IGCSE Mathematics - International (0607) — May–June 2025, Paper 33

17 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 - place value and ordering

Write the number 15 036 in words.

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Question 2 · 3 marks · Number - fractions, decimals and percentages

Write 7/15 as a percentage. Give your answer correct to 2 decimal places.

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Question 3 · 3 marks · Geometry - vocabulary of the circle

X and Y are points on a circle, centre O. Complete each sentence with a mathematical term. OX is a .................... of the circle. XY is a .................... of the circle.

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Question 4 · 4 marks · Number - the four operations

These are the ingredients needed to make 8 biscuits: 70 g butter, 90 g sugar, 1 egg, 140 g flour, 40 g chocolate. An egg has a mass of 45 g. Work out the total mass of the…

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Question 5 · 3 marks · Algebra - substitution into formulae

A company uses this formula to work out the number of people who can safely work in an office. N = (L × W) / 15 L is the length of the office in metres. W is the width of the…

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Question 6 · 2 marks · Number - percentages

A shirt costs $45. The cost of the shirt is increased by 7%. Work out the increase in the cost of the shirt.

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Question 7 · 4 marks · Geometry - angles on a straight line and parallel lines

In the diagram, ABC is a straight line. AP is parallel to BQ. Angle PBQ = 70° and angle QBC = 55°. At P the angle is marked y°. At B, angle ABP is marked x°. Work out the value of…

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Question 8 · 5 marks · Number - powers and roots

Work out. 17^3

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Question 9 · 5 marks · Algebra - solving linear equations

Solve. x/2 - 1 = 5

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Question 10 · 4 marks · Mensuration - area and unit conversion

Geeta's garden is a rectangle 15.2 m long and 8.5 m wide. She puts 50 g of grass seed on each square metre of the garden. Work out the mass of grass seed she uses. Give your…

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Question 11 · 3 marks · Probability - relative frequency and bias

A 6-sided die, numbered 1 to 6, is thrown 400 times. The frequencies are: 1 → 100, 2 → 20, 3 → 80, 4 → 70, 5 → 110, 6 → 20. Give reasons why this is a biased die.

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Question 12 · 3 marks · Mensuration - volume of a cylinder

This cylinder has diameter 6 cm and length 11 cm. Work out the volume of the cylinder. Give the units of your answer.

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Question 13 · 3 marks · Sets - set notation and Venn diagrams

The Venn diagram shows the number of elements in each region: A only contains 15, A ∩ B contains 7, B only contains 11, and outside both A and B (inside U) contains 3. Find n(A').

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Question 14 · 2 marks · Trigonometry - right-angled triangles

A right-angled triangle has a horizontal base of 4.4 m and a vertical right-hand side of 2.5 m, with the right angle at the bottom-right. The angle at the bottom-left vertex…

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Question 15 · 2 marks · Statistics - mean of grouped data

The table shows scores grouped into class intervals, with mid-values and frequencies. Score (x) Mid-value Frequency --- --- --- 0 < x ≤ 10 5 24 10 < x ≤ 20 81 20 < x ≤ 30 195…

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Question 16 · 4 marks · Number - simple interest

Mike invests $2500 in an account paying simple interest at a rate of R% per year. At the end of 5 years, the value of his investment is $2800. Work out the value of R.

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Question 17 · 8 marks · Graphs - sketching cubic functions

On the diagram, sketch the graph of y = x^3 + 6x^2 + 2x - 20 for values of x between -6 and 3.

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← May–June 2025 Paper 41 · May–June 2025 Paper 32 →

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