Cambridge O Level

* 3 4 6 3 1 1 6 5 8 5 *

ADDITIONAL MATHEMATICS 4037/22

Paper 2 May/June 2022

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (PQ) 311245
© UCLES 2022 [Turn over
 2

Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax 2 + bx + c = 0 ,

- b ! b 2 - 4ac
x=
2a

Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r

n
where n is a positive integer and e o =
n!
r (n - r) !r!

Arithmetic series un = a + (n - 1) d
1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2

Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r

2. TRIGONOMETRY

Identities

sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A

Formulae for ∆ABC

a b c
= =
sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2

© UCLES 2022 4037/22/M/J/22

 3

1 DO NOT USE A CALCULATOR IN THIS QUESTION.

6+ x
A curve has equation y= where x H 0 . Find the exact value of y when x = 6 . Give your
3+ x
answer in the form a + b c , where a, b and c are integers. [3]

2
y

5
y = f (x)
y = g(x)

0 1 2.5 x
–1

The diagram shows the graphs of y = f (x) and y = g (x) , where y = f (x) and y = g (x) are straight
lines. Solve the inequality f (x) G g (x) . [5]

© UCLES 2022 4037/22/M/J/22 [Turn over

 4

3 Find the possible values of k for which the equation kx 2 + (k + 5) x - 4 = 0 has real roots. [5]

2 1
4 Variables x and y are related by the equation y = 1 + + where x 2 0 . Use differentiation to find
x x2
the approximate change in x when y increases from 4 by the small amount 0.01. [5]

© UCLES 2022 4037/22/M/J/22

 5

x3 - 1
2
625
5 (a) Solve the equation = 5. [3]
125 x
3

(b) On the axes, sketch the graph of y = 4e x + 3 showing the values of any intercepts with the
coordinate axes. [2]

O x

© UCLES 2022 4037/22/M/J/22 [Turn over

 6

6 (a) In this question, i is a unit vector due east and j is a unit vector due north.

A cyclist rides at a speed of 4 ms−1 on a bearing of 015°. Write the velocity vector of the cyclist in
the form xi + yj, where x and y are constants. [2]

(b) A vector of magnitude 6 on a bearing of 300° is added to a vector of magnitude 2 on a bearing of

230° to give a vector v. Find the magnitude and bearing of v. [5]

© UCLES 2022 4037/22/M/J/22

 7

e 4x tan x
7 Differentiate y = with respect to x. [4]
ln x

© UCLES 2022 4037/22/M/J/22 [Turn over

 8

8 The function f is defined by f (x) = 3 sin 2 x - 2 cos x for 2 G x G 4 , where x is in radians.

(a) Find the x-coordinate of the stationary point on the curve y = f (x) . [5]

© UCLES 2022 4037/22/M/J/22

 9

(b) Solve the equation f (x) = 1 - 3 cos x . [5]

© UCLES 2022 4037/22/M/J/22 [Turn over

 10

9 In this question all lengths are in centimetres.

a
2z T
O
rad

The diagram shows a circle, centre O, radius a. The lines PT and QT are tangents to the circle at P and
Q respectively. Angle POQ is 2z radians.

(a) In the case when the area of the sector OPQ is equal to the area of the shaded region, show that
tan z = 2z . [4]

© UCLES 2022 4037/22/M/J/22

 11

(b) In the case when the perimeter of the sector OPQ is equal to half the perimeter of the shaded
region, find an expression for tan z in terms of z. [3]

© UCLES 2022 4037/22/M/J/22 [Turn over

 12

10 (a) A geometric progression has first term a and common ratio r, where r 2 0 . The second term of
this progression is 8. The sum of the third and fourth terms is 160.

(i) Show that r satisfies the equation r 2 + r - 20 = 0 . [4]

(ii) Find the value of a. [3]

© UCLES 2022 4037/22/M/J/22

 13

(b) An arithmetic progression has first term p and common difference 2. The qth term of this
progression is 14.
A different arithmetic progression has first term p and common difference 4. The sum of the first
q terms of this progression is 168.

Find the values of p and q. [6]

© UCLES 2022 4037/22/M/J/22 [Turn over

 14

11
y
P Q

y=1

y = 1 + cos x

O R x

The diagram shows part of the line y = 1 and one complete period of the curve y = 1 + cos x , where
x is in radians. The line PQ is a tangent to the curve at P and at Q. The line QR is parallel to the y-axis.
Area A is enclosed by the line y = 1 and the curve. Area B is enclosed by the line y = 1, the line PQ
and the curve.

Given that area A : area B is 1 : k find the exact value of k. [9]

© UCLES 2022 4037/22/M/J/22

 15

Continuation of working space for Question 11.

Question 12 is printed on the next page.

© UCLES 2022 4037/22/M/J/22 [Turn over
 16

2
d2y
2 =f 4 p . Given that the gradient of the curve is 3 at the point (1, −1),
x +1 4
12 A curve is such that
dx x
find the equation of the curve. [7]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2022 4037/22/M/J/22

 Cambridge O Level
* 5 9 3 1 3 3 5 8 5 2 *

MATHEMATICS (SYLLABUS D) 4024/12

Paper 1 May/June 2024

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary working clearly.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (PQ/SG) 331859/2
© UCLES 2024 [Turn over
 2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER

1 (a) Here are five temperatures in °C.

4 1 -6 0 -2

Write these temperatures in order, starting with the lowest.

.................... , .................... , .................... , .................... , .................... [1]

lowest

(b) Write these numbers in order of size, starting with the smallest.
3
0.45 40%
8

.................... , .................... , .................... [1]

smallest

2 (a) Shade one more small square so the diagram has one line of symmetry.

[1]

(b) Shade one more small square so the diagram has rotational symmetry of order 2.

[1]

© UCLES 2024 4024/12/M/J/24

 3

3 Olga writes a list of five numbers.

The median of the numbers is 12.

The mode of the numbers is 11.
The range of the numbers is 10.

The sum of the numbers is 75.

Find the five numbers in Olga’s list.

.................... , .................... , .................... , .................... , .................... [3]

4 (a) Convert 4 kilograms to grams.

............................................... g [1]

(b) Convert 250cm 3 to litres.

......................................... litres [1]

© UCLES 2024 4024/12/M/J/24 [Turn over

 4

5 In this question all dimensions are given in centimetres.

(a)
11

6 NOT TO
SCALE

The diagram shows a parallelogram.

Find the perimeter of the parallelogram.

............................................ cm [1]

(b)
y

NOT TO
SCALE
4

13

The diagram shows a trapezium.

The area of the trapezium is 36cm 2 .

Find the value of y.

y = ................................................. [2]

© UCLES 2024 4024/12/M/J/24

 5

6 (a) Jack uses number cards to make a 2-digit number.

Complete the missing card to give a 2-digit number that is not a prime number.

.......
3
[1]

(b) Mei says:

When I add two multiples of 3, the answer is always a multiple of 6.

Give an example to show that Mei is wrong.

....................................................................................................................................................... [1]

2 1
7 (a) Work out ' .
7 3

................................................. [1]
5 3
(b) Work out + .
6 4
Give your answer as a mixed number.

................................................. [2]

© UCLES 2024 4024/12/M/J/24 [Turn over

 6

8 (a) A train leaves station A at 07 43.

The train arrives at station B at 10 27.

Work out the time the train takes to travel from station A to station B.

................ hours ................ minutes [1]

(b) A bus leaves the bus station at 06 25.

It arrives at the airport at 07 05.
The distance from the bus station to the airport is 24 km.

Calculate the average speed of the bus for this journey.

Give your answer in km/h.

......................................... km/h [3]

9 There are red pens, blue pens and black pens in a box.

There are x red pens.

The number of blue pens is 5 more than the number of red pens.
The number of black pens is 2 times the number of blue pens.

(a) Write an expression, in terms of x, for the total number of pens in the box.
Give your expression in its simplest form.

................................................. [2]

(b) The total number of pens in the box is 27.

Find the number of red pens in the box.

................................................. [2]

© UCLES 2024 4024/12/M/J/24

 7

10 The scale drawing shows part of a field, ABCD.

The scale is 1 cm to 50 m.

C
North

Scale: 1 cm to 50 m

(a) Measure the bearing of C from B.

................................................. [1]

(b) D is 250 m from C and 300 m from A.

Use a ruler and compasses only to complete the scale drawing of the field ABCD. [2]

(c) There is a path across the field.

The path is equidistant from AB and BC.

Use a straight edge and compasses only to construct the path. [2]

© UCLES 2024 4024/12/M/J/24 [Turn over

 8

11 By writing each number correct to 1 significant figure, estimate the value of

5.32 + 3.97
.
878

................................................. [2]

12 (a) a = 5b + 7

Find the value of a when b =-2 .

a = ................................................. [1]

(b) c = 4d - 9

Rearrange the formula to make d the subject.

d = ................................................. [2]

© UCLES 2024 4024/12/M/J/24

 9

13 Kamal records the number of phone calls he receives at work each day for 20 days.
The results are shown in the table.

Number of phone calls 0 to 5 6 to 10 11 to 15 16 or more

Frequency 9 5 4 2

(a) Find the relative frequency of Kamal receiving 0 to 5 phone calls at work in one day.

................................................. [1]

(b) Kamal works for 160 days.

Find the number of these days Kamal would expect to receive 11 or more phone calls at work.

................................................. [2]

14 (a) Write 42 000 000 in standard form.

