB̂ Q.
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11
(a) Complete the tree diagram below that represents these events.
Answer (a)
5 red
9
6 red
10
.......... blue
red
..........
..........
blue
.......... blue
[1]
(b) Expressing your answer as a fraction in its simplest form, calculate the probability that both
counters are the same colour.
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12
17 For
D C Examiner’s
Use
3q X
A B
2p
ABCD is a parallelogram.
X is the point on BC such that BX : XC = 2 : 1.
→ →
AB = 2p and AD = 3q.
→
Answer (a) AC = ............................ [1]
→
(b) AX ,
→
Answer (b) AX = .......................... [1]
→
(c) XD .
→
Answer (c) XD = ........................... [1]
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13
(a) A – B,
(b) B–1.
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14
20 The graph shows the cumulative frequency curve for the ages of 60 employees. For
Examiner’s
60 Use
50
40
Cumulative
frequency 30
20
10
0
15 20 25 30 35 40 45 50 55 60 65
Age (years)
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15
(ii) x2 – xy – 2y2.
2
(b) Simplify x2 + 4x .
x – 16
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16
(i) Write down the lower bound of the length of the string.
Give your answer in centimetres.
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17
23 For
B Examiner’s
Use
15
sin 17
8
cos 17
15
tan 8
θ
A C
32 cm
(a) AB,
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18
factor 2.
Answer (a)
5
Q
4
P
3
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1
–2
–3
–4
R
–5
–6
[2]
(b) Describe fully the single transformation that maps triangle P onto triangle Q.
............................................................................................................................................. [2]
(c) Find the matrix representing the transformation that maps triangle Q onto triangle R.
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19
25 The diagram is the speed-time graph for the first 20 seconds of a cyclist’s journey. For
Examiner’s
Use
12
10
Speed 8
(metres per second)
6
0
0 2 4 6 8 10 12 14 16 18 20
Time (t seconds)
(b) By drawing a tangent, find the acceleration of the cyclist when t = 18.
(c) On the grid in the answer space, sketch the distance-time graph for
the first 16 seconds of the cyclist’s journey.
Answer (c)
140
120
100
Distance
(metres) 80
60
40
20
0
0 2 4 6 8 10 12 14 16
Time (t seconds)
[2]
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20
North
A B
(b) A house D, inside the triangle, is more than 35 km from B and closer to B than to A.
Shade the region on your diagram that represents the possible positions
of the house D. [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.
www.XtremePapers.net
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Ordinary Level
*9964901203*
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.
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.
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 80.
DC (SLM) 29094
© UCLES 2010 [Turn over
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2
1 Evaluate
(a) 5–2,
7 5
(b) 1 1 ÷ 2 1 .
5 3
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3
3 (a) In a town, 11 000 people out of the total population of 50 000 are aged under 18. For
Examiner’s
What percentage of the population is aged under 18? Use
(b) A company employing 1200 workers increased the number of workers by 15%.
4 Evaluate
(a) 91 + 90,
(b) 冢冣
1 2.
9
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4
5 By writing each number correct to 1 significant figure, estimate the value of For
Examiner’s
48.9 × 0.2072 . Use
3.94
6 (a) Solve 3 = 2.
x–1
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5
7 (a) On the regular hexagon below, draw all the lines of symmetry. For
Examiner’s
Use
[1]
(b) On the grid below, draw a quadrilateral with rotational symmetry of order 2.
[1]
8 The table shows the record minimum monthly temperatures, in °C, in Vostok and London.
Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Vostok –36 – 47 – 64 –70 –71 –71 –74 –75 –72 – 61 – 45 –35
London –10 –9 –8 –2 –1 5 7 6 3 –4 –5 –7
Find
(a) the difference between the temperatures in Vostok and London in July,
(b) the difference between the temperatures in Vostok in February and June.
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6
(c) Find the smallest positive integer, n, such that 168n is a square number.
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7
(b) f –1(x).
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8
x – 3y = 17
Answer x = .....................................
y = ..................................... [3]
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9
14 A straight line passes through the points P (–8, 10) and Q (4, 1). For
Examiner’s
Find Use
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10
15 For
Examiner’s
C Use
D
O Q
38° B
A
Find
(a) DÂC,
(b) DB̂ C,
(c) CB̂ Q.
