IGCSE Mathematics 0580 Paper 43, May/June 2026

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0580/43 · May/June 2026

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Complete the statement. $\frac{4}{7} = \frac{}{56}$

[1]

Work out $55 %$ of $12.2$ .

[1]

Calculate $\frac{0.7 - {3.5}^{3}}{{4.2}^{2}}$ giving your answer correct to 2 significant figures.

[2]

Kit and Jo are changing some money. The exchange rate is $$ 1 = 0.93 e u r o s$ .

Kit changes $$ 350$ into euros. Calculate the amount, in euros, that Kit receives.

[1]

Jo changes $150 euros$ into dollars ($$). Calculate the amount, in dollars, that Jo receives.

[1]

Ruta and Zoli share some money in the ratio $7 : 3$ . Ruta receives $$ 420$ more than Zoli. Work out how much money Ruta and Zoli each receive.

[3]

The table shows the time 9 students each spent studying for a test and the number of errors each student made in the test.

study time (minutes)	$5$	$8$	$11$	$15$	$18$	$21$	$25$	$27$	$31$
number of errors	$35$	$34$	$30$	$25$	$24$	$20$	$13$	$9$	$6$

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

[2]

What type of correlation is shown in the scatter diagram?

[1]

Draw a line of best fit on the scatter diagram.

[1]

Another student studies for 13 minutes. Use your line of best fit to estimate the number of errors this student is expected to make in the test.

[1]

The point $A$ is on the top of a vertical building. The horizontal distance from the base of the building to $B$ is $22 m$ . $A B = 25 m$ and the height of the building is $h m$ .

Find the value of $h$ .

[3]

Work out the angle of depression of $B$ from $A$ .

[2]

$A B$ and $C D$ are parallel lines. $A D$ and $B C$ are straight lines that intersect at $X$ . Angle $A B X = y^{\circ}$ .

Complete the statement with a geometrical reason. Angle $D C X = y^{\circ}$ because ...........................................................................................................

[1]

b(i)

Triangle $A B X$ is similar to triangle $D C X$ . $C X = 5 cm$ , $X D = 8 cm$ and $A D = 20 cm$ . Find $B X$ .

[2]

b(ii)

Angle $C X D = {80.5}^{\circ}$ . Work out the area of triangle $C X D$ .

[2]

The table shows the marks of 100 students in a test.

mark	$0 < x ⩽ 20$	$20 < x ⩽ 40$	$40 < x ⩽ 60$	$60 < x ⩽ 80$	$80 < x ⩽ 100$
frequency	$4$	$20$	$31$	$34$	$11$

Write down the modal class.

[1]

Calculate an estimate of the mean.

[4]

Llew cycles to school.

The speed–time graph shows the first 10 seconds of his journey. By drawing a suitable tangent, estimate the acceleration at $t = 2$ .

[2]

Llew cycles to school at an average speed of $18.9 kilometres per hour$ . Write this speed in metres per second.

[2]

The table shows some values for $y = 3 \times 2^{x} - 5$ correct to 1 decimal place.

$x$	$- 2$	$- 1.5$	$- 1$	$- 0.5$	$0$	$0.5$	$1$	$1.5$	$2$
$y$		$- 3.9$		$- 2.9$		$- 0.8$	$1$	$3.5$	$7$

Complete the table.

[3]

Draw the graph of $y = 3 \times 2^{x} - 5$ for $- 2 ⩽ x ⩽ 2$ .

[4]

By drawing a suitable line on the graph, solve the equation $3 \times 2^{x} = 7$ .

[2]

Find the equation of the asymptote to the graph of $y = 3 \times 2^{x} - 5$ .

[1]

Sketch the graph of $y = \cos x$ for $0^{\circ} ⩽ x ⩽ 360^{\circ}$ .

[2]

Solve the equation $3 \cos x + 1 = 0$ for $0^{\circ} ⩽ x ⩽ 360^{\circ}$ .

[3]

The diagram shows triangle $A B C$ . $B C = 15 cm$ , $A C = 15 \sqrt{3} cm$ and angle $A B C = 120^{\circ}$ .

Show that triangle $A B C$ is an isosceles triangle.

[4]

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

[3]

$A$ is the point $(5, 2)$ and $B$ is the point $(- 3, 6)$ .

Calculate the length of $A B$ .

[3]

Find the equation of the line perpendicular to $A B$ that passes through the point $(- 2, 5)$ . Give your answer in the form $y = m x + c$ .

[4]

The sides of a triangle are $5 cm$ , $7 cm$ and $11 cm$ . Find the size of the largest angle in this triangle.

[3]

A rectangle measures $4.2 cm$ by $6.8 cm$ . Each measurement is given correct to the nearest millimetre. Calculate the lower bound of the area of the rectangle.

