Make a the subject of F = ma.

a = F/m. Divide both sides by m.

Make x the subject of y = x + 7.

x = y − 7. Subtract 7 from both sides.

Make h the subject of V = Ah.

h = V/A. Divide both sides by A.

Make x the subject of y = 2x + 1.

x = (y − 1)/2. Subtract 1, then divide everything by 2.

Make r the subject of C = 2πr.

r = C/(2π). Divide both sides by 2π.

Changing the subject of a formula · Cambridge IGCSE Mathematics

In plain words

A formula such as v = u + at tells you v if you know the rest. But what if you know v and want t? Changing the subject means rearranging the formula so a different letter is on its own. It's solving an equation with letters instead of numbers.

Three things to know

Treat the letter you want as x, and undo everything around it, doing the same to both sides.
If the letter you want is squared, square-root both sides at the end.
If it appears twice, get both terms on one side and factorise it out.

Worked example

Make x the subject of y = 3x − 5.

Add 5 to both sides: y + 5 = 3x.
Divide both sides by 3.
x = (y + 5)/3.

Tips and tricks

Divide the whole of the other side, not just part of it. x = y + 5/3 is wrong.
Substituting numbers into a formula: write it out with the numbers in before using a calculator.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Changing the subject of a formula: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Make a the subject of F = ma.
- a = Fm
- a = F/m (the answer)
- a = m/F
- a = F − m
Divide both sides by m.
Make x the subject of y = x + 7.
- x = y + 7
- x = y − 7 (the answer)
- x = 7 − y
- x = y/7
Subtract 7 from both sides.
Make h the subject of V = Ah.
- h = V/A (the answer)
- h = VA
- h = A/V
- h = V − A
Divide both sides by A.
Make x the subject of y = 2x + 1.
- x = 2y − 1
- x = (y + 1)/2
- x = (y − 1)/2 (the answer)
- x = y/2 − 1
Subtract 1, then divide everything by 2.
Make r the subject of C = 2πr.
- r = 2πC
- r = C/(2π) (the answer)
- r = C − 2π
- r = 2π/C
Divide both sides by 2π.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Changing the subject of a formula

Cambridge IGCSE Mathematics 0580 · 9 marks · papermunch.org

Name ______________________________ Date ______________

Make t the subject of v = u + at.[2]
Show answerHide answer
t = (v − u)/a.
I got this one
Make r the subject of A = πr².[2]
Show answerHide answer
r = √(A/π).
I got this one
Make x the subject of y = (x + 2)/3.[2]
Show answerHide answer
x = 3y − 2.
I got this one
Make x the subject of ax + b = cx + d.[3]
Show answerHide answer
x = (d − b)/(a − c). ax − cx = d − b, so x(a − c) = d − b.
I got this one

Answers: Changing the subject of a formula

1. t = (v − u)/a.
2. r = √(A/π).
3. x = 3y − 2.
4. x = (d − b)/(a − c). ax − cx = d − b, so x(a − c) = d − b.