................................................. [1]

(b) Evaluate `1.3 # 10 -4j + `7.4 # 10 -3j .

Give your answer in standard form.

................................................. [2]

© UCLES 2024 4024/12/M/J/24 [Turn over

 10

15
D

C NOT TO
SCALE

7 8

A 5 B

Triangle ABC is mathematically similar to triangle CBD.

AB = 5cm , AC = 7cm and BC = 8cm .

Calculate BD.

BD = ............................................ cm [2]

© UCLES 2024 4024/12/M/J/24

 11

16
y
5

–1 0 x
1 2 3 4 5
–1

The region R is defined by these inequalities.

y H 2x

x+y G 4

xH0

Find and label region R. [3]

© UCLES 2024 4024/12/M/J/24 [Turn over

 12

17
B

A
120°
20° NOT TO
SCALE

y° x°
C
D

A, B, C and D are points on a circle, centre O.

Angle BAD = 120° and angle OBC = 20° .

(a) Find the value of x.

x = ................................................. [2]

(b) Find the value of y.

y = ................................................. [2]

© UCLES 2024 4024/12/M/J/24

 13
1
18 (a) Evaluate 125 - 3 .

................................................. [1]
3

(b) Simplify e o .
a3 2
4a

................................................. [2]

19 (a) The mass of a bag of almonds is 125 g, correct to the nearest gram.

Write down the lower bound of the mass of the bag of almonds.

............................................... g [1]

(b) The mass of a large box is 500 g, correct to the nearest 10 grams.
The mass of a small box is 250 g, correct to the nearest 10 grams.

Calculate the upper bound of the difference between the mass of a large box and the mass of a
small box.

............................................... g [2]

© UCLES 2024 4024/12/M/J/24 [Turn over

 14

2 - 4x
20 f (x) =
5
(a) Find f -1 (x) .

f -1 (x) = ................................................. [3]

(b) Simplify f (x) - f (2x) .

................................................. [2]

© UCLES 2024 4024/12/M/J/24

 15

21 The table shows the heights of 180 sunflowers.

Height (h cm) 100 1 h G 120 120 1 h G 140 140 1 h G 150 150 1 h G 160
Frequency 28 60 68 24

Complete the histogram.

5
Frequency
density 4

0
100 110 120 130 140 150 160 h
Height (cm)

[3]

© UCLES 2024 4024/12/M/J/24 [Turn over

 16

22
y
6

-3 -2 -1 0 1 2 3 4 x
-1

-2

-3

-4

-5

-6

1 x
The diagram shows the graph of y = + .
x 2
(a) By drawing a tangent, estimate the gradient of the curve when x = 2 .

................................................. [2]
1 5x
(b) By drawing a suitable line on the grid, find the solutions of - +1 = 0 .
x 2

x = ....................., x = .................... [3]

© UCLES 2024 4024/12/M/J/24

 17

3 -1
23 A =e o
2 0

(a) Find A -1 .

A -1 = f p [2]

(b) AX = b l
7
4
Find X.

X= [2]

© UCLES 2024 4024/12/M/J/24 [Turn over

 18

x 5
24 Solve - =1.
x-1 x-3

x = ................................................. [4]

© UCLES 2024 4024/12/M/J/24

 19

25
C

NOT TO
X SCALE

A
a

O B
b

OCB is a triangle.

A is a point on OC such that OA | AC = 1 | 3.

X is the midpoint of BC.
OA = a and OB = b .

Find the position vector of X.

Give your answer as simply as possible in terms of a and b.

................................................. [3]

© UCLES 2024 4024/12/M/J/24

 20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 4024/12/M/J/24

 Cambridge O Level
* 0 0 0 0 8 9 7 9 4 4 *

MATHEMATICS (SYLLABUS D) 4024/12

Paper 1 October/November 2022

2 hours

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary working clearly.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (RW/CGW) 303251/3
© UCLES 2022 [Turn over
 2

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER

1 (a) Work out 80 ' 0.02 .

................................................. [1]
3
(b) Evaluate 1000 .

................................................. [1]

2 (a) Put one pair of brackets into this calculation to make it correct.

4 + 4 # 4 - 4 = 4

[1]

(b) Work out - 6 # (- 3 + 7) .

................................................. [1]

3 Write 7.54 # 10 - 4 as an ordinary number.

................................................. [1]

© UCLES 2022 4024/12//O/N/22

 3

4 Sam has six square tiles labelled A, B, C, D, E and F.

A B C

D E F

When Sam places tiles E and F side by side the resulting rectangle has no lines of symmetry and no
rotational symmetry.

E F

Write down the two tiles that Sam should place side by side to make a rectangle that has

(a) one line of symmetry only,

................................................. [1]

(b) rotational symmetry of order 2.

................................................. [1]

© UCLES 2022 4024/12//O/N/22 [Turn over

 4

5 The perimeter of a regular hexagon is equal to the perimeter of a regular octagon.

Each edge of the octagon is 9 cm long.

Find the length of one edge of the hexagon.

............................................ cm [2]

11 2
6 (a) Work out - .
15 3

................................................. [1]
3
(b) Work out ' 6.
10
Write your answer as a fraction in its simplest form.

................................................. [2]

© UCLES 2022 4024/12//O/N/22

 5

7
C

y°

NOT
B x° TO
SCALE

A D

In the diagram, AD, AB and BC are three sides of a regular pentagon and DC is a diagonal of the
pentagon.
AB is parallel to DC.

(a) Find the value of x.

x = ................................................. [2]

(b) Find the value of y.

y = ................................................. [1]

© UCLES 2022 4024/12//O/N/22 [Turn over

 6

8
B

NOT TO
SCALE

A C

ABC is an isosceles triangle with AB = BC .

t : BAC
The ratio ABC t = 2 : 5.

t .
Find ABC

t = ................................................. [2]
ABC

9 By writing each number correct to 1 significant figure, estimate the value of

47.5 + 36.1
.
64.9 ' 17.7

................................................. [2]

© UCLES 2022 4024/12//O/N/22

 7

10 (a) Write 420 as the product of its prime factors.

................................................. [2]

(b) Given that 1512 = 2 3 # 3 3 # 7 , find the highest common factor of 420 and 1512.

................................................. [1]

11 Azra has a spinner.

The sections are coloured red, blue, yellow or green.
The relative frequency of the spinner landing on red, blue or yellow is shown in the table.

Colour on spinner Red Blue Yellow Green

Relative frequency 0.15 0.3 0.2

(a) Find the relative frequency of the spinner landing on green.

................................................. [2]

(b) Azra spins the spinner 150 times.

How many times would she expect the spinner to land on blue?

................................................. [1]

© UCLES 2022 4024/12//O/N/22 [Turn over

 8

12 (a) Represent the inequality - 4 G x 1 2 on the number line below.

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x

[1]

(b) Solve the inequality.

10 - n 1 2n - 5

................................................. [2]

13 Sophie cycles 2600 metres in 12 minutes.

Work out Sophie’s average speed in kilometres per hour.

......................................... km/h [3]

© UCLES 2022 4024/12//O/N/22

 9

14 The scale drawing shows a plot of land, PQRS.

The scale is 1 cm to 20 m.

Q
North

S R

Scale: 1 cm to 20 m

(a) A path crosses the land.

The path is equidistant from SP and SR.
Use a straight edge and compasses only to construct the path. [2]

(b) Priya walks from point P to the path on a bearing of 104°.

(i) Draw a line to represent Priya’s walk. [1]

(ii) Find the actual distance from P to where Priya meets the path.

.............................................. m [2]

(c) A car park is to be built on the plot of land.

On the scale drawing the area of the car park will be 2 cm 2 .

Find the actual area of the car park.

........................................... m 2 [2]

© UCLES 2022 4024/12//O/N/22 [Turn over

 10

15
y

A (0, 6) C (p, 6)

NOT TO
SCALE

0 x
B (p, 0)

The diagram shows the points A (0, 6), B ( p, 0) and C ( p, 6).

The equation of the line AB is 3y + 4x = 18 .

(a) Find the value of p.

p = ................................................. [1]

(b) Write down the three inequalities that define the region inside triangle ABC.

.................................................

.................................................

................................................. [2]

© UCLES 2022 4024/12//O/N/22

 11

16 P is the point ( - 2 , 1) and Q is the point (6, 13).

M is the midpoint of the line PQ.

(a) Find the coordinates of M.

( ...................... , ...................... ) [1]

(b) (i) Find the gradient of the line PQ.

................................................. [2]

(ii) Write down the gradient of a line that is perpendicular to the line PQ.

................................................. [1]

© UCLES 2022 4024/12//O/N/22 [Turn over

 12

17 (a) Simplify.

(x 2) 3

................................................. [1]

(b) t- 2 = 9

Find the value of t.

t = ................................................. [1]

(c) 5 # 50 = 5k

Find the value of k.

k = ................................................. [1]

© UCLES 2022 4024/12//O/N/22

 13

18 x is directly proportional to the square of (y + 1) .

When y = 2 , x = 45.

Find x when y = 4 .

x = ................................................. [2]

19 Solve.
3x - 1 x + 2 5
+ =
6 4 3

x = ................................................. [4]

© UCLES 2022 4024/12//O/N/22 [Turn over

 14

20 The table shows some information about the times each of 100 children spent reading in one day.

Time (t mins) x 1 t G 30 30 1 t G 40 40 1 t G 45 45 1 t G 60
Frequency 32 23 15 30
Frequency
1.6 2.3
density

(a) Find the value of x in the interval x 1 t G 30 .

x = ................................................. [1]

(b) On the grid, draw a histogram to represent the data for the 100 children.

