O Level Mathematics 4024 Paper 11, Oct/Nov 2023

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4024/11 · Oct/Nov 2023

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Work out $6 + 4 \div 2$ .

[1]

Work out $40 \times 0.3$ .

[1]

Write these numbers in order of size, starting with the smallest. $\frac{1}{5} \frac{3}{25} 13 % 0.1$

[2]

Work out the temperature that is 20 degrees higher than $- 12^{\circ} C$ .

[1]

Work out the difference between $- 4^{\circ} C$ and $10^{\circ} C$ .

[1]

Kasia buys 12 apples. Each apple costs 65 cents. Work out how much Kasia pays. Give your answer in dollars.

[2]

Yasmin asks 20 people how many pets they own. The results are shown in the bar chart.

Find the range.

[1]

Find the fraction of the 20 people who own 3 pets.

[1]

The diagram shows a straight line crossing two parallel lines.

Work out the value of $x$ .

[1]

Work out the value of $y$ .

[1]

By writing each number correct to 1 significant figure, estimate the value of $\frac{53.7}{2.61 + 7.48} .$

[2]

Convert $78 mm$ to $cm$ .

[1]

Convert $3 m^{2}$ to ${cm}^{2}$ .

[1]

The scatter diagram shows the ages of ten people and the time they each take to complete a task.

Write down the type of correlation shown on the scatter diagram.

[1]

By drawing a line of best fit, estimate the time taken by a person aged 50 to complete the task.

[2]

Four exterior angles of a pentagon are $150^{\circ}$ , $100^{\circ}$ , $45^{\circ}$ and $35^{\circ}$ . Calculate the size of the remaining exterior angle.

[2]

Calculate the interior angle of a regular decagon.

[2]

Evaluate $4^{2} + \sqrt[3]{27}$ .

[1]

Evaluate $5^{- 1} \times 5^{3}$ .

[2]

The scale drawing shows the positions of two boats $A$ and $B$ . The scale is $1 : 20 000$ .

Find the actual distance of boat $A$ from boat $B$ in kilometres.

[2]

Using compasses and a straight edge only, construct the locus of points that are equidistant from $A$ and $B$ .

[2]

A ship, $S$ , is equidistant from $A$ and $B$ . $S$ is on a bearing of $105^{\circ}$ from $A$ . Mark and label the position of $S$ on the scale drawing.

[1]

Work out $1 \frac{3}{5} \div 1 \frac{2}{3}$ .

[2]

Write 36 as a product of its prime factors.

[2]

Bus $A$ leaves the bus station every 36 minutes. Bus $B$ leaves the bus station every 48 minutes. The two buses both leave the bus station at 0930. Find the next time when the two buses leave the bus station together.

[3]

$B$ , $C$ and $D$ are points on the circle, centre $O$ . $A B$ and $A C$ are tangents to the circle. Angle $B A C = 38^{\circ}$ . Work out

angle $A B C$

[1]

angle $B O C$

[2]

angle $B D C$ .

[1]

The region $R$ is defined by these inequalities. $1 ⩽ x ⩽ 3$ $2 ⩽ y ⩽ 3$ $y ⩾ \frac{x}{2} + 1$ Find and label region $R$ .

[4]

$y$ is directly proportional to the square root of $x$ . When $x = 16$ , $y = 2$ . Find $y$ when $x = 25$ .

[2]

In a sports club of 40 members: • 22 members run ( $R$ ) • 24 cycle ( $C$ ) • 14 sail ( $S$ ) • 3 cycle and sail but do not run • 9 run and cycle but do not sail • 5 run and sail but do not cycle • 6 run only. Complete the Venn diagram.

[3]

Use set notation to describe the shaded subset in the Venn diagram.

[1]

The diagram shows the speed–time graph for part of a car journey.

Calculate the acceleration of the car in the first 10 seconds of the journey.

[1]

The car travels $700 m$ in $T$ seconds. Find the value of $T$ .

[3]

$A = (\begin{array}{cc} - 2 & 1 \\ 4 & 3 \end{array}) B = (\begin{array}{cc} 3 & 2 \\ - 1 & 1 \end{array})$

Find $A^{- 1}$ .

[2]

Find $A B$ .

[2]

Factorise $6 a - 9$ .

