IGCSE Mathematics 0580 Paper 31, May/June 2026

Question paper and mark scheme80 marks28 questions

Solve it on ExamPal

Practise

Untimed. Write on the paper and check as you go.

Start

Exam

Timed, with a clock you set, like sitting the real paper.

Start

Opens full screen.

Download PDF Mark scheme

100%

Opening the question paper

Read as textThe questions and the mark scheme as plain text. Easier to read on a phone.

Question paper

0580/31 · May/June 2026

Download PDF

The table shows a shopping bill for three items. Complete the table.

[3]

Write $7 \times 7 \times 7 \times 7 \times 7 \times 7$ as a power of 7.

[1]

Calculate ${17.4}^{2}$ .

[1]

Arya changes 250 pounds into dollars. The exchange rate is 1 pound = $1.26 . Calculate the amount that Arya receives.

[1]

Find 18% of $65.

[1]

The bar chart shows the number of each type of book sold in a shop on one day. Work out the percentage of books sold that are cookery.

[3]

Write these numbers in order, starting with the smallest. $\sqrt[3]{0.1} \frac{4}{9} 45 % 0.443$

[2]

The travel graph shows the journey of a train from Central station to Parkway station.

For how many minutes does the train stop between Central and Parkway?

[1]

Write down the time the train arrives at Parkway.

[1]

The train leaves Parkway at 14 33 and returns to Central at a constant speed. The return journey takes 21 minutes. Complete the graph to show this return journey.

[1]

Solve.

$6 + x = 2$

[1]

$5 x + 2 = 18$

[2]

a(i)

On the diagram, draw the line of symmetry.

[1]

a(ii)

On the diagram, shade one more square so that it has one line of symmetry.

[1]

On the diagram, shade one more square so that it has rotational symmetry of order 2.

[1]

The table shows how 40 students travel to school.

Complete the table.

[2]

Complete the pie chart.

[2]

The scale diagram shows the positions of town $A$ and town $B$ . The scale is $1 cm$ represents $15 km$ .

Measure the bearing of town $B$ from town $A$ .

[1]

Find the actual distance $A B$ .

[2]

Write one of the symbols $<$ , $>$ or $=$ in each statement to make it correct. $\frac{5}{8} ........................... 62.5 %$ ${0.2}^{2} ........................... 0.4$ $\frac{2}{3} ........................... 0.67$

[2]

Put one pair of brackets into each calculation to make it correct.

$10 + 12 - 8 \times 5 = 30$

[1]

$10 + 20 \times 7 \div 5 = 30$

[1]

Write down the reciprocal of $\frac{5}{7}$ .

[1]

The diagram shows a cuboid. Calculate the surface area of the cuboid.

[3]

A sphere has a radius of $6.4 cm$ . Calculate the volume of the sphere.

[2]

The scatter diagram shows the number of hot drinks sold by a cafe9 each day and the average temperature for that day.

These are the results for two more days. Plot this information on the scatter diagram.

[1]

What type of correlation is shown in the scatter diagram?

[1]

c(i)

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

[1]

c(ii)

One day the average temperature was $24^{\circ} C$ . Use your line of best fit to estimate the number of hot drinks sold.

[1]

The diagram shows a circle inside a rectangle. The shaded area is $450 {cm}^{2}$ . Find the radius of the circle.

[4]

Write down the smallest integer that satisfies $x > - 8$ .

[1]

Represent the inequality $- 4 ⩽ x < 3$ on the number line.

[2]

$A$ , $B$ , $C$ and $D$ are points on the circumference of a circle with centre $O$ . $A B = A D$ and angle $B D C = 52^{\circ}$ . $B D$ is a diameter of the circle. Calculate angle $A B C$ .

[3]

$P = 5 x + 4 y$ Find the value of $x$ when $P = 18$ and $y = - 3$ .

[3]

Factorise. $6 x^{2} + 12 x$

[2]

Calculate $(8.7 \times 10^{8}) + (2.4 \times 10^{7})$ . Write your answer in standard form.

[2]

Joseph invests $36\,000 at a rate of 6.2% per year compound interest. Calculate the total interest earned at the end of 4 years.

[3]

Calculate the interior angle of a regular pentagon.

[2]

Ali drives 56km at an average speed of 48km/h. He then drives for 30 minutes at 54km/h. Calculate the average speed for his whole journey.

[4]

a(i)

These are the first four terms of a sequence. $3 7 11 15$ Find the $n th$ term.

[2]

a(ii)

Show that 603 is a term in the sequence.

[2]

The $n th$ term of a different sequence is $n^{2} - 6$ . Find the first three terms of this sequence.

