Rearranging formulae Revision Notes for AQA GCSE Maths

Rearranging formulae

What is the subject of a formula?

infoNote

The subject of a formula is the single letter that appears by itself on one side of the equals sign. This variable is what the formula calculates or finds.

For example:

In $P = 2l + 2w$ , P is the subject
In $A = \frac{1}{2}bh$ , A is the subject

When you rearrange a formula, you change which letter becomes the subject by using algebraic methods, similar to solving equations.

Method for finding missing values

When you need to find a value that isn't currently the subject of a formula, follow this two-step process:

Step 1: Substitute the known values into the formula Step 2: Solve the resulting equation to find the missing value

This approach works when you know most values but need to find one specific unknown.

Rearranging to change the subject

To make a different letter the subject of a formula, you must perform the same operation to both sides until your chosen letter stands alone on one side.

chatImportant

Key principles:

Do the same thing to both sides - this keeps the formula balanced
Work systematically - undo operations in reverse order
Isolate your target letter - get it by itself on one side

Step-by-step approach:

Identify which letter you want as the new subject
Use inverse operations to move other terms to the opposite side
Continue until your chosen letter is isolated

Worked examples

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Worked Example 1: Finding a missing value

When Alicia works h hours normal time and v hours overtime weekly, she earns: $P = 8h + 12v$

If she worked 32 normal hours and earned £328 total, find her overtime hours:

$328 = 8 \times 32 + 12v$
$328 = 256 + 12v$
$72 = 12v$
$v = 6$

Alicia worked 6 hours overtime.

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Worked Example 2: Making p the subject

Starting with $N = 2p + 3q^2$ , rearrange to make p the subject:

$N = 2p + 3q^2$ (subtract $3q^2$ from both sides)
$N - 3q^2 = 2p$ (divide both sides by 2)
$p = \frac{N - 3q^2}{2}$

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Worked Example 3: Making Q the subject

Starting with $R = 1 - 5Q$ , rearrange to make Q the subject:

$R = 1 - 5Q$ (add $5Q$ to both sides)
$R + 5Q = 1$ (subtract R from both sides)
$5Q = 1 - R$ (divide both sides by 5)
$Q = \frac{1 - R}{5}$

Tip: When you want a term to be positive, start by adding it to both sides.

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Worked Example 4: Making h the subject

Starting with $A = \frac{1}{2}bh$ , rearrange to make h the subject:

$A = \frac{1}{2}bh$ (multiply both sides by 2)
$2A = bh$ (divide both sides by b)
$h = \frac{2A}{b}$

Tip: The new subject can appear on either side of the formula - it doesn't matter which.

Common techniques

Dealing with fractions

When your target letter is in a fraction, multiply both sides by the denominator to eliminate the fraction first.

Dealing with brackets

If your target letter is inside brackets, you may need to expand the brackets first, then rearrange.

Working with negative terms

Add the negative term to both sides to make it positive, then continue rearranging.

Exam tips

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Key Points to Remember:

Show every step clearly in your working
Check your answer by substituting back into the original formula
Keep fractions in their simplest form
Write your final answer clearly - state what the new subject equals

Remember!

The subject of a formula is the single letter that stands alone on one side
Always do the same operation to both sides when rearranging
Use inverse operations to move terms across the equals sign
Substitute known values first, then solve for unknown values
Check your rearranged formula by substituting test values

Rearranging formulae (AQA GCSE Maths): Revision Notes