GCSE Maths: Completing the