IGCSE Mathematics (0580) — October–November 2023, Paper 22

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 · Number — decimal places

Write 24.07839 correct to 2 decimal places.

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Question 2 · 1 mark · Number — directed numbers

Write down the number that is 9 greater than −23.

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Question 3 · 2 marks · Algebra — substitution into formula

v = u + at. Find the value of v when u = 30, a = −2 and t = 7.

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Question 4 · 1 mark · Number — unit conversion

Change 62 000 millimetres into kilometres.

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Question 5 · 2 marks · Geometry — angles, parallel lines

The diagram shows two intersecting straight lines crossing two parallel lines. Angles of 50° and x° are marked at one intersection and 114° at another. NOT TO SCALE. Find the…

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Question 6 · 2 marks · Number — prime numbers

Explain why 111 is not a prime number.

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Question 7 · 2 marks · Geometry — bearings

P and Q are two points. North lines are shown at both P and Q. The bearing of P from Q is given by an angle of 39° between the east direction at Q and the line QP. NOT TO SCALE.…

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Question 8 · 3 marks · Number — fractions (non-calculator)

Without using a calculator, work out 3 1/8 − 1 3/4. You must show all your working and give your answer as a mixed number in its simplest form.

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Question 9 · 2 marks · Number — prime factorisation

Write 90 as a product of its prime factors.

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Question 10 · 2 marks · Algebra — expanding and simplifying

Expand and simplify. 2(t + w) + 3(w − t)

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Question 11 · 4 marks · Geometry — similar shapes

The two shapes are mathematically similar. The smaller shape has a side of 6.3 cm corresponding to 9 cm on the larger shape, and a side of 5 cm corresponding to h cm on the larger…

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Question 12 · 3 marks · Kinematics — speed-time graphs

The diagram shows a speed–time graph for 16 seconds of a car journey. The car travels at 10 m/s, constant until 12 seconds, then decelerates uniformly to 0 m/s at 16 seconds. NOT…

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Question 13 · 4 marks · Algebra — indices

3^(3p) × 3^(2p) = 729. Find the value of p.

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Question 14 · 3 marks · Algebra — changing the subject

y = 2w² − x. Rearrange the formula to make w the subject.

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Question 15 · 3 marks · Sets — Venn diagrams, set notation

On the Venn diagram (sets P and Q in universal set ξ), shade the region P ∪ Q'.

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Question 16 · 2 marks · Algebra — LCM with indices

Find the lowest common multiple (LCM) of 12x⁸ and 8x¹².

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Question 17 · 4 marks · Geometry — circle theorems

A, B and C are points on a circle, centre O. Angle OBA = 28°. NOT TO SCALE. Find angle ACB.

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Question 18 · 4 marks · Mensuration — surface area of cylinder

A solid cylinder has radius 5 cm and height 8 cm. Calculate the total surface area of the cylinder.

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Question 19 · 4 marks · Algebra — sequences (linear)

Find the nth term of the sequence: 11, 8, 5, 2, −1, …

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Question 20 · 3 marks · Number — bounds

The area of a rectangle is 55.2 cm², correct to 1 decimal place. The length of the rectangle is 9 cm, correct to the nearest cm. Calculate the upper bound of the width of the…

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Question 21 · 4 marks · Algebra — intersection of line and curve

The line y = x + 1 intersects the curve y = x² + x − 3 at two points. Find the coordinates of the two points.

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Question 22 · 2 marks · Algebra — inverse proportion

x is inversely proportional to the square root of w. When w = 16, x = 3. Find x in terms of w.

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Question 23 · 2 marks · Statistics — histograms, frequency density

Some students record their reaction times. The table shows the results. Reaction time (t seconds) 0 < t ≤ 6 6 < t ≤ 10 --- --- --- Frequency 18 16 On a histogram, the height of…

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Question 24 · 4 marks · Algebra — algebraic fractions, factorising

Simplify. (ax − 2a − x + 2) / (a² − 1)

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Question 25 · 2 marks · Calculus — differentiation

The derivative of 2ax⁷ + 3xᵏ is 42x⁶ + 15x^(k−1). Find the value of a and the value of k.

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Question 26 · 3 marks · Vectors — position vectors

The diagram shows a parallelogram OPQT. The position vector of P is a and the position vector of T is b. K is on PQ so that PK : KQ = 3 : 1. The lines OK and TQ are extended to…

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