IGCSE Mathematics (0980) — May–June 2025, Paper 22

24 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 · Geometry - symmetry

The diagram shows a 4 by 4 grid of small squares. Three squares are shaded: the top row has shaded squares in the 2nd and 4th columns, and the bottom-left square is also shaded.…

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Question 2 · 3 marks · Geometry - scale drawings and bearings

The scale drawing shows the positions of two villages, P and Q. The scale is 1 cm represents 0.5 km. Find the actual distance between village P and village Q.

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Question 3 · 3 marks · Geometry - angles and parallel lines

The diagram shows two straight lines intersecting two parallel lines (not to scale). The two parallel lines are horizontal. The upper parallel line is crossed by two transversals;…

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Question 4 · 2 marks · Probability

There are seven cards showing the numbers 1, 2, 3, 4, 5, 6 and 7. Samira picks one of these cards at random and replaces it. Find the probability that she picks an odd number.

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Question 5 · 4 marks · Transformations - translation

The grid shows triangle T with vertices at (-1, 1), (-1, 3) and (-2, 1), and triangle U. Translate triangle T by the vector (0, -2) (column vector with top component 0 and bottom…

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Question 6 · 5 marks · Algebra - linear equations

Solve. 8x + 7 = 39

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Question 7 · 3 marks · Algebra - sequences

These are the first 4 terms of a sequence. 11 8 5 2 Find the next term of this sequence.

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Question 8 · 2 marks · Number - factors and multiples

Find the highest common factor (HCF) of 36 and 54.

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Question 9 · 6 marks · Vectors and coordinate geometry

A is the point (3, -1). Vector AB = (2, -4) (column vector with top component 2 and bottom component -4). Vector AC = 2 x vector AB. Find the coordinates of the point C.

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Question 10 · 2 marks · Mensuration - arcs and sectors

The diagram shows a sector of a circle, centre O (not to scale). The two straight edges (radii) each have length 18 cm and the angle between them at O is 45 degrees. The length of…

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Question 11 · 3 marks · Number - standard form

Write 0.007 08 in standard form.

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Question 12 · 2 marks · Geometry - circle theorems

The diagram (not to scale) shows a circle with points P, Q and R on the circle. R is at the upper left, P is at the right and Q is at the lower right. QR is a diameter of the…

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Question 13 · 11 marks · Statistics - mean of grouped data

100 students solve a puzzle. The table shows information about the time taken by each student to solve the puzzle. Time (t seconds) 20 < t <= 40 40 < t <= 60 60 < t <= 100 --- ---…

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Question 14 · 2 marks · Number - recurring decimals to fractions

Write the recurring decimal 0.25(5) (i.e. 0.25 with the 5 recurring, = 0.2555...) as a fraction.

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Question 15 · 6 marks · Graphs - reciprocal functions

The diagram shows the graph of y = 2/x - 1. Write down the coordinates of the point where the graph crosses the x-axis.

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Question 16 · 4 marks · Mensuration - surface area of solids

The diagram (not to scale) shows a solid made by joining a hemisphere to a cylinder. The hemisphere sits on top of the cylinder. The radius of both the hemisphere and the cylinder…

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Question 17 · 4 marks · Number - indices

Find the value of 125^(2/3).

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Question 18 · 4 marks · Number - surds

Rationalise the denominator of 9/sqrt(3). Give your answer in its simplest form.

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Question 19 · 7 marks · Algebra - algebraic fractions

Write as a single fraction in its simplest form. (5a/6) x (3b/a)

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Question 20 · 4 marks · Algebra - variation

y is proportional to 1/sqrt(x). When x = 9, y = 2. Find the value of y when x = 36.

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Question 21 · 9 marks · Graphs - cubic functions and intercepts

The diagram shows the graph of y = 3x - x^3. The graph crosses the x-axis at A, at O and at B. The turning points of the graph are at P and at Q. Find the x-coordinate of A and…

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Question 22 · 4 marks · Trigonometry - exact values

Write down the exact value of tan 60 degrees.

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Question 23 · 3 marks · Vectors - position vectors in geometry

The diagram (not to scale) shows a trapezium OABC. O is at the lower left, A is at the lower right, B is at the upper left and C is at the upper right. The vector a runs along OA…

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Question 24 · 5 marks · Algebra - simultaneous equations (line and curve)

The line y = 7x + 3 intersects the curve y = x^2 + 5x - 12 at the points A and B. Find the coordinates of A and B.

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