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GCSE Maths / Edexcel

Rearranging formulae

Change the subject of a formula by using inverse operations and keeping both sides balanced.

AlgebraFoundation and HigherGrades 4 to 7Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Rearranging formulae

Pearson Edexcel GCSE Maths algebra A5: understand, use, and rearrange formulae to change the subject.

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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

The subject of a formula is the letter on its own. In y = 3x + 4, y is the subject.

Rearranging a formula means making a different letter the subject.

Treat the formula like an equation: whatever you do to one side, do to the other side.

Use inverse operations to undo the formula. Work backwards from the operations around the letter you want.

If the final answer needs a whole expression divided, use brackets or a clear fraction bar. For example, (y + 4) / 3 is not the same as y + 4 / 3.

In Edexcel answers, the final subject should be clearly on its own, usually on the left-hand side.

Key ruleTo make x the subject, isolate x using inverse operations.

Worked examples

One-step rearrangement

Make x the subject of y = x + 5.

  1. Subtract 5 from both sides.
  2. y - 5 = x.

Answer: x = y - 5

Two-step rearrangement

Make x the subject of y = 3x - 4.

  1. The x term has been multiplied by 3 and then 4 has been subtracted.
  2. Undo the subtraction first: add 4 to both sides, giving y + 4 = 3x.
  3. Undo the multiplication by 3: divide the whole of y + 4 by 3.

Answer: x = (y + 4) / 3

Formula with three letters

Make a the subject of v = u + at.

  1. Subtract u from both sides: v - u = at.
  2. Divide by t.

Answer: a = (v - u) / t

Common mistakes

  • Moving a term without applying the same inverse operation to both sides.
  • Dividing only one term in the numerator instead of the whole expression.
  • Stopping when the new subject is still multiplied by another letter.
  • Losing a negative sign during the rearrangement.

Quick exercise

Try these before moving to the exam-style questions.

  1. Make x the subject of y = x - 9.
  2. Make m the subject of c = 5m.
  3. Make p the subject of q = 2p + 7.
  4. Make h the subject of A = bh.
  5. Make n the subject of t = 6n - 1.
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 styleFoundationNon-calculator2 marks

Make x the subject of y = x + 8.

rearranging formulaeinverse operationsfoundation algebra
Standard exam styleFoundation and HigherEither3 marks

Make t the subject of s = 4t - 7.

change the subjectformulaemethod marks
ChallengeHigherEither4 marks

Make x the subject of y = ax + b.

rearranging formulaehigher algebraletters as constants