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11
(a) Complete the tree diagram below that represents these events.
Answer (a)
5 red
9
6 red
10
.......... blue
red
..........
..........
blue
.......... blue
[1]
(b) Expressing your answer as a fraction in its simplest form, calculate the probability that both
counters are the same colour.
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12
17 For
D C Examiner’s
Use
3q X
A B
2p
ABCD is a parallelogram.
X is the point on BC such that BX : XC = 2 : 1.
→ →
AB = 2p and AD = 3q.
→
Answer (a) AC = ............................ [1]
→
(b) AX ,
→
Answer (b) AX = .......................... [1]
→
(c) XD .
→
Answer (c) XD = ........................... [1]
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13
(a) A – B,
(b) B–1.
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14
20 The graph shows the cumulative frequency curve for the ages of 60 employees. For
Examiner’s
60 Use
50
40
Cumulative
frequency 30
20
10
0
15 20 25 30 35 40 45 50 55 60 65
Age (years)
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15
(ii) x2 – xy – 2y2.
2
(b) Simplify x2 + 4x .
x – 16
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16
(i) Write down the lower bound of the length of the string.
Give your answer in centimetres.
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17
23 For
B Examiner’s
Use
15
sin 17
8
cos 17
15
tan 8
θ
A C
32 cm
(a) AB,
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18
factor 2.
Answer (a)
5
Q
4
P
3
–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1
–2
–3
–4
R
–5
–6
[2]
(b) Describe fully the single transformation that maps triangle P onto triangle Q.
............................................................................................................................................. [2]
(c) Find the matrix representing the transformation that maps triangle Q onto triangle R.
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19
25 The diagram is the speed-time graph for the first 20 seconds of a cyclist’s journey. For
Examiner’s
Use
12
10
Speed 8
(metres per second)
6
0
0 2 4 6 8 10 12 14 16 18 20
Time (t seconds)
(b) By drawing a tangent, find the acceleration of the cyclist when t = 18.
(c) On the grid in the answer space, sketch the distance-time graph for
the first 16 seconds of the cyclist’s journey.
Answer (c)
140
120
100
Distance
(metres) 80
60
40
20
0
0 2 4 6 8 10 12 14 16
Time (t seconds)
[2]
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20
North
A B
(b) A house D, inside the triangle, is more than 35 km from B and closer to B than to A.
Shade the region on your diagram that represents the possible positions
of the house D. [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.
www.XtremePapers.net
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Ordinary Level
* 7 2 4 6 9 8 1 4 2 3 *
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.
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.
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 80.
DC (NH/SW) 49516/2
© UCLES 2012 [Turn over
2
1 (a) On the diagram below, shade two more squares to make a pattern that has rotational
symmetry of order 2.
[1]
(b) On the diagram below, shade two more squares to make a pattern that has only one line of
symmetry.
[1]
2 (a) Evaluate 8 – 5 × 4 + 3.
3 (a) The diagram shows the fuel gauge in Abid’s car. For
Examiner’s
1 Use
2
1 3
4 4
0 1
1
2
1 3
4 4
0 1
Draw an arrow on the gauge above to indicate that the tank is approximately 4 full.
5
[1]
4 Factorise completely
(b) x2 – x – 6.
5 An empty lorry has a mass of 4.3 tonnes, correct to the nearest tenth of a tonne. For
Examiner’s
(a) What is the lower bound for the mass of the empty lorry? Use
(b) The total mass of the lorry and its load is 6.8 tonnes, correct to the nearest tenth of a tonne.
22
6 Given that π = 3.141592654, find the difference between 7 and π, correct to two significant
figures.
7 (a) Jane puts some red balloons and some blue balloons into a bag. For
The ratio of red balloons to blue balloons is 3 : 4. Examiner’s
There are 84 balloons in the bag. Use
46°
m
11
n
61°
12 46°
9
73°
Find m and n.
Answer m = ...................................
n = .............................. [2]
9 Buses following route A leave the bus station every five minutes. For
Buses following route B leave the bus station every six minutes. Examiner’s
Buses following route C leave the bus station every nine minutes. Use
What is the next time when buses following all three routes leave the bus station together?
3x + 5y = 0
2x – 3y = 19
Answer x = ....................................
y = ............................... [3]
11 Evaluate For
Examiner’s
(a) 3 – 2 , Use
5 7
(b) 12 ÷ 13 .
3 4
12
1
0.2 2 √⎯2 3 0.83 8 81
14 Sachin and Zaheer play a game of tennis and a game of badminton. For
The results of the games are independent and the games cannot be drawn. Examiner’s
3 Use
The probability that Sachin wins the game of tennis is 4 .
3
The probability that Zaheer wins the game of badminton is 5 .
(b) What is the probability that Zaheer wins just one of the games?
For
15 (a) Write 83 in the form 2k. Examiner’s
Use
16 (a) The profits of a company were $5 million in 2009 and $8 million in 2010.
(a) Write down, in standard form, the number of locusts in this swarm.
18 Solve For
Examiner’s
(a) 5x – 2 = 1, Use
(b) 3 – y ⭐ 1,
(c) 2t – 1 = 1 – t .
4 3
The number of black and white counters in each diagram is shown in the table below.
Diagram number 1 2 3 4 5 6
Number of white 1 4 9 16
counters
Number of black 0 2 6 12
counters
(b) Write an expression, in terms of n, for the number of white counters in the nth diagram.
(c) By considering the number patterns in the table, write an expression, in terms of n, for the
number of black counters in the nth diagram.
Line 2: y = 2 – x
Line 3: y = 2x – 1
Line 4: 2y – 8 = 3x
(b) Which two lines intersect the y-axis at the same point?
(c) Which line passes through the points (1, 1) and (–3, 5)?
(d) Find the midpoint of the line segment joining (1, 1) and (–3, 5).
21 A group of 100 students was asked how many minutes each spent talking on their mobile phone For
during one day. Examiner’s
The histogram summarises this information. Use
2
Frequency
density
0
0 10 20 30 40 50 60 70 80 90
Time (mins)
(i) find the number of students who spent between 0 and 10 minutes talking on their
mobile phone,
(ii) estimate the number of students who spent between 25 and 65 minutes talking on their
mobile phone.
(b) A pie chart is drawn to represent the information shown in the histogram.
Calculate the angle of the sector that represents the students who spent
between 0 and 10 minutes talking on their mobile phone.
1 1 1 For
22 b = c + d Examiner’s
Use
(a) Evaluate b when c = 3 and d = 8.
23 The diagram shows the speed-time graph of a car travelling between two road junctions. For
Examiner’s
Use
15
10
Speed
(m / s)
0
0 10 20 30 40 50 60
Time (t secs)
(c) Calculate the distance travelled by the car between t = 15 and t = 58.
24 For
A 8 B Examiner’s
Use
D Y
C 4
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..............................................................................................................................................[2]
(i) f(2),
(ii) f(–1),
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.
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.
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.
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 80.
DC (CW/SW) 49517/2
© UCLES 2012 [Turn over
2
(a) Find the difference between the outside temperature and the freezer temperature.
[1]
x+2 For
7 (a) Solve ⭐ 2. Examiner’s
3 Use
(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.
(b) Find the lower bound, in metres, of the perimeter of the rug.
2 3.
9 (a) Evaluate + For
5 8 Examiner’s
Use
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
b(a – b)
11 c= For
a Examiner’s
Use
(a) Find c when a = 4 and b = –2.
(a) Calculate m – 2n .
Answer
冢 冣 [1]
Answer s = ...............................
t = ............................... [2]
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.
15
A B
65
4
D C
16 For
Examiner’s
Use
C
A B
D
(b) A different regular shape will fit exactly into the space at B.
(b) Write the following numbers in order of size, starting with the smallest.
23 32 40 5–1
(i) f(–2),
(ii) f –1(x).
(b) g(y) = y2 – 3y + 1
20 The table below shows the populations of some countries in 2010. For
Examiner’s
Use
Country Population
Indonesia 2.4 × 108
Mexico
Russia 1.4 × 108
Senegal 1.4 × 107
South Korea 4.8 × 107
(c) Calculate the difference in population between South Korea and Senegal.
Give your answer in standard form.
(a) Complete the tree diagram to show the probabilities of the possible outcomes.
&ODVV$ &ODVV%
%R\
%R\
*LUO
%R\
*LUO
*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.
22 The diagrams below show the first three patterns in a sequence. For
Examiner’s
Use
Pattern number 1 2 3 4 5
Number of dots 5 8
[1]
23 The table summarises the times, in minutes, taken by a group of people to complete a puzzle. For
Examiner’s
Use
Time (t minutes) 0<t⭐4 4<t⭐8 8 < t ⭐ 12 12 < t ⭐ 16 16 < t ⭐ 20
Frequency 4 8 7 4 2
Frequency
0 2 4 6 8 10 12 14 16 18 20
Time (t minutes)
[2]
(c) How many people took more than 8 minutes to complete the puzzle?
...................................................................................................................................................
.............................................................................................................................................. [1]
How much more than the cash price will she pay overall for the car?
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
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
er
s.
General Certificate of Education Ordinary Level
co
m
* 3 9 0 6 7 5 5 8 0 8 *
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.
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.
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 80.
DC (SLM/CGW) 64207/3
© UCLES 2013 [Turn over
2
5
10
20
12
25
5
Work out
2 Evaluate
4 (a) Complete the statement in the answer space using one of these symbols.
G 1 = 2 H
27
Answer 0.65 ............................... [1]
40
(b) Express 7% as a decimal.
5 For
Examiner’s
Use
6 Q
X
P
Calculate PQ.
8 (a) One approximate solution of the equation sin x° = 0.53 is x = 32. For
Examiner’s
Use this value of x to find the solution of the equation that lies between 90° and 180°. Use
(b)
A
13
5
D C 12 B
9 Ahmed pays a total of $81 for wood, paint and a hammer. For
Examiner’s
(a) The amounts he pays for the wood, paint and hammer are in the ratio 4 : 3 : 2. Use
(b) When Ahmed paid $81 he had received a 10% discount on the normal price.
10 b = m (a – c)
(a) A ......................................................... has four equal sides and four angles of 90°. [1]
(c) A ......................................................... has just one pair of opposite angles equal and
12
6 9 1
The three cards above can be rearranged to make three-digit numbers, for example 916.
13 For
Examiner’s
Use
Speed
(m/s)
0 10 20 30 40 50 60 70
Time (t seconds)
The diagram shows the speed-time graph for 70 seconds of a car’s journey.
After 20 seconds the car reaches a speed of v m/s.
During the 70 seconds the car travels 1375 m.
(a) Calculate v.
(b) Calculate the acceleration of the car during the first 20 seconds.
14 For
Examiner’s
Use
T
A 32°
D
O
Find
(a) ATO
t ,
(b) TDO
t ,
(c) t .
ABT
15 For
A Examiner’s
Use
D C
(a) Construct the locus of all points, inside the quadrilateral ABCD, which are
(b) On the diagram, shade the region inside the quadrilateral containing the points that are
(a) Maryam decorates each cake with a ribbon around the outside.
The length of the ribbon for the larger cake is 66 cm.
(b) Maryam uses 1600 m3 of cake mixture to make the smaller cake.
Find the volume of cake mixture she uses to make the larger cake.
(a) p + q,
(b) 2p ÷ q.
18 Eighty cyclists were each asked the distance (in kilometres) they cycled last week. For
Examiner’s
Use
80
70
60
50
Cumulative
frequency 40
30
20
10
0
0 20 40 60 80 100 120
Distance (kilometres)
19 The diagram shows the metal cover for a circular drain. For
Water drains out through the shaded sections. Examiner’s
Use
C
D
O
O is the centre of circles with radii 1 cm, 2 cm, 3 cm, 4 cm and 5 cm.
The cover has rotational symmetry of order 6 and BOC t = 40°.
(a) Calculate the area of the shaded section ABCD, giving your answer in terms of π.
55
(b) The total area of the metal (unshaded) sections of the cover is π cm2. For
3 Examiner’s
Use
(i) Calculate the total area of the shaded sections, giving your answer in terms of π.
(ii) Calculate the fraction of the total area of the cover that is metal (unshaded).
Give your answer in its simplest form.
20 (a) Evaluate
(i) 50 + 52,
R R R R R
p p p p p
Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5
22 For
y Examiner’s
7 Use
5
B
4
2
A
1
x
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
–1
–2
–3
–4
–5
(b) The rotation 90° clockwise, centre (1, 1), maps triangle A onto triangle D.
(c) Find the matrix of the transformation that maps triangle A onto triangle B.
Answer
[1]
23 For
y Examiner’s
Use
7
T
6
2 S R
x
0 1 2 3 4 5 6 7 8
(iii) the equation of the line with gradient 3 that passes through S.
(b) One of the inequalities that defines the shaded region RST is x G 6 .
Write down the other two inequalities that define this region.
Answer .................................................
............................................ [2]
24 (a) A = e o B =e o
4 3 2 -3 For
Examiner’s
1 2 1 1 Use
(i) Find 2A – B.
Answer
[2]
(c)
M N
Use set notation to describe the shaded subset in the Venn diagram.
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.
er
s.
General Certificate of Education Ordinary Level
co
m
* 0 2 1 5 8 3 0 0 9 3 *
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.
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.
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 80.
DC (SLM/SW) 64206/2
© UCLES 2013 [Turn over
2
1 Evaluate
4 2
(a) - ,
7 5
Odd Even
Red 6 9
Blue 5 3
3 (a) Write these lengths in order of size, starting with the shortest� For
Examiner’s
500 m 5 cm 50 km 500 mm Use
3 C
B
2 A
D
1 E
G I
F H
0 1 2 3 4 5 x
3
A
2
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x
–1
–2
–3
–4
(b) Rotate triangle A through 90° clockwise about the point (–1, 3)�
Label the image C� [1]
7 The diagram shows a scale used to measure the water level in a river� For
Examiner’s
Use
m
2.0
1.5
1.0
0.5
0
–0.5
–1.0
June
–1.5
–2.0
–2.5
The table shows the reading, in metres, at the beginning of each month�
(a) The diagram shows the water level at the beginning of June�
(b) Work out the difference between the highest and lowest levels shown in the table�
(c) The August reading was 0�4 m higher than the July reading�
3 × 2 + 1 2 = 49 [1]
A B
[1]
11 A photo is 10 cm long�
It is enlarged so that all dimensions are increased by 20%�
(b) Find the ratio of the area of the enlarged photo to the area of the original photo�
Give your answer in the form k : 1�
(b) Shade the region inside the triangle containing points that are closer to A than to B and
more than 6 cm from C� [2]
B C
A=e o B=e o
2 3 -2 4 For
13 Examiner’s
-2 0 -3 1 Use
(a) Find A – B �
Answer
[2]
14 (a) Sofia earns $7�60 for each hour she works� For
She starts work at 7�45 a�m� and finishes at 4�30 p�m� Examiner’s
She stops work for half an hour for lunch� Use
e o �
9xy 6 2
(b) Simplify
x3y2
17 For
Examiner’s
Use
45°
45°
3
2
18 The table shows information about the annual coffee production of some countries in 2010� For
Examiner’s
Use
Country Number of bags per year
Brazil
Vietnam 1.85 × 107
Colombia 9.2 × 106
Indonesia 8.5 × 106
Complete the table with the coffee production for Brazil, using standard form� [1]
(b) How many more bags of coffee were produced in Vietnam than in Colombia?
19 (a) Keith records the number of letters he receives each day for 20 days� For
His results are shown in the table� Examiner’s
Use
(b) Over the same 20 days, Emma received a mean of 1�7 letters each day�
3x 2x - 1
20 (a) Solve + = 3� For
4 2 Examiner’s
Use
Mark (m) 0 1 m G 10 10 1 m G 20 20 1 m G 30 30 1 m G 40 40 1 m G 50 50 1 m G 60
Frequency 4 12 14 22 18 10
Mark (m) m G 10 m G 20 m G 30 m G 40 m G 50 m G 60
Cumulative
frequency
[1]
80
70
60
50
Cumulative
frequency 40
30
20
10
0
0 10 20 30 40 50 60
Mark
[2]
His sister Kiran leaves college at 13 10 and cycles home on the same road at a constant
speed of 16 km/h�
(a) On the same grid, draw the distance-time graph for Kiran’s journey�
College 12
10
8
Distance
from home 6
(km)
4
Home 0
13 00 13 10 13 20 13 30 13 40 13 50 14 00
Time of day [2]
(b) How far was Kiran from home when she passed Varun?