[2]

The diagram shows a cuboid, $A B C D E F G H$ . $A B = 18 cm$ , $B C = 14 cm$ and $A E = 16 cm$ . Calculate the length of the diagonal $A G$ .

[3]

a(i)

$f (x) = 3 x + 1 g (x) = 5 - 3 x$ Find $x$ when $f (x) = g (x)$ .

[2]

a(ii)

$f (x) = 3 x + 1 g (x) = 5 - 3 x$ Find $g^{- 1} (x)$ .

[2]

a(iii)

$f (x) = 3 x + 1 g (x) = 5 - 3 x$ Find $g g (x)$ . Give your answer in its simplest form.

[2]

$h (x) = 2^{2 x}$ Find $x$ when $h^{- 1} (x) = 2$ .

[2]

Lee invests $$ 2000$ in an account that pays simple interest at a rate of $3.5$ per year. Work out the total value of the investment at the end of 4 years.

[3]

Mia invests $$ 3000$ in an account that pays compound interest at a rate of $3.2$ per year. Find the number of complete years it takes for the value of Mia's investment to become greater than $$ 4800$ .

[3]

Ryan invests some money. The value of the investment increases exponentially at a rate of $r %$ per year. At the end of 6 years, the value of the original investment has increased by $19.4 %$ . Find the value of $r$ .

[3]

Find the coordinates of the turning points of the graph $y = 8 x^{3} - 6 x + 5$ . You must show all your working.

[5]

Determine whether each turning point is a maximum or a minimum. Show how you decide.

[3]

The diagram shows a frustum. Calculate the volume of the frustum.

[5]

Mark scheme

0580/43 · May/June 2026

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1 · 1 mark

1 mark
32

2 · 1 mark

1 mark
6.71

3 · 2 marks

2 marks
–2.4 cao

4a · 1 mark

1 mark
325.5[0]

4b · 1 mark

1 mark
161.29

5 · 3 marks

3 marks
735 315

6a · 2 marks

2 marks
3 points correctly plotted

6b · 1 mark

1 mark
Negative

6c · 1 mark

1 mark
Ruled line of best fit

6d · 1 mark

1 mark
Reading from their line of best fit at 13

7a · 3 marks

3 marks
11.9 or 11.87….

7b · 2 marks

2 marks
28.3 or 28.4 or 28.34 to 28.42..

8a · 1 mark

1 mark
Alternate angles [are equal]

8b(i) · 2 marks

2 marks
7.5

8b(ii) · 2 marks

2 marks
19.7 or 19.72 to 19.73

9a · 1 mark

1 mark
60, 80

9b · 4 marks

4 marks
55.6

10a · 2 marks

B1
Ruled tangent drawn at t = 2
B1
0.15 to 0.4

10b · 2 marks

2 marks
5.25

11a · 3 marks

3 marks
–4.3 –3.5 –2

11b · 4 marks

4 marks
Correct graph

11c · 2 marks

M1
y = 2 drawn
A1
FT their curve and y = 2 drawn

11d · 1 mark

1 mark
y = –5

12a · 2 marks

2 marks
Correct sketch to go through (0, 1), (90, 0), (270, 0) and (360, 1)

12b · 3 marks

3 marks
109.5 and 250.5

13a · 4 marks

M2
[sin BAC =] (15 sin 120)/(15√3) oe
A1
angle BAC = 30
A1
180 – 120 – 30 = 30 with one of: BCA = 30 or BAC = BCA or a comment that two angles are the same.

13b · 3 marks

3 marks
7.5

14a · 3 marks

3 marks
8.94 or 8.944 to 8.945

14b · 4 marks

4 marks
[y =] 2x + 9 final answer

15 · 3 marks

3 marks
132 or 132.2 or 132.17 to 132.18

16 · 2 marks

2 marks
28.0125

17 · 3 marks

3 marks
27.9 or 27.85 to 27.86

18a(i) · 2 marks

2 marks
2/3 oe

18a(ii) · 2 marks

2 marks
(5 – x)/3 oe final answer

18a(iii) · 2 marks

2 marks
9x – 10 final answer

18b · 2 marks

2 marks
16

19a · 3 marks

3 marks
2280 final answer

19b · 3 marks

3 marks
15

19c · 3 marks

3 marks
3[.00..] or 2.999…. nfww

20a · 5 marks

B2
[dy/dx =] 24x^2 – 6
M1
setting their derivative = 0 or dy/dx = 0
B2
(1/2, 3) and (-1/2, 7)

20b · 3 marks

3 marks
(-1/2, 7) maximum with correct reason AND (1/2, 3) minimum with correct reason

21 · 5 marks

5 marks
2870 or 2865 to 2866 nfww

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