Frequency
2
density

0 t
0 10 20 30 40 50 60
Time (minutes)
[3]

© UCLES 2022 4024/12//O/N/22

 15

3x 2
21 f (x) = 1 + g (x) =
2 1-x

(a) Find f -1 (x) .

f -1 (x) = ................................................. [3]

(b) Solve g (x) = f (- 4) .

x = ................................................. [3]

22 Factorise.

(a) 9p 2 - q 2

................................................. [1]

(b) ac - 3bc + a - 3b

................................................. [2]

© UCLES 2022 4024/12//O/N/22 [Turn over

 16

23 Adam and Ben buy tickets for the cinema and the theatre.

(a) Adam buys 5 cinema tickets and 4 theatre tickets.

Ben buys 7 cinema tickets and 9 theatre tickets.

Complete the matrix, X, to represent this information.

Cinema Theatre

f p
Adam
X=
Ben

[1]

(b) Cinema tickets cost $11 each and theatre tickets cost $30 each.
The matrix Y represents this information.

11
Y =e o
30

(i) P = XY

Find the matrix P.

P= [2]

(ii) Explain what the elements in matrix P represent.

.............................................................................................................................................

............................................................................................................................................. [1]

© UCLES 2022 4024/12//O/N/22

 17

24 sin x° = sin 50° and 90 1 x 1 180 .

Find the value of x.

x = ................................................. [1]

x 2 - 4x
25 Simplify .
x 2 - x - 12

................................................. [3]

© UCLES 2022 4024/12//O/N/22 [Turn over

 18

26
A

NOT TO
SCALE

a B

OAC is a triangle and B is a point on AC such that AB : BC = 3 : 2.

OA = a and OB = b .

(a) Find OC in terms of a and b, giving your answer in its simplest form.

OC = ................................................. [3]
2
(b) D is a point on OC such that OD = b - a .
5
Show that OABD is a trapezium.

[2]

© UCLES 2022 4024/12//O/N/22

 19

BLANK PAGE

© UCLES 2022 4024/12//O/N/22

 20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2022 4024/12//O/N/22

 Cambridge O Level
* 5 1 1 4 5 6 4 3 6 1 *

MATHEMATICS (SYLLABUS D) 4024/21

Paper 2 May/June 2024

2 hours 30 minutes

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 100.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (DE/SW) 331860/4
© UCLES 2024 [Turn over
 2

1 (a) The cost of a ticket to watch a basketball match is $67.60 .

(i) The total money received from ticket sales for one match is $1 183 000.

Find the number of tickets sold for this match.

................................................. [1]

(ii) The cost of one ticket at $67.60 is 4% more than the cost of one ticket last year.

Calculate the cost of one ticket last year.

$ ................................................. [2]

(b) The number of seats in the basketball stadium is 20 545.

The number of seats sold for the first match of the season is 19 340.

Calculate the percentage of the seats in the stadium that are sold.

.............................................. % [1]

(c) A team plays 41 matches.

For the 41 matches, the mean number of seats sold per match is 16 440.
The total number of seats sold for the first 21 matches is 329 000.

Calculate the mean number of seats sold per match for the last 20 matches.

................................................. [3]

© UCLES 2024 4024/21/M/J/24

 3

(d) The table shows the salaries of three basketball players.

Basketball player Salary ($)

Stephen 8.27 # 10 6
Joe 4.29 # 10 6
Tristan 3.64 # 10 7

(i) Find the difference between the salaries of Tristan and Stephen.

$ ................................................. [1]

(ii) The total Joe earns is his salary plus a bonus of $x.
The total he earns is 102.5% of his salary.

Calculate the value of x.

x = ................................................ [2]

© UCLES 2024 4024/21/M/J/24 [Turn over

 4

2 (a) The temperature at midday was recorded at ten different heights on a mountain.
The results are shown in the table.

Height (m) 300 825 600 425 900 100 1250 1450 1125 1350
Temperature (°C) 3.0 - 0.8 0.0 1.2 -1.9 3.5 - 4.6 - 6.4 - 4.0 - 3.8

(i) Complete the scatter diagram.

The first five points have been plotted for you.

0
250 500 750 1000 1250 1500 Height
(m)
–1

–2
Temperature
(°C)
–3

–4

–5

–6

–7

[2]

(ii) Describe the type of correlation shown in the scatter diagram.

................................................. [1]

(iii) Draw a line of best fit on the scatter diagram. [1]

(iv) Another reading is taken at a height of 1000 m.

Use your line of best fit to estimate the temperature at this height.

............................................. °C [1]

© UCLES 2024 4024/21/M/J/24

 5

(b) The table summarises the times taken by 80 adults to climb the mountain.

Time taken (h hours) 5.5 1 h G 6.5 6.5 1 h G 7.5 7.5 1 h G 8 8 1 h G 8.5 8.5 1 h G 10.5
Frequency 8 15 20 23 14

(i) Calculate an estimate of the mean time.

........................................ hours [3]

(ii) A histogram is drawn to show this information.

The height of the bar representing 5.5 1 h G 6.5 is 8 mm.

Calculate the height of the bar representing 8 1 h G 8.5 .

.......................................... mm [1]

© UCLES 2024 4024/21/M/J/24 [Turn over

 6

3 (a)
Q

NOT TO
SCALE

142°
P R

Triangle PQR is isosceles with PQ = QR .

The exterior angle of the triangle at R is 142°.

Calculate angle PQR.

Angle PQR = ................................................ [2]

(b)
A B

NOT TO
E SCALE

D C

The diagonals of trapezium ABCD meet at E.

Show that triangle ABE is similar to triangle CDE.

Give a reason for each statement you make.

.....................................................................................................................................................

.....................................................................................................................................................

.....................................................................................................................................................

..................................................................................................................................................... [3]

© UCLES 2024 4024/21/M/J/24

 7

4 (a) Two of the factors of 50 are square numbers.

One of these square numbers is 1.

Find the other square number that is a factor of 50.

................................................. [1]

(b) A = 2 x - 1 # 3 2y # 7
B = 2x+3 # 3 y # 5

The numbers A and B are written as the product of their prime factors, where x and y are positive
integers.

(i) Find the highest common factor (HCF) of A and B in terms of x and y.

................................................. [2]

(ii) Find the lowest common multiple (LCM) of A and B in terms of x and y.

................................................. [2]

© UCLES 2024 4024/21/M/J/24 [Turn over

 8

5 (a) Two companies move boxes.

Company A charges $0.50 for each box plus a fixed fee of $125.
Company B charges only a fixed fee of $350.

Find the number of boxes moved when Company A charges the same as Company B.

................................................. [2]

(b) The maximum mass a van can carry is exactly 770 kg.
The van carries boxes each of mass 4 kg, correct to the nearest kilogram.

Find the upper bound for the number of boxes this van can carry.

................................................. [2]

(c) A lorry contains boxes of three sizes S, M and L.

The ratio of the number of boxes S : M = 2 : 7.
The ratio of the number of boxes S : L = 5 : 4.
The lorry contains 72 boxes of size L.

Find the total number of boxes in the lorry.

................................................. [3]

© UCLES 2024 4024/21/M/J/24

 9

6
y
6

2
B
1

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
A
–1

–2

–3

–4

–5

–6

–7

–8

1
(a) Triangle A is mapped onto triangle P by a translation of e o.
-3
Draw triangle P. [2]

(b) Describe fully the single transformation that maps triangle A onto triangle B.

.....................................................................................................................................................

..................................................................................................................................................... [3]

(c) Transformation M is a reflection in the line y = -1.

Transformation R is a rotation 90° clockwise about (1, 1).
RM(B) = Q.

Draw triangle Q. [3]

© UCLES 2024 4024/21/M/J/24 [Turn over

 10

7 (a) A cuboid has dimensions 5 cm by 12 cm by h cm.

The volume of the cuboid is 480 cm 3 .

Calculate the value of h.

h = ................................................ [2]

(b)
C

NOT TO
65° SCALE
B D
16

A E
21

ABCDE is a pentagon.
AE is parallel to BD.
AE = 21 cm, BD = 16 cm and DE = 8 cm.
Angle DEA = 90° and angle CBD = 65°.

(i) Calculate angle BAE.

Angle BAE = ................................................ [3]

© UCLES 2024 4024/21/M/J/24

 11

(ii) The area of pentagon ABCDE is 200 cm 2 .

Calculate the length of BC.

BC = ........................................... cm [5]

© UCLES 2024 4024/21/M/J/24 [Turn over

 12

2x
8 (a) (i) Complete the table for y = .
5

x 0 1 2 3 4 5
y 0.2 0.4 0.8 1.6 3.2

[1]
2x
(ii) On the grid, draw the graph of y = for 0 G x G 5.
5
y
7

0 1 2 3 4 5 x

[3]

© UCLES 2024 4024/21/M/J/24

 13

(iii) 2 x + 3 = 100
2x 5
(a) Show that = .
5 2

[2]

(b) By drawing a suitable line on the grid, solve 2 x + 3 = 100 .

x = ................................................ [2]

(b)
y

NOT TO
SCALE

O x

This is a sketch of the graph y = a + bx - x 2 .

