IGCSE Mathematics 0580 Paper 13, May/June 2026

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Question paper

0580/13 · May/June 2026

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Write down the number that is 1 more than 4999 499.

[1]

Write the number 707 700 in words.

[1]

$A$ and $B$ are points on the circumference of a circle, centre $O$ . Write down the mathematical name for

the line $A B$

[1]

the shaded region.

[1]

A car hire company uses this formula to work out the hire cost, in dollars. $cost = fixed charge + rate per day \times number of days$ Find the cost of hiring a car for 7 days when the fixed charge is $140 and the rate per day is $30.

[2]

Sam takes 75 minutes to make a cake. The time taken to make the cake is in the ratio $preparing : cooking : decorating = 6 : 10 : 9$ .

Work out the number of minutes Sam takes to decorate the cake.

[2]

Sam starts making the cake at 12 42. Find the time Sam finishes making the cake.

[1]

A book has 420 pages. Meg reads 14 pages each day. Meg has read $\frac{1}{3}$ of the number of pages so far. Find how many days it will take Meg to finish reading the rest of the book.

[3]

Raj records the temperature, in °C, at midday for each of 8 days. These are the results. $1, 10, 8, - 3, - 2, 10, 7, 9$

Calculate the mean.

[2]

Find the median.

[2]

When another temperature is recorded, the range increases by 5. Find the two possible values of this temperature.

[2]

Ben asks some children to choose their favourite type of snack. The pie chart shows the results.

Measure the sector angle for crisps.

[1]

Find the fraction of the children who chose chocolate. Give your answer in its simplest form.

[2]

8 more children chose fruit than those who chose nuts. Work out the number of children who chose fruit.

[2]

$A$ , $B$ and $C$ are points on the circumference of the circle, centre $O$ . $D A E$ is a tangent to the circle at $A$ . $D E$ is parallel to $B C$ . $B O E$ is a straight line.

Write down the two geometrical reasons to explain why angle $A O E = 55^{\circ}$ .

[2]

Find the value of $x$ .

[1]

Find the value of $y$ .

[2]

$K = 2 x + \sqrt{y}$ Find the value of $K$ when $x = 5$ and $y = 169$ .

[2]

$\frac{2}{5}$ of the area of a shape is blue, $\frac{3}{7}$ is green and the rest is red.

What fraction of the shape is red?

[3]

$12 {cm}^{2}$ of the shape is green. Find the total area of the shape.

[2]

Factorise. $5 c - 15 c^{2} d$

[2]

Complete the table of values for $y = 6 x - x^{2} - 4$ .

[2]

On the grid, draw the graph of $y = 6 x - x^{2} - 4$ for $0 ⩽ x ⩽ 6$ .

[4]

On the grid, draw the line $y = 3$ .

[1]

Use your graph to solve $6 x - x^{2} - 4 = 3$ .

[2]

The diagram shows a right-angled triangular prism. On the $1 {cm}^{2}$ grid, complete the net of this prism. One face has been drawn for you.

[3]

Find the volume of the triangular prism.

[2]

In a restaurant the cost of a pizza is $25. The restaurant reduces the cost of the pizza to $19. Work out the percentage decrease in the cost.

[2]

In another restaurant, the cost of a pizza is $15. This restaurant adds a service charge of 10% to each pizza. Find the cost of a pizza, including the service charge.

[2]

The area of a circle is $36 π {cm}^{2}$ . Find the radius of the circle.

[2]

Convert $850 {cm}^{3}$ into litres.

[1]

Write down the value of $\sqrt[3]{27}$ .

[1]

Write $5^{- 1}$ as a decimal.

[2]

Write 84 as a product of its prime factors.

[2]

96 can be written as $2^{P} \times 3$ . Find the value of $P$ .

[1]

Use your answers to 19(a) and 19(b) to find the lowest common multiple (LCM) of 84 and 96. Leave your answer as a product of prime numbers.

[1]

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

[2]

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

[3]

On the grid, draw the image of shape $A$ after a rotation 180°, centre $(0, 0)$ .

[2]

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of $\frac{341 \times 0.47}{9.8}$ .

[2]

In this question, all lengths are in centimetres. The area, in ${cm}^{2}$ , of the rectangle is $5 x + 8$ . Write an equation to show this information and solve it to find the value of $x$ .

[3]

Solve the simultaneous equations. $x + 5 y = 9$ $4 x + 6 y = 1$

[3]

Mark scheme

0580/13 · May/June 2026

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1 · 1 mark

1 mark
4 999 500

2 · 1 mark

1 mark
Seven hundred [and] seven thousand [and] seven hundred

3a · 1 mark

1 mark
Chord

3b · 1 mark

1 mark
Sector

4 · 2 marks

2 marks
350

5a · 2 marks

2 marks
27

5b · 1 mark

1 mark
13 57

6 · 3 marks

3 marks
20

7a · 2 marks

2 marks
5

7b · 2 marks

2 marks
7.5 or $7 \frac{1}{2}$ cao

7c · 2 marks

2 marks
–8 15

8a · 1 mark

1 mark
80

8b · 2 marks

2 marks
$\frac{7}{18}$

8c · 2 marks

2 marks
24

9a · 2 marks

2 marks
Angle between tangent and radius = 90 Angles in a triangle add to 180

9b · 1 mark

1 mark
35

9c · 2 marks

2 marks
110

10 · 2 marks

2 marks
23

11a · 3 marks

3 marks
$\frac{6}{35}$ nfww

11b · 2 marks

2 marks
28

12 · 2 marks

2 marks
5c(1 – 3cd) final answer

13a · 2 marks

2 marks
–4, 1, 4

13b · 4 marks

4 marks
Correct curve

13c · 1 mark

1 mark
Line $y = 3$ drawn

13d · 2 marks

2 marks
1.5 to 1.7 , 4.3 to 4.5

14a · 3 marks

3 marks
Correct net of triangular prism

14b · 2 marks

2 marks
24

15a · 2 marks

2 marks
24

15b · 2 marks

2 marks
16.5[0]

16 · 2 marks

2 marks
6

17 · 1 mark

1 mark
0.85[0] oe

18a · 1 mark

1 mark
3

18b · 2 marks

2 marks
0.2 cao

19a · 2 marks

2 marks
$2^{2} \times 3 \times 7$ or $2 \times 2 \times 3 \times 7$

19b · 1 mark

1 mark
5

19c · 1 mark

1 mark
$2^{5} \times 3 \times 7$

20a · 2 marks

2 marks
Translation $(\begin{array}{c} 2 \\ - 7 \end{array})$

20b · 3 marks

3 marks
Enlargement (sf) $\frac{1}{2}$ oe (centre) (0, 0) oe

20c · 2 marks

2 marks
Triangle plotted at (–4, –2), (–2, –2), (–3, –6)

21 · 2 marks

M1
$\frac{300 \times 0.5}{10}$
A1
15

22 · 3 marks

B1
6(x – 1) = 5x + 8 or 6x – 6 = 5x + 8
B2
14 final answer

23 · 3 marks

3 marks
[x = ] –3.5 or $- 3 \frac{1}{2}$ or $- \frac{7}{2}$ [y = ] 2.5 or $2 \frac{1}{2}$ or $\frac{5}{2}$

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