Standard formulae and rearranging
Rearranging formulae is a stepping stone between substitution A2 and solving equations A17. OCR Foundation tests simple one-step rearrangements; Higher includes squares, square roots, and formulas with the new subject appearing twice.
What "subject" means
The subject of a formula is the variable on its own (usually on the left).
- In A = πr², A is the subject.
- "Make r the subject" means rearrange so r is alone on one side.
The recipe — inverse operations
To change the subject:
- Identify the operations applied to the desired variable (in order).
- Apply the inverse operations to BOTH sides, in reverse order.
Mathematics is "do the same to both sides".
✦Worked example— Example — single inverse step
C = 2πr. Make r the subject.
- r is multiplied by 2π.
- Divide both sides by 2π: r = C / (2π).
✦Worked example— Example — multiple steps
v = u + at. Make a the subject.
- u is added; subtract u from both sides: v − u = at.
- a is multiplied by t; divide by t: a = (v − u)/t.
✦Worked example— Example — square or square root
A = πr². Make r the subject.
- A/π = r².
- r = √(A/π) (positive square root for length).
T = 2π√(L/g). Make L the subject.
- T/(2π) = √(L/g).
- (T/(2π))² = L/g.
- L = g(T/(2π))² = gT²/(4π²).
✦Worked example— Example — variable on both sides (Higher)
a = (b + c)/(b − c). Make b the subject.
- a(b − c) = b + c (multiply both sides by (b − c)).
- ab − ac = b + c.
- ab − b = c + ac.
- b(a − 1) = c(a + 1).
- b = c(a + 1)/(a − 1).
Standard formulae you should know
- Speed: s = d/t.
- Area: A = πr², A = ½bh, A = lw.
- Pythagoras: c² = a² + b².
- KE: E = ½mv².
- Compound interest (Higher): A = P(1 + r)ⁿ.
OCR mark scheme conventions
- M1 for one correct rearrangement step.
- M1 + A1 for full rearrangement.
- For the answer, simplification expected (e.g. don't leave 2 × 3 — write 6).
⚠Common mistakes
- Adding when you should multiply (or vice versa).
- Square-rooting only one side.
- With variable on both sides, forgetting to factorise.
- Forgetting that the inverse of squaring is square root (not "÷ 2").
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves