IGCSE Mathematics (0580) — October–November 2023, Paper 21

22 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 — angles in a triangle

The diagram shows an isosceles triangle. The apex angle is 41° and x° is one of the two equal base angles. NOT TO SCALE. Find the value of x.

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Question 2 · 3 marks · Statistics — mode

The stem-and-leaf diagram shows the time, in minutes, it takes each of 15 people to complete a race. 1 6 6 7 2 1 3 3 4 5 6 7 7 7 3 0 1 1 Key: 1 6 represents 16 minutes. Find the…

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Question 3 · 2 marks · Algebra — solving linear equations

Complete the statement: When x = ..........., x + 3 = 8.

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Question 4 · 3 marks · Number — money, multiplication

The table shows some information about Amir's shopping. Complete the table. Fruit Cost per kilogram Number of kilograms Amir buys Cost --- --- --- --- Oranges $2.35 3.2 $...…

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Question 5 · 3 marks · Algebra — factorising

Factorise completely. 42mk − 35m

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Question 6 · 3 marks · Statistics — scatter diagrams

For each of 10 people working in an office, the scatter diagram shows their salary (x-axis, $0 to $80 000) and the value of their car (y-axis, $0 to $10 000). One of these people…

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Question 7 · 1 mark · Number — currency conversion

The exchange rate between Singapore dollars and euros is 1 Singapore dollar = 0.62 euros. Find the value of 161.20 euros in Singapore dollars.

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Question 8 · 1 mark · Number — fractions

Calculate 7 3/11 × 3 3/10.

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Question 9 · 2 marks · Number — HCF

Find the highest common factor (HCF) of 140 and 126.

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Question 10 · 5 marks · Algebra — indices

Simplify. n⁵ × n

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Question 11 · 3 marks · Algebra — solving inequalities

Solve. 4(2x − 3) ≥ 43 + 3x

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Question 12 · 3 marks · Number — recurring decimals to fractions

Write 0.42̇ (0.4 recurring 2) as a fraction in its simplest form. You must show all your working. (The recurring decimal is 0.4222...)

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Question 13 · 3 marks · Number — exponential decay

At the end of 2021 there were 27 000 rhinos living in the wild. The number of rhinos is expected to decrease exponentially by 3% each year. Work out the number of rhinos expected…

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Question 14 · 4 marks · Sets — Venn diagrams, forming equations

The Venn diagram shows information about the number of elements in sets A, B and ξ. The regions are: A only = 5x, A∩B = x + 5, B only = 12 − x, and outside both = 15. n(ξ) = 52.…

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Question 15 · 5 marks · Algebra — linear inequalities, regions

By shading the unwanted regions of the grid, draw and label the region R which satisfies these inequalities: y 1, x ≤ 2, y ≥ x + 2.

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Question 16 · 3 marks · Number — bounds

P = 2w + 2h. w = 11 and h = 9.5, both correct to 2 significant figures. Find the lower bound and the upper bound for P.

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Question 17 · 3 marks · Geometry — circle theorems, tangent

A, B and C are points on the circumference of a circle, centre O. Tangent DE touches the circle at C. Angle BCE = 53° and angle ACO = 20°. NOT TO SCALE. Find the value of x, where…

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Question 18 · 3 marks · Trigonometry — sine rule

A triangle has a side of length 8.3 cm with an angle of 105° between it and a side of length 16.2 cm; y° is the angle opposite the 8.3 cm side. NOT TO SCALE. Calculate the value…

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Question 19 · 4 marks · Graphs — trigonometric functions

Sketch the graph of y = cos x for 0° ≤ x ≤ 360°.

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Question 20 · 6 marks · Algebra — algebraic fractions, factorising

Write as a single fraction in its simplest form. (10x² − 60x) / (x² − x − 30)

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Question 21 · 4 marks · Geometry — angle between line and plane (3D)

The diagram shows a cuboid ABCDEFGH. AB = 15.1 cm, BC = 4.5 cm and CG = 9.2 cm. NOT TO SCALE. Calculate the angle that the diagonal BH makes with the face ADHE.

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Question 22 · 4 marks · Mensuration — area of rhombus and sectors

ABCD is a rhombus with side length 13.6 cm. Angle ABC = 41°. BAC is a sector of a circle with centre B. DAC is a sector of a circle with centre D. NOT TO SCALE. Calculate the…

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