IGCSE Mathematics (0580) — May–June 2023, Paper 43

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 · Number — ratio and percentage

Tomas sells a computer, a bike and a phone. The amounts he receives are in the ratio computer : bike : phone = 14 : 17 : 9. Calculate the amount he receives for the phone as a…

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Question 2 · 8 marks · Statistics — stem-and-leaf diagram

Anna records the number of text messages she receives for 14 days: 17, 15, 31, 38, 31, 22, 13, 18, 21, 27, 28, 21, 31, 29. Complete the stem-and-leaf diagram (stems 1, 2, 3) and…

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Question 3 · 10 marks · Geometry — measurement, scale drawing

The scale drawing shows two sides, AB and BC, of a field. The scale is 5 centimetres represents 200 metres. Measure angle ABC.

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Question 4 · 13 marks · Geometry — bearings

A, B and C are three towns and the bearing of C from A is 114°. B is due south of A and AC = BC. NOT TO SCALE. Calculate the bearing of B from C.

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Question 5 · 12 marks · Trigonometry — cosine rule

ABC is a scalene triangle on horizontal ground. AYX is a straight vertical post, held in place by two straight wires XB and YC. AC = 4.8 m, BC = 5.6 m and angle ACB = 20.4°. NOT…

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Question 6 · 15 marks · Statistics — cumulative frequency diagram

The cumulative frequency table shows information about the speed of each of 200 cars as they pass a speed camera. Speed (v km/h) v ≤ 70 v ≤ 80 v ≤ 90 v ≤ 95 v ≤ 100 v ≤ 120 ---…

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Question 7 · 10 marks · Graphs — recognising function types

The diagram shows the graph of a function. Put a ring around the word which correctly identifies the type of function: reciprocal, quadratic, cubic, exponential, linear.

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Question 8 · 12 marks · Algebra — forming and solving linear equations

A shop sells shirts for $x and jackets for $(x + 27). The shop sells 4 shirts and 3 jackets for a total of $194.75. Write down and solve an equation to find the cost of one shirt.

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Question 9 · 10 marks · Mensuration — area of square and sectors

The diagram shows a shape made from a square ABCD and two equal sectors of a circle. The square has side 11 cm. MAB and DCN are straight lines. NOT TO SCALE. Calculate the area of…

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Question 10 · 12 marks · Graphs — table of values (exponential)

The table shows some values for y = 2x − 3. x −2 −1 0 0.5 1 1.5 2 2.5 --- --- --- --- --- --- --- --- --- y −2.75 −1.58 −0.17 1 2.66 Complete the table.

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Question 11 · 9 marks · Coordinate geometry — length

M has coordinates (4, 1) and N has coordinates (−2, −7). Find the length of MN.

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Question 12 · 8 marks · Calculus — differentiation

The equation of a curve is y = x⁴ − 8x² + 5. Find the derivative, dy/dx, of y = x⁴ − 8x² + 5.

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