IGCSE Mathematics (0980) — May–June 2025, Paper 42

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

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Question 1 · 1 mark · Geometry - properties of quadrilaterals and 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 quadrilateral.

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Question 2 · 1 mark · Geometry - nets and 3D solids

The diagram shows the net of a solid. The net consists of a central rectangle with a smaller rectangle attached above it and another below it, and a triangle attached to each of…

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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.

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Question 4 · 2 marks · Mensuration - area of a trapezium

ABCD is a trapezium (NOT TO SCALE). DC is the top parallel side of length 10 cm, and AB is the bottom parallel side of length 12 cm. The perpendicular height between the parallel…

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Question 5 · 1 mark · Number - currency conversion

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

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Question 6 · 3 marks · Mensuration - volume of a cone 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]

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Question 7 · 2 marks · Algebra - rearranging formulae

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

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Question 8 · 1 mark · Number - calculator use and order of operations

Calculate. (2.1^2 - 1.9) / 0.5

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Question 9 · 3 marks · Algebra - simultaneous linear equations

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

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Question 10 · 3 marks · Algebra - forming and solving linear 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…

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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.

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Question 12 · 2 marks · Number - bounds of measurement

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…

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Question 13 · 4 marks · Geometry - similar triangles (lengths)

Triangle ABC and triangle PQR are mathematically similar (NOT TO SCALE). In triangle ABC: AB = 9 cm, AC = 12 cm, BC = 16 cm, with the angles at B and C marked. In triangle PQR…

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Question 14 · 2 marks · Algebra - factorising by grouping

Factorise. 5x - 10 - ax + 2a

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Question 15 · 2 marks · Geometry - angles of regular polygons

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

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Question 16 · 4 marks · Probability - complementary events

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.

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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.

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Question 18 · 4 marks · Geometry - circle theorems (angles in the same segment, cyclic quadrilateral)

A, B, C, D and E lie on a circle (NOT TO SCALE). Chords are drawn joining these points. The angle at D in triangle/region marked z is z degrees. At E the angle marked x is x…

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Question 19 · 6 marks · Functions - evaluating a function

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

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Question 20 · 13 marks · Trigonometry - right-angled triangle (tangent)

The diagram shows a quadrilateral ABCD (NOT TO SCALE). CD = 10 m and DB = 12 m. Angle DBA = 90 degrees, angle CDB = 56 degrees and angle ADB = 34 degrees. D and B are joined; C is…

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Question 21 · 4 marks · Indices - laws of indices (multiplication)

Simplify. 3t^5 x 5t^3

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Question 22 · 5 marks · Probability - Venn diagrams

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

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Question 23 · 3 marks · Algebra - simplifying algebraic fractions (factorising)

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

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Question 24 · 8 marks · Algebra - forming equations from speed/time/distance ('show that')

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 =…

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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.

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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.

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Question 27 · 4 marks · Trigonometry - angle between a line and a plane (3D)

The diagram shows a cube ABCD as the base, with P a vertex of the top face directly above the vertex diagonally opposite A on the base (NOT TO SCALE). A and B are front base…

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