(c) Find Varun’s speed for the first 20 minutes of his journey�
Give your answer in kilometres per hour�
(d) On the grid below, draw the speed-time graph for Varun’s journey�
25
20
Speed 15
(km/h)
10
0
13 00 13 10 13 20 13 30 13 40 13 50 14 00
Time of day [2]
© UCLES 2013 4024/12/M/J/13
19
23 For
B Examiner’s
C Use
68°
O
A
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���������������������������������������������������������������������������������������������������������������������������������������������������
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���������������������������������������������������������������������������������������������������������������������������������������������������
���������������������������������������������������������������������������������������������������������������������������������������������������
���������������������������������������������������������������������������������������������������������������������������������������������� [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.
er
s.
Cambridge Ordinary Level
co
m
* 4 3 3 8 1 5 0 9 2 8 *
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.
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.
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 80.
DC (RW/KN) 81743/3
© UCLES 2014 [Turn over
2
B
[1]
(b) Shade four more small triangles in the shape below to make a pattern
with rotational symmetry of order 3.
[1]
3
9
4.3 5.6
(b) Write down all the integers that satisfy the inequality - 4 G 2x 1 4 .
5.25
4.8
280°
The shape has two straight sections of length 5.25 cm and 4.8 cm.
The curved part is the arc of the major sector of a circle, radius 3 cm.
The angle of the major sector is 280°.
The total length of wire needed to make the figure is ^a + brh cm.
Answer a = ....................................................
b = .................................................... [2]
8 (a) By writing each number correct to one significant figure, estimate the value of
28.6 + 47.7
.
0.47 # 21.4
a-4
9 Make a the subject of the formula y = .
3-a
(b) The times of some buses from Aytown to Deetown are shown.
Aytown 07 04 08 04 08 56 09 00 09 32 10 56
Beetown - - 09 05 - 09 41 11 05
Ceetown 07 18 08 18 09 14 - - 11 14
Deetown 07 35 08 35 09 31 09 28 10 05 11 31
What time is the latest bus from Ceetown that she can catch?
11
North
North
7 11 15 19
Write down an expression, in terms of n, for the nth term of this sequence.
3un - 4 = u n + 1
Answer u2 = ..................................................
u4 = .................................................. [2]
(b) Simplify
(i) 1 ' x - 5 ,
Age (y years) 10 G y 1 20 20 G y 1 40 40 G y 1 45 45 G y 1 50 50 G y 1 65
Frequency p 20 8 q 18
2
Frequency
density
0
10 20 30 40 50 60 70
Age (y years)
(i) p,
(ii) q.
16
A D
38°
66°
B F C
Find
(a) DFC
t ,
(b) ABC
t ,
(c) t .
AED
(i) 4 ^2t + 3h + 5,
25x 3 y 2 - 15x 2 y .
18
Speed
(m/s)
blue boat
4
red boat
0
0 10 20 30 40 50 60
Time (seconds)
Two boats, one red and one blue, leave a harbour at the same time.
They travel in the same direction.
The speed-time graphs for the boats are shown, for the first minute of their journey.
(a) Find the acceleration of the blue boat in the last 10 seconds.
(b) Find which boat is ahead after one minute and by what distance.
(b) One molecule of water is made up of two atoms of hydrogen and one atom of oxygen.
The mass of one atom of hydrogen is 1.67 # 10 - 24 g.
The mass of one atom of oxygen is 2.66 # 10 - 23 g.
Answer a = ....................................................
b = .................................................... [2]
Write down
(b) Another straight line cuts the x-axis at P ^- 4, 0h and passes through Q ^2, 18h.
22 (a) Construct, using ruler and compasses only, an equilateral triangle ABC.
The side AB has been drawn for you.
[1]
(b) Construct the locus of points, inside triangle ABC, which are
(c) A point X lies within triangle ABC, is nearer to A than to C and is less than 4 cm from A.
23 (a) A spherical tennis ball and a spherical beach ball have diameters in the ratio 1 : 3.
The surface area of the beach ball is 153 cm2.
Find y when x = 5.
............ round
4 round
10
square
............
