IGCSE Mathematics (0580) — May–June 2025, Paper 13

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

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Question 1 · 4 marks · Number

Write the number 70 000 000 in words.

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Question 2 · 2 marks · Geometry

Write down the mathematical name for an angle between 90° and 180°.

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Question 3 · 5 marks · Number

Write down sqrt(169) .

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Question 4 · 3 marks · Geometry

The diagram shows a quadrilateral with sides of equal length. The bottom-left interior angle is a° and the bottom-right interior angle is 2a°. Write down the mathematical name for…

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Question 5 · 2 marks · Number - sequences

Find the next term in each sequence. 1, 5, 10, 16, 23, ...

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Question 6 · 4 marks · Statistics

These are the lengths of time, in minutes, of seven phone calls. 10 22 5 7 35 8 75 Find the median.

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Question 7 · 3 marks · Number - ratio and proportion

70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French. Find the number of students…

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Question 8 · 6 marks · Geometry - mensuration and nets

The diagram shows two faces of a net of a cuboid on a 1 cm² grid. The two drawn faces together form a 6 cm by 2 cm rectangle divided into two 3 cm by 2 cm faces. Complete the…

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Question 9 · 3 marks · Geometry - mensuration

The diagram shows the net of a square-based pyramid. The perpendicular height of each triangle is 4 cm. The base has side length 5 cm. Calculate the surface area of the pyramid.

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Question 10 · 3 marks · Algebra - graphs

Line A has equation y = 3x + 1. Line B has equation y = 3x - 1. Draw a ring around the description that is correct. - Line A intersects line B - Line A has a steeper gradient than…

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Question 11 · 6 marks · Statistics - pie charts

Jo asks 90 people whether they prefer pop, rock, classical, jazz or folk music. The pie chart shows some of the results. The 'Pop' sector has a central angle of 120° and the…

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Question 12 · 3 marks · Number - sets and Venn diagrams

A music group has 30 members. 7 members play a flute (F) and play a clarinet (C). 12 members play a flute. 1 member does not play a flute and does not play a clarinet. Use this…

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Question 13 · 2 marks · Number - estimation

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 62.5 / (9.7 × 0.52) .

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Question 14 · 2 marks · Geometry - mensuration

The diagram shows a trapezium. The two parallel sides are 4 cm and 10 cm, and the perpendicular distance between them is h cm. The area of the trapezium is 42 cm². Work out the…

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Question 15 · 3 marks · Algebra - inequalities

Write down the inequality represented on the number line. The number line runs from -6 to 5. There is a filled (solid) circle at -4 and an open (unfilled) circle at 3, with the…

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Question 16 · 3 marks · Algebra - equations and percentages

On Monday the cost of a concert ticket is $x. On Tuesday the cost of a ticket for the same concert is 20% more than the cost on Monday. Jack buys 4 tickets on Monday and 5 tickets…

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Question 17 · 3 marks · Algebra - indices

Simplify. y^4 × y^6

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Question 18 · 5 marks · Geometry - circle theorems

The diagram shows a circle, centre O. P and S are points on the circle. POR is a straight line. QRST is a tangent to the circle at S. Angle OPS = 25°, angle x° is marked at S…

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Question 19 · 2 marks · Geometry - mensuration (sectors)

The diagram shows a sector of a circle with radius 3 cm and sector angle 60°. Calculate the area of the sector. Give your answer in terms of pi in its simplest form.

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Question 20 · 2 marks · Number - factors and multiples

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

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Question 21 · 4 marks · Algebra - equations

In this question, all lengths are in centimetres. The triangle has sides 2x + 1, 9 and x + 3. The rectangle has dimensions (2x - 1) by x. The perimeter of the triangle is equal to…

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Question 22 · 2 marks · Algebra - rearranging formulae

g = h/3 - 8 Rearrange the formula to make h the subject.

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Question 23 · 2 marks · Geometry - similarity

Rectangle A has width 8 cm and height x cm. Rectangle B has width 2 cm and height 1.5 cm. Rectangle A is mathematically similar to rectangle B. Work out the value of x.

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Question 24 · 3 marks · Number - fractions

Work out 3 1/2 - 1 4/7. Give your answer as a mixed number in its simplest form.

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Question 25 · 3 marks · Algebra - simultaneous equations

Solve the simultaneous equations. 8x + 5y = 4 2x - y = 10

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