[2]

The diagram shows a right-angled triangle. Calculate the value of $x$ .

[2]

Find the equation of the line parallel to $y = 4 x + 3$ that passes through $(2, 9)$ .

[2]

The diagram shows a right-angled triangle. Calculate the value of $x$ .

[2]

Mark scheme

0580/31 · May/June 2026

Download PDF

1 · 3 marks

B1
for 8.88
B1
FT for 21.62 – their 8.88
B1
FT for their12.74 ÷ 5.2

2a · 1 mark

1 mark
7^6

2b · 1 mark

1 mark
302.76

3 · 1 mark

1 mark
315[.00]

4 · 1 mark

1 mark
11.7[0]

5 · 3 marks

3 marks
36

6 · 2 marks

2 marks
0.443 4/9 45% $\sqrt[3]{0.1}$

7a · 1 mark

1 mark
7

7b · 1 mark

1 mark
14 27

7c · 1 mark

1 mark
Ruled line from (1433, 27) to (1454, 0)

8a · 1 mark

1 mark
–4 final answer

8b · 2 marks

2 marks
3.2 oe final answer

9a(i) · 1 mark

1 mark
Correct line of symmetry drawn on grid

9a(ii) · 1 mark

1 mark
Correct shading of 2 squares to give line symmetry

9b · 1 mark

1 mark
Correct shading of 2 squares to give rotational symmetry of order 2

10a · 2 marks

2 marks
72 135 153

10b · 2 marks

2 marks
Accurate pie chart

11a · 1 mark

1 mark
124

11b · 2 marks

2 marks
114

12 · 2 marks

2 marks
= < <

13a · 1 mark

1 mark
10 + (12 – 8) × 5 = 30

13b · 1 mark

1 mark
(10 + 20 × 7) ÷ 5 = 30

14 · 1 mark

1 mark
7/5 or 1 2/5 or 1.4

15a · 3 marks

3 marks
158

15b · 2 marks

2 marks
1100 or 1098 or 1098.0 to 1098.2…

16a · 1 mark

1 mark
(18, 40) and (28, 21) plotted

16b · 1 mark

1 mark
Negative

16c(i) · 1 mark

1 mark
Acceptable ruled line of best fit

16c(ii) · 1 mark

1 mark
their reading at 24

17 · 4 marks

4 marks
6.33 or 6.332 to 6.333…

18a · 1 mark

1 mark
–7

18b · 2 marks

2 marks
Correct inequality line showing –4 ⩽ x < 3

19 · 3 marks

3 marks
83

20a · 3 marks

3 marks
6 final answer

20b · 2 marks

2 marks
6x(x + 2) final answer

21 · 2 marks

2 marks
8.94 × 10^8

22 · 3 marks

3 marks
9790 or 9793[…..]

23 · 2 marks

2 marks
108

24 · 4 marks

4 marks
49.8 nfww

25a(i) · 2 marks

2 marks
4n – 1 oe final answer

25a(ii) · 2 marks

M1
4n – 1 = 603
M1
n = (603 + 1)/4 = 151

25b · 2 marks

2 marks
– 5 – 2 3

26 · 2 marks

2 marks
21.1 or 21.09… to 21.10

27 · 2 marks

2 marks
[y =] 4x + 1 oe final answer

28 · 2 marks

2 marks
48.2 or 48.18 to 48.19

Questions

1
Question 13 marks
Mark scheme ›
2
Question 22 marks
Mark scheme ›
3
Question 31 mark
Mark scheme ›
4
Question 41 mark
Mark scheme ›
5
Question 53 marks
Mark scheme ›
6
Question 62 marks
Mark scheme ›
7
Question 73 marks
Mark scheme ›
8
Question 83 marks
Mark scheme ›
9
Question 93 marks
Mark scheme ›
10
Question 104 marks
Mark scheme ›
11
Question 113 marks
Mark scheme ›
12
Question 122 marks
Mark scheme ›
13
Question 132 marks
Mark scheme ›
14
Question 141 mark
Mark scheme ›
15
Question 155 marks
Mark scheme ›
16
Question 164 marks
Mark scheme ›
17
Question 174 marks
Mark scheme ›
18
Question 183 marks
Mark scheme ›
19
Question 193 marks
Mark scheme ›
20
Question 205 marks
Mark scheme ›
21
Question 212 marks
Mark scheme ›
22
Question 223 marks
Mark scheme ›
23
Question 232 marks
Mark scheme ›
24
Question 244 marks
Mark scheme ›
25
Question 256 marks
Mark scheme ›
26
Question 262 marks
Mark scheme ›
27
Question 272 marks
Mark scheme ›
28
Question 282 marks
Mark scheme ›