Learn Extracted exam questions IGCSE Mathematics 0580 Mathematics June 2025 Question Paper 12
0580 Mathematics June 2025 Question Paper 12
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2 Write three-quarters as
(a) a decimal
[1]
(b) a percentage % [1]
(a) a decimal ................................................. [1]
(b) a percentage. ..............................................% [1]
1 Write the number sixteen thousand and sixty-two in figures [1]
3 Write down the value of
(a) 36
[1]
(b) 103 [1]
36 (a) ................................................. [1]
(b) 103. ................................................. [1]
6
Shade 5 2 of the rectangle. [1] 1
4 The diagram shows a line AB and a point P. B P A
(a) Measure the length of line AB in millimetres mm [1]
(b) Draw a line through point P that is perpendicular to line AB. [1]
(a) Measure the length of line AB in millimetres. .......................................... mm [1]
(b) Draw a line through point P that is perpendicular to line AB. [1]
5 Complete this statement.
10 weeks is days. [1] , ,
7 (a) Find the value of the reciprocal of 3 1 [1]
(b) Write 2 3
- as a fraction [1]
(a) Find the value of the reciprocal of 3 7 ................................................. [1] - as a fraction.
(b) Write 2 3 ................................................. [1]
8 Put one pair of brackets into each calculation to make it correct.
(a) 12 4 2 3 16 '
=-
[1]
(b) 3 4 5 7 5
=- [1]
' + - - 12 16 2 3 4 =- [1] (a) - - + - 3 4 5 5 7 =- [1]
-
-
-
- 3 4 5 5 7 =- [1] (b)
-
-
9 Write these fractions in order, starting with the smallest. 8 5 12 11 3 2 4 3 24 13
1 1 1 1 [2]
smallest
10 A cuboid has length 5 cm, width 2 cm and height 3 cm.
(a) Draw a net of the cuboid on the 1 cm2 grid.
[3]
(b) Work out the volume of the cuboid.
Give the units of your answer [2] , ,
(a) Draw a net of the cuboid on the 1 cm2 grid. [3]
(b) Work out the volume of the cuboid. Give the units of your answer. .......................................... ................. [2]
11 0 2 2 3 4 7
For these six numbers
(a) write down the mode
[1]
(b) work out the range
[1] .
(c) work out the median
[1]
(d) work out the mean [2] 12 Tim has a method for multiplying a number by 99.
He shows his method for 53 99
. 53 100 53 5300 53 5247
=
=
= 53 99
Work out 85 99
using Tim’s method [2] , ,
(a) write down the mode ................................................. [1]
(b) work out the range ................................................. [1] .
(c) work out the median ................................................. [1]
(d) work out the mean. ................................................. [2] 12 Tim has a method for multiplying a number by 99. He shows his method for 53 . 99 # 53 99 # - 100 53 53 = # - 53 5300 = 5247 = using Tim’s method. 99 Work out 85 # ................................................. [2]
13 (a) 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]
(b) Write down two geometrical properties of a rectangle. 1 2 [2]
(c)
The parallel sides of a trapezium have lengths 6 cm and 4 cm.
The area of the trapezium is 15 cm2.
On the 1 cm2 grid, draw a trapezium with these lengths and area.
[3] , ,
13 (a) 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]
(b) Write down two geometrical properties of a rectangle. 1. ........................................................................................................................................................ 2. ........................................................................................................................................................ [2]
(c) The parallel sides of a trapezium have lengths 6 cm and 4 cm. The area of the trapezium is 15 cm2. On the 1 cm2 grid, draw a trapezium with these lengths and area. [3]
14 (a) Complete the table of values for ( )( ) y x x 3 2
. x -4 -3 -2 -1 0 1 2 3 y 6 -4 -4
[3]
(b) On the grid, draw the graph of ( )( ) y x x 3 2
- for x 4 3 G G
.
- 4 -7 -6 -5
- 4 -3 -2 -1 1 2 3 4 5 6 -3 -2 -1 0 1 2 3 x y [4] , ,
(c) Write down the coordinates of the lowest point of the graph.
( , ) [1]
(d) Write down the equation of the line of symmetry of the graph [1]
(e) Use your graph to solve the equation ( )( ) x x 3 2 3 +
= .
x = or x = [2] 15 Beth thinks of a positive number, n.
She squares n then subtracts 55.
The answer is 9.
Work out the value of n.
n = [2] , ,
( ) )( + - 2 3 = x x y . 14 (a) Complete the table of values for 0 1 2 3 x -1 -2 -3 -4 6 y -4 -4 [3] ( ) )( + - 2 3 = x x y for - . 3 4 G G x
( ) )( + - 2 3 = x x y for - . 3 4 G G x (b) On the grid, draw the graph of y 6 5 4 3 2 1 x 0 - 4 -1 -2 1 2 3 -3 -1 -2 -3 - 4 -5 -6 -7 [4] , ,
(c) Write down the coordinates of the lowest point of the graph. ( ...................... , ...................... ) [1]
(d) Write down the equation of the line of symmetry of the graph. ................................................. [1]
(e) Use your graph to solve the equation ( ) )( + - 2 3 3 = . x x x = .......................................... or x = .......................................... [2] 15 Beth thinks of a positive number, n. She squares n then subtracts 55. The answer is 9. Work out the value of n. n = ................................................ [2]
16 The diagram shows a point P and three triangles, A, B and C, on a 1 cm2 grid. C A B P 0 x y
- 4
- 4
- 5
- 6 -3 -2 -1 1 2 3 4 5 6 7 -3 -2 -1 1 2 3 4 5 6
(a) Find the area of triangle B cm2 [1]
(b) (i) Write down the coordinates of point P.
( , ) [1]
(ii) Work out the coordinates of point P after a translation by the vector 20 12
e o.
( , ) [1]
(c) Draw the image of triangle A after a reflection in the line y 1 =- . [2]
(d) Describe fully the single transformation that maps
(i) triangle A onto triangle B [3]
(ii) triangle A onto triangle C [3] , ,
(a) Find the area of triangle B. .......................................... cm2 [1]
(b) (i) Write down the coordinates of point P. ( ...................... , ...................... ) [1] - 20 e o.
e o. (ii) Work out the coordinates of point P after a translation by the vector 12 ( ...................... , ...................... ) [1] , ,
(c) Draw the image of triangle A after a reflection in the line y 1 =- . [2]
(d) Describe fully the single transformation that maps (i) triangle A onto triangle B ............................................................................................................................................. ............................................................................................................................................. [3]
(ii) triangle A onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3]
17 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of . . . 17 8 10 3 5 5 + [2] 18 Find the highest common factor (HCF) of 66 and 110 [2] 19 (a) P is a prime number.
Write down the value of P that satisfies the inequality P 13 19 1 1 .
P = [1]
(b) Write down the inequality represented on the number line. x 8 7 6 5 4 3 2 1 0 -1 -2 -3
[2] , ,
20 J K %
Use set notation to describe the shaded region [1] 21 Work out 2 9 7 1 1 5
.
Give your answer as a mixed number in its simplest form [3] 22 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 1 G [2] , ,
23 (a) Factorise.
x
xy 9 6
[2]
(b) Expand and simplify.
( )( ) x x 2 3 4 +
[2] 24 Solve the simultaneous equations.
x y x y 5 2 3 3 4 27 +
=
x = y = [3] , ,
23 (a) Factorise. x - 6 9 xy ................................................. [2]
(b) Expand and simplify. ( ) )( + - 2 3 4 x x ................................................. [2] 24 Solve the simultaneous equations. + 2 3 5 = x y + 27 3 4 = x y x = ................................................ y = ................................................ [3]