O Level Mathematics 4024 Paper 11, Oct/Nov 2024

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4024/11 · Oct/Nov 2024

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At midday the temperature is $- 2^{\circ} C$ . At $6 p m$ the temperature is $4^{\circ} C$ .

Find the difference between these temperatures.

[1]

The temperature at midnight is $9^{\circ} C$ lower than the temperature at midday. Find the temperature at midnight.

[1]

Amber and Pablo share $$ 280$ in the ratio $2 : 5$ . Work out Pablo’s share.

[2]

Here are eight integers. $- 1 - 5 - 1 - 3 - 3 2 - 1 - 7$ Find

the mode

[1]

the median.

[2]

Shade one more small square so the diagram has one line of symmetry.

[1]

Here is a regular polygon. Complete the description of the rotational symmetry of this polygon. The polygon has rotational symmetry of order ....................................

[1]

Simplify. $2 a - 3 b + 4 b - 5 a$

[2]

Expand. $5 (3 x - 2)$

[1]

The table shows the time spent on a homework task and the number of errors made for some students in a class.

Time (minutes)	$79$	$92$	$91$	$85$	$82$	$95$	$60$	$65$	$63$	$70$
Number of errors	$5$	$1$	$3$	$3$	$5$	$0$	$9$	$7$	$8$	$7$

Complete the scatter diagram. The first 6 points have been plotted for you.

[2]

On the scatter diagram, draw a line of best fit.

[1]

Another of the students in the class made 6 errors. Use your line of best fit to estimate the time this student spent on the homework task.

[1]

By writing each number correct to 1 significant figure, calculate an estimate for the value of $\frac{3.1 \times 26.7}{6.9 - 2.3}$

[2]

These are the first four terms of a sequence. $2 8 14 20$

Find the next number in the sequence.

[1]

Find an expression, in terms of $n$ , for the $n th$ term of this sequence.

[2]

The grid shows triangle $A$ and triangle $B$ .

Describe fully the single transformation that maps triangle $A$ onto triangle $B$ .

[3]

Triangle $A$ is mapped onto triangle $C$ by the translation $(\begin{array}{c} - 3 \\ 2 \end{array})$ . Draw triangle $C$ .

[2]

Solve the simultaneous equations. Show your working. $\begin{aligned} 3 a + b & = - 4 \\ 2 a + 3 b & = 9 \end{aligned}$

[3]

Point $A (2, 4)$ is joined to point $B (5, - 2)$ by a straight line.

Find the coordinates of the midpoint of $A B$ .

[1]

Find the gradient of the line $A B$ .

[2]

Write 0.000257 in standard form.

[1]

Work out $\frac{2 \times 10^{4}}{4 \times 10^{- 5}}$ . Give your answer in standard form.

[2]

Work out $2 \frac{1}{5} \div \frac{3}{4}$ . Give your answer as a mixed number in its simplest form.

[2]

Write 360 as a product of its prime factors.

[2]

Find the smallest positive integer $n$ such that $360 n$ is a cube number.

[1]

A sector of a circle with angle $60^{\circ}$ has arc length $4 π c m$ . Find the area of the sector. Give your answer, as simply as possible, in terms of $π$ .

[4]

Express as a single matrix. $2 (\begin{array}{cc} 3 & - 1 \\ 2 & 4 \end{array}) - (\begin{array}{cc} 1 & 3 \\ - 2 & 5 \end{array})$

[2]

b(i)

$A = (\begin{array}{cc} 4 & k \\ 2 & 1 \end{array})$ . The determinant of $A$ is 10. Find the value of $k$ .

[1]

b(ii)

Find $A^{- 1}$ .

[1]

The diagram shows the lines $y = 2 x + 1$ and $x + y = 2$ .

The region $R$ is defined by these three inequalities. $y ⩽ 2 x + 1 x + y ⩽ 2 y ⩾ - 2$ On the diagram, shade and label the region $R$ .

[2]

The point $(k, k - 2)$ lies in the region $R$ where $k$ is an integer. List the possible values of $k$ .

[2]

50 adults each take part in a quiz. The cumulative frequency diagram shows their scores.

Use the diagram to find an estimate of the interquartile range.

[2]

20% of the adults win a prize for getting a high score in the quiz. Use the diagram to work out the minimum score needed to win a prize.

[2]

Use the diagram to complete the frequency table.

