IGCSE Mathematics (0580) — 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 · Symmetry

The diagram shows a 4 by 4 grid of small squares. In the top row, the 2nd and 4th squares (from the left) are shaded grey. In the bottom row, the 1st square (leftmost) is shaded…

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Question 2 · 3 marks · 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. The drawing shows P with a North arrow above it, and Q lower and to the right…

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Question 3 · 3 marks · Angles - parallel lines

The diagram (NOT TO SCALE) shows two straight lines intersecting two parallel lines. On the upper parallel line, the left intersection makes an angle of 45 degrees and the right…

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Question 4 · 2 marks · Probability

There are 7 cards, numbered 1, 2, 3, 4, 5, 6, 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 (-2, 1), (-2, 3), (-1, 1), and triangle U with vertices at (1, -1), (3, -1), (3, -2), drawn on an x-y grid from -4 to 4 on both axes.…

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Question 6 · 5 marks · Algebra - linear equations

Solve. 8x + 7 = 39

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Question 7 · 3 marks · 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 - HCF

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

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Question 9 · 6 marks · Vectors

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

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Question 10 · 2 marks · Mensuration - arc length

The diagram (NOT TO SCALE) shows a sector of a circle, centre O. The two radii have length 18 cm and the angle at O between them is 45 degrees. The length of the arc is npi cm.…

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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 · Circle theorems

The diagram (NOT TO SCALE) shows a circle with points P, Q and R on the circumference. QR is a diameter passing through the circle. R is at the top left, P is at the right, and Q…

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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 0.25 recurring (the 5 is recurring, i.e. 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, drawn on axes with x from -8 to 8 and y from -5 to 5. The curve has two branches (a reciprocal-type curve shifted down by 1). Write…

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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 radius of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 5…

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Question 17 · 4 marks · Indices - fractional powers

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

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Question 18 · 4 marks · Surds - rationalising denominators

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

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Question 19 · 7 marks · Algebraic fractions - multiplication

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

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Question 20 · 4 marks · Variation - inverse proportion

y is inversely proportional to the square root of x, i.e. y 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, roots

The diagram (NOT TO SCALE) 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 (a minimum in the third…

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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-like figure with points O, A, B, C and M. O is at the lower left, A is on the lower line to the right of O (vector OA = a). B is above…

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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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← May–June 2025 Paper 23 · May–June 2025 Paper 21 →

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