Show WorkingWorked example 1: change the subject of a formula
Make x the subject of y = 3x − 3.
- Add 3 to both sides: y + 3 = 3x.
- Divide both sides by 3: x = y + 33.
Answer x = (y + 3)÷3
AlgebraFoundation and Higher (some Higher only)
Rearranging formulae GCSE questions with answers
8 rearranging formulae questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.
Rearranging a formula means making a different letter the subject, using the same inverse steps as solving an equation. On Higher the formulae have powers and roots too, such as making u the subject of v² = u² + 2as.
01 / Quiz yourselfTry it, then tap to check
Rearranging formulae questions to try
Work each one out on paper first. Then open the answer and compare your working with ours, step by step.
01 / Change the subject of a formulaBoth tiers
Make x the subject of y = 10 − 5x.
Show the answer and working
- Add 5x to both sides: y + 5x = 10.
- Subtract y from both sides: 5x = 10 − y.
- Divide both sides by 5: x = 10 − y5.
Answer x = (10 − y)÷5
02 / Change the subject of a formulaBoth tiers
The perimeter of a rectangle is given by P = 2a + 2b.
Make a the subject of the formula.
Show the answer and working
- Subtract 2b from both sides: P − 2b = 2a.
- Divide both sides by 2: a = P − 2b2. (This is the same as P2 − b.)
Answer a = (P − 2b)÷2
03 / Change the subject of a formulaBoth tiers
Make x the subject of y = 3x + 12.
Show the answer and working
- Subtract 12 from both sides: y − 12 = 3x.
- Divide both sides by 3: x = y − 123.
Answer x = (y − 12)÷3
04 / Change the subject of a formulaBoth tiers
In physics, v = u + at.
Make u the subject of the formula.
Show the answer and working
- Subtract at from both sides: v − at = u.
- So u = v − at.
Answer u = v − at
05 / Rearrange harder formulaeHigher only
In physics, v2 = u2 + 2as.
Make u the subject of the formula, where u is positive.
Show the answer and working
- Subtract 2as from both sides: u2 = v2 − 2as.
- Square root both sides: u = √v2 − 2as.
Answer u = √v2 − 2as
06 / Rearrange harder formulaeHigher only
Make y the subject of ky + m = ny + w.
Show the answer and working
- Get the y terms on one side and everything else on the other: ky − ny = w − m.
- Factorise the left side: y(k − n) = w − m.
- Divide both sides by k − n: y = w − mk − n.
Answer y = (w − m)÷(k − n)
07 / Rearrange harder formulaeHigher only
Make x the subject of y = 3x + 5x.
Show the answer and working
- Multiply both sides by x: xy = 3x + 5.
- Get the x terms on one side: xy − 3x = 5.
- Factorise: x(y − 3) = 5.
- Divide by y − 3: x = 5y − 3.
Answer x = 5÷(y − 3)
08 / Rearrange harder formulaeHigher only
Make x the subject of y = 3x2 − 4, where x is positive.
Show the answer and working
- Add 4 to both sides: y + 4 = 3x2.
- Divide both sides by 3: x2 = y + 43.
- Square root both sides: x = √(y + 4)÷3.
Answer x = √(y + 4)÷3
02 / What's covered2 kinds of question
Rearranging formulae at GCSE and where marks go
- Change the subject of a formulaBoth tiers
- Rearrange harder formulaeHigher only
Worked example 2: rearrange harder formulae
Make x the subject of y = 8x + 1x.
- Multiply both sides by x: xy = 8x + 1.
- Get the x terms on one side: xy − 8x = 1.
- Factorise: x(y − 8) = 1.
- Divide by y − 8: x = 1y − 8.
Answer x = 1÷(y − 8)
A common mistake
Undoing the steps in the wrong order. To make x the subject of y = 3x + 5, take away 5 first, then divide by 3: x = (y − 5)/3, not y/3 − 5.
03 / Practise itiPhone and iPad
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