The graph crosses the x-axis at integer values of x.

Find the value of a and the value of b.

a = ................................................

b = ................................................ [3]
© UCLES 2024 4024/21/M/J/24 [Turn over
 14

9
North

NOT TO
SCALE

A
176
B

132

The diagram shows the positions of three ports A, B and C.

The bearing of port B from port A is 107°.
The bearing of port C from port A is 192°.
AB = 176 km and AC = 132 km.

(a) Find the bearing of A from B.

................................................. [1]

(b) Calculate BC.

BC = .......................................... km [4]

© UCLES 2024 4024/21/M/J/24

 15

(c) Boat B leaves port B at 10.00 am.

It sails directly to port A at an average speed of 48 km/h.

Boat C leaves port C at 10.15 am.

It sails directly to port A and arrives there 7 minutes before boat B.

Find the average speed of boat C in km/h.

........................................ km/h [5]

© UCLES 2024 4024/21/M/J/24 [Turn over

 16

4p + 3t
10 (a) r=
2
Find the value of p when r = 10 and t = - 2 .

p = ................................................ [3]

(b)

w°
NOT TO
SCALE
2w°

(w + 10)° (w – 15)°

The diagram shows a quadrilateral.

Form an equation in w and solve it to find the size of the largest angle in the quadrilateral.

Largest angle = ................................................ [4]

© UCLES 2024 4024/21/M/J/24

 17

2k 2 - 5k - 3
(c) Simplify .
k2 - 9

................................................. [3]
2 5
(d) Solve + = 1.
x+3 x-2
Show all your working and give your answers correct to 2 decimal places.

x = .................... or x = .................... [6]

© UCLES 2024 4024/21/M/J/24 [Turn over

 18

11 (a) On any day in January, the probability the temperature at a weather station is above 14 °C is 0.35 .

(i) There are 31 days in January.

Find the number of days in January when you would expect the temperature to be
above 14 °C.

................................................. [1]

(ii) The temperature on two consecutive days in January is recorded.

(a) Complete the tree diagram.

First day Second day

Above 14 °C
0.35

Above 14 °C

0.35
........... 14 °C or below

Above 14 °C
...........
...........
14 °C or below

........... 14 °C or below
[2]

(b) Find the probability that the temperature is above 14 °C on both days.

................................................. [1]

(c) Find the probability that the temperature is above 14 °C on only one of the two days.

................................................. [2]

© UCLES 2024 4024/21/M/J/24

 19

(b) In a group of 14 children:

• 8 wear red T-shirts

• 1 wears a green T-shirt
• 5 wear blue T-shirts.

Two children are chosen from the group at random.

Find the probability that they wear different coloured T-shirts.

................................................. [3]

© UCLES 2024 4024/21/M/J/24

 20

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 4024/21/M/J/24

 Cambridge O Level
* 7 4 1 9 3 6 9 3 1 6 *

ADDITIONAL MATHEMATICS 4037/23

Paper 2 October/November 2022

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages. Any blank pages are indicated.

DC (LO) 319572
© UCLES 2022 [Turn over
 2

Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax 2 + bx + c = 0 ,

- b ! b 2 - 4ac
x=
2a

Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r

where n is a positive integer and eno = n!

r (n - r) !r!

Arithmetic series un = a + (n - 1) d
1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2

Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r

2. TRIGONOMETRY

Identities

sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A

Formulae for ∆ABC

a b c
= =
sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2

© UCLES 2022 4037/23/O/N/22

 3

1 Solve the following inequality.

(2x + 3) (x - 4) 2 (3x + 4) (x - 1) [5]

© UCLES 2022 4037/23/O/N/22 [Turn over

 4

2 The tangent to the curve y = ax 2 - 5x + 2 at the point where x = 2 has equation y = 7x + b . Find
the values of the constants a and b. [5]

3 Solve the equation lg (2x - 1) + lg (x + 2) = 2 - lg 4 . [5]

© UCLES 2022 4037/23/O/N/22

 5

4 The line y = kx + 6 intersects the curve y = x 3 - 4x 2 + 3kx + 2 at the point where x = 2 .

(a) Find the value of k. [2]

(b) Show that, for this value of k, the line cuts the curve only once. [4]

© UCLES 2022 4037/23/O/N/22 [Turn over

 6

cos x 1 - sin x
5 (a) Show that + = 2 sec x . [4]
1 - sin x cos x

i i
cos 1 - sin
(b) Hence solve the equation 2 + 2 = 8 cos 2 i for - 360° 1 i 1 360° . [4]
i i 2
1 - sin cos
2 2

© UCLES 2022 4037/23/O/N/22

 7

6 The first four terms in ascending powers of x in the expansion (3 + ax) 4 can be written as
3
81 + bx + cx 2 + x 3 . Find the values of the constants a, b and c. [6]
2

n
7 Given that C4 = 13 # n C2 , find the value of n C8 . [5]

© UCLES 2022 4037/23/O/N/22 [Turn over

 8

3
8 (a) Particle A starts from the point with position vector e o and travels with speed 26 ms -1 in the
-2
12
direction of the vector e o. Find the position vector of A after t seconds. [3]
5

67
(b) At the same time, particle B starts from the point with position vector e o. It travels with speed
-18
3
20 ms -1 at an angle of a above the positive x‑axis, where tan a = . Find the position vector of B
4
after t seconds. [4]

© UCLES 2022 4037/23/O/N/22

 9

(c) Hence find the time at which A and B meet, and the position where this occurs. [3]

© UCLES 2022 4037/23/O/N/22 [Turn over

 10

9 The equation of a curve is y = kxe - 2x , where k is a constant.

dy
(a) Find . [2]
dx

(b) Find the coordinates of the stationary point on the curve y = 10xe - 2x . [3]

© UCLES 2022 4037/23/O/N/22

 11

(c) Use your answer to part (a) to find y 4xe - 2x

dx . [3]

1
(d) Find the exact value of y
0
4xe - 2x dx . [2]

© UCLES 2022 4037/23/O/N/22 [Turn over

 12

10 (a) The third term of an arithmetic progression is 10 and the sum of the first 8 terms is 116. Find the
first term and common difference. [5]

© UCLES 2022 4037/23/O/N/22

 13

(b) Find the sum of nineteen terms of the progression, starting with the twelfth term. [4]

© UCLES 2022 4037/23/O/N/22 [Turn over

 14

11
5a R
S
b

Q
3b

O 2a P

In the vector diagram, OP = 2a , SR = 5a , OS = 3b and QR = b .

(a) Given that PX = mPS , write OX in terms of a, b and m. [3]

(b) Given that OX = n OQ , write OX in terms of a, b and n. [2]

© UCLES 2022 4037/23/O/N/22

 15

(c) Find the values of m and n. [4]

OX
(d) Write down the value of . [1]
OQ

PX
(e) Find the value of . [1]
XS

© UCLES 2022 4037/23/O/N/22

 16

BLANK PAGE

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2022 4037/23/O/N/22

 * 0000800000001 *

,










,

Cambridge O Level

¬OŠ. 4mHuOªEŠ]y5€W
¬er{Tªo‚Wy [‚|f3’‚
¥eEU5UeUU•¥EEUeU U
* 5 9 4 1 1 2 8 8 9 9 *

ADDITIONAL MATHEMATICS 4037/22

Paper 2 October/November 2024

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (SL) 344964
© UCLES 2024 [Turn over
 * 0000800000002 *

DO NOT WRITE IN THIS MARGIN

2
,










,

Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax 2 + bx + c = 0 ,

- b ! b 2 - 4ac
x=

DO NOT WRITE IN THIS MARGIN

2a

Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r

n n!
where n is a positive integer and e o =
r (n - r) !r!

Arithmetic series un = a + (n - 1) d

DO NOT WRITE IN THIS MARGIN

1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2

Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r

2. TRIGONOMETRY

DO NOT WRITE IN THIS MARGIN

Identities

sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A

Formulae for ∆ABC

a b c
= =
sin A sin B sin C
DO NOT WRITE IN THIS MARGIN

a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2

ĬÍĊ®Ġ´íÈõÏĪÅĊàû·þ×
© UCLES 2024 ĬåôüÑĞûĨàĈó¸ºĂĖċĚĂ
ĥõÕÕõµĥµĥÕµąÅĕÅĕåÕ
4037/22/O/N/24
 * 0000800000003 *
DO NOT WRITE IN THIS MARGIN

3
,










,

1 Solve the following simultaneous equations.

y 3
=
x 2

y 4 27
= [3]
x 5 16
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÏĊ®Ġ´íÈõÏĪÅĊàù·þ×
© UCLES 2024 ĬåóûÙĬ÷ĘÙòþñĞúÂċĪĂ
ĥõåĕµÕąÕõåĥąÅõåÕµÕ
4037/22/O/N/24 [Turn over
 * 0000800000004 *

DO NOT WRITE IN THIS MARGIN

4
,










,

2 Variables x and y are related by the equation y = x 1 + 2x .

dy
(a) Find . [3]
dx

DO NOT WRITE IN THIS MARGIN

(b) It is given that when y = 12 , x = 4 . Find the approximate change in x when y increases from 12
by the small amount 0.06. [3]

DO NOT WRITE IN THIS MARGIN

(c) Find the x-coordinate of the stationary point on the curve y = x 1 + 2x . [2]

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN

ĬÍĊ®Ġ´íÈõÏĪÅĊÞû·Ā×
© UCLES 2024 ĬåóúÙĢąđÞðąúÀÖĤěĒĂ
ĥÅõĕõÕąõĕąĕąąõąÕåÕ
4037/22/O/N/24
 * 0000800000005 *
DO NOT WRITE IN THIS MARGIN

5
,










,

3 DO NOT USE A CALCULATOR IN THIS QUESTION.

The polynomial p is defined by p (x) = ax 3 - 3x 2 - 3x + b , where a and b are constants.

