A4AlgebraFoundation & Higher

Substitution & Formulae

A formula is a rule connecting quantities, like $A = l w$ for the area of a rectangle. Substituting means putting numbers in; rearranging means changing which letter is the subject.

35 min Video by Maths Genie AQA GCSE Maths

Changing the Subject of a FormulaWatch the walkthrough, then read the notes below.

Open on YouTube

What you'll learn

Substitute values into expressions and formulae
Use BIDMAS when substituting
Change the subject of a formula
Work with formulae from real contexts

Substituting values

Replace each letter with its value and work out the answer using BIDMAS. Be careful with powers and negative numbers.

1Square first:

4^{2} = 16

2Then

3 \times 16 = 48

Answer

48

Changing the subject

To make a different letter the subject, use inverse operations to get it on its own — exactly like solving an equation, but with letters.

v = u + a t \Rightarrow t = \frac{v - u}{a}

Rearranged to make t the subject.

Tip — Whatever you do to one side of a formula, do to the other.

Remember these

A = l w

Substitute numbers for letters.

inverse operations rearrange a formula

Get the new subject on its own.

Watch out for these

Working out

3 a^{2}

when

a = 4

(3 \times 4)^{2} = 144

Powers before multiplying:

3 \times 16 = 48

Only changing one side when rearranging.

Apply each inverse operation to both sides.

Key takeaways

Substitute by replacing letters with values and using BIDMAS.
Powers and brackets come before multiplication.
Rearrange formulae with inverse operations on both sides.

Test yourself

Ready to practise Substitution & Formulae? Pick a mode and earn XP & Dobloons.