[1]

Factorise $4 b^{2} - 25$ .

[1]

Simplify $\frac{2 c^{2} - 8 c}{2 c^{2} - 5 c - 12}$ .

[3]

$f (x) = \frac{x}{4} + 3 g (x) = 2 (x - 1)$

Find $f (- 8)$ .

[1]

Find $f^{- 1} (x)$ .

[2]

$f (p) = g (p + 5)$ Find the value of $p$ .

[3]

In the diagram, $O A B C$ is a parallelogram. $\vec{O A} = a$ and $\vec{O C} = c$ . $X$ is the midpoint of $A C$ . $Y$ is the point on $A B$ where $A Y : Y B = 2 : 1$ . Express, as simply as possible, in terms of $a$ and $c$

$\vec{A C}$

[1]

the position vector of $X$

[2]

$\vec{Y X}$ .

[2]

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

[4]

Mark scheme

4024/11 · Oct/Nov 2023

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1a · 1 mark

1 mark
8

1b · 1 mark

1 mark
12

2 · 2 marks

2 marks
0.1, $\frac{3}{25}$ , 13%, $\frac{1}{5}$

3a · 1 mark

1 mark
8

3b · 1 mark

1 mark
14

4 · 2 marks

2 marks
7.8[0]

5a · 1 mark

1 mark
4

5b · 1 mark

1 mark
$\frac{5}{20}$ oe fraction

6a · 1 mark

1 mark
70

6b · 1 mark

1 mark
110

7 · 2 marks

2 marks
50, 3 and 7 seen and final answer 5

8a · 1 mark

1 mark
7.8

8b · 1 mark

1 mark
30 000

9a · 1 mark

1 mark
Positive

9b · 2 marks

B1
Ruled line of best fit
B1
Reading their straight line of best fit at 50

10a · 2 marks

2 marks
30

10b · 2 marks

2 marks
144

11a · 1 mark

1 mark
19

11b · 2 marks

2 marks
25

12a · 2 marks

2 marks
1.76 to 1.84

12b · 2 marks

2 marks
Acceptable bisector of $A B$ with correct arcs

12c · 1 mark

1 mark
$S$ marked on a bearing of 105° from $A$ and on their bisector

13 · 2 marks

2 marks
$\frac{24}{25}$

14a · 2 marks

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

14b · 3 marks

3 marks
11 54

15a · 1 mark

1 mark
71

15b · 2 marks

2 marks
142

15c · 1 mark

1 mark
71

16 · 4 marks

B1
$x = 1$ and $x = 3$ correctly drawn
B1
$y = 2$ and $y = 3$ correctly drawn
B1
$y = \frac{x}{2} + 1$ correctly drawn
1 mark
Correct region $R$ identified

17 · 2 marks

2 marks
$\frac{5}{2}$ oe

18a · 3 marks

3 marks
Correct Venn diagram

18b · 1 mark

1 mark
$G \cap H \cap F^{'}$ oe

19a · 1 mark

1 mark
2

19b · 3 marks

3 marks
40

20a · 2 marks

2 marks
$- \frac{1}{10} (\begin{array}{cc} 3 & - 1 \\ - 4 & - 2 \end{array})$ oe

20b · 2 marks

2 marks
$(\begin{array}{cc} - 7 & - 3 \\ 9 & 11 \end{array})$

21a · 1 mark

1 mark
$3 (2 a - 3)$ final answer

21b · 1 mark

1 mark
$(2 b + 5) (2 b - 5)$ final answer

21c · 3 marks

B1
$2 c (c - 4)$ seen
B1
$(2 c + 3) (c - 4)$ seen
1 mark
$\frac{2 c}{2 c + 3}$ final answer

22a · 1 mark

1 mark
1

22b · 2 marks

2 marks
$4 (x - 3)$ or $4 x - 12$ final answer

22c · 3 marks

3 marks
$- \frac{20}{7}$ oe

23a · 1 mark

1 mark
$c - a$

23b · 2 marks

2 marks
$\frac{1}{2} a + \frac{1}{2} c$ oe simplified vector

23c · 2 marks

2 marks
$- \frac{1}{2} a - \frac{1}{6} c$ oe simplified vector

24 · 4 marks

4 marks
$\frac{1}{5}$ oe

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