IGCSE Math RevisionQuestion 1
\(y\) is directly proportional to \(x\). When \(x = 3\), \(y = 12\).
Find \(y\) when \(x = 7\).
Show the worked answer
- \(y = kx\): \(12 = 3k\), so \(k = 4\).
- \(y = 4 \times 7 = 28\)
Answer: \(y = 28\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.8
Cambridge IGCSE Maths 0580 Direct and Inverse Proportion Questions
Direct and Inverse Proportion questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 8 questions
- 8 Extended
- 6 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.8 Proportion Extended only
Extended: Express direct and inverse proportion algebraically and use it to find unknown quantities.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Direct and Inverse Proportion questions: Extended
Extended content, for Papers 2 and 4.
Question 2
\(y\) varies directly as the square of \(x\), and \(y = 48\) when \(x = 4\).
Work out \(y\) when \(x = 5\).
Show the worked answer
- \(y = kx^2\): \(48 = 16k\), so \(k = 3\).
- \(y = 3 \times 25 = 75\)
Answer: \(y = 75\)
Question 3
\(y\) is inversely proportional to \(x\). When \(x = 3\), \(y = 8\).
Find \(y\) when \(x = 6\).
Show the worked answer
- \(y = \frac{k}{x}\): \(8 = \frac{k}{3}\), so \(k = 24\).
- \(y = \frac{24}{6} = 4\)
Answer: \(y = 4\)
Question 4
\(y\) varies inversely as the square of \(x\), and \(y = 4\) when \(x = 3\).
Work out the value of \(y\) when \(x = 6\).
Show the worked answer
- \(y = \frac{k}{x^2}\): \(4 = \frac{k}{9}\), so \(k = 36\).
- \(y = \frac{36}{36} = 1\)
Answer: \(y = 1\)
Question 5
\(y\) is directly proportional to \(\sqrt{x}\). When \(x = 9\), \(y = 12\).
Find \(x\) when \(y = 20\).
Show the worked answer
- \(y = k\sqrt{x}\): \(12 = 3k\), so \(k = 4\).
- \(20 = 4\sqrt{x}\), so \(\sqrt{x} = 5\) and \(x = 25\).
Answer: \(x = 25\)
Question 6
The time taken to build a wall is inversely proportional to the number of workers. \(6\) workers take \(15\) days.
How many days do \(9\) workers take?
Show the worked answer
- \(t = \frac{k}{w}\): \(k = 6 \times 15 = 90\).
- \(t = \frac{90}{9} = 10\)
Answer: \(10\) days
Question 7
The distance, \(d\) metres, an object falls is directly proportional to the square of the time, \(t\) seconds. It falls \(20\) m in \(2\) seconds.
How far does it fall in \(5\) seconds?
Show the worked answer
- \(d = kt^2\): \(20 = 4k\), so \(k = 5\).
- \(d = 5 \times 25 = 125\)
Answer: \(125\) m
Question 8
\(y\) is directly proportional to \(x^3\).
When \(x\) is multiplied by \(3\), what is \(y\) multiplied by?
Show the worked answer
- \(y = kx^3\). Replacing \(x\) by \(3x\) gives \(k(3x)^3 = 27kx^3\).
Answer: \(27\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test direct and inverse proportion?
Direct and Inverse Proportion is Extended content (syllabus 2.8), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more direct and inverse proportion questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.