IGCSE Mathematics (0580) — May–June 2025, Paper 43

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

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Question 1 · 1 mark · Statistics - averages

Find the median of these numbers. 5 11 11 13 17 21

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Question 2 · 3 marks · Geometry - scale drawing and construction

In triangle ABC, AC = 21 m and BC = 15.9 m. Using a ruler and compasses only, complete the scale drawing of the triangle. Use a scale of 1 cm to represent 3 m. The side AB is…

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Question 3 · 2 marks · Number - types of number

From this list, write down a natural number. The list is: 2/5 sqrt(15) 23 sqrt(144) -2 0.8

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Question 4 · 3 marks · Mensuration - area of compound shapes

The diagram shows a pentagon made from two congruent trapeziums (NOT TO SCALE). The pentagon has a flat horizontal base of width 14 cm and is symmetrical about a vertical line.…

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Question 5 · 2 marks · Mensuration - units and conversions

Convert 780 cm^2 into m^2.

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Question 6 · 2 marks · Number - standard form

One titanium atom has a mass of 7.95 x 10^-23 grams. Calculate the number of titanium atoms in 1 kg of titanium. Give your answer in standard form.

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Question 7 · 3 marks · Sets - set notation

E (universal set) = {x : x is an integer and 1 <= x <= 12} E = {even numbers} M = {multiples of 3} Find n(M).

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Question 8 · 4 marks · Algebra - factorisation

Factorise. 28xy - 12x

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Question 9 · 3 marks · Algebra - indices

Simplify. 5x^5 y x 7x^3 y^2

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Question 10 · 5 marks · Algebra - expansion of brackets

Expand and simplify. 2x - x(5 - x^2)

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Question 11 · 8 marks · Algebra - sequences and nth term

The table shows three sequences. Complete the table (find the 6th term and the nth term for each sequence). 1st term 2nd term 3rd term 4th term 5th term 6th term nth term --- ---…

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Question 12 · 3 marks · Number - laws of indices

sqrt( 10^400 / (10^220 x 10^80) ) = 10^k Find the value of k.

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Question 13 · 6 marks · Coordinate geometry - straight line graphs

Line L has the equation y = 2(x - 5). Find the coordinates of the point where line L intersects the y-axis.

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Question 14 · 3 marks · Number - compound interest

Jess invests $1400 in an account. The account pays compound interest at a rate of r% per year. At the end of 4 years the value of her investment is $1523.15. Find the value of r.

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Question 15 · 3 marks · Algebra - inverse proportion

m is inversely proportional to the square root of (t + 2). m = 0.5 when t = 23. Find m when t = 98.

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Question 16 · 5 marks · Algebra - linear inequalities and regions

A grid is provided with x-axis from -4 to 5 and y-axis from -2 to 7. By shading the unwanted regions of the grid, draw and label the region R which satisfies these three…

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Question 17 · 1 mark · Sets - Venn diagrams

In the Venn diagram, shade the region (A union B) (intersection) C'. (The Venn diagram shows three intersecting circles labelled A (top left), B (top right) and C (bottom centre)…

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Question 18 · 8 marks · Mensuration - volume of a cuboid

The diagram shows a solid cuboid with sides of length 4.5 cm, 8 cm and 13.2 cm (NOT TO SCALE). Calculate the volume of the cuboid.

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Question 19 · 4 marks · Statistics - cumulative frequency diagrams

The table shows some information about the heights of 200 plants. Height (h cm) Cumulative frequency --- --- h <= 30 6 h <= 40 42 h <= 50 76 h <= 60 170 h <= 70 190 h <= 80 200…

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Question 20 · 5 marks · Probability - combined events

Stephan has two bags, A and B, each containing red sweets and yellow sweets only. He picks two sweets at random, one from bag A and the other from bag B. The probability that…

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Question 21 · 4 marks · Mensuration - areas of triangles and sectors

The diagram shows an equilateral triangle ABC with all sides of length 12 cm (NOT TO SCALE). With A at the top apex, B at the bottom right and C at the bottom left, base CB = 12…

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Question 22 · 4 marks · Number - bounds

A metal cube has mass 14.2 g, correct to 1 decimal place. Find the lower bound of the mass of the cube.

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Question 23 · 4 marks · Mensuration - volume of a frustum / cone

The diagram shows a frustum made by removing a small cone from a large cone (NOT TO SCALE). The frustum is shown as the upper part (wider top, narrower bottom) with the removed…

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Question 24 · 4 marks · Statistics - histograms with unequal intervals

The histogram shows information about the distance some people travel to work. The horizontal axis is Distance (km) from 0 to 50 and the vertical axis is Frequency density from 0…

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Question 25 · 5 marks · Trigonometry - graphs of trigonometric functions

Sketch the graph of y = sin x for 0 degrees <= x <= 360 degrees. (Axes are provided with y from -1 to 1 and x from 0 to 360 degrees.)

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Question 26 · 5 marks · Vectors - vector geometry

The diagram shows a quadrilateral OXPY with diagonals meeting at T (NOT TO SCALE). Y is top-left, P is top-right, O is bottom-left and X is bottom-right. The diagonals OP and XY…

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