$Score (s)$	$0 < s ⩽ 20$	$20 < s ⩽ 40$	$40 < s ⩽ 60$	$60 < s ⩽ 80$	$80 < s ⩽ 100$
Frequency					$8$

[2]

$x$ is inversely proportional to the square root of $y$ . When $x = 2$ , $y = 16$ . Find $y$ when $x = 32$ .

[2]

$(a x^{n})^{3} = 4 x^{10}$ Work out the value of $a$ and the value of $n$ .

[2]

The diagram shows the speed–time graph for a journey. Calculate the total distance travelled.

[2]

$f (x) = 3 x^{2} + 5$

Work out $f (- 1)$ .

[1]

Solve $f (2 x) = 17$ .

[3]

A rectangle has length $32 c m$ and width $15 c m$ . Each measurement is given correct to the nearest centimetre.

Write down the upper bound for the length.

[1]

Calculate the upper bound for the difference between the length and the width.

[1]

Simplify. $\frac{2 x^{2} + 5 x - 3}{2 x^{2} + 6 x}$

[3]

The diagram shows a cuboid. $E H = 6 c m$ , $H G = 2 c m$ and $E C = 7 c m$ . Calculate $C G$ .

[3]

Solve. $\frac{x}{x - 1} - \frac{3}{2 x - 1} = 1$

[4]

Mark scheme

4024/11 · Oct/Nov 2024

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1a · 1 mark

1 mark
6

1b · 1 mark

1 mark
–11

2 · 2 marks

2 marks
200

3a · 1 mark

1 mark
–1

3b · 2 marks

2 marks
–2

4a · 1 mark

1 mark
Grid completed with rotational symmetry of order 2

4b · 1 mark

1 mark
3

5a · 2 marks

2 marks
–3a + b final answer

5b · 1 mark

1 mark
15x – 10 final answer

6a · 2 marks

2 marks
Four points plotted correctly

6b · 1 mark

1 mark
Ruled line of best fit

6c · 1 mark

1 mark
Reading their straight line of best fit at 6 errors

7 · 2 marks

2 marks
3, 30, 7 and 2 seen as rounded values and final answer 18

8a · 1 mark

1 mark
26

8b · 2 marks

2 marks
6n – 4 oe final answer

9a · 3 marks

B1
Enlargement
B1
[scale factor] 3
B1
[Centre] (3, 4)

9b · 2 marks

2 marks
Triangle drawn with vertices at (–2, 5) (–2, 3) and (–1, 3)

10 · 3 marks

M1
Correct method to eliminate one variable
A2
a = –3 b = 5

11a · 1 mark

1 mark
(3.5 oe, 1)

11b · 2 marks

2 marks
–2

12a · 1 mark

1 mark
2.57 × 10–4 cao

12b · 2 marks

2 marks
5 × 10^8 cao

13 · 2 marks

2 marks
$2 \frac{14}{15}$ cao

14a · 2 marks

2 marks
2^3 × 3^2 × 5 or 2 × 2 × 2 × 3 × 3 × 5

14b · 1 mark

1 mark
75

15 · 4 marks

4 marks
24π nfww

16a · 2 marks

2 marks
$(\begin{array}{cc} 5 & - 5 \\ 6 & 3 \end{array})$

16b(i) · 1 mark

1 mark
–3

16b(ii) · 1 mark

1 mark
$\frac{1}{10} (\begin{array}{cc} 1 & - their k \\ - 2 & 4 \end{array})$ oe

17a · 2 marks

2 marks
Correct region shaded

17b · 2 marks

2 marks
0, 1, 2

18a · 2 marks

2 marks
49 to 53

18b · 2 marks

2 marks
74 to 76

18c · 2 marks

2 marks
14, 13, 8, 7

19 · 2 marks

2 marks
$\frac{1}{16}$ oe nfww

20 · 2 marks

B1
[a = ] 8
B1
[n = ] 15

21 · 2 marks

2 marks
400

22a · 1 mark

1 mark
8

22b · 3 marks

3 marks
1 or –1 nfww

23a · 1 mark

1 mark
32.5

23b · 1 mark

1 mark
18

24 · 3 marks

3 marks
$\frac{2 x - 1}{2 x}$ or $1 - \frac{1}{2 x}$ final answer nfww

25 · 3 marks

3 marks
3 nfww

26 · 4 marks

4 marks
2 nfww

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