(a) Given that x = 2 and x =-1 are roots of the equation p (x) = 0 , find a and b. [3]
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

(b) Solve the equation p (x) = 0 . [2]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÏĊ®Ġ´íÈõÏĪÅĊÞù·Ā×
© UCLES 2024 ĬåôùÑĨĉġÛĊü¯ĜÞ¸ěĢĂ
ĥÅąÕµµĥĕąõÅąąĕĥĕµÕ
4037/22/O/N/24 [Turn over
 * 0000800000006 *

DO NOT WRITE IN THIS MARGIN

6
,










,

4 Use a graphical method to solve the inequality 2x - 8 2 4 . [5]

10

DO NOT WRITE IN THIS MARGIN

6

DO NOT WRITE IN THIS MARGIN

–8 –6 –4 –2 0 2 4 6 8 x

–2

–4

DO NOT WRITE IN THIS MARGIN

–6

–8
DO NOT WRITE IN THIS MARGIN

ĬÑĊ®Ġ´íÈõÏĪÅĊßù¶þ×
© UCLES 2024 ĬåóùÎĞġīÓýĉÆüÖÕ³ĒĂ
ĥĕåÕµĕĥµÅĕĥąÅĕÅÕĥÕ
4037/22/O/N/24
 * 0000800000007 *
DO NOT WRITE IN THIS MARGIN

7
,










,

5 Solve the following equations.

(a) log 2 x 2 + log 16 x = 18 [4]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

(b) e 2x + 1 - 10e -2x - 1 = 3 [4]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÓĊ®Ġ´íÈõÏĪÅĊßû¶þ×
© UCLES 2024 ĬåôúÖĬĝěæûøăàÞā³ĢĂ
ĥĕÕĕõõąÕÕĥµąÅõåĕõÕ
4037/22/O/N/24 [Turn over
 * 0000800000008 *

DO NOT WRITE IN THIS MARGIN

8
,










,

6 DO NOT USE A CALCULATOR IN THIS QUESTION.

Write (5 - 3) ( 6 + 2) -2 in the form a + b 3 , where a and b are constants. [5]

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÑĊ®Ġ´íÈõÏĪÅĊÝù¶Ā×
© UCLES 2024 ĬåôûÖĢďĎÑõïČþĂããĚĂ
ĥåąĕµõąõµÅÅąąõąĕĥÕ
4037/22/O/N/24
 * 0000800000009 *
DO NOT WRITE IN THIS MARGIN

9
,










,

7 A class of 10 students includes Abby and Ben.

(a) A group of 5 students is to be selected from the class. Find the number of possible groups in the
following cases.

(i) There are no restrictions. [1]

DO NOT WRITE IN THIS MARGIN

(ii) The group includes both Abby and Ben. [2]

(iii) The group includes either Abby or Ben, but not both. [2]
DO NOT WRITE IN THIS MARGIN

(b) All 10 students are arranged in a line. How many arrangements are possible if there are exactly
three students between Abby and Ben? [3]
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÓĊ®Ġ´íÈõÏĪÅĊÝû¶Ā×
© UCLES 2024 ĬåóüÎĨēĞèăĂ½Úú÷ãĪĂ
ĥåõÕõĕĥĕåµĕąąĕĥÕõÕ
4037/22/O/N/24 [Turn over
 * 0000800000010 *

DO NOT WRITE IN THIS MARGIN

10
,










,

8 Solve the equation cot 2 2i + 3 cosec 2i = 9 for -90° G i G 90° . [6]

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÑĊ®Ġ´íÈõÏĪÅĊàù¸þ×
© UCLES 2024 ĬåñûÏĤėČÏîøâĢĄÇěĢĂ
ĥõĥÕµõåõĕõÅÅąÕąĕÕÕ
4037/22/O/N/24
 * 0000800000011 *
DO NOT WRITE IN THIS MARGIN

11
,









,

9 In this question time is measured in seconds.

(a) A particle is moving in a straight line with constant velocity of 6 ms -1 . At time t = 0 , it passes
a fixed point A. At time t = 5 it suddenly changes direction and moves with a different constant
velocity along the same straight line. It passes the point A again at time t = 15. Sketch the
velocity−time graph for the motion. [3]

v
DO NOT WRITE IN THIS MARGIN

0
5 10 15 t

−6
DO NOT WRITE IN THIS MARGIN

(b) Another particle is moving in a straight line with constant acceleration. At time t = 0 it passes
a fixed point B with velocity -8 ms -1 . It passes the point B again at time t = 20 . Sketch the
velocity−time graph for the motion. [3]

v
DO NOT WRITE IN THIS MARGIN

0
5 10 15 20 t
DO NOT WRITE IN THIS MARGIN

ĬÓĊ®Ġ´íÈõÏĪÅĊàû¸þ×
© UCLES 2024 Ĭåòü×ĦěüêČĉħ¶üēěĒĂ
ĥõĕĕõĕÅĕąąĕÅąµĥÕÅÕ
4037/22/O/N/24 [Turn over
 * 0000800000012 *

DO NOT WRITE IN THIS MARGIN

12
,









,

x2
10 The diagram shows part of the curve y = x - and the line y =-4 . The curve and the line intersect
4
at the point A.

O x

DO NOT WRITE IN THIS MARGIN

h
x2
y = x-
4

y =- 4
A

(a) The maximum point on the curve is at a perpendicular distance h from the line y =-4 .

DO NOT WRITE IN THIS MARGIN

Find the value of h. [4]

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN

ĬÑĊ®Ġ´íÈõÏĪÅĊÞù¸Ā×
© UCLES 2024 Ĭåòù×ĠĩíÍĆĂĠĘرċĪĂ
ĥÅÅĕµĕŵĥåĥÅŵÅÕÕÕ
4037/22/O/N/24
 * 0000800000013 *
DO NOT WRITE IN THIS MARGIN

13
,









,

(b) Find the exact x-coordinate of A. [3]

DO NOT WRITE IN THIS MARGIN

(c) Find the acute angle between the tangent to the curve at A and the line y =-4 . [4]
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÓĊ®Ġ´íÈõÏĪÅĊÞû¸Ā×
© UCLES 2024 ĬåñúÏĪĥýìôïéÄàĥċĚĂ
ĥŵÕõõåÕõÕµÅÅÕåĕÅÕ
4037/22/O/N/24 [Turn over
 * 0000800000014 *

DO NOT WRITE IN THIS MARGIN

14
,









,

11 In this question i is a unit vector in the positive x-direction and j is a unit vector in the positive
y-direction. Time is in seconds and distances are in metres.

The diagram shows the initial positions and velocities of two particles, A and B, that move in the
x-y plane.

y
Particle B
5 ms–1
(2 3, 9) 3

DO NOT WRITE IN THIS MARGIN

10 ms–1

Particle A 60°
O x

Particle A starts from the origin O at time t = 0 . It moves with constant speed 10 ms -1 in the direction
60° above the x-axis.

DO NOT WRITE IN THIS MARGIN

(a) Find the exact values of the components of the velocity of particle A in the x-direction and the
y-direction. [2]

DO NOT WRITE IN THIS MARGIN

(b) Find, in terms of t, the position vector of particle A at time t. [1] DO NOT WRITE IN THIS MARGIN

ĬÍĊ®Ġ´íÈõÏĪÅĊÝüµĂ×
© UCLES 2024 ĬåòüÎĨĚõÚöüĆĠõġ»ĒĂ
ĥĥµĕµĕĥõĕŵąąĕąÕĕÕ
4037/22/O/N/24
 * 0000800000015 *
DO NOT WRITE IN THIS MARGIN

15
,









,

5
Particle B starts from the point (2 3, 9) at time t = 0 . It moves with constant speed ms -1 parallel to
3
the positive x-axis.

(c) Find, in terms of t, the position vector of particle B at time t. [2]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

(d) Hence show that the particles collide. [4]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

Question 12 is printed on the next page.

ĬÏĊ®Ġ´íÈõÏĪÅĊÝúµĂ×
© UCLES 2024 ĬåñûÖĢĖąßĄąÃ¼ýµ»ĢĂ
ĥĥÅÕõõąĕąµĥąąõĥĕąÕ
4037/22/O/N/24 [Turn over
 * 0000800000016 *

DO NOT WRITE IN THIS MARGIN

16
,









,

12 A metal tank is in the shape of a cuboid with a square base of side x m and an open top. The tank has
a volume of 5 m 3 . Given that x can vary, and that the area of the metal used to make the tank is a
minimum, find the dimensions of the tank. [6]

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
ĬÍĊ®Ġ´íÈõÏĪÅĊßüµĄ×
© UCLES 2024 ĬåñúÖĬĨĄÜþþÌĚáėëĚĂ
ĥÕĕÕµõąµĥĕĕąÅõÅĕĕÕ
4037/22/O/N/24
 Cambridge IGCSE™
* 9 9 6 5 8 9 0 9 6 0 *

ADDITIONAL MATHEMATICS 0606/23

Paper 2 May/June 2024

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 12 pages.

