IGCSE Mathematics (0580) — October–November 2023, Paper 23

22 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 · 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 2 · 2 marks · Number — cube numbers

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

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Question 3 · 3 marks · Statistics — median from stem-and-leaf

The stem-and-leaf diagram shows the heights, in centimetres, of some plants. 10 4 8 11 1 3 4 6 12 2 3 6 9 13 2 6 9 Key: 10 4 represents 10.4 cm. Find the median height.

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Question 4 · 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 5 · 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 6 · 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 7 · 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 8 · 2 marks · Number — HCF

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

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Question 9 · 3 marks · Algebra — substitution and rearrangement

P = (2wy²)/3. Find the positive value of y when P = 108 and w = 8.

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Question 10 · 3 marks · Vectors — scalar multiplication

AB = (7, −3) is a column vector. Find 3·AB.

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Question 11 · 4 marks · Mensuration — volume of sphere, density

A bronze sphere has radius 3.6 cm. The density of bronze is 8.05 g/cm³. Find the mass of the sphere. Give your answer in kilograms, correct to the nearest gram. [The volume, V, of…

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Question 12 · 3 marks · Number — reverse percentage

Oliver sent 22% more messages in June than in May. He sent 305 messages in June. Find how many more messages he sent in June than in May.

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Question 13 · 4 marks · Algebra — linear inequalities, regions

The graph of y = 2x + 1 is drawn on the grid. By shading the unwanted regions of the grid, find and label the region R which satisfies these inequalities: y ≥ 2x + 1, y ≥ 1, 4x +…

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Question 14 · 2 marks · Statistics — box-and-whisker plots

The box-and-whisker plot shows information about the mass, in kg, of some parcels (scale 1 to 3.5 kg). Find the mass of the heaviest parcel.

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Question 15 · 3 marks · Algebra — changing the subject

T = √(3d − e). Rearrange the formula to make d the subject.

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Question 16 · 4 marks · Mensuration — cylinder

A cylinder with height 12.5 cm has a curved surface area of 105π cm². Calculate the volume of the cylinder.

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Question 17 · 4 marks · Algebra — fractional indices

Simplify. (64y²⁷)^(2/3)

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Question 18 · 3 marks · Number — percentage change, proportion

F is proportional to the product of m and a. Calculate the percentage change in F when m is increased by 40% and a is decreased by 15%.

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Question 19 · 4 marks · Trigonometry — sine rule (ambiguous case)

In triangle PQR, PQ = 18 cm, RQ = 13.5 cm and angle QPR = 42°. NOT TO SCALE. Calculate the obtuse angle PRQ.

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Question 20 · 3 marks · Algebra — expanding three brackets

(x + a)(x + 2)(2x + 3) is equivalent to 2x³ + bx² + cx − 18. Find the value of each of a, b and c.

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Question 21 · 6 marks · Geometry — 3D Pythagoras

The diagram shows a cuboid ABCDEFGH. AB = 14 cm, BC = 5 cm and CG = 8 cm. M is the midpoint of HG. NOT TO SCALE. Calculate BM.

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Question 22 · 5 marks · Algebra — intersection of line and curve

Find the coordinates of the point where the line 4x + y = 9 intersects the curve y + x² = 5. You must show all your working.

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