IGCSE Mathematics - International (0607) — May–June 2025, Paper 41

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

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Question 1 · 5 marks · Statistics - averages and measures of spread

150 students are each asked how many texts they sent the previous day. The results are shown in the table. Number of texts 0 1 2 3 4 5 6 --- --- --- --- --- --- --- --- Frequency…

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Question 2 · 3 marks · Number - percentages

Find 42 as a percentage of 60.

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Question 3 · 3 marks · Algebra - expanding brackets

Expand. x^2(3x - 2)

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Question 4 · 2 marks · Sets - set notation and Venn diagrams

Use set notation to describe each of the shaded regions. First diagram: a Venn diagram with universal set U containing two overlapping sets A and B. The shaded region is the part…

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Question 5 · 1 mark · Algebra - substitution into formulae

s = (u + v)/2 × t Find s when u = 4.3, v = 9.5 and t = 8.5 .

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Question 6 · 7 marks · Geometry - Pythagoras' theorem

Triangle ABC is the cross-section of a prism. AC = 5.7 cm, NC = 3.6 cm and the length of the prism is 8 cm. Angle ABN = 72° and angle ANC = 90°. N lies on BC and AN is the…

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Question 7 · 3 marks · Algebra - indices

Simplify. 2x^3 y^4 × (4x^2 y)^3

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Question 8 · 2 marks · Vectors - column vectors

The diagram shows point A(-4, 3) and point B(5, -2) on a coordinate grid. Point A is translated to point B. Find vector AB (the column vector representing the translation from A…

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Question 9 · 8 marks · Number - exponential growth and decay

The value of a car depreciates exponentially by 15% each year. On 1 January 2023 its value was $20 400. Find the value of the car on 1 January 2022.

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Question 10 · 6 marks · Mensuration - volume of a cylinder

The diagram shows a solid cylinder and a solid cone. The radius of the cylinder is 5 cm and its height is 12 cm. The height of the cone is 15 cm. The volume of the cylinder is…

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Question 11 · 11 marks · Functions - graphs of functions (GDC)

f(x) = x^3 / ((x + 2)(x - 3)) Sketch the graph of y = f(x) for values of x between -10 and 10.

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Question 12 · 8 marks · Trigonometry - cosine rule

The diagram shows a triangular field. AB = 140 m and BC = 260 m. Angle ABC = 68°. Show that AC = 244.8 m correct to 1 decimal place.

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Question 13 · 8 marks · Algebra - forming and rearranging equations

Pierre drives from town P to town Q and then to town R. The distance from P to Q is 112 km. The distance from Q to R is 87 km. The average speed from P to Q is x km/h. The average…

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Question 14 · 5 marks · Statistics - mean of grouped data

Ahmed records the mass of each of 50 pumpkins. The results are shown in the table. Mass (m kg) 0 < m ≤ 2 2 < m ≤ 5 5 < m ≤ 10 10 < m ≤ 15 15 < m ≤ 25 --- --- --- --- --- ---…

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Question 15 · 3 marks · Mensuration - similar solids (length and volume ratio)

These two bottles are mathematically similar. The capacity of the small bottle is 0.5 litres. The capacity of the large bottle is 1 litre. The height of the large bottle is 25 cm.…

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