DC (KN/SG) 332423/3
© UCLES 2024 [Turn over
 2

Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax 2 + bx + c = 0 ,

- b ! b 2 - 4ac
x=
2a

Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r

n
where n is a positive integer and e o =
n!
r (n - r) !r!

Arithmetic series un = a + (n - 1) d
1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2

Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r

2. TRIGONOMETRY

Identities

sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A

Formulae for ∆ABC

a b c
= =
sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2

© UCLES 2024 0606/23/M/J/24

 3

1 The point A has coordinates (1, 4) and the point B has coordinates (5, 6). The perpendicular bisector of
AB intersects the x-axis at the point C and the y-axis at the point D. Given that O is the origin, find the
area of triangle OCD. [5]

2 Given that the equation kx 2 + (2k - 1) x + k + 1 = 0 has no real roots, find the set of possible values
of k. [4]

© UCLES 2024 0606/23/M/J/24 [Turn over

 4

3 (a)

y
10

-2 -1 0 1 2 3 4 5 6 x
-1

-2

-3

Draw the graphs of y = 2x - 5 and y = 4 - x for - 2 G x G 6 . [4]

(b) Use your graphs to solve the inequality 4 - x G 2x - 5 . [2]

© UCLES 2024 0606/23/M/J/24

 5

10
1
4 (a) Find and simplify the term independent of x in the expansion of ex 2 - o . [2]
2x 3

(b) DO NOT USE A CALCULATOR IN THIS PART OF THE QUESTION.

(i) Use the binomial theorem to show that `1 + 2 2j - `1 - 2 2j = k 2 , where k is an integer

4 4

to be found. [4]

`1 + 2 2j - `1 - 2 2j
4 4

(ii) Hence write in the form a + b 2 , where a and b are integers. [2]
1+ 2

© UCLES 2024 0606/23/M/J/24 [Turn over

 6

1 + 2 sin 2 x r r
5 (a) The function f is defined by f (x) = for - 1 x 1 .
cos 2 x 2 2
2
(i) Show that f (x) can be written as a tan x + b , where a and b are integers. [2]

(ii) Hence solve the equation f (x) = 4 . [3]

(iii) Hence also find the gradient of the curve y = f (x) at each of the points where y = 4 . [4]

© UCLES 2024 0606/23/M/J/24

 7

(b) Solve the equation 50 cos 2 i = 5 sin i + 47 for 0° G i G 360° . [5]

© UCLES 2024 0606/23/M/J/24 [Turn over

 8

6 DO NOT USE A CALCULATOR IN THIS QUESTION.

(a) Given that x - 3 and x+1 are both factors of 2x 3 - 3x 2 - 8x - 3, solve the equation
2x 3 - 3x 2 - 8x - 3 = 0 . [2]

(b) The polynomial p (x) = x 3 + ax 2 + bx + c , where a, b and c are constants, has remainder - 5
4
when divided by x - 1. The curve y = p (x) has stationary points at x = and x = 2 .
3
(i) Find the values of a, b and c. [7]

(ii) Hence use the second derivative test to show that the stationary point at x = 2 is a minimum.
[2]

© UCLES 2024 0606/23/M/J/24

 9

7
C

i rad
O A B
5 cm 4 cm

In the diagram, AD and BC are arcs of circles with common centre O.

ODC and OAB are straight lines with OA = 5 cm and AB = 4 cm . Angle BOC = i radians .
The area of the shaded region ABCD is 4r cm 2 .

(a) Find i. [3]

(b)
C

i rad
O A B
5 cm 4 cm

The straight line AC is added to the diagram and the region ACD is now shaded.
Find the perimeter of the shaded region ACD. [5]

© UCLES 2024 0606/23/M/J/24 [Turn over

 10

d2y dy 3
8 A curve is such that b r
l e
3r r o
2 = cos 4x - 4 . Given that dx = 4 at the point 16 , 4 on the curve, find
dx
the equation of the curve. [7]

© UCLES 2024 0606/23/M/J/24

 11

9
y
x=9
y = 4 + `3x - 1j
-1

O B x

The diagram shows a sketch of part of the curve y = 4 + (3x - 1) -1 and the line x = 9 .
The point A has x-coordinate 1. The tangent to the curve at A meets the x-axis at the point B.
Find the area of the shaded region. [10]

Question 10 is printed on the next page.

© UCLES 2024 0606/23/M/J/24 [Turn over

 12

10
A B

O D C

The diagram shows a parallelogram OABC. The point D divides the line OC in the ratio 2 : 3.
OA = a and OC = c
The point P lies on AD such that OP = m OB and AP = nAD , where m and n are scalars.
Find two expressions for OP , each in terms of a, c and a scalar, and hence show that P divides both
DA and OB in the ratio m : n, where m and n are integers to be found. [7]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2024 0606/23/M/J/24

 Cambridge IGCSE™
* 7 0 2 9 1 0 6 8 3 8 *

ADDITIONAL MATHEMATICS 0606/12

Paper 1 February/March 2023

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.

INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 16 pages.

DC (PQ/CT) 312456/2
© UCLES 2023 [Turn over
 2

Mathematical
MathematicalFormulae
Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax 2 + bx + c = 0 ,

- b ! b 2 - 4ac
x=
2a

Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r

n
where n is a positive integer and e o =
n!
r (n - r) !r!

Arithmetic series un = a + (n - 1) d
1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2

Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r

2. TRIGONOMETRY

Identities

sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A

Formulae for ∆ABC

a b c
= =
sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2

© UCLES 2023 0606/12/F/M/23

 3

1 Find the exact values of k such that the straight line y = 1-k-x is a tangent to the curve
y = kx 2 + x + 2k . [4]

© UCLES 2023 0606/12/F/M/23 [Turn over

 4

2 A curve has equation y = (5 - x) (x + 2) 2 .

(a) Find the x-coordinates of the stationary points on the curve. [4]

(b) On the axes below, sketch the graph of y = (5 - x) (x + 2) 2 , stating the coordinates of the points
where the curve meets the axes. [3]

O x

© UCLES 2023 0606/12/F/M/23

 5

(c) Find the values of k for which the equation k = (5 - x) (x + 2) 2 has one distinct root only. [3]

© UCLES 2023 0606/12/F/M/23 [Turn over

 6

Find the coefficient of x 8 in the expansion of `1 - x 2jb2x - l .

10
1
3 [5]
x

© UCLES 2023 0606/12/F/M/23

 7

4 (a) Write 3 lg x - 2 lg y 2 - 3 as a single logarithm to base 10. [3]

5
(b) Solve the equation log3 x + log x 3 = . [5]
2

© UCLES 2023 0606/12/F/M/23 [Turn over

 8

The table shows values of the variables x and y, which are related by an equation of the form y = Ab x ,
2
5
where A and b are constants.

x 1 1.5 2 2.5
y 2.0 11.3 128 2896

(a) Use the data to draw a straight line graph of ln y against x 2 . [2]

ln y
8

2
0 1 2 3 4 5 6 7 x

–1
© UCLES 2023 0606/12/F/M/23
 9

(b) Use your graph to estimate the values of A and b. Give your answers correct to 1 significant figure.
[5]

(c) Estimate the value of y when x = 1.75. [2]

(d) Estimate the positive value of x when y = 20 . [2]

© UCLES 2023 0606/12/F/M/23 [Turn over

 10

- 25 17 26
6 Given that f m (x) = (5x + 2) , f l (6) = and f (6) = , find an expression for f (x) . [8]
3 3

© UCLES 2023 0606/12/F/M/23

 11

7 (a) A 5-character password is to be formed from the following 13 characters.

Letters A B C D E

Numbers 9 8 7 6 5

Symbols * # !

No character may be used more than once in any password.

(i) Find the number of possible passwords that can be formed. [1]

(ii) Find the number of possible passwords that contain at least one symbol. [2]

(b) Given that 16 # n C12 = (n - 10) # n + 1 C11 , find the value of n. [3]

© UCLES 2023 0606/12/F/M/23 [Turn over

 12

8
y

3
y = 2-
6y = 9 - 2x x-1

O A C x

3
The diagram shows part of the curve y = 2 - and the straight line 6y = 9 - 2x . The curve
x-1
intersects the x-axis at point A and the line at point B. The line intersects the x-axis at point C. Find
the area of the shaded region ABC, giving your answer in the form p + ln q , where p and q are rational
numbers. [11]

© UCLES 2023 0606/12/F/M/23

 13

Additional working space for Question 8.

© UCLES 2023 0606/12/F/M/23 [Turn over

 14

9 In this question, all lengths are in metres.

J2 + 12tN
(a) A particle P has position vector KK OO at a time t seconds, t H 0 .
L 5 - 5t P

(i) Write down the initial position vector of P. [1]

(ii) Find the speed of P. [2]

J 158N
(iii) Determine whether P passes through the point with position vector KK OO . [2]
L- 48 P

© UCLES 2023 0606/12/F/M/23

 15

(b)
O

a b c

A B C

The diagram shows the triangle OAC. The point B lies on AC such that AB : AC = 1: 4 . Given that
OA = a , OB = b and OC = c , find c in terms of a and b. [3]

Question 10 is printed on the next page.

