IGCSE Mathematics (0580) — May–June 2023, Paper 11

25 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

Work out the number of months in 5 years.

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Question 2 · 2 marks

Write 3752 correct to the nearest 10.

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Question 3 · 3 marks

Magazines cost $3.40 each. Rosina has $15 to buy as many magazines as possible. Complete the statement. Rosina can buy ................ magazines and will have $ ................…

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Question 4 · 1 mark

Write down the mathematical name of a 4-sided shape that has rotational symmetry of order 2 and no lines of symmetry.

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Question 5 · 2 marks · Statistics

The numbers are: 21, 8, 15, 32, 3, 29, 19, 45, 8. Calculate the mean of these numbers.

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Question 6 · 1 mark · Number

A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes.

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Question 7 · 2 marks · Number

Write these numbers in order, starting with the smallest: 15/213, 0.071, 0.7, 7%.

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Question 8 · 1 mark · Number

Write the fraction 24/84 in its simplest form.

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Question 9 · 2 marks · Algebra

Simplify 3a − 5b − a − 6b.

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Question 10 · 2 marks · Algebra

The cost of hiring a bicycle, $C, for y hours is given by the formula C = 12 + 3.5y. Maria pays $36.50 to hire this bicycle. Work out the number of hours she hires the bicycle for.

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Question 11 · 2 marks · Vectors

a = (3, 7) and b = (−2, 5) (column vectors). Work out a − 2b.

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Question 12 · 3 marks · Geometry

The diagram shows a pair of parallel lines and a straight line, with one marked angle 52° and an angle x° in the alternate position. Write down the geometrical reason why the…

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Question 13 · 2 marks · Mensuration

Calculate the volume of a sphere with diameter 4.8 cm. [The volume, V, of a sphere with radius r is V = (4/3)πr³.]

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Question 14 · 2 marks · Number

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of (6.7 × 2.1) / (18 − 5.9). You must show all your working.

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Question 15 · 2 marks · Probability

Eric has four colours of paint. The table shows the probability that he uses each colour: Red 0.3, Blue 0.35, Green 0.13, Yellow x. Find the value of x.

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Question 16 · 2 marks · Algebra

Factorise completely 8x² − 20x.

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Question 17 · 4 marks · Algebra

The nth term of a sequence is 10 − n². Write down the first three terms of this sequence.

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Question 18 · 2 marks · Number

The length, l metres, of a piece of wood is 3.6 metres, correct to the nearest 10 centimetres. Complete this statement about the value of l: ... ⩽ l < ...

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Question 19 · 2 marks · Number

Calculate 1 ÷ (6.4 × 10⁻⁵). Give your answer in standard form.

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Question 20 · 3 marks · Number

Without using a calculator, work out 2 1/7 ÷ 5/9. You must show all your working and give your answer as a mixed number in its simplest form.

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Question 21 · 3 marks · Geometry

The diagram shows a right-angled triangle with angles 4x° and (3x − 1)° (and the right angle). Use the information in the diagram to write down and solve an equation to find the…

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Question 22 · 2 marks · Trigonometry

The diagram shows a right-angled triangle with the side opposite y° equal to 7.5 cm and the side adjacent to y° equal to 12.8 cm. Calculate the value of y.

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Question 23 · 2 marks · Geometry

Triangle ABC is similar to triangle DEF. In ABC, AB = 5.6 cm and BC = 7.2 cm. In DEF, DE = h cm and EF = 8.1 cm. Calculate the value of h.

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Question 24 · 3 marks · Sets

𝓔 = {a, b, c, d, e, f, g, h, i, j, k}, F = {f, a, c, e}, B = {b, a, c, k}. Complete the Venn diagram (two overlapping sets F and B within the universal set).

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Question 25 · 5 marks · Algebra

At a cinema, an adult ticket costs $a and a child ticket costs $c. Farah buys 3 adult tickets and 4 child tickets for $38.50. Complete the equation: 3a + 4c = ...

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