IGCSE Mathematics (0580) — October–November 2023, Paper 43

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

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Question 1 · 12 marks · Number — currency conversion

The table shows the amount received when exchanging $100 in some countries: Wales 77.05 pounds, India 7437.05 rupees, China 671.20 yuan, Spain 85.35 euros. Brad changes $250 to…

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Question 2 · 11 marks · Number — percentages

The table shows the number of each type of bird seen in a garden on Monday. Type of bird Frequency Pie chart sector angle --- --- --- Goldfinch 8 96° Jay 6 Starling 11 Robin 5…

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Question 3 · 9 marks · Transformations — rotation

Triangles A and B are drawn on a grid. Describe fully the single transformation that maps triangle A onto triangle B.

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Question 4 · 7 marks · Geometry — polygons

Find the size of one interior angle of a regular 10-sided polygon.

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Question 5 · 14 marks · Statistics — histograms

Indira records the time taken for workers to travel to work. The table and histogram each show part of this information. Time (t minutes) 0 < t ≤ 10 10 < t ≤ 25 25 < t ≤ 40 40 < t…

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Question 6 · 12 marks · Functions — evaluation

f(x) = 5x − 3, g(x) = 64^x, h(x) = 2/(x + 1) (x ≠ −1). Find f(2).

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Question 7 · 11 marks · Graphs — table of values (trigonometric)

Complete the table of values for y = 3 cos 2x°. Values given to 1 dp. x 0 10 20 30 40 45 50 60 70 80 90 --- --- --- --- --- --- --- --- --- --- --- --- y 3.0 2.8 2.3 1.5 0.5 −0.5…

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Question 8 · 17 marks · Trigonometry — right-angled triangle

The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. OB = 6 cm, BC = 2 cm, obtuse angle AOC = 135° and angle BCO = 90°. NOT TO SCALE. Show that angle…

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Question 9 · 14 marks · Coordinate geometry — length, triangle types

A is the point (0, 2), B is the point (3, 3) and C is the point (4, 0). Determine if triangle ABC is scalene, isosceles or equilateral. You must show all your working.

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Question 10 · 14 marks · Algebra — expanding and simplifying

Expand and simplify. 4(2x − 1) − 6(3 − x)

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Question 11 · 9 marks · Graphs — quadratic, intercepts

The diagram shows a sketch of y = 18 + 5x − 2x². The curve crosses the x-axis at A and C, and the y-axis at B. NOT TO SCALE. Find the coordinates of the points A, B and C.

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October–November 2023 Paper 42 →

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