O Level Mathematics 4024 Paper 22, May/June 2025

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4024/22 · May/June 2025

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The diagram shows part of a pattern with rotational symmetry of order 4. Complete the diagram.

[1]

Write eighteen thousand and twelve in figures.

[1]

Write down a prime number between 20 and 30.

[1]

Find the reciprocal of $\frac{1}{9}$ .

[1]

Write the ratio $175 ml : 2.5 litres$ in its simplest form.

[2]

Dan, Erika and Fatik share $$ 540$ in the ratio $4 : 5 : 3$ . Find the amount that Erika receives.

[2]

Find the value of $x$ and the value of $y$ .

[2]

Convert $6.1 m^{2}$ to ${cm}^{2}$ .

[1]

In a survey, students are asked to choose their favourite type of movie. The table shows the results.

Type of movie	Romance	Thriller	Science Fiction	Other
Relative frequency	0.1		0.35	0.3

Calculate the relative frequency of a student choosing Thriller.

[2]

500 students take part in the survey. Calculate the number of students who choose Science Fiction.

[1]

Chris wants to exchange $$ 350$ for euros (€) at the bank. The bank only gives euros in multiples of €5. The exchange rate is $$ 1 = € 0.92$ . Calculate the number of euros he receives and his change from $$ 350$ .

[3]

Calculate the interior angle of a regular octagon.

[2]

On the Venn diagram, shade the region represented by $(A \cap B)^{'}$ .

[1]

In a class of 22 students: • 12 play the piano • 9 play the guitar • 6 do not play the piano or the guitar. Find the number of students who play both the piano and the guitar. You may use the Venn diagram to help you.

[2]

Simplify. $\frac{7 x^{2} y^{5}}{x^{3} y^{2}}$

[2]

Zaya invests $$ 4500$ in a savings account. The account pays simple interest at a rate of 3.2% per year. Calculate the value of the investment at the end of 5 years.

[3]

Aisha invests $$ 2750$ in a different savings account. This account pays compound interest at a rate of 2.1% per year. Calculate the total amount of interest she receives at the end of 3 years.

[3]

Factorise. $7 h x + 6 f y - 21 f x - 2 h y$

[2]

A bag contains 9 red counters and 3 green counters. Lee takes two counters from the bag at random without replacement.

Complete the tree diagram.

[2]

Work out the probability that both counters are red.

[1]

$P Q R S$ is a cyclic quadrilateral. $A P B$ is a tangent to the circle at $P$ . Angle $S P B = 37^{\circ}$ and angle $P S Q = 85^{\circ}$ .

Find angle $P Q S$ .

[1]

Find angle $Q R S$ .

[2]

These are the first four patterns in a sequence made from black beads and from white beads.

Complete the table for Pattern 5.

Pattern number	1	2	3	4	5
Number of white beads	5	7	9	11
Total number of beads	6	10	15	21

[1]

b(i)

Find an expression for the number of white beads in Pattern $n$

[2]

b(ii)

Find an expression for the total number of beads in Pattern $n$ .

[2]

Bill has only 88 white beads but lots of black beads. Pattern $p$ is the largest possible pattern he can make using these beads. Work out the value of $p$ .

[2]

The population of Kenya is $5.71 \times 10^{7}$ people. The area of Kenya is $6 \times 10^{5} {km}^{2}$ . The population density is the number of people per ${km}^{2}$ . Calculate the population density of Kenya.

[2]

$f (x) = \frac{10 - x}{3}$ Find $f (- 8)$ .

[1]

$g (x) = 4 x + 3$ Find $g^{- 1} (x)$ .

[2]

300 students take part in a competition. The table shows information about their scores.

Score ( $s$ )	$0 < s ⩽ 30$	$30 < s ⩽ 40$	$40 < s ⩽ 60$	$60 < s ⩽ 70$	$70 < s ⩽ 100$
Frequency	24	70	88	76	42

Calculate an estimate of the mean score.

[4]

On the grid, complete the histogram to represent the data in the table.

[3]

Complete the table of values for $y = x^{3} - 5 x + 4$ .

$x$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$y$		$6$	$8$	$4$	$0$	$2$	$16$

[1]

Draw the graph of $y = x^{3} - 5 x + 4$ for $- 3 ⩽ x ⩽ 3$ .

[4]

By drawing a suitable straight line on the grid, find the solutions of the equation $x^{3} - 5 x - 3 = 0$ .

[3]

$A B C D$ and $E F G D$ are rectangles.

a(i)

Show that $C D = x - 1$ .

[1]

a(ii)

The area of rectangle $A B C D$ is $\frac{1}{5}$ of the area of rectangle $E F G D$ . Form an equation in $x$ and show that it simplifies to $x^{2} - 6 x + 3 = 0$ .

[3]

b(i)

Use the quadratic formula to solve the equation $x^{2} - 6 x + 3 = 0$ . You must show all your working and give your answers correct to 2 decimal places.

[3]

b(ii)

Calculate the shaded area.

[2]

The diagram shows a solid formed by joining a cone to a hemisphere. The diameter of the cone is $14 cm$ and the diameter of the hemisphere is $14 cm$ . The total height of the solid is $24 cm$ .

