IGCSE Mathematics 0580 Paper 13, Oct/Nov 2025

Question paper and mark scheme80 marks27 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

0580/13 · Oct/Nov 2025

Download PDF

Measure the length of line $A B$ in centimetres.

[1]

Draw a line that is parallel to line $A B$ .

[1]

Write the number 83042 in words.

[1]

Write down the value of the 7 in the number 346709.

[1]

c(i)

Write 8453 correct to the nearest hundred

[1]

c(ii)

Write 8453 correct to the nearest ten.

[1]

Measure angle $a$ .

[1]

Write down the mathematical name of this type of angle.

[1]

Ben records the favourite sport of each of 20 students. Football Cricket Hockey Rugby Football Tennis Rugby Football Football Rugby Tennis Football Rugby Football Cricket Football Rugby Football Cricket Cricket Complete the frequency table. You may use the tally column to help you.

[2]

The diagram shows quadrilateral $A B C D$ on a $1 {cm}^{2}$ grid.

Write down the coordinates of point $B$ .

[1]

Write down the mathematical name of quadrilateral $A B C D$ .

[1]

Find the area of quadrilateral $A B C D$ .

[1]

On the grid, plot the point $E$ at $(- 3, 2)$ .

[1]

Anna thinks of a number, she multiplies it by 2 and then finds the square root. The answer is 12. What number did Anna think of?

[2]

A journey starts at 1055 and ends at 1610. Find how long the journey takes. Give your answer in hours and minutes.

[1]

These are the masses, in kg, of each of 11 bags. 23 16 8 10 27 19 4 17 13 4 14

Complete the stem-and-leaf diagram to show this information.

[2]

Find the median.

[1]

Find the value of

$2^{5}$

[1]

$6^{0}$ .

[1]

The diagram shows an isosceles triangle between a pair of parallel lines.

Find the value of $x$ .

[2]

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

[2]

Sam buys 3 apples at 40 cents each. He also buys 5 peaches. The total cost is $3.45 . Find the cost of 1 peach.

[3]

Pears cost 55 cents each. Bananas cost 36 cents each. Write an expression, in cents, for the cost of $x$ pears and $y$ bananas.

[2]

Simplify. $3 y - 4 y + 2 y$

[1]

b(i)

Solve. $x + 5 = 19$

[1]

b(ii)

Solve. $6 x - 5 = 7$

[2]

Write down the inequality represented on the number line.

[2]

Victoria invests $2000 at a rate of 5% per year simple interest. Calculate the value of her investment after 4 years.

[3]

Complete each statement.

$0.0000047 m^{2} = ....................... {cm}^{2} .$

[1]

$8500 {cm}^{3} = ....................... litres .$

[1]

Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13. Jo receives $1400. Find the total amount of money they share.

[3]

$k^{x} \times k^{5} = k^{20}$ Find the value of $x$ .

[1]

Expand and simplify. $(x + 5) (x - 4)$

[2]

Factorise. $21 r^{3} - 7 r$

[2]

The diameter of a circle is 16cm. Find the area of the circle. Leave your answer in terms of $π$ .

[2]

Find the number of sides of a regular polygon with interior angle 160°.

[2]

The height, $h cm$ , of a door is 180cm, correct to the nearest centimetre. Complete this statement about the value of $h$ .

[2]

These are the first four terms of a sequence. –6 1 8 15

Write down the next term.

[1]

Write down the term-to-term rule.

[1]

c(i)

Find the $n$ th term.

[2]

c(ii)

Is 688 a term in this sequence? Explain how you decide.

[2]

The diagram shows triangles $A$ and $B$ . Describe fully the single transformation that maps triangle $A$ onto triangle $B$ .

[3]

Use set notation to describe the shaded region.

[1]

b(i)

$E = {people in a club}$ $T = {people who play tennis}$ $S = {people who go swimming}$ There are 60 people in the club. 36 people go swimming. Complete the Venn diagram.

[2]

b(ii)

Find $n (T^{'})$ .

[1]

The scale on a map is 1cm represents 12km. Write this in the ratio $1 : n$ .

[1]

The bearing of $B$ from $A$ is 070°. Find the bearing of $A$ from $B$ .

[2]

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

[3]

There are 2 sets of traffic lights on Li’s journey to work. The probability he stops at the first set of traffic lights is 0.4 . The probability he stops at the second set of traffic lights is 0.7 .

Complete the tree diagram.

[2]

Work out the probability that Li does not stop at both sets of traffic lights.

