IGCSE Mathematics 0580 Paper 13, May/June 2025

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Question paper

0580/13 · May/June 2025

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Write the number 70000000 in words.

[1]

b(i)

Write down the value of the 5 in the number 0.25 . Give your answer as a fraction.

[1]

b(ii)

Find the value of the reciprocal of 0.25 .

[2]

Write down the mathematical name for an angle between 90° and 180°.

[1]

Write down the mathematical term that describes two polygons that are the same shape and size.

[1]

Write down $\sqrt{169}$ .

[1]

Work out the value of $2^{4}$ .

[1]

Work out the value of $10^{- 2}$ .

[1]

Work out $- 18 \div - 4$ .

[1]

Work out $1.6 \times 0.02$ .

[1]

The diagram shows a quadrilateral with sides of equal length.

Write down the mathematical name for this quadrilateral.

[1]

Work out the value of $a$ .

[2]

Find the next term in each sequence.

1, 5, 10, 16, 23, $\dots$

[1]

1, 2, 4, 8, 16, $\dots$

[1]

These are the lengths of time, in minutes, of seven phone calls. 10 22 5 7 35 8 75

a(i)

Find the median.

[2]

a(ii)

Find the range.

[1]

The longest phone call is 75 minutes. Write 75 minutes in hours.

[1]

70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French. Find the number of students who study German.

[3]

The diagram shows two faces of a net of a cuboid on a $1 {cm}^{2}$ grid.

Complete the statement. The dimensions of the cuboid are .......... cm by .......... cm by .......... cm.

[1]

On the grid, complete a net of the cuboid.

[3]

Work out the volume of the cuboid.

[2]

The diagram shows the net of a square-based pyramid. The perpendicular height of each triangle is $4 cm$ . The base has side length $5 cm$ .

Calculate the surface area of the pyramid.

[2]

Write down the number of edges of the square-based pyramid.

[1]

Line $A$ has equation $y = 3 x + 1$ . Line $B$ has equation $y = 3 x - 1$ . Draw a ring around the description that is correct. Line $A$ intersects line $B$ Line $A$ has a steeper gradient than line $B$ Line $A$ is perpendicular to line $B$ Line $A$ is parallel to line $B$ Line $A$ and Line $B$ intersect the $y$ -axis at the same point

[1]

On the grid, draw the graph of $y = 2 x - 1$ .

[2]

Jo asks 90 people whether they prefer pop, rock, classical, jazz or folk music. The pie chart shows some of the results.

Work out the number of people who prefer pop.

[2]

The sector angle for classical is $80^{\circ}$ . Draw this sector on the pie chart.

[1]

c(i)

9 people prefer jazz and the rest prefer folk. Work out the size of the sector angle for jazz.

[2]

c(ii)

Complete the pie chart.

[1]

A music group has 30 members. 7 members play a flute ( $F$ ) and play a clarinet ( $C$ ). 12 members play a flute. 1 member does not play a flute and does not play a clarinet.

Use this information to complete the Venn diagram.

[2]

Find $n (C)$ .

[1]

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of $\frac{62.5}{9.7 \times 0.52} .$

[2]

The diagram shows a trapezium. The area of the trapezium is $42 {cm}^{2}$ . Work out the value of $h$ .

[2]

Write down the inequality represented on the number line.

[2]

Write down the smallest integer that satisfies the inequality $d > - 3 \frac{1}{4}$ .

[1]

On Monday the cost of a concert ticket is $$ x$ . On Tuesday the cost of a ticket for the same concert is 20% more than the cost on Monday. Jack buys 4 tickets on Monday and 5 tickets on Tuesday. Jack pays $$ 270$ in total. Work out the value of $x$ .

[3]

Simplify.

$y^{4} \times y^{6}$

[1]

$\frac{p^{5}}{p^{8}}$

[1]

$(w^{4})^{3}$

[1]

The diagram shows a circle, centre $O$ . $P$ and $S$ are points on the circle. $P O R$ is a straight line. $Q R S T$ is a tangent to the circle at $S$ .

Find the value of $x$ . Give a geometrical reason for your answer.

[2]

Find the value of $y$ .

[3]

The diagram shows a sector of a circle with radius $3 cm$ and sector angle $60^{\circ}$ . Calculate the area of the sector. Give your answer in terms of $π$ in its simplest form.

[2]

Find the highest common factor (HCF) of 36 and 54.

[2]

In this question, all lengths are in centimetres. The perimeter of the triangle is equal to the perimeter of the rectangle. Form an equation and solve it to find the value of $x$ .

[4]

$g = \frac{h}{3} - 8$ Rearrange the formula to make $h$ the subject.

[2]

Rectangle $A$ is mathematically similar to rectangle $B$ . Work out the value of $x$ .

[2]

Work out $3 \frac{1}{2} - 1 \frac{4}{7}$ . Give your answer as a mixed number in its simplest form.

[3]

Solve the simultaneous equations. $8 x + 5 y = 4$ $2 x - y = 10$

[3]

Mark scheme

0580/13 · May/June 2025

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1a · 1 mark

1 mark
Seventy million(s) cao

1b(i) · 1 mark

1 mark
$\frac{5}{100}$ or $\frac{1}{20}$

1b(ii) · 2 marks

2 marks
4

2a · 1 mark

1 mark
Obtuse

2b · 1 mark

1 mark
Congruent

3a · 1 mark

1 mark
13

3b · 1 mark

1 mark
16

3c · 1 mark

1 mark
$\frac{1}{100}$ or 0.01

3d · 1 mark

1 mark
$\frac{9}{2}$ or 4.5 or $4 \frac{1}{2}$

3e · 1 mark

1 mark
0.032

4a · 1 mark

1 mark
Rhombus

4b · 2 marks

2 marks
60

5a · 1 mark

1 mark
31

5b · 1 mark

1 mark
32

6a(i) · 2 marks

2 marks
10

6a(ii) · 1 mark

1 mark
70

6b · 1 mark

1 mark
1.25 or $1 \frac{1}{4}$

7 · 3 marks

3 marks
20

8a · 1 mark

1 mark
3, 3, 5

8b · 3 marks

3 marks
Fully correct net

8c · 2 marks

2 marks
45

9a · 2 marks

2 marks
65

9b · 1 mark

1 mark
8

10a · 1 mark

1 mark
Circle around the statement Line A is parallel to line B

10b · 2 marks

2 marks
Correct graph of $y = 2 x - 1$

11a · 2 marks

2 marks
30 nfww

11b · 1 mark

1 mark
Sector 80° drawn on pie chart

11c(i) · 2 marks

2 marks
36

11c(ii) · 1 mark

1 mark
Completed pie chart

12a · 2 marks

2 marks
Venn diagram with 5, 7, 17 in subsets and 1 outside

12b · 1 mark

1 mark
24

13 · 2 marks

M1
$\frac{60}{10 \times 0.5}$
A1
12

14 · 2 marks

2 marks
6 nfww

15a · 2 marks

2 marks
–4 ⩽ x < 3

15b · 1 mark

1 mark
–3 cao

16 · 3 marks

3 marks
27

17a · 1 mark

1 mark
$y^{10}$

17b · 1 mark

1 mark
$p^{- 3}$ or $\frac{1}{p^{3}}$

17c · 1 mark

1 mark
$w^{12}$

18a · 2 marks

2 marks
25 base angles of an isosceles triangle are equal

18b · 3 marks

3 marks
140

19 · 2 marks

2 marks
$\frac{3}{2} π$ , $1 \frac{1}{2} π$ , or $1.5 π$

20 · 2 marks

2 marks
18

21 · 4 marks

M3
3x = 15
A1
5

22 · 2 marks

2 marks
3(g + 8) or 3g + 24

23 · 2 marks

2 marks
6 nfww

24 · 3 marks

3 marks
$1 \frac{13}{14}$ cao nfww

25 · 3 marks

3 marks
[x = ] 3 final answer nfww [y = ] –4

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