AAAarubi AcademyGCSE Maths Edexcel first
Join nowSign in
GCSE Maths / Edexcel

Inverse proportion

Recognise inverse proportion, use products or formulae, and solve worker-time and Higher inverse-square problems.

Ratio, Proportion and RatesFoundation and HigherGrades 5 to 8Skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Inverse proportion

Pearson Edexcel GCSE Maths ratio R13 and R14: solve inverse proportion problems and recognise inverse proportion graphically.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

In inverse proportion, as one quantity increases, the other decreases by the linked multiplier.

A common example is workers and time: more workers usually means less time for the same job.

For simple inverse proportion, x multiplied by y stays constant. This can be written as y = k / x.

Do not treat inverse proportion like direct proportion. Doubling x means y halves, not doubles.

At Higher tier, y may be inversely proportional to x². Then y = k / x².

Key ruleFor inverse proportion, xy = constant, so y = k / x.

Worked examples

Workers and time

6 workers take 8 hours. How long would 12 workers take at the same rate?

  1. 12 workers is twice as many as 6.
  2. Twice as many workers take half the time.
  3. 8 / 2 = 4.

Answer: 4 hours

Use y = k / x

y is inversely proportional to x. When x = 3, y = 20. Find y when x = 5.

  1. Use y = k / x.
  2. 20 = k / 3, so k = 60.
  3. When x = 5, y = 60 / 5.

Answer: 12

Higher inverse square

y is inversely proportional to x². When x = 2, y = 18. Find y when x = 6.

  1. Use y = k / x².
  2. 18 = k / 4, so k = 72.
  3. When x = 6, y = 72 / 36.

Answer: 2

Common mistakes

  • Multiplying both quantities by the same factor as if it were direct proportion.
  • Using y = kx instead of y = k / x.
  • Forgetting to square x in inverse-square questions.
  • Not checking whether the answer should get bigger or smaller.

Quick exercise

Try these before moving to the exam-style questions.

  1. 4 workers take 9 hours. How long would 8 workers take?
  2. y is inversely proportional to x. y = 15 when x = 4. Find k.
  3. y = k / x and k = 48. Find y when x = 6.
  4. 10 machines take 6 hours. How long would 5 machines take?
  5. y is inversely proportional to x². y = 10 when x = 3. Find k.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundation and HigherCalculator3 marks

5 workers take 12 hours to complete a job. How long would 10 workers take at the same rate?

inverse proportionworkers and timefoundation ratio
Standard exam styleFoundation and HigherEither4 marks

y is inversely proportional to x. When x = 8, y = 6. Find y when x = 12.

inverse proportion formulaconstant productmethod marks
ChallengeHigherCalculator5 marks

y is inversely proportional to x². When x = 5, y = 12. Find y when x = 10.

inverse square proportionhigher ratioformula