IGCSE Mathematics (0580) — October–November 2023, Paper 42

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

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Question 1 · 11 marks · Transformations — translation

Triangle T is drawn on a grid (vertices at (2, 3), (6, 3), (6, 5)). Translate triangle T by the vector (−7, 1). Label the image K.

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Question 2 · 11 marks · Statistics — range

Daisy records her 50 homework marks. The table shows the results. Homework mark 15 16 17 18 19 20 --- --- --- --- --- --- --- Frequency 1 3 19 11 10 6 Write down the range.

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Question 3 · 15 marks · Number — percentage decrease

The value of Priya's car decreases by 10% every year. The value today is $7695. Calculate the value of the car after one year.

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Question 4 · 12 marks · Mensuration — sectors and cones

The diagram shows a sector of a circle that is made into a cone by joining OA to OB. The sector angle is x° and the radius of the sector is 7.5 cm. The base radius of the cone is…

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Question 5 · 9 marks · Algebra — forming and solving equations

In a shop the cost of a fiction book is $x and the cost of a reference book is $(x + 2). The cost of 11 fiction books is the same as the cost of 10 reference books. Find the value…

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Question 6 · 7 marks · Trigonometry — Pythagoras and trig in right-angled triangle

The diagram shows a right-angled triangle. The hypotenuse is (2t + 3) cm, one leg is t cm (opposite the angle w°) and the other leg is 5 cm. NOT TO SCALE. Find the value of w.

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Question 7 · 16 marks · Trigonometry — angles of elevation (3D)

The diagram shows a right-angled triangle PQR on horizontal ground. X is vertically above R and the angle of elevation of X from P is 21°. XR = 2.8 m and RQ = 7.1 m. NOT TO SCALE.…

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Question 8 · 9 marks · Probability

Two fair dice. Dice A is numbered 1, 2, 2, 2, 3, 6. Dice B is numbered 2, 3, 3, 4, 4, 4. Dice A is rolled once. Write down the probability that it lands on the number 6.

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Question 9 · 8 marks · Calculus — differentiation

The diagram shows a sketch of the graph of y = 4x³ − x⁴. The graph crosses the x-axis at the origin O and at the point A. The point B is a maximum point. NOT TO SCALE.…

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Question 10 · 7 marks · Geometry — congruent triangles

ABCDEF is a regular hexagon. DF, DA and DB are diagonals. NOT TO SCALE. Complete the following statements using three different triangles: Triangle DEF is congruent to triangle…

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Question 11 · 14 marks · Functions — evaluation

f(x) = 1 − 3x, g(x) = (x − 1)², h(x) = 3/x (x ≠ 0). Find g(3).

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Question 12 · 11 marks · Vectors — column vectors

O is the origin (0, 0), A is the point (8, 1) and B is the point (2, 5). NOT TO SCALE. Write OB as a column vector.

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