[2]

Sam writes 851000 in standard form as $85.1 \times 10^{4}$ . Explain why $85.1 \times 10^{4}$ is not a number in standard form.

[1]

Mark scheme

0580/13 · Oct/Nov 2025

Download PDF

1a · 1 mark

1 mark
5.6

1b · 1 mark

1 mark
Ruled line parallel to AB

2a · 1 mark

1 mark
Eighty-three thousand [and] forty-two

2b · 1 mark

1 mark
700

2c(i) · 1 mark

1 mark
8500

2c(ii) · 1 mark

1 mark
8450

3a · 1 mark

1 mark
123

3b · 1 mark

1 mark
Obtuse

4 · 2 marks

2 marks
4 8 1 5 2

5a · 1 mark

1 mark
(–1, 2)

5b · 1 mark

1 mark
trapezium

5c · 1 mark

1 mark
16

5d · 1 mark

1 mark
Point plotted at (–3,2)

6 · 2 marks

2 marks
72

7 · 1 mark

1 mark
5[hours] 15[minutes] cao

8a · 2 marks

2 marks
0 4 4 8
1 0 3 4 6 7 9
2 3 7

0	4 4 8
1	0 3 4 6 7 9
2	3 7

8b · 1 mark

1 mark
14

9a · 1 mark

1 mark
32

9b · 1 mark

1 mark
1

10a · 2 marks

2 marks
70

10b · 2 marks

1 mark
110
1 mark
Angles on a straight line add to 180 oe nfww

11a · 3 marks

3 marks
45

11b · 2 marks

2 marks
55x + 36y final answer

12a · 1 mark

1 mark
y

12b(i) · 1 mark

1 mark
14

12b(ii) · 2 marks

2 marks
2

13 · 2 marks

2 marks
–5 ⩽ x < 1 oe

14 · 3 marks

3 marks
2400 nfww

15a · 1 mark

1 mark
0.047

15b · 1 mark

1 mark
8.5

16 · 3 marks

3 marks
4800

17a · 1 mark

1 mark
15

17b · 2 marks

2 marks
x² + x – 20 final answer

17c · 2 marks

2 marks
7r(3r² – 1) final answer

18 · 2 marks

2 marks
64π

19 · 2 marks

2 marks
18

20 · 2 marks

B1
179.5
B1
180.5

21a · 1 mark

1 mark
22

21b · 1 mark

1 mark
Add 7

21c(i) · 2 marks

2 marks
7n – 13 oe final answer

21c(ii) · 2 marks

1 mark
7n – 13 = 688 oe 7n = 701
1 mark
No, 701 is not divisible by 7 oe nfww

22 · 3 marks

B1
Enlargement
B1
Centre (0,0)
B1
[Scale factor] 3

23a · 1 mark

1 mark
A ∩ B

23b(i) · 2 marks

B1
14 in correct place
B1
6 in correct place

23b(ii) · 1 mark

1 mark
40

24a · 1 mark

1 mark
1 200 000

24b · 2 marks

2 marks
250

25 · 3 marks

3 marks
1 1/4 cao

26a · 2 marks

2 marks
Correct tree diagram

26b · 2 marks

2 marks
0.18 oe

27 · 1 mark

1 mark
In standard form the value is written as a × 10ⁿ where 1 ⩽ a < 10 and 85.1 is greater than 10 oe

Questions

1
Question 12 marks
Mark scheme ›
2
Question 24 marks
Mark scheme ›
3
Question 32 marks
Mark scheme ›
4
Question 42 marks
Mark scheme ›
5
Question 54 marks
Mark scheme ›
6
Question 62 marks
Mark scheme ›
7
Question 71 mark
Mark scheme ›
8
Question 83 marks
Mark scheme ›
9
Question 92 marks
Mark scheme ›
10
Question 104 marks
Mark scheme ›
11
Question 115 marks
Mark scheme ›
12
Question 124 marks
Mark scheme ›
13
Question 132 marks
Mark scheme ›
14
Question 143 marks
Mark scheme ›
15
Question 152 marks
Mark scheme ›
16
Question 163 marks
Mark scheme ›
17
Question 175 marks
Mark scheme ›
18
Question 182 marks
Mark scheme ›
19
Question 192 marks
Mark scheme ›
20
Question 202 marks
Mark scheme ›
21
Question 216 marks
Mark scheme ›
22
Question 223 marks
Mark scheme ›
23
Question 234 marks
Mark scheme ›
24
Question 243 marks
Mark scheme ›
25
Question 253 marks
Mark scheme ›
26
Question 264 marks
Mark scheme ›
27
Question 271 mark
Mark scheme ›