IGCSE Mathematics (0580) — May–June 2023, Paper 21

21 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 · Geometry

The diagram shows angles at points B, C and D with CDE a straight line. Angle ABC-region marks: angle at B = 104°, angle at A = 71°, angle at C = 56°. Find angle ADE.

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Question 2 · 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 3 · 4 marks · Geometry

The diagram shows a straight line intersecting two parallel lines, with angle 58° marked, and angles a° and b°. Find the value of a and the value of b, giving a geometrical reason…

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Question 4 · 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 5 · 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 6 · 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 7 · 2 marks · Ratio

The scale of a map is 1 : 125 000. On a map, the length of an island is 9.4 cm. Calculate the actual length of the island, giving your answer in kilometres.

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Question 8 · 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 9 · 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 10 · 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 11 · 6 marks · Transformations

The grid shows triangles A, B and C. Describe the single transformation that maps triangle A onto triangle B.

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Question 12 · 4 marks · Geometry

AO, OB and OC are all radii of the circle. AB = BC. Therefore triangle AOB is congruent to triangle COB. Draw a ring around the correct criterion for this statement (SAS, RHS,…

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Question 13 · 3 marks · Number

Anya invests $6000 in an account that pays compound interest at a rate of r % per year. At the end of 8 years, the account has earned $621.70 in interest. Calculate the value of r.

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Question 14 · 3 marks · Algebra

y is directly proportional to the square of (x + 3). When x = 2, y = 5. Find y when x = 1.

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Question 15 · 3 marks · Probability

A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Calculate the probability that one button…

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Question 16 · 3 marks · Vectors

Find the magnitude of the vector (−4, 5) (column vector).

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Question 17 · 2 marks · Algebra

Simplify (81x¹²)^(3/4).

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Question 18 · 4 marks · Trigonometry

The diagram shows the position of three towns U, V and W. U is due west of V and angle UVW = 125°. UV = 27.3 km and VW = 62.4 km. Calculate the bearing of U from W.

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Question 19 · 5 marks · Trigonometry

On the diagram, sketch the graph of y = cos x for 0° ⩽ x ⩽ 360°.

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Question 20 · 7 marks · Graphs

The table shows some values for y = 3x² − 2x − 1 for x = −1, −0.5, 0, 0.5, 1, 1.5. Complete the table (the missing y-values).

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Question 21 · 6 marks · Calculus

A curve has equation y = x³ − 12x. Find the gradient of the curve at the point (1, −11).

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