GCSE & IGCSE maths practice

Rearranging formulae questions and answers

Rearranging a formula (changing the subject) means getting one letter on its own, using inverse operations in the reverse order. The first questions need one or two steps; the later ones have powers and roots, and the Higher ones have the subject appearing twice, where you collect it on one side and factorise.

10 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 26 Oct 2026.

Start the questions Linear equations: lesson and examples

Where rearranging formulae comes up

GCSE (AQA, Edexcel, OCR)	Rearranging formulae to change the subject: Foundation and Higher.
Cambridge IGCSE (0580)	Core: simple formulas (the subject appears once, with no power or root of it). Extended: the subject appears twice, or there's a power or root of it.
Edexcel International GCSE (4MA1)	Foundation: the subject appears once. Higher: the subject may appear twice or as a power.

The method

Undo what's been done to the subject, in reverse order: brackets and fractions first, then + and −, then × and ÷, then powers and roots.
Whatever you do to one side, do to the whole of the other side.
If the subject appears twice: get every term with the subject on one side, factorise it out, then divide by the bracket.
Type your answer with the subject first if you like, e.g. x = (y - 5)/3.

Rearranging formulae questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Make $x$ the subject of $y = 3x + 5$ .

x =

Question 2Warm-upFoundation

Make $r$ the subject of $C = 2\pi r$ .

r =

Question 3Warm-upFoundation

Make $t$ the subject of $v = u + at$ .

t =

Exam-style

Question 4Exam-styleFoundation

Make $x$ the subject of $y = \dfrac{x}{4} - 2$ .

x =

Question 5Exam-styleFoundation

Make $r$ the subject of $A = \pi r^2$ , where $r$ is positive.

r =

Question 6Exam-styleFoundation

Make $v$ the subject of $E = \tfrac{1}{2}mv^2$ , where $v$ is positive.

v =

Question 7Exam-styleHigher

Make $x$ the subject of $ax + 3 = bx + 7$ .

x =

Question 8Exam-styleHigher

Make $x$ the subject of $y = \dfrac{x + 2}{x - 3}$ .

x =

Challenge

Question 9ChallengeHigher

Make $l$ the subject of $T = 2\pi\sqrt{\dfrac{l}{g}}$ .

l =

Question 10ChallengeHigher

Make $f$ the subject of $\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}$ .

f =

Common mistakes

Dividing only part of a side: from 3x = y − 5, x = (y − 5)/3, not y − 5/3.
Square-rooting before isolating the square: from A = πr², divide by π first.
With the subject twice, trying to divide before collecting the terms together.

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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