IGCSE Mathematics - International (0607) — May–June 2025, Paper 22

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

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Question 1 · 2 marks · Number - powers and indices

Work out (0.02)^3.

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Question 2 · 2 marks · Number - prime numbers

This is a list of numbers. 31 33 35 37 39 41 From this list, write down all the prime numbers.

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Question 3 · 1 mark · Number - fractions

Write the fraction 24/64 in its lowest terms.

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Question 4 · 1 mark · Mensuration - units and conversions

Convert 250 cm^3 into m^3.

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Question 5 · 1 mark · Geometry - properties of shapes

A quadrilateral has exactly one pair of parallel sides. Write down the mathematical name of this quadrilateral.

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Question 6 · 4 marks · Number - ratio and proportion

Share 120 in the ratio 2 : 3.

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Question 7 · 3 marks · Statistics - frequency tables

At a school, 50 students are asked their favourite car colour. The table shows the results. Colour Red Blue White Silver Black --- --- --- --- --- --- Frequency 7 x 15 16 x Find…

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Question 8 · 7 marks · Algebra - expanding brackets

Expand and simplify. 5(2x - 1) - 3(3 + 4x)

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Question 9 · 3 marks · Statistics - mode from frequency table

The table shows the marks scored by each of 60 students in a science test. Mark 0 1 2 3 4 5 6 7 8 9 10 --- --- --- --- --- --- --- --- --- --- --- --- Frequency 2 14 5 3 7 6 5 1 7…

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Question 10 · 2 marks · Sets - set notation and Venn diagrams

Use set notation to describe each of the shaded regions. The first Venn diagram (universal set U) shows two overlapping sets A and B. The whole rectangle is shaded except for set…

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Question 11 · 2 marks · Algebra - laws of indices

Simplify. (5x)^3 / (1/x)^4

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Question 12 · 3 marks · Mensuration - volume of solids

In this question all lengths are in centimetres. A solid is made by joining a cuboid to a pyramid (NOT TO SCALE). The diagram shows a square-based cuboid with a square-based…

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Question 13 · 5 marks · Trigonometry - right-angled triangles

The diagram shows two right-angled triangles joined along a common vertical side of length x cm (NOT TO SCALE). In the left triangle, the hypotenuse is 10 cm, the angle at the…

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Question 14 · 2 marks · Algebra - LCM of algebraic expressions

Find the lowest common multiple (LCM) of these expressions. 2x^3 y^4 3x^2 z^3 4y^2 z

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Question 15 · 4 marks · Probability - combined events

An unbiased die is numbered 2, 3, 4, 4, 5, 6. Zaira rolls the die three times. Find the probability that Zaira rolls an odd number two or more times.

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Question 16 · 6 marks · Algebra - sequences (linear)

Find the next term and the nth term in the sequence. 12, 14, 16, 18, 20, ....

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Question 17 · 5 marks · Geometry - circle theorems

The diagram shows a circle, centre O (NOT TO SCALE). AOBP is a straight line. PC is a tangent to the circle. Points A, D, C and B lie on the circle, with D and C on the upper arc.…

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Question 18 · 3 marks · Algebra - forming and rearranging expressions

Apples cost $2.50 per kilogram. The total cost of x kg of apples and y kg of pears is $10. Find the cost of 1 kg of pears. Give your answer in terms of x and y.

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Question 19 · 6 marks · Functions - evaluating functions

f(x) = 1/(5x - 4), x != 0.8 Find f(2).

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Question 20 · 5 marks · Number - surds

Rationalise the denominator. (sqrt(3) - sqrt(2)) / (sqrt(3) + sqrt(2))

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Question 21 · 8 marks · Coordinate geometry - equation of a line

Line L is perpendicular to the line with equation y = 2x + 1. Line L passes through the point (3, 12). Find the equation of the line L.

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