IGCSE Mathematics - International (0607) — May–June 2025, Paper 21

22 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 - types of number

This is a list of numbers. 3.142 sqrt(125) 125 81 7 2/3 From this list write down a cube number.

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Question 2 · 2 marks · Number - approximation and rounding

Write 0.003 094 8 correct to 3 significant figures.

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Question 3 · 2 marks · Geometry - angles and triangles

The diagram shows triangle ABD with point C on the straight line BCD. Lines BA, AD and AC are drawn. The angle ADC at D is marked 68 degrees. In the diagram AC = BC = AD (shown by…

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Question 4 · 2 marks · Geometry - symmetry

A regular pentagon is shown. Draw all the lines of symmetry of this regular pentagon.

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Question 5 · 3 marks · Number - fractions

Work out 1 3/7 x 4 2/3. Give your answer as a mixed number in its simplest form.

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Question 6 · 7 marks · Geometry - transformations

The grid shows triangles A, B and C. Describe fully the single transformation that maps triangle A onto triangle B.

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Question 7 · 2 marks · Number - ratio and proportion

The ratio a : b = 7 : 12. The ratio b : c = 8 : 5. Find the ratio a : b : c in its simplest form.

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Question 8 · 2 marks · Statistics - mean

The mean of 9 numbers is 8. When an extra number is included, the mean is 7.7. Find the extra number.

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Question 9 · 4 marks · Algebra - factorisation

Factorise. 4x^2 y^3 - 6xy^4

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Question 10 · 2 marks · Number - standard form

Work out 4 x 10^18 + 3.2 x 10^17. Give your answer in standard form.

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Question 11 · 2 marks · Algebra - inequalities

Solve. 7 - 3x 2x - 8

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Question 12 · 3 marks · Number - HCF and LCM, indices

P = 2^3 x 3^a x 5^b x 7 Q = 2 x 3^5 x 7^c The highest common factor (HCF) of P and Q is 2 x 3^4 x 7. The lowest common multiple (LCM) of P and Q is 2^3 x 3^5 x 5^2 x 7. Find the…

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Question 13 · 5 marks · Geometry - circle theorems

A, B, C, D, E and F are points on a circle, centre O. Angle FAB = 75 degrees and angle BCD = 113 degrees. Find angle BFE.

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Question 14 · 3 marks · Algebra - sequences

These are the first 5 terms of a sequence. 1 7 17 31 49 Find the next term of the sequence.

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Question 15 · 3 marks · Algebra - quadratic equations

Solve. 2x^2 - 5x - 3 = 0

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Question 16 · 5 marks · Coordinate geometry - straight line equations

A is the point (-3, 2) and B is the point (5, -8). Find the equation of the perpendicular bisector of AB.

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Question 17 · 4 marks · Statistics - cumulative frequency

The cumulative frequency diagram shows the heights of 120 plants. Use the cumulative frequency diagram to estimate the interquartile range.

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Question 18 · 6 marks · Algebra - functions

f(x) = 3x - 2 g(x) = 5 - x Find f(-4).

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Question 19 · 3 marks · Algebra - expanding brackets

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

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Question 20 · 5 marks · Trigonometry - trigonometric equations

Solve tan x = sqrt(3) for values of x between 0 degrees and 360 degrees.

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Question 21 · 4 marks · Algebra - variation (inverse proportion)

y is inversely proportional to x^3. y = 1 when x = 2. Find y in terms of x.

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Question 22 · 4 marks · Number - surds

Simplify. sqrt(120) x sqrt(27)

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