Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Direct & Inverse Proportion — exam questions
10 original Incandio exam-style questions on Direct & Inverse Proportion, 25 marks, about 31 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Direct & Inverse Proportion — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
6 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statements 2.5 · 1.7. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
y is directly proportional to x. Write down a formula connecting y and x, using k as the constant of proportionality.
(Total for Question 1 = 1 mark)
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(2)Work out
6 identical pens cost £4.50. Work out the cost of 10 of these pens.
(Total for Question 2 = 2 marks)
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(3)Find
y is directly proportional to x. When x = 8, y = 20. Find y when x = 14.
(Total for Question 3 = 3 marks)
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(1)Explain why
A student claims that if y is inversely proportional to x then y falls by the same amount every time x increases by 1. Explain why the claim is wrong.
(Total for Question 4 = 1 mark)
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(3)Work out
The cost each person pays to hire a hall is inversely proportional to the number of people sharing it. When 5 people share, each pays £12. Work out what each person pays when 8 people share.
(Total for Question 5 = 3 marks)
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(3)Find
The energy stored in a spring is directly proportional to the square of its extension. A spring extended by 3 cm stores 45 joules. Find the energy stored when the same spring is extended by 5 cm.
energy stored = ............................
(Total for Question 6 = 3 marks)
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(3)Show that
The time taken to fill a tank is inversely proportional to the rate at which water flows in. At 12 litres per minute the tank fills in 25 minutes. Show that at 20 litres per minute it fills in 15 minutes.
(Total for Question 7 = 3 marks)
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(2)Calculate
A pack of 8 tins costs £5.36 and a pack of 12 tins costs £7.92. Calculate which pack is better value for money.
(Total for Question 8 = 2 marks)
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(3)Work out
5 workers build a wall in 12 days. Work out how long 8 workers would take, assuming every worker works at the same rate.
(Total for Question 9 = 3 marks)
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(4)Work out
The force between two magnets is inversely proportional to the square of the distance between them. At a distance of 4 cm the force is 7.5 newtons. Work out the distance at which the force is 30 newtons.
distance = ............................
(Total for Question 10 = 4 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain Direct & Inverse Proportion to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Robert Boyle over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Direct & Inverse Proportion — Quantities that scale together, quantities that trade off, and the algebraic y = kx² machinery of Higher Tier proportion.
- All of Incandio Mathematics · Incandio Exam Practice