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GCSE Maths / Edexcel

Direct proportion

Recognise direct proportion, scale quantities using the same multiplier, and use y = kx or Higher proportional formulae.

Ratio, Proportion and RatesFoundation and HigherGrades 4 to 7Skill

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

Pearson Edexcel GCSE Maths ratio R10 and R13: solve direct proportion problems and recognise proportional relationships.

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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

Two quantities are directly proportional when they increase or decrease by the same multiplier.

If x doubles, y doubles. If x is multiplied by 5, y is also multiplied by 5.

For a linear direct proportion relationship, y = kx, where k is the constant of proportionality.

A direct proportion graph is a straight line through the origin. If it does not pass through the origin, it is not directly proportional.

At Higher tier, y can be directly proportional to x² or another power. Find k first, then use the formula.

Key ruleFor direct proportion, y = kx unless the question states another power such as y is proportional to x².

Worked examples

Multiplier method

3 notebooks cost 7.50 pounds. How much do 8 notebooks cost?

  1. One notebook costs 7.50 / 3 = 2.50 pounds.
  2. 8 notebooks cost 8 x 2.50.

Answer: 20 pounds

Use y = kx

y is directly proportional to x. When x = 4, y = 20. Find y when x = 7.

  1. Use y = kx.
  2. 20 = 4k, so k = 5.
  3. When x = 7, y = 5 x 7.

Answer: 35

Higher square proportion

y is directly proportional to x². When x = 3, y = 45. Find y when x = 5.

  1. Use y = kx².
  2. 45 = k x 9, so k = 5.
  3. When x = 5, y = 5 x 25.

Answer: 125

Common mistakes

  • Adding the same amount instead of multiplying by the same scale factor.
  • Using y = k + x instead of y = kx.
  • Forgetting that a direct proportion graph must pass through the origin.
  • Using y = kx for a Higher question that says y is proportional to x².

Quick exercise

Try these before moving to the exam-style questions.

  1. 5 pencils cost 2.00 pounds. How much do 8 pencils cost?
  2. y is directly proportional to x. y = 12 when x = 3. Find y when x = 8.
  3. If 4 kg costs 9 pounds, how much does 10 kg cost?
  4. y = kx and y = 18 when x = 6. Find k.
  5. y is proportional to x². y = 32 when x = 4. Find y when x = 5.
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 styleFoundationCalculator3 marks

4 tickets cost 18 pounds. Work out the cost of 10 tickets.

direct proportionunitary methodfoundation ratio
Standard exam styleFoundation and HigherEither4 marks

y is directly proportional to x. When x = 6, y = 42. Find y when x = 11.

y = kxconstant of proportionalitymethod marks
ChallengeHigherCalculator5 marks

y is directly proportional to x². When x = 4, y = 80. Find y when x = 7.

direct proportionsquare proportionhigher ratio