Watch out
Applying an inverse operation to only one term.
Scottish National 5 Mathematics
National 5 Maths Changing the subject
Rearrange linear formulae and formulae involving a simple square or square root.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Identify the operations applied to the required subject.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Changing the subject is an assessed part of Scottish National 5 Mathematics in the algebra area. Rearrange linear formulae and formulae involving a simple square or square root.
Identify the operations applied to the required subject.
Undo them in reverse order on both sides.
If the subject is squared, take the appropriate square root at the final step.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- Use inverse operations on both sides of the formula.
Check
Expand, factorise or substitute back into the original expression to verify the result.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Changing the subject worked example
Make r the subject of A = πr²
- Divide by π: r² =
- Take the positive square root for a radius.
Answer: r = √
Watch out
- Applying an inverse operation to only one term.
- Forgetting that a physical length is positive.