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AlgebraTopic Summary

Knowledge Organiser: Rearranging Formulae

Part of Rearranging Formulae · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Rearranging Formulae within Rearranging Formulae for GCSE Mathematics. Revise Rearranging Formulae in Algebra for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 6

Practice

14 questions

Recall

11 flashcards

Knowledge Organiser: Rearranging Formulae

Key Terms
  • Subject: The letter on its own on one side of a formula (e.g. v in v = u + at)
  • Rearrange: Change which letter is the subject
  • Inverse operation: The opposite operation used to "undo" steps
  • Formula: An equation that shows the relationship between variables
  • Collect: Gather all terms containing the required letter onto one side
Must-Know Facts
  • Use reverse BIDMAS: undo + or − first, then × or ÷, then powers or roots
  • Whatever you do to one side, do the same to the other
  • If the letter appears twice, collect those terms on one side first then factorise
  • If the letter is under a root, isolate the root then square both sides
  • If the letter is squared, isolate it then take the square root (± applies)
Key Methods
  • Single occurrence: isolate the letter using inverse operations step by step
  • Letter under fraction: multiply both sides by the denominator first
  • Letter appears twice: expand brackets, collect letter terms, factorise, divide
  • Letter squared: rearrange to x² = …, then x = ±√…
  • Square root: rearrange to √x = …, then x = (…)²
Key Formulas
  • Inverse operations: +↔−, ×↔÷, square↔√, cube↔∛
  • Letter twice: collect terms → factorise → divide (e.g. ax + bx = x(a + b))
  • Fraction: multiply by denominator before any other step
Common Mistakes
  • Only dividing part of the numerator: When multiplying out a fraction, multiply ALL terms on both sides
  • Not factorising when the subject appears twice: Must factorise to get the subject as a single term
  • Square root giving only positive answer: x² = 9 gives x = ±3 — remember both roots
  • Order of operations when rearranging: Work in reverse BIDMAS — deal with + and − before × and ÷

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Keep building this topic

Read this section alongside the surrounding pages in Rearranging Formulae. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 3: Subject Appears Twice (Higher)Making a Letter the StarThe Method: Reverse BIDMAS

Practice Questions for Rearranging Formulae

Make b the subject of the formula: a = b + c

  • A. b = a + c
  • B. b = c − a
  • C. b = a − c
  • D. b = ac
1 markfoundation

The circumference of a circle is given by the formula: C = 2πr Make r the subject of the formula.

2 marksfoundation

Quick Recall Flashcards

What does 'rearranging a formula' produce?
An equivalent formula expressing a different variable as the subject. E.g. v = u + at rearranges to a = (v − u)/t.
What is the 'subject' of a formula?
The variable that stands alone on one side of the equals sign. In v = u + at, v is the subject.

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Worked Example 3: Subject Appears Twice (Higher)

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Rearranging Formulae