IGCSE Mathematics - International (0607) — May–June 2025, Paper 23

23 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 · Number - order of operations

Work out. 2 - 5 x 3 + 7

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Question 2 · 3 marks · Number - types of number

This is a list of numbers. 20 21 22 23 24 25 26 27 From the list write down the square number.

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Question 3 · 2 marks · Algebra - simplifying expressions

Simplify. 2x - 3y - x - 2y

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Question 4 · 3 marks · Geometry - angles in polygons

A regular polygon has 20 sides. Work out the size of one interior angle of the polygon.

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Question 5 · 4 marks · Number - ratio and proportion

Ganpreet and Rahul share $240 in the ratio 7 : 5. Show that the value of Rahul's share is $100.

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Question 6 · 5 marks · Algebra - simultaneous equations

The cost of a bar of chocolate is $c. The cost of a packet of sweets is $p. The total cost of 5 bars of chocolate and 2 packets of sweets is $13. The total cost of 7 bars of…

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Question 7 · 3 marks · Number - fractions

Work out 5 1/3 ÷ 1 3/5. Give your answer as a mixed number in its simplest form.

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Question 8 · 5 marks · Geometry - transformations

The diagram shows triangle T with vertices at (2, 1), (4, 1) and (4, 2) on a coordinate grid, and triangle P drawn to the left of the y-axis. Translate triangle T by the vector…

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Question 9 · 2 marks · Number - indices

Find the value of 16^(-3/2).

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Question 10 · 4 marks · Geometry - circle theorems

A, B, C, D and E lie on the circle. The diagram (not to scale) shows the cyclic pentagon ABCDE inscribed in a circle, with TU a tangent to the circle at C. Angle ABD = 70° (marked…

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Question 11 · 5 marks · Number - surds

Simplify. sqrt(27) - 2 sqrt(75)

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Question 12 · 4 marks · Geometry - mensuration (sectors)

The diagram (not to scale) shows a sector of a circle with radius 8 cm. The area of the sector is 8π cm^2. The perimeter of the sector is (a + bπ) cm. Find the value of a and the…

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Question 13 · 2 marks · Number - standard form

Work out. 4.9 x 10^199 + 4.9 x 10^197

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Question 14 · 5 marks · Trigonometry - trigonometric functions

f(x) = cos x, 0° <= x <= 360° Write down the exact value of f(0).

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Question 15 · 2 marks · Algebra - indices

y^(2k) x y^3 = 1/y Find the value of k.

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Question 16 · 2 marks · Algebra - changing the subject of a formula

Rearrange 4y - 3x = 1 - py to write y in terms of p and x.

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Question 17 · 3 marks · Algebra - quadratic functions and completing the square

The diagram (not to scale) shows a sketch of the graph of y = x^2 + ax + b. The point (1, -2) is a minimum. The curve crosses the y-axis at -1. Find the value of a and the value…

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Question 18 · 3 marks · Algebra - inequalities

Solve. 3(2x + 1) 5 - 4x

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Question 19 · 2 marks · Algebra - logarithms

Solve. Give each answer as an exact value. 2^x = 5

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Question 20 · 3 marks · Algebra - sequences

These are the first 5 terms of a sequence. 3 6 12 24 48 Find the next term of the sequence.

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Question 21 · 4 marks · Geometry - Pythagoras in 3D

The diagram (not to scale) shows a triangular prism. The cross-section is a right-angled triangle EAB. AE = 3 cm, AB = 4 cm and BC = 12 cm. Work out the length of BF.

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Question 22 · 2 marks · Algebra - algebraic fractions

Write as a single fraction in its simplest form. 2 - 3/(x - 2)

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Question 23 · 6 marks · Probability - combined events

Bag A contains 4 white balls and 3 black balls. Bag B contains 5 white balls and 4 black balls. Ranjit picks a ball at random from Bag A and replaces it. Ranjit also picks a ball…

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