............ round
6
10
square
square
............
3 -1 5 3
25 A=c m B=c m
-2 4 0 -2
(a) Find 3A - B .
Answer f p
[2]
Answer f p
[2]
1 0
(c) Find the 2 # 2 matrix X, where AX = c m.
0 1
Answer f p
[2]
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.
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.
er
s.
Cambridge Ordinary Level
co
m
* 5 4 5 6 0 0 5 3 9 8 *
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.
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.
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 80.
DC (RW/KN) 81742/2
© UCLES 2014 [Turn over
2
2 Tasnim records the temperature, in °C, at 6 a.m. every day for 10 days.
-6 -3 0 -2 -1 -7 -5 2 -1 -3
(a) Find the difference between the highest and the lowest temperatures.
3 7
3 It is given that 1n1 .
4 8
(a) Write down a decimal value of n that satisfies this inequality.
Bus station 09 56 10 26 10 56 11 26 11 56
City Hall 10 03 10 33 11 03 11 33 12 03
Railway station 10 17 10 47 11 17 11 47 12 17
Hospital 10 28 10 58 11 28 11 58 12 28
Airport 10 43 11 13 11 43 12 13 12 43
(a) How long does the bus take to get from the bus station to the airport?
Write down the latest time that Chris can take a bus from the City Hall to be at the airport in time.
(b) Shade in two more small squares in this shape to make a pattern with
exactly 2 lines of symmetry.
[1]
A
64°
1 3
9 (a) Evaluate + .
7 4
(b) By writing each number correct to one significant figure, estimate the value of
41.3
.
9.79 # 0.765
P Q
[1]
Using a Venn diagram, or otherwise, find the number of children who own a dog, but
not a cat.
J80 60 J0.8N
40N K O
M=K O N=K 1 O
K O
L70 90 50P
L1.2P
(a) Work out MN.
Answer [2]
Answer ...............................................................................................................................................
............................................................................................................................................................
....................................................................................................................................................... [1]
13 f ^xh = 2 - 3x
Find
(a) f ^- 5h,
(b) f -1 ^xh.
(a) Write down the upper bound of the length of the garden.
(b) Work out the lower bound of the perimeter of the garden.
15
y
5
4
L
3
x
0 1 2 3 4 5
Answer ...................................................................
.............................................................. [2]
y
7
3
B
2
C A
1
x
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
Answer f p [1]
(b) Find the matrix representing the transformation that maps triangle A onto triangle C.
Answer f p [1]
(c) Triangle A is mapped onto triangle D by an enlargement, scale factor 2, centre ^5, 0h.
(b) A regular octagon, an equilateral triangle and a regular n-sided polygon fit together at a point.
octagon
a°
Find a.
19 (a) Evaluate
3
(i) 216 ,
J 3a 2 b N- 2
(b) Simplify K 4
O .
L12ab P
20 The diagram shows the speed-time graph for 100 seconds of a car’s journey.
The car accelerates uniformly from a speed of v m/s to a speed of 3v m/s in 50 seconds.
It then continues at a constant speed.
3v
Speed
(m/s)
v
0
0 50 100
Time (t seconds)
(a) Find, in terms of v, the acceleration of the car in the first 50 seconds.
(b) The car travels 2500 metres during the 100 seconds.
Find v.
(c) Find the speed of the car, in kilometres per hour, when t = 75.
(a) Complete the tree diagram to show the possible outcomes and their probabilities.
2 black
9
black
3
10
red
............
............ black
............ red
red
............
[1]
B 12 C
15
A D
E
G F
24 Some students were asked how long they had each spent doing homework the day before.
The results are summarised in the table.
(a) On the grid, draw a frequency polygon to represent this information for the girls and
another frequency polygon for the boys.
Frequency
(c) Make a comment comparing the distribution of the times spent by the girls with the
times spent by the boys.
Answer
............................................................................................................................................................
....................................................................................................................................................... [1]
25 In quadrilateral ABCD
angle A = ^2y + xh °
angle B = ^3y + xh °
angle C = ^2y + 10h °
angle D = ^3x + 5h °
(a) By finding the sum of the angles in the quadrilateral, show that 7y + 5x = 345.
[1]
7y + 5x = 345
2y + x = 90
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.
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.