© UCLES 2023 0606/12/F/M/23 [Turn over

 16

10 (a) It is given that 2 + cos i = x for 1 1 x 1 3 and 2 cosec i = y for y 2 2 . Find y in terms of x.
[4]

z z
(b) Solve the equation 3 cos = 3 sin for - 4r 1 z 1 4r . [5]
2 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.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.

© UCLES 2023 0606/12/F/M/23

 * 0000800000001 *

,










,

Cambridge O Level

¬WŠ. 4mHuOªEŠ^|5€W
¬l5sQžŠ¤U‡†‡8¤rdŽ‚
¥ee•5u¥UU e EUe5•U
* 4 4 8 8 8 7 1 2 3 0 *

MATHEMATICS (SYLLABUS D) 4024/22

Paper 2 October/November 2024

2 hours 30 minutes

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use either your calculator value or 3.142.

INFORMATION
● The total mark for this paper is 100.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (DE/CGW) 336455/4
© UCLES 2024 [Turn over
 * 0000800000002 *

DO NOT WRITE IN THIS MARGIN

2
,










,

1 (a) These are the contents of a bag of mixed fruit.

Pineapple 96 g

Mango 84 g

Papaya 60 g

Calculate the mass of mango as a percentage of the total mass of the mixed fruit.

DO NOT WRITE IN THIS MARGIN

.............................................. % [2]

(b) Tom makes a drink by mixing juice and water in the ratio 3 : 7.
He makes 1.4 litres of this drink.

Calculate the amount of juice Tom uses.

Give your answer in millilitres.

DO NOT WRITE IN THIS MARGIN

............................................. ml [2]

(c) The cost of a fruit drink is directly proportional to the amount of juice it contains.
A fruit drink containing 125 ml of juice costs $1.50 .

Calculate the cost of a fruit drink containing 175 ml of juice.

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN

ĬÕĊ®Ġ´íÈõÏĪÅĊßú·þ×
$ ................................................. [2]
© UCLES 2024 Ĭì·ôÔĪþĆÞúôĬĀĚÂĜĖĂ
ĥõµĕõĕåµĥÅõÅÅĕÅõµÕ
4024/22/O/N/24
 * 0000800000003 *
DO NOT WRITE IN THIS MARGIN

3
,










,

(d) Kofi has a bag containing nuts and raisins.

There are 285 g of raisins in the bag.
The remaining 62% of the mass in the bag is nuts.

Calculate the mass of nuts in the bag.

DO NOT WRITE IN THIS MARGIN

............................................... g [2]
DO NOT WRITE IN THIS MARGIN

(e) The mass of mixed nuts and seeds in a bag is 500 g, correct to the nearest 10 g.
The mass of nuts in the bag is 350 g, correct to the nearest 5 g.

Calculate the upper bound and the lower bound of the mass of seeds in the bag.
DO NOT WRITE IN THIS MARGIN

Upper bound = .............................................. g

Lower bound = .............................................. g [3]

DO NOT WRITE IN THIS MARGIN

Ĭ×Ċ®Ġ´íÈõÏĪÅĊßü·þ×
© UCLES 2024 Ĭì¸óÜĠĂöÛĀýÝÜĢĖĜĦĂ
ĥõÅÕµõÅÕõµåÅÅõåµåÕ
4024/22/O/N/24 [Turn over
 * 0000800000004 *

DO NOT WRITE IN THIS MARGIN

4
,










,

2 (a) The table shows the age and value of 10 cars of the same model.

Age (years) 3 3 4 4 5 5 5 6 8 8
Value ($) 5500 6200 4200 4000 4000 3700 4500 3000 1500 2000

(i) Complete the scatter diagram.

The first 6 points have been plotted for you.

DO NOT WRITE IN THIS MARGIN

7000

6000

5000

4000
Value ($)
3000

2000

DO NOT WRITE IN THIS MARGIN

1000

0
0 1 2 3 4 5 6 7 8 9 10 11 12
Age (years)
[2]

(ii) Draw a line of best fit. [1]

(iii) Use your line of best fit to find an estimate for the value of a car of this model that is 7 years

DO NOT WRITE IN THIS MARGIN

old.

$ ................................................. [1]

(iv) Jay has a car of this model that is 12 years old and he wants to find its value.

Explain why Jay should not use this scatter diagram to find an estimate for the value of this
car.

.............................................................................................................................................
DO NOT WRITE IN THIS MARGIN

............................................................................................................................................. [1]

ĬÕĊ®Ġ´íÈõÏĪÅĊÝú·Ā×
© UCLES 2024 Ĭì¸òÜĦôóàĂĆæú¾¸ČĎĂ
ĥÅĕÕõõÅõĕĕÕÅąõąµµÕ
4024/22/O/N/24
 * 0000800000005 *
DO NOT WRITE IN THIS MARGIN

5
,










,

(b) Jay records the distances travelled by 50 cars.

The frequency table shows the results.

Distance (d thousand km) 10 1 d G 40 40 1 d G 50 50 1 d G 60 60 1 d G 100

Frequency 8 14 11 17

(i) Work out the fraction of the cars that have travelled more than 50 000 km.
Give your answer in its simplest form.
DO NOT WRITE IN THIS MARGIN

................................................. [1]

(ii) Find the interval that contains the median.

................................................. [1]

(iii) Calculate an estimate of the mean distance travelled.

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

............................ thousand km [3]

DO NOT WRITE IN THIS MARGIN

Ĭ×Ċ®Ġ´íÈõÏĪÅĊÝü·Ā×
© UCLES 2024 Ĭì·ñÔĤðăÙøûģÞ¶ĤČĞĂ
ĥÅĥĕµĕåĕąĥąÅąĕĥõåÕ
4024/22/O/N/24 [Turn over
 * 0000800000006 *

DO NOT WRITE IN THIS MARGIN

6
,










,

3 (a)
NOT TO
SCALE

0.6

DO NOT WRITE IN THIS MARGIN

1.2

The diagram shows a tank.

The tank is a cuboid with length 1.2 m, width 0.6 m and height h m.
The volume of the tank is 1.8 m 3 .

(i) Calculate the value of h.

DO NOT WRITE IN THIS MARGIN

h = ................................................ [2]

(ii) Fuel is pumped into the empty tank at a rate of 0.2 m 3 per minute.

Calculate the time taken to fill the tank to 90% of its volume.
Give your answer in minutes and seconds.

DO NOT WRITE IN THIS MARGIN

............ minutes ............ seconds [3]

DO NOT WRITE IN THIS MARGIN

ĬÙĊ®Ġ´íÈõÏĪÅĊàü¶þ×
© UCLES 2024 Ĭì¸ñÏĪĘĉÑóĊĚ¾¾āäĎĂ
ĥĕÅĕµµåµÅąåÅÅĕŵõÕ
4024/22/O/N/24
 * 0000800000007 *
DO NOT WRITE IN THIS MARGIN

7
,










,

(b)
E F
NOT TO
SCALE
110 B
A

H G
70
DO NOT WRITE IN THIS MARGIN

D 80 C

The diagram shows a tank with an open top.

The tank is a prism with trapezium ABCD as its cross-section.
AD = BC = 70 cm , CD = 80 cm and AB = 110 cm .
The base of the tank is a square.

Calculate the total surface area of the outside of the tank.

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÛĊ®Ġ´íÈõÏĪÅĊàú¶þ×
.......................................... cm 2 [5]
© UCLES 2024 Ĭì·ò×ĠĜùèą÷Ï̶ÕäĞĂ
ĥĕµÕõÕÅÕÕõõÅÅõåõĥÕ
4024/22/O/N/24 [Turn over
 * 0000800000008 *

DO NOT WRITE IN THIS MARGIN

8
,










,

4 (a) Anya buys 4 shirts and 3 hats.

She pays $100 and receives $21.50 in change.
Each shirt costs the same amount.
Each hat costs $13.50 .

Work out the cost of one shirt.

DO NOT WRITE IN THIS MARGIN

$ ................................................. [3]

(b) The exchange rate between dollars ($) and euros (€) is $1 = €0.91 .

Anya buys a new camera for $150.

She sees the same camera for sale online for €140.

Calculate the difference between the price in dollars and the price in euros.

DO NOT WRITE IN THIS MARGIN

Give your answer in dollars, correct to the nearest cent.

$ ................................................. [2]

(c) Anya invests $600 in a savings account.

The account pays compound interest at a rate of r % per year.
At the end of 3 years the total interest is $21.86 .

DO NOT WRITE IN THIS MARGIN

Calculate the value of r.

DO NOT WRITE IN THIS MARGIN

ĬÙĊ®Ġ´íÈõÏĪÅĊÞü¶Ā×
r = ................................................ [3]
© UCLES 2024 Ĭì·ó×ĦĪðÓċðؼĚ÷´ĖĂ
ĥåĥÕµÕÅõµÕąÅąõąõõÕ
4024/22/O/N/24
 * 0000800000009 *
DO NOT WRITE IN THIS MARGIN

9
,










,

1 1 2 2 2 5 6 7 8

Mandeep has these 9 number cards.

(a) She takes one of the 9 cards at random, notes the number and replaces it.

Find the probability that the card shows an odd number.

DO NOT WRITE IN THIS MARGIN

................................................. [1]

(b) Mandeep takes one of the 9 cards at random, notes the number and replaces it.
She then takes a second card at random.

Find the probability that both cards show the number 1.

