IGCSE Mathematics (0580) — October–November 2023, Paper 13

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

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Question 1 · 1 mark · Geometry — congruence

The diagram shows a shaded shape and several other shapes labelled A, B, C, D and E. Write down the letter of the shape that is congruent to the shaded shape.

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Question 2 · 4 marks · Number — factors

Write down all the factors of 32.

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Question 3 · 2 marks · Geometry — symmetry

Draw the lines of symmetry on this rhombus.

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Question 4 · 2 marks · Number — cube numbers

From this list, write down a cube number: 61, 63, 64, 66, 68, 69.

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Question 5 · 1 mark · Number — time calculations

Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives.

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Question 6 · 3 marks · Statistics — range from stem-and-leaf

Jamie records the masses of two samples of oranges, type A and type B. The stem-and-leaf diagram shows the mass, in grams, of each of 30 oranges of type A: 17 6 8 8 9 18 0 1 2 2 4…

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Question 7 · 3 marks · Geometry — constructions

In triangle LMN, LN = 7.5 cm and MN = 8 cm. Using a ruler and compasses only, construct triangle LMN. Leave in your construction arcs. The line LM has been drawn for you.

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Question 8 · 2 marks · Mensuration — surface area of cube

The surface area of a cube is 73.5 cm². Find the length of one side of the cube.

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Question 9 · 2 marks · Geometry — angles in polygons

The diagram shows an equilateral triangle. Two exterior angles, each x°, are marked. NOT TO SCALE. Find the value of x.

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Question 10 · 2 marks · Vectors — addition

a = (4, 9), b = (−6, 1), c = (13, −2) are column vectors. Work out a + b.

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Question 11 · 2 marks · Algebra — factorising

Factorise completely. 15v² − 3v

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Question 12 · 3 marks · Probability — total probability

Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Bus Walk Car Other --- --- --- ---…

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Question 13 · 3 marks · Number — fractions (non-calculator)

Without using a calculator, work out 1 5/6 ÷ 11/15. You must show all your working and give your answer as a mixed number in its simplest form.

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Question 14 · 3 marks · Geometry — quadrilaterals, rotation

The diagram shows triangle ABC with angle ABC = 112° and angle ACB = 44°. M is the midpoint of AC. NOT TO SCALE. Triangle ABC is rotated 180° about centre M. The image and the…

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Question 15 · 2 marks · Number — simple interest

Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years.

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Question 16 · 2 marks · Algebra — solving linear equations

Solve the equation. 5x + 7 = 9x − 3

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Question 17 · 3 marks · Coordinate geometry — equation of a line

Line L is drawn on the grid. Find the equation of line L in the form y = mx + c.

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Question 18 · 2 marks · Algebra — forming expressions

A bar of chocolate costs $3 and a bag of sweets costs $5. Write down an expression for the total cost, in dollars, of x bars of chocolate and y bags of sweets.

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Question 19 · 4 marks · Probability

A bag contains these cards: 1, 7, 3, 9, 4, 5, 2. One of these cards is picked at random. Find the probability that the number on the card is greater than 3.

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Question 20 · 2 marks · Mensuration — arc length

The diagram shows a sector of a circle with radius r cm and sector angle 72°. The arc length is 9.35 cm. NOT TO SCALE. Calculate the value of r.

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Question 21 · 3 marks · Sets — Venn diagrams

ξ = {2, 4, 8, 9, 10, 12}, Q = {square numbers}, R = {multiples of 4}. Use this information to complete the Venn diagram (sets Q and R).

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Question 22 · 2 marks · Number — HCF

Find the highest common factor (HCF) of 48 and 80.

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Question 23 · 3 marks · Algebra — simultaneous equations

Solve the simultaneous equations. You must show all your working. 3x + 5y = 23 and 6x − 4y = 11.

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← October–November 2023 Paper 21 · October–November 2023 Paper 12 →

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