IGCSE Mathematics (0580) — October–November 2024, Paper 23

26 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

From the list of numbers 61 62 63 64 65 66 67 68 69, write down a cube number.

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Question 2 · 1 mark

A train journey starts at 23 30 and finishes at 07 15 the next day. Find the time taken for this journey.

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Question 3 · 2 marks

Simplify. 3p - t - p - 4t

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Question 4 · 3 marks

The scale drawing shows the positions of town K and town L. The scale is 1 cm represents 10 km. Find the actual distance between town K and town L.

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Question 5 · 4 marks

Each student in a class of 20 students records the number of coins in their pockets. Number of coins 0 1 2 3 4 5 6 --- --- --- --- --- --- --- --- Frequency 3 1 7 8 0 0 1 Find the…

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Question 6 · 1 mark

The diagram shows three lines meeting at a point (NOT TO SCALE). One angle is 80°, with a right angle marked, and an angle w° below. Find the value of w.

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Question 7 · 2 marks

Solve the equation. 7 - h = 3 - 5h

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Question 8 · 2 marks

Sacha buys b books and m magazines. The cost of each book is $12 and the cost of each magazine is $5. Write an expression, in terms of b and m, for the total cost of the books and…

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Question 9 · 2 marks

Find the size of an interior angle of a regular 15-sided polygon.

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Question 10 · 3 marks

Without using a calculator, work out 2 1/4 - 1 11/12. You must show all your working and give your answer as a fraction in its simplest form.

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Question 11 · 2 marks

Solve the simultaneous equations. 3p - 2q = 7 p + 2q = 1

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Question 12 · 2 marks

V = cube root of (x/y). Rearrange the formula to write x in terms of V and y.

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Question 13 · 4 marks

Find the nth term of this sequence. 21, 13, 5, -3, -11, ...

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Question 14 · 4 marks

A, B, C and D lie on the circle (NOT TO SCALE). TAS is a tangent to the circle at A. Angle SAD = 37°, angle DAC = 41° (at A), with angles x° at C and y° at B marked. Find the…

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Question 15 · 2 marks

The box-and-whisker diagram shows information about the heights of some plants (Height in cm, axis 10-80). Find the median height.

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Question 16 · 3 marks

The diagram shows triangle ABC (NOT TO SCALE) with AC = 17.2 cm, CB = 11.1 cm, AB = 20.3 cm and angle CAB = 33.14° (at A). Calculate the shortest distance from C to AB.

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Question 17 · 4 marks

Simplify. 18x^18 ÷ 3x^3

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Question 18 · 3 marks

Two mathematically similar solids have volumes 81 cm^3 and 24 cm^3. The height of the smaller solid is 4.8 cm. Calculate the height of the larger solid.

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Question 19 · 2 marks

y is inversely proportional to sqrt(x + 2). When x = 2, y = 3. Find y in terms of x.

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Question 20 · 3 marks

Solve the equation tan x + 2 = 0 for 0° <= x <= 360°.

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Question 21 · 2 marks

The Venn diagram (three sets A, B, C) shows the number of elements in each region: A only 1, A∩B only 3, B only 5, A∩C only 1, A∩B∩C 5, B∩C only 2, C only 6, outside 2. A region…

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Question 22 · 4 marks

The diagram shows a cuboid with a diagonal PB (NOT TO SCALE). AB = 12 cm, BC = 5 cm and the height (PA / vertical edge) is 4 cm. Calculate the angle between the diagonal PB and…

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Question 23 · 2 marks

Write x^2 + 8x - 7 in the form (x + a)^2 + b.

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Question 24 · 3 marks

A rectangle has an area of 150 m^2, correct to the nearest square metre. The length of the rectangle is 22 m, correct to the nearest metre. Calculate the upper bound of the width…

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Question 25 · 4 marks

Simplify. (3x - 2 - 3xy + 2y) / (1 - y^2)

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Question 26 · 4 marks

In the diagram (NOT TO SCALE), OA = a and OB = b. AK : KB = 2 : 1. OK = KC. Find AC in terms of a and b. Give your answer in its simplest form.

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