IGCSE Mathematics 0580 Paper 12, May/June 2025

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0580/12 · May/June 2025

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Write the number sixteen thousand and sixty-two in figures.

[1]

Write three-quarters as

a decimal

[1]

a percentage.

[1]

Write down the value of

$\sqrt{36}$

[1]

$10^{3}$ .

[1]

The diagram shows a line $A B$ and a point $P$ .

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

[1]

Draw a line through point $P$ that is perpendicular to line $A B$ .

[1]

Complete this statement. 10 weeks is ...................... days.

[1]

Shade $\frac{2}{5}$ of the rectangle.

[1]

Find the value of the reciprocal of $\frac{1}{3}$ .

[1]

Write $2^{- 3}$ as a fraction.

[1]

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

$- 12 + 4 \div 2 - 3 = - 16$

[1]

$- 3 - 4 + 5 - 7 = - 5$

[1]

Write these fractions in order, starting with the smallest. $\frac{5}{8} \frac{11}{12} \frac{2}{3} \frac{3}{4} \frac{13}{24}$ ................. < ................. < ................. < ................. < ................. smallest

[2]

A cuboid has length $5 cm$ , width $2 cm$ and height $3 cm$ .

Draw a net of the cuboid on the $1 {cm}^{2}$ grid.

[3]

Work out the volume of the cuboid. Give the units of your answer.

[2]

0 2 2 3 4 7 For these six numbers

write down the mode

[1]

work out the range

[1]

work out the median

[1]

work out the mean.

[2]

Tim has a method for multiplying a number by 99. He shows his method for $53 \times 99$ . $\begin{aligned} 53 \times 99 & = 53 \times 100 - 53 \\ = 5300 - 53 \\ = 5247 \end{aligned}$ Work out $85 \times 99$ using Tim's method.

[2]

A quadrilateral has the geometrical properties • 4 equal length sides • 2 lines of symmetry • rotational symmetry of order 2. Write down the mathematical name of this quadrilateral.

[1]

Write down two geometrical properties of a rectangle. 1. ........................................................................................................................................................ 2. ........................................................................................................................................................

[2]

The parallel sides of a trapezium have lengths $6 cm$ and $4 cm$ . The area of the trapezium is $15 {cm}^{2}$ . On the $1 {cm}^{2}$ grid, draw a trapezium with these lengths and area.

[3]

Complete the table of values for $y = (x + 3) (x - 2)$ .

[3]

On the grid, draw the graph of $y = (x + 3) (x - 2)$ for $- 4 ⩽ x ⩽ 3$ .

[4]

Write down the coordinates of the lowest point of the graph.

[1]

Write down the equation of the line of symmetry of the graph.

[1]

Use your graph to solve the equation $(x + 3) (x - 2) = 3$ .

[2]

Beth thinks of a positive number, $n$ . She squares $n$ then subtracts 55. The answer is 9. Work out the value of $n$ .

[2]

The diagram shows a point $P$ and three triangles, $A$ , $B$ and $C$ , on a $1 {cm}^{2}$ grid.

Find the area of triangle $B$ .

[1]

b(i)

Write down the coordinates of point $P$ .

[1]

b(ii)

Work out the coordinates of point $P$ after a translation by the vector $(\begin{array}{c} - 20 \\ 12 \end{array})$ .

[1]

Draw the image of triangle $A$ after a reflection in the line $y = - 1$ .

[2]

d(i)

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

[3]

d(ii)

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

[3]

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of $\frac{17.8 + 10.3}{5.5}$ .

[2]

Find the highest common factor (HCF) of 66 and 110.

[2]

$P$ is a prime number. Write down the value of $P$ that satisfies the inequality $13 < P < 19$ .

[1]

Write down the inequality represented on the number line.

[2]

Use set notation to describe the shaded region.

[1]

Work out $2 \frac{7}{9} \times 1 \frac{1}{5}$ . Give your answer as a mixed number in its simplest form.

[3]

The mass, $m kg$ , of a stone is $3.2 kg$ , correct to the nearest $100 g$ . Complete this statement about the value of $m$ . .......................................... $⩽ m <$ ..........................................

