IGCSE Mathematics (0580) — May–June 2023, Paper 41

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

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Question 1 · 13 marks · Ratio

An orchard has 1250 trees in the ratio apple : pear : cherry = 12 : 9 : 4. Calculate the number of apple trees.

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Question 2 · 16 marks · Mensuration

The diagram shows a solid triangular prism ABCDEF of length 15 cm. AB = 6.4 cm, EB = 5.7 cm and the volume of the prism is 145 cm³. Show that angle EBA = 32°, correct to the…

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Question 3 · 13 marks · Statistics

The table shows the mass of 1000 eggs: 40<m⩽50 freq 126, 50<m⩽56 freq 520, 56<m⩽64 freq 154, 64<m⩽70 freq 200. Calculate an estimate of the mean.

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Question 4 · 14 marks · Mensuration

The diagram shows a right-angled triangle PQR with PQ = 8 cm and QR = 24 cm (right angle at Q). Calculate the area of triangle PQR.

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Question 5 · 13 marks · Statistics

There are 160 people in a village. The cumulative frequency diagram shows information about their ages. Find an estimate for the median age.

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Question 6 · 14 marks · Coordinate geometry

In square ABCD, A = (−2, 1) and B = (1, 5). C = (a, b) where a and b are both positive integers. Find the coordinates of C and the coordinates of D.

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Question 7 · 18 marks · Algebra

Factorise fully 27y² − 3.

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Question 8 · 12 marks · Algebra

A tailor makes x dresses and y shirts in one week. He makes at least 4 dresses; no more than 7 shirts; less than 14 dresses and shirts altogether; the number of shirts is more…

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Question 9 · 8 marks · Sets

The Venn diagram shows set X and set Y. X contains r, t, l, e, a; Y contains h, e, s, c, a (with e, a in the intersection). List the elements of X.

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Question 10 · 9 marks · Functions

f(x) = x − 4, g(x) = 2x + 5, h(x) = 3ˣ. Find f(−3).

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