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 β first, then Γ or Γ·, 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 (Β± 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 xΒ² = β¦, then x = Β±ββ¦
- Square root: rearrange to βx = β¦, then x = (β¦)Β²
Key Formulas
- Inverse operations: +ββ, ΓβΓ·, squareββ, cubeββ
- Letter twice: collect terms β factorise β 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: xΒ² = 9 gives x = Β±3 β remember both roots
- Order of operations when rearranging: Work in reverse BIDMAS β deal with + and β before Γ and Γ·
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.
Practice questions for Rearranging Formulae
Make b the subject of the formula: a = b + c
The circumference of a circle is given by the formula: C = 2Οr Make r the subject of the formula.
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 β 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.