IGCSE Mathematics (0580) — May–June 2025, Paper 33

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

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Question 1 · 3 marks · Number - multiples, squares and cubes

Here is a list of numbers: 2 6 16 18 24 26 27 33 From this list, write down the number that is a multiple of 12.

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Question 2 · 1 mark · Geometry - symmetry

The diagram shows a grid of 6 columns by 4 rows of unit squares, with some squares shaded grey. The shaded squares form a pattern: in the top row the two end squares (columns 1…

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Question 3 · 1 mark · Number - order of operations

Put one pair of brackets into this calculation to make it correct. 80 ÷ 8 + 2 × 3 = 24

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Question 4 · 3 marks · Algebra - travel graphs

Tim drives home from work. The travel graph shows his journey. Write down the time Tim leaves work.

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Question 5 · 2 marks · Number - calculator use, powers and roots

Calculate. (2.8^5 − 0.3^2) / sqrt(5) Give your answer correct to 2 decimal places.

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Question 6 · 1 mark · Probability - probability scale

In a bag of counters, 6 of the counters are blue. The arrow on the probability scale shows the probability of picking a blue counter at random. The probability scale runs from 0…

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Question 7 · 1 mark · Number - time

The local time in Japan is 3 1/2 hours ahead of the local time in India. Find the time in Japan when it is 21 45 in India.

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Question 8 · 1 mark · Number - currency exchange

Mia changes $350 into euros. The exchange rate is $1 = 0.92 euros. Calculate the amount Mia receives.

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Question 9 · 4 marks · Geometry - angles, parallel lines

ABC is a straight line. BD is parallel to AE. Find the value of x. Give a geometrical reason for your answer.

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Question 10 · 2 marks · Algebra - linear equations

Solve. 4p + 11 = 25

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Question 11 · 4 marks · Algebra - expanding brackets and simplifying

Expand and simplify. 5(x − 2) + 3(x − 7)

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Question 12 · 5 marks · Statistics - bar charts

Kai opens his restaurant from Tuesday to Saturday each week. He counts the number of customers each day for two weeks. The bar chart shows some of the results. In week 1 there…

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Question 13 · 4 marks · Number - percentage change

In May a shop makes a profit of $542. In June the shop makes a profit of $600. Calculate the percentage increase in the profit from May to June.

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Question 14 · 3 marks · Number - simple interest

Meg invests $2500 at a rate of 4.6% per year simple interest. Calculate the total amount of her investment at the end of 3 years.

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Question 15 · 7 marks · Number - problem solving with rates

The table gives information about the costs of hiring bikes. Type of bike Cost for first day Cost for each extra day --- --- --- Road $25 $20 Mountain $40 $35 Electric $70 $50…

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Question 16 · 5 marks · Geometry - scale drawings

The scale drawing shows a path from S to P. The scale is 1 cm represents 2.5 km. Work out the actual distance between S and P.

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Question 17 · 6 marks · Geometry - transformations (translation)

Sue describes the single transformation that maps shape A onto shape B as a translation by the vector (7 over 1). Explain why Sue is incorrect.

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Question 18 · 2 marks · Geometry - circle terminology

The diagram shows a circle with two points C and D on the circle joined by a straight line CD (a line drawn across the circle, not through the centre). Points C and D lie on the…

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Question 19 · 6 marks · Algebra - tables of values for reciprocal graphs

Complete the table of values for y = 20/x. x 1 2 3 4 5 --- --- --- --- --- --- y 20 10 4

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Question 20 · 3 marks · Probability - relative frequency

A spinner is numbered 1, 2, 3, 4 and 5. Rinesh spins the spinner many times. He works out the relative frequency that the spinner lands on each number. Number 1 2 3 4 5 --- ---…

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Question 21 · 8 marks · Number - standard form, ordering

These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A = 35 800 B = 7.8 × 10^2 C = 1.5 × 10^6 D = 535 E = 2…

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Question 22 · 4 marks · Mensuration - volume of a cylinder

The diagram shows a solid cylinder with height 10 cm. The volume of the cylinder is 478 cm^3. Find the radius of the cylinder.

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Question 23 · 2 marks · Geometry - Pythagoras' theorem

The diagram shows a right-angled triangle (not to scale). The top side is 35 cm, the right-hand vertical side is 22 cm, and the hypotenuse (the sloping side from the top-left…

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Question 24 · 2 marks · Trigonometry - right-angled triangles

The diagram shows a right-angled triangle (not to scale). The angle at the top vertex is 52°, the vertical right-hand side (adjacent to the 52° angle) is 18.4 cm, and the…

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