DO NOT WRITE IN THIS MARGIN

................................................. [2]

(c) Mandeep takes two of the 9 cards at random without replacement.

She calculates the product of the two numbers shown.

Find the probability that the product is less than 5.

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

................................................. [3]

ĬÛĊ®Ġ´íÈõÏĪÅĊÞú¶Ā×
© UCLES 2024 Ĭì¸ôÏĤĦĀæíāđĠĢã´ĦĂ
ĥåĕĕõµåĕååÕÅąĕĥµĥÕ
4024/22/O/N/24 [Turn over
 * 0000800000010 *

DO NOT WRITE IN THIS MARGIN

10
,










,

x
6 (a) Complete the table for y = (2x 2 - x - 10) .
4

x -3 -2 -1 0 1 2 3
y 0 1.75 0 -2.25 -2 3.75

[1]

DO NOT WRITE IN THIS MARGIN

x
(b) Draw the graph of y = (2x 2 - x - 10) for - 3 G x G 3.
4
y
6

DO NOT WRITE IN THIS MARGIN

2

–3 –2 –1 0 1 2 3 x
–1

–2

–3

DO NOT WRITE IN THIS MARGIN

–4

–5

–6

–7

–8

–9
DO NOT WRITE IN THIS MARGIN

– 10
[3]

ĬÙĊ®Ġ´íÈõÏĪÅĊßü¸þ×
© UCLES 2024 Ĭì¶óÎĨĢĪÍĄ÷îØĜēČĞĂ
ĥõąĕµÕĥõĕĥąąąÕąõÅÕ
4024/22/O/N/24
 * 0000800000011 *
DO NOT WRITE IN THIS MARGIN

11
,









,

x 2
(c) The equation (2x - x - 10) = k has exactly two solutions.
4
Use your graph to find the possible values of k.

k = .................... or k = .................... [2]

(d) By drawing a suitable line on the grid, find the solutions of 2x 3 - x 2 - 10x = 2x - 4 .
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

x = .................... , x = .................... , x = .................... [4]

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÛĊ®Ġ´íÈõÏĪÅĊßú¸þ×
© UCLES 2024 ĬìµôÖĢĞĚìöĊ»ĄĤÇČĎĂ
ĥõõÕõµąĕąĕÕąąµĥµÕÕ
4024/22/O/N/24 [Turn over
 * 0000800000012 *

DO NOT WRITE IN THIS MARGIN

12
,









,

7 (a) Solve.

4x + 7 = 16

DO NOT WRITE IN THIS MARGIN

x = ................................................ [2]

(b) Solve.

5 (4 - y) = 30

DO NOT WRITE IN THIS MARGIN

y = ................................................ [2]

(c) Write down all the integers that satisfy this inequality.
3
- Gx13
2

DO NOT WRITE IN THIS MARGIN

................................................. [2]

DO NOT WRITE IN THIS MARGIN

ĬÙĊ®Ġ´íÈõÏĪÅĊÝü¸Ā×
© UCLES 2024 ĬìµñÖĬĐďÏüā´âÀĥĜĦĂ
ĥÅåÕµµąµĥµåąÅµÅµÅÕ
4024/22/O/N/24
 * 0000800000013 *
DO NOT WRITE IN THIS MARGIN

13
,









,

4y - x
(d) Rearrange the formula y = to make x the subject.
3x
DO NOT WRITE IN THIS MARGIN

x = ................................................ [3]
2 2
12x - 3y
(e) Simplify 2 .
2x + 8x - xy - 4y
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

ĬÛĊ®Ġ´íÈõÏĪÅĊÝú¸Ā×
................................................. [4]
© UCLES 2024 Ĭì¶òÎĞĔğêþðõö¸±ĜĖĂ
ĥÅÕĕõÕĥÕõÅõąÅÕåõÕÕ
4024/22/O/N/24 [Turn over
 * 0000800000014 *

DO NOT WRITE IN THIS MARGIN

14
,









,

8
A

NOT TO
D SCALE
5.6
2.7

DO NOT WRITE IN THIS MARGIN

B E

3.9
9.8

ADB and AEC are straight lines.

BC is parallel to DE.
BC = 9.8 cm , BD = 2.7 cm , DE = 5.6 cm and CE = 3.9 cm .

DO NOT WRITE IN THIS MARGIN

(a) Complete the missing angles and reasons to show that triangle ABC is similar to triangle ADE.

In triangle ABC and triangle ADE,

angle BAC = angle ............. because common angle

angle ABC = angle ............. because ................................................................................

angle ACB = angle ............. because ................................................................................

As the three pairs of angles are equal, triangle ABC is similar to triangle ADE.

DO NOT WRITE IN THIS MARGIN

[3]

(b) Show that AD = 3.6 cm and AE = 5.2 cm .

DO NOT WRITE IN THIS MARGIN

[4]

ĬÕĊ®Ġ´íÈõÏĪÅĊÞùµĂ×
© UCLES 2024 ĬìµôÏĤğėÜČûÚÚĝµìĎĂ
ĥĥÕÕµµåõĕÕõÅąĕąµąÕ
4024/22/O/N/24
 * 0000800000015 *
DO NOT WRITE IN THIS MARGIN

15
,









,

(c) Calculate angle DAE.

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

Angle DAE = ................................................ [3]

(d) Calculate the area of triangle ABC.

DO NOT WRITE IN THIS MARGIN

.......................................... cm 2 [2]
DO NOT WRITE IN THIS MARGIN

Ĭ×Ċ®Ġ´íÈõÏĪÅĊÞûµĂ×
© UCLES 2024 Ĭì¶ó×ĦģħÝîĆďþĕġìĞĂ
ĥĥåĕõÕÅĕąååÅąõĥõĕÕ
4024/22/O/N/24 [Turn over
 * 0000800000016 *

DO NOT WRITE IN THIS MARGIN

16
,









,

9 (a)
A
B NOT TO
SCALE
126°

O
C

DO NOT WRITE IN THIS MARGIN

E
D 10.5

A, B, C and D are points on a circle, centre O.

AOD and OCE are straight lines.
DE is a tangent to the circle at D.
Angle ABC = 126° and DE = 10.5 cm .

Calculate the radius of the circle.

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN

............................................ cm [5]
DO NOT WRITE IN THIS MARGIN

ĬÕĊ®Ġ´íÈõÏĪÅĊàùµĄ×
© UCLES 2024 Ĭì¶ò×ĠđĢÚôýĘà¹Ã¼ĖĂ
ĥÕõĕµÕŵĥąÕÅÅõÅõąÕ
4024/22/O/N/24
 * 0000800000017 *
DO NOT WRITE IN THIS MARGIN

17
,









,

(b)

NOT TO
SCALE
O

82°

Q
P
DO NOT WRITE IN THIS MARGIN

P and Q are points on a different circle, centre O.

The angle of the minor sector POQ is 82°.
The length of the minor arc PQ is 7.3 cm.

Calculate the area of the major sector.

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

.......................................... cm 2 [5]
DO NOT WRITE IN THIS MARGIN

Ĭ×Ċ®Ġ´íÈõÏĪÅĊàûµĄ×
© UCLES 2024 ĬìµñÏĪčĒßĆôÑüÁė¼ĦĂ
ĥÕąÕõµåÕõõąÅÅĕåµĕÕ
4024/22/O/N/24 [Turn over
 * 0000800000018 *

DO NOT WRITE IN THIS MARGIN

18
,









 ,

10 The cost of apples is x cents per kilogram.

Mina spends $9 on apples.

(a) Write down an expression for the mass, in kilograms, of apples Mina receives.

............................................. kg [1]

(b) The cost of pears is 40 cents per kilogram more than the cost of apples.

DO NOT WRITE IN THIS MARGIN

Mina spends $9 on pears.
The mass of pears Mina receives is 0.75 kg less than the mass of apples.

Form an equation in x and show that it simplifies to x 2 + 40x - 48 000 = 0 .

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN
[4]

(c) Solve the equation x 2 + 40x - 48 000 = 0 .

Show your working.
DO NOT WRITE IN THIS MARGIN

ĬÕĊ®Ġ´íÈõÏĪÅĊÝù·Ă×
x = .................... or x = .................... [3]
© UCLES 2024 Ĭì·òÎĞęøØûƮĻçĄĞĂ
ĥąĕÕµÕĥµÅµÕąÅÕÅõµÕ
4024/22/O/N/24
 * 0000800000019 *
DO NOT WRITE IN THIS MARGIN

19
,









 ,

(d) Narinder buys 1.5 kg of apples and 0.8 kg of pears.

Work out the total amount he pays in dollars.

DO NOT WRITE IN THIS MARGIN

$ ................................................. [2]
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

Ĭ×Ċ®Ġ´íÈõÏĪÅĊÝû·Ă×
© UCLES 2024 Ĭì¸ñÖĬĕĈáýûûĘÃóĄĎĂ
ĥąĥĕõµąÕÕÅąąÅµåµåÕ
4024/22/O/N/24
 * 0000800000020 *

DO NOT WRITE IN THIS MARGIN

20
,










,

BLANK PAGE

DO NOT WRITE IN THIS MARGIN

DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS MARGIN

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
ĬÕĊ®Ġ´íÈõÏĪÅĊßù·Ą×
© UCLES 2024 Ĭì¸ôÖĢħāÖăôô¶ğÑĔĦĂ
ĥµµĕµµąõµĥõąąµąµµÕ
4024/22/O/N/24