Calculate the volume of the solid.

[3]

Show that the total surface area of the solid is $712 {cm}^{2}$ , correct to the nearest integer.

[5]

A smaller solid is mathematically similar to this solid. The total surface area of the smaller solid is $242 {cm}^{2}$ . Calculate the total height of the smaller solid.

[3]

The diagram shows a triangular field $A B C$ . $A B = 150 m$ , $B C = 187 m$ and angle $A B C = 112^{\circ}$ .

Fencing is needed for the perimeter of the field. Fencing is sold in rolls of length $20 m$ . Calculate the number of rolls of fencing needed.

[5]

Calculate the shortest distance from $B$ to $A C$ .

[4]

Zara cycles a distance of 500 metres, correct to the nearest 5 metres. This takes 24.7 seconds, correct to the nearest 0.1 seconds. Calculate the lower bound of her average speed.

[3]

Express as a single fraction in its simplest form. $\frac{5}{2 x + 1} - \frac{2}{4 x - 3}$

[3]

Mark scheme

4024/22 · May/June 2025

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1 · 1 mark

1 mark
Diagram completed correctly.

2a · 1 mark

1 mark
18 012 cao

2b · 1 mark

1 mark
23 or 29

2c · 1 mark

1 mark
9

3a · 2 marks

2 marks
7 : 100 cao

3b · 2 marks

2 marks
225

4 · 2 marks

B1
[x =] 52
B1
[y =] 128

5 · 1 mark

1 mark
61 000

6a · 2 marks

2 marks
0.25 or $\frac{1}{4}$ or 25%

6b · 1 mark

1 mark
175

7 · 3 marks

3 marks
[€]320 [$]2.17

8 · 2 marks

2 marks
135

9a · 1 mark

1 mark
Venn diagram with region $(A \cup B)^{'}$ shaded

9b · 2 marks

2 marks
5

10 · 2 marks

2 marks
$\frac{7 y^{3}}{x}$ or $7 y^{3} x^{- 1}$ final answer

11a · 3 marks

3 marks
5220

11b · 3 marks

3 marks
176.91

12 · 2 marks

2 marks
$(7 x - 2 y) (h - 3 f)$ or $(2 y - 7 x) (3 f - h)$ final answer

13a · 2 marks

2 marks
Correct tree diagram First counter $\frac{3}{12}$ oe Second counter $\frac{3}{11}, \frac{9}{11}, \frac{2}{11}$ oe

13b · 1 mark

1 mark
$\frac{6}{11}$ oe

14a · 1 mark

1 mark
37

14b · 2 marks

2 marks
122

15a · 1 mark

1 mark
$\frac{13}{28}$

15b(i) · 2 marks

2 marks
2n + 3 oe final answer

15b(ii) · 2 marks

2 marks
$\frac{1}{2} n^{2} + \frac{5 n}{2} + 3$ oe final answer

15c · 2 marks

2 marks
42

16 · 2 marks

2 marks
95 or 95.2 or 95.16 to 95.17

17a · 1 mark

1 mark
6

17b · 2 marks

2 marks
$\frac{x - 3}{4}$ oe final answer

18a · 4 marks

4 marks
52.4 or $52 \frac{2}{5}$

18b · 3 marks

3 marks
Correct histogram drawn

19a · 1 mark

1 mark
– 8

19b · 4 marks

4 marks
Correct smooth curve

19c · 3 marks

M1
Ruled line y = 7
A2
–1.95 to –1.7 –0.8 to –0.5 2.3 to 2.6

20a(i) · 1 mark

1 mark
$2 x - 3 - (x - 2)$ leading to $x - 1$

20a(ii) · 3 marks

M1
$3 (x - 1) = \frac{1}{5} (2 x - 3) (x + 3)$ oe
B1
$2 x^{2} - 3 x + 6 x - 9$ or better
A1
$15 x - 15 = 2 x^{2} - 3 x + 6 x - 9$ oe leading to $x^{2} - 6 x + 3 = 0$

20b(i) · 3 marks

B2
$\frac{[-] - 6 \pm \sqrt{(- 6)^{2} - 4 \times 1 \times 3}}{2 \times 1}$ oe
B1
5.45 and 0.55

20b(ii) · 2 marks

2 marks
53.4 or 53.38 to 53.41

21a · 3 marks

3 marks
1590 or 1591 or 1590.6 to 1590.9

21b · 5 marks

M4
$\frac{1}{2} \times 4 \times π \times 7^{2}$ oe + $7 \times π \times \sqrt{17^{2} + 7^{2}}$ oe
A1
712.07 to 712.3

21c · 3 marks

3 marks
14[.0] or 13.98 to 13.99…

22a · 5 marks

5 marks
31 cao

22b · 4 marks

4 marks
92.8 to 92.9…

23 · 3 marks

3 marks
$[\frac{497.5}{24.75} oe =] 20.1 [0 \dots] nfww$

24 · 3 marks

3 marks
$\frac{16 x - 17}{(2 x + 1) (4 x - 3)}$ or $\frac{16 x - 17}{8 x^{2} - 2 x - 3}$ final answer

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