IGCSE Mathematics (0580) — May–June 2025, Paper 42

27 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

Start with Question 1 →
Question 1 · 1 mark · Geometry - properties of shapes / symmetry

A quadrilateral has these properties: - the diagonals are the only lines of symmetry - it has rotational symmetry of order 2. Write down the mathematical name of this…

Answer this question and get it marked →
Question 2 · 1 mark · Geometry - nets and 3D solids

The diagram shows the net of a solid. The net consists of a central rectangle (the base) with a square flap above it and another rectangle below it, and two triangular flaps…

Answer this question and get it marked →
Question 3 · 3 marks · Number - ratio and proportion

Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B.

Answer this question and get it marked →
Question 4 · 2 marks · Mensuration - area

The diagram shows a trapezium ABCD (not to scale). DC = 10 cm is the top parallel side and AB = 12 cm is the bottom parallel side. The perpendicular distance between the two…

Answer this question and get it marked →
Question 5 · 1 mark · Number - currency conversion

Scott changes $300 into pounds (£). The exchange rate is £1 = $1.20. Calculate the amount Scott receives.

Answer this question and get it marked →
Question 6 · 3 marks · Mensuration - volume and density

A solid wooden cone has base radius 4 cm and height 12 cm. The density of the wood is 0.74 g/cm^3. Calculate the mass of the cone. [Density = Mass ÷ Volume]

Answer this question and get it marked →
Question 7 · 2 marks · Algebra - rearranging formulae

y = mx + c Rearrange the formula to make m the subject.

Answer this question and get it marked →
Question 8 · 1 mark · Number - calculator use / order of operations

Calculate. (2.1^2 - 1.9) / 0.5

Answer this question and get it marked →
Question 9 · 3 marks · Algebra - simultaneous equations

Solve the simultaneous equations. You must show all your working. 2w - 3y = 11 3w + y = 11

Answer this question and get it marked →
Question 10 · 3 marks · Algebra - forming and solving equations

A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $n. The cost of a child ticket is $(n - 10). The total cost of the tickets is $277.50. Find the…

Answer this question and get it marked →
Question 11 · 2 marks · Number - reverse percentages

In a sale, the original price of a shirt is reduced by 15%. The sale price of the shirt is $23.63. Find the original price of the shirt.

Answer this question and get it marked →
Question 12 · 2 marks · Number - bounds

The length of a rectangle is 16 cm, correct to the nearest centimetre. The width of the rectangle is 14 cm, correct to the nearest centimetre. Calculate the lower bound of the…

Answer this question and get it marked →
Question 13 · 4 marks · Geometry - similar triangles

The diagram shows two mathematically similar triangles (not to scale). Triangle ABC has AB = 9 cm, AC = 12 cm and BC = 16 cm, with equal base angles marked at B and C. Triangle…

Answer this question and get it marked →
Question 14 · 2 marks · Algebra - factorising by grouping

Factorise. 5x - 10 - ax + 2a

Answer this question and get it marked →
Question 15 · 2 marks · Geometry - angles in polygons

The interior angle of a regular polygon is 172°. Find the number of sides of this polygon.

Answer this question and get it marked →
Question 16 · 4 marks · Probability

On any day, the probability that the weather will be sunny is 0.7. Find the probability that on any day the weather will not be sunny.

Answer this question and get it marked →
Question 17 · 10 marks · Number - simple interest

Alex invests $400 at a rate of 2.3% per year simple interest. Find the total amount Alex has at the end of 5 years.

Answer this question and get it marked →
Question 18 · 4 marks · Geometry - circle theorems

The diagram shows five points A, B, C, D and E lying on a circle (not to scale), with chords drawn between them. At vertex C, angle DCE = 26° and angle ECB = 52°. At vertex E,…

Answer this question and get it marked →
Question 19 · 6 marks · Algebra - functions

f(x) = x + 1 g(x) = 5 - 2x h(x) = 2^x Find f(-3).

Answer this question and get it marked →
Question 20 · 13 marks · Trigonometry - right-angled triangles

The diagram shows a quadrilateral ABCD. CD = 10 m and DB = 12 m. Angle DBA = 90°, angle CDB = 56° and angle ADB = 34°. Calculate the length of AB.

Answer this question and get it marked →
Question 21 · 4 marks · Algebra - laws of indices

Simplify. 3t^5 × 5t^3

Answer this question and get it marked →
Question 22 · 5 marks · Probability - Venn diagrams

The Venn diagram shows information about the 33 students in a class. E = {number of students in a class}, G = {number of students who study geography}, H = {number of students who…

Answer this question and get it marked →
Question 23 · 3 marks · Algebra - algebraic fractions / factorising

Simplify. (h^2 + 4h) / (h^2 - 16)

Answer this question and get it marked →
Question 24 · 8 marks · Algebra - forming equations / speed-distance-time

Ahmed walks 2 km at a speed of x km/h. He then walks a further 3 km at a speed of (x + 1) km/h. The total time he takes to walk the 5 km is 1 1/4 hours. Show that 5x^2 - 15x - 8 =…

Answer this question and get it marked →
Question 25 · 5 marks · Coordinate geometry - perpendicular bisector

P is the point (8, 0) and Q is the point (20, 6). Find the equation of the perpendicular bisector of PQ. Give your answer in the form y = mx + c.

Answer this question and get it marked →
Question 26 · 2 marks · Calculus - differentiation of powers

y = ax^11 + 3x^b dy/dx = 44x^10 + 18x^c Find the values of a, b and c.

Answer this question and get it marked →
Question 27 · 4 marks · Trigonometry - 3D / angle between line and plane

The diagram shows a cube (not to scale). The base is ABCD and the top vertex above C is P; the cube has edges of equal length and AP is a space diagonal from base vertex A to the…

Answer this question and get it marked →

← May–June 2025 Paper 43 · May–June 2025 Paper 41 →

← All IGCSE Mathematics (0580) past papers