O Level Mathematics 4024 Paper 12, Oct/Nov 2023

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4024/12 · Oct/Nov 2023

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Work out.

$0.05 \times 0.3$

[1]

$600 \div 0.2$

[1]

$20 - 12 \div (8 - 6)$

[1]

This rectangle is split into squares of two different sizes. Find the fraction of the rectangle that is shaded grey.

[1]

Find the decimal which is exactly halfway between $\frac{3}{5}$ and 68%.

[1]

Write 4.07382 correct to 3 decimal places.

[1]

Evaluate $\sqrt[3]{64}$ .

[1]

Sonu records the temperature, in °C, at midnight every day for 12 days. Here are the results in order, starting with the coldest. -6 -5 -3 -2 -1 -1 T 5 5 6 6 7

Find the range of the temperatures.

[1]

The median temperature is 1°C. Find the value of T.

[1]

Anna and Ria share some money in the ratio 5 : 9. Ria receives $8 more than Anna. Work out the total amount of money that is shared.

[2]

AB and CD are parallel lines. EC and FB are parallel lines. Angle ABF = 73°.

Find the value of x.

[1]

Find the value of y.

[1]

Shape A and triangles P and Q are drawn on a centimetre square grid.

Describe fully the single transformation that maps triangle P onto triangle Q.

[3]

Shape B is an enlargement of shape A. The centre of enlargement is (5, 5). The area of shape B is 27 cm^2. Draw shape B on the grid.

[3]

Write the number 0.00493 in standard form.

[1]

Evaluate $(4 \times 10^{9}) \times (2 \times 10^{- 2})$ . Give your answer in standard form.

[1]

Write 180 as the product of its prime factors.

[2]

Expressed as the product of their prime factors, $36 = 2^{2} \times 3^{2}$ $and$ $N = 2^{2} \times 3 \times k$ , $where$ k > 3. 180 is the lowest common multiple (LCM) of 36 and N. Find the value of k.

[1]

By writing each number correct to 1 significant figure, estimate the value of $\sqrt{\frac{1240 \times 3.8}{11.2}}$ .

[2]

Solve $7 m - 13 ⩽ 8$ .

[2]

Solve the simultaneous equations. Show all your working. 5x + 4y = 14 3x - 2y = 15

[3]

A list of eight numbers has a mean of 12. The first five numbers have a mean of 9. Find the sum of the three remaining numbers.

[2]

Measure angle ABC.

[1]

Using compasses and a straight edge only, construct the perpendicular bisector of AC.

[2]

On the diagram, shade the region inside triangle ABC that is • nearer to A than to C and • more than 6 cm from B.

[2]

The second term of a linear sequence is 28. The fifth term of the sequence is 16. Find the first term, the third term and the fourth term of this sequence.

[2]

These are the first five terms of a different sequence. 3 9 19 33 51 Find an expression for the nth term of this sequence.

[2]

$T = \sqrt{P - 4}$

Work out the value of T when P = 40.

[1]

Rearrange the formula to make P the subject.

[2]

The heights of 80 plants are measured. The table shows the results.

Height ( $h$ centimetres)	$h ⩽ 2$	$h ⩽ 4$	$h ⩽ 6$	$h ⩽ 8$	$h ⩽ 10$	$h ⩽ 12$
Cumulative frequency	4	18	42	60	72	80

Draw a cumulative frequency diagram to show this information.

[2]

Use your diagram to find an estimate for the interquartile range.

[2]

Plants are sold when they are taller than H centimetres. 28 of these plants are sold. Find the value of H.

[2]

The diagram shows the speed–time graph of part of a journey for two cyclists, A and B.

Find the acceleration of cyclist A during the first 20 seconds.

[1]

Find which cyclist travelled further in the first 20 seconds and by how many metres.

[3]

Express as a single fraction in its simplest form. $\frac{x + 1}{8} + \frac{3 x}{4} - \frac{5 x}{16}$

[2]

Factorise.

2cd + ce - 6d - 3e

[2]

3v^2 - 27t^2

[2]

Diagram A shows a sector of a circle, centre D and radius $\frac{3}{4} y cm$ . The obtuse angle EDF = 6x°. Diagram B shows a sector of a circle, centre P and radius $y cm$ . The sector angle is x°.

The length of the major arc EF is 9 times the length of the arc QR. Show that x = 20.

[3]

Find the value of y when the area of sector QPR is equal to $2 π {cm}^{2}$ .

[2]

$(\begin{array}{cc} x & 3 \\ 2 & x + 1 \end{array})$ $(\begin{array}{c} x - 1 \\ 2 \end{array})$ = $(\begin{array}{c} 2 x + 6 \\ y \end{array})$

Show that x^2 - 3x = 0.

[2]

b(i)

Solve x^2 - 3x = 0.

[2]

b(ii)

Find the value of y when x > 0.

