IGCSE Mathematics (0580) — May–June 2025, Paper 41

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 · Algebra and graphs - linear equations

Solve. 4c - 9 = 13

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Question 2 · 2 marks · Number - calculation and accuracy

Work out. (16.71 + 46.13) / sqrt(8.6^2 - 3.5^2) Give your answer correct to 2 significant figures.

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Question 3 · 3 marks · Number - currency conversion and unit comparison

In the USA, one gallon of fuel costs $4.83. In the UK, one litre of fuel costs £1.62. The exchange rate is £1 = $1.215. 1 gallon = 3.785 litres In which country does 1 litre of…

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Question 4 · 7 marks · Transformations - describing transformations

Describe fully the single transformation that maps shape A onto shape B.

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Question 5 · 6 marks · Algebra and graphs - sequences (cubes)

These are the first 5 terms of a sequence. 1 8 27 64 125 Find the 10th term of this sequence.

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Question 6 · 2 marks · Algebra and graphs - expanding brackets

Expand. 5x^2(3x - 2)

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Question 7 · 2 marks · Algebra and graphs - inequalities on a number line

Write down the inequality in y shown by the number line. The number line for y runs from -2 to 5. There is a filled (closed) circle at y = -1.5 with the line shaded to the right,…

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Question 8 · 4 marks · Number - percentages and money

Hadi buys a dishwasher. He can either pay a single payment of $980 or he can pay using a monthly plan. The monthly plan is 20% of $980 plus 12 payments of $75.25. Hadi uses the…

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Question 9 · 2 marks · Number - reverse percentages

In a sale, the original price of a sewing machine is reduced by $38. This is an 8% reduction in the original price. Work out the original price of the sewing machine.

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Question 10 · 6 marks · Number - factors

Write down all the factors of 18.

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Question 11 · 3 marks · Mensuration - scale and area

A warehouse has a floor area of 800 m^2. The plan of the warehouse is drawn to a scale of 1 : 50. Calculate the floor area on the plan. Give your answer in square centimetres.

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Question 12 · 3 marks · Trigonometry - shortest distance / perpendicular

The diagram shows triangle PQR (not to scale). Angle QPR = 42° at P, angle PQR = 115° (the interior angle at Q), and PQ = 12.5 cm. R is the upper-right vertex. Calculate the…

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Question 13 · 3 marks · Algebra and graphs - rearranging formulae

Make x the subject of this formula. A = w^2 + 5x^2

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Question 14 · 11 marks · Algebra and graphs - tables of values for cubic

The table shows some values for y = 5x^2 - x^3 - 4. x -2 -1 0 1 2 3 4 5 --- ---- ---- --- --- --- --- --- --- y 24 -4 8 14 -4 Complete the table.

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Question 15 · 9 marks · Statistics - estimated mean of grouped data

The height of each of 140 basketball players is recorded. The table shows the results. Height (h cm) 160 < h <= 180 180 < h <= 185 185 < h <= 190 190 < h <= 200 200 < h <= 210 ---…

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Question 16 · 3 marks · Number - compound interest (finding the rate)

Mateo invests $1250 at a rate of r% per year compound interest. At the end of 6 years the total value of his investment is $1484. Calculate the value of r.

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Question 17 · 10 marks · Trigonometry - cosine rule

The diagram shows a quadrilateral ABCD. In triangle ABD, AB = 9.6 cm, BD = 12.1 cm and angle ABD = 56°. Calculate AD.

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Question 18 · 3 marks · Algebra and graphs - completing the square

2x^2 + 12x - 2 can be written in the form a(x + b)^2 - c. Find the values of a, b and c.

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Question 19 · 4 marks · Mensuration - arc length and perimeter of a sector

The diagram (not to scale) shows a major sector of a circle with radius 7.5 cm. The angle of the removed minor sector at the centre is 126°, so the major sector has an angle of…

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Question 20 · 9 marks · Trigonometry - 3D problems (angle between line and plane)

The diagram shows a pyramid OABCD. The pyramid has a square base, ABCD, with sides 10.5 cm. The vertex O is vertically above the centre of the base, M. The height of the pyramid…

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Question 21 · 3 marks · Number - laws of indices

(16^(5m)) / 4 = 64^(2n) Find m in terms of n.

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Question 22 · 3 marks · Number - upper and lower bounds

I = V/R V is 50, correct to the nearest 10. R is 13, correct to the nearest integer. Calculate the upper bound of I.

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