IGCSE Mathematics (0580) — May–June 2025, Paper 23

24 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 · Probability

The probability of picking a green pen from a box is 0.17. Find the probability of not picking a green pen from the box.

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Question 2 · 4 marks · Geometry - angle properties

The diagram (not to scale) shows quadrilateral ABCD with various lines extended. ABCD is a quadrilateral. CDE is a straight line. AFB is an isosceles triangle. At vertex A, angle…

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Question 3 · 2 marks · Geometry - symmetry of solids

The diagram shows a pyramid ABCDE with a square base. M is the centre of the square base. E is vertically above M. Write down the number of planes of symmetry of this pyramid.

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Question 4 · 1 mark · Statistics - correlation

The number of ice creams sold increases as the temperature rises. What type of correlation does this statement describe?

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Question 5 · 7 marks · Transformations

The grid shows triangle A (small shaded triangle) and triangle B. Describe fully the single transformation that maps triangle A onto triangle B.

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Question 6 · 3 marks · Statistics - stem-and-leaf diagrams

There are 15 giraffes in a group. The table gives information about the heights of the 15 giraffes. Information --- One giraffe has a height of 2.6 m No giraffe is shorter than…

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Question 7 · 5 marks · Number - fractions

Work out. 5/6 − 7/12 Give your answer as a fraction in its simplest form.

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Question 8 · 4 marks · Number - prime factors

Write 42 as a product of its prime factors.

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Question 9 · 5 marks · Algebra - quadratic equations

Solve. 5x^2 = 12 − 17x

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Question 10 · 4 marks · Algebra - simultaneous equations

Solve the simultaneous equations. 4x − 5y = 13 3x − 2y = 8

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Question 11 · 4 marks · Probability - possibility diagrams

Angela picks a number at random from the numbers 1, 2 and 3. She then picks a number at random from the numbers 4, 5 and 6. She adds the two numbers to find the total. Complete…

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Question 12 · 5 marks · Vectors

v = (2, −3) as a column vector (top component 2, bottom component −3). Find 5v.

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Question 13 · 4 marks · Geometry - circle theorems

A, B, C and D are points on a circle. EF is a tangent to the circle at A. AB is parallel to DC. Find angle DCB, giving a geometrical reason.

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

Find the lowest common multiple (LCM) of 15xy^3 and 18x^4y.

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Question 15 · 6 marks · Number - surds

Simplify. sqrt(27) + sqrt(12)

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Question 16 · 3 marks · Number - recurring decimals to fractions

Write 0.3̇2̇8̇ as a fraction in its simplest form. (The recurring decimal is 0.3 with 2 and 8 recurring, i.e. 0.3282828...)

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Question 17 · 3 marks · Geometry - similar solids

Solid A is mathematically similar to solid B. The diagram (NOT TO SCALE) shows two similar triangular prisms: Solid A is the smaller, with height 7 cm; Solid B is the larger, with…

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Question 18 · 4 marks · Algebra - changing the subject

Make t the subject of the formula. 2 = m(1 − t) / (pt)

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Question 19 · 3 marks · Algebra - simplifying algebraic fractions

Simplify. (7x − x^2) / (49 − x^2)

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Question 20 · 3 marks · Geometry - arc length

The diagram (NOT TO SCALE) shows a sector of a circle, centre O. The radius of the circle is 6 cm. The minor sector angle AOB is 40° (A above B, both on the circle). Calculate the…

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Question 21 · 6 marks · Calculus - differentiation

Differentiate x^3 − 3x^2 + 1.

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Question 22 · 8 marks · Algebra - functions

f(x) = 2x + 5, g(x) = x − 4, h(x) = 5^x. Find f(3).

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Question 23 · 6 marks · Trigonometry - exact values

Write down the value of cos 90°.

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Question 24 · 7 marks · Coordinate geometry - midpoint

A is the point (a, 12) and B is the point (b, 27). Find the y-coordinate of the midpoint of AB.

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