[2]

A shop sells hats (H), scarves (S) and gloves (G). A group of 40 people are asked which items they buy in the shop. Some of the results are shown in the Venn diagram.

2 people buy all three items. Those people that buy both a hat and a scarf also buy gloves. 4 people buy exactly two items. Use this information to complete the Venn diagram.

[2]

Work out $n (S$ $\cap$ (H $\cup$ G)').

[1]

OAB is a triangle. P lies on AB and AP : PB = 2 : 3. $\vec{O A} = 4 a$ and $\vec{O P} = 3 a + 2 b$ .

a(i)

Find, in terms of a and b, giving your answer in its simplest form $\vec{A P}$

[1]

a(ii)

Find, in terms of a and b, giving your answer in its simplest form $\vec{O B}$

[3]

Q is a point on OA such that $\vec{Q P}$ is parallel to $\vec{O B}$ . Find $\vec{Q P}$ .

[1]

Mark scheme

4024/12 · Oct/Nov 2023

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1a · 1 mark

1 mark
0.015

1b · 1 mark

1 mark
3000

1c · 1 mark

1 mark
14

2 · 1 mark

1 mark
$\frac{5}{21}$ cao

3a · 1 mark

1 mark
0.64 cao

3b · 1 mark

1 mark
4.074 cao

3c · 1 mark

1 mark
4

4a · 1 mark

1 mark
13

4b · 1 mark

1 mark
3

5 · 2 marks

2 marks
28

6a · 1 mark

1 mark
73

6b · 1 mark

1 mark
107

7a · 3 marks

B1
Rotation
B1
90° clockwise oe
B1
[centre] (0, 0)

7b · 3 marks

3 marks
Shape drawn at (–7, 2), (–1, 2), (–1, –4), (–4, –4), (–4, –1), (–7, –1)

8a · 1 mark

1 mark
$4.93 \times 10^{- 3}$ cao

8b · 1 mark

1 mark
$8 \times 10^{7}$ cao

9a · 2 marks

2 marks
$2^{2} \times 3^{2} \times 5$ or $2 \times 2 \times 3 \times 3 \times 5$

9b · 1 mark

1 mark
5 cao

10 · 2 marks

2 marks
1000 and 4 and 10 seen as rounded values and final answer 20

11 · 2 marks

2 marks
$m ⩽ 3$ or $3 ⩾ m$ final answer

12 · 3 marks

M1
Correct method to eliminate one variable
A2
$[x =] 4$ $[y =] - \frac{3}{2}$ oe

13 · 2 marks

2 marks
51

14a · 1 mark

1 mark
47 to 51

14b · 2 marks

2 marks
Acceptable bisector of line AC with correct arcs

14c · 2 marks

2 marks
Correct region shaded

15a · 2 marks

2 marks
32 24 20

15b · 2 marks

2 marks
$2 n^{2} + 1$ oe final answer

16a · 1 mark

1 mark
6

16b · 2 marks

2 marks
$T^{2} + 4$ final answer

17a · 2 marks

2 marks
Correct cumulative frequency diagram

17b · 2 marks

2 marks
Strict FT their UQ – their LQ evaluated

17c · 2 marks

2 marks
Correct reading of H when CF is 52

18a · 1 mark

1 mark
$\frac{6}{20}$ oe

18b · 3 marks

3 marks
B 20 nfww

19 · 2 marks

2 marks
$\frac{9 x + 2}{16}$ final answer

20a · 2 marks

2 marks
$(c - 3) (2 d + e)$ final answer

20b · 2 marks

2 marks
$3 (v - 3 t) (v + 3 t)$ final answer

21a · 3 marks

M2
$\frac{360 - 6 x}{360} \times 2 π \times \frac{3 y}{4} = 9 \times \frac{x}{360} \times 2 π y$ or $2 π \times \frac{3 y}{4} - \frac{6 x}{360} \times 2 π \times \frac{3 y}{4} = 9 \times \frac{x}{360} \times 2 π y$
A1
At least one extra step of rearrangement leading to $x = 20$

21b · 2 marks

2 marks
6

22a · 2 marks

M1
$x (x - 1) + 3 \times 2 [= 2 x + 6]$
A1
$x^{2} - x + 6 = 2 x + 6$ leading to $x^{2} - 3 x = 0$

22b(i) · 2 marks

2 marks
3, 0

22b(ii) · 2 marks

2 marks
12

23a · 2 marks

2 marks
Venn diagram completed correctly

23b · 1 mark

1 mark
10 cao

24a(i) · 1 mark

1 mark
2b – a final answer

24a(ii) · 3 marks

3 marks
$\frac{3}{2} a + 5 b$ final answer or $\frac{3 a + 10 b}{2}$ final answer

24b · 1 mark

1 mark
$\frac{3}{5} a + 2 b$ oe

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