[2]

Factorise. $9 x - 6 x y$

[2]

Expand and simplify. $(2 x + 3) (x - 4)$

[2]

Solve the simultaneous equations. $\begin{aligned} 5 x + 2 y & = 3 \\ 3 x + 4 y & = 27 \end{aligned}$

[3]

The diagram shows a shape made from two different semicircles, with the same centre. The radius of the large semicircle is $7 cm$ . The radius of the small semicircle is $4 cm$ . Work out the perimeter of the shape. Give your answer in terms of $π$ .

[3]

Mark scheme

0580/12 · May/June 2025

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1 · 1 mark

1 mark
16 062

2a · 1 mark

1 mark
0.75

2b · 1 mark

1 mark
75

3a · 1 mark

1 mark
6

3b · 1 mark

1 mark
1000 cao

4a · 1 mark

1 mark
83

4b · 1 mark

1 mark
ruled perpendicular line through *P*

5 · 1 mark

1 mark
70

6 · 1 mark

1 mark
14 squares shaded

7a · 1 mark

1 mark
3

7b · 1 mark

1 mark
$\frac{1}{8}$ cao

8a · 1 mark

1 mark
$- 12 + 4 \div (2 - 3) = - 16$

8b · 1 mark

1 mark
$- 3 - (4 + 5 - 7) = - 5$

9 · 2 marks

2 marks
$\frac{13}{24} \frac{5}{8} \frac{2}{3} \frac{3}{4} \frac{11}{12}$

10a · 3 marks

3 marks
Fully correct net

10b · 2 marks

B1
30
B1
cm $^{3}$

11a · 1 mark

1 mark
2

11b · 1 mark

1 mark
7

11c · 1 mark

1 mark
2.5 or $2 \frac{1}{2}$

11d · 2 marks

2 marks
3

12 · 2 marks

M1
$85 \times 99$ $85 \times 100 - 85$ $8500 - 85$
A1
8415

13a · 1 mark

1 mark
rhombus

13b · 2 marks

2 marks
two properties stated that are better than any applying to all quadrilaterals.

13c · 3 marks

3 marks
A correct drawing of a trapezium with perpendicular height 3 cm and parallel sides 4 cm and 6 cm

14a · 3 marks

3 marks
[6], 0, [−4], -6, -6, [−4], 0, 6

14b · 4 marks

4 marks
Correct curve

14c · 1 mark

1 mark
( $- 0.5$ , $k$ ) where $- 6.6 ⩽ k < - 6$

14d · 1 mark

1 mark
$x = - 0.5$ oe

14e · 2 marks

2 marks
$- 3.6$ to $- 3.4$ $2.4$ to $2.6$

15 · 2 marks

2 marks
8

16a · 1 mark

1 mark
6

16b(i) · 1 mark

1 mark
4, –3

16b(ii) · 1 mark

1 mark
–16, 9

16c · 2 marks

2 marks
Triangle drawn with coordinates $(1, - 2)$ , $(2, - 2)$ and $(2, - 5)$

16d(i) · 3 marks

B1
Enlargement
B1
[scale factor] 2
B1
[centre] (–1, 0)

16d(ii) · 3 marks

B1
Rotation
B1
90° clockwise
B1
[centre] (2, 3)

17 · 2 marks

M1
$\frac{20 + 10}{6}$ nfww
A1
5 nfww

18 · 2 marks

2 marks
22

19a · 1 mark

1 mark
17

19b · 2 marks

2 marks
$- 2 ⩽ x < 7$ final answer

20 · 1 mark

1 mark
$J \cup K$

21 · 3 marks

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

22 · 2 marks

2 marks
3.15 3.25

23a · 2 marks

2 marks
$3 x (3 - 2 y)$ final answer

23b · 2 marks

2 marks
$2 x^{2} - 5 x - 12$ final answer

24 · 3 marks

3 marks
[ $x =$ ] $- 3$ [ $y =$ ] 9 nfww

25 · 3 marks

3 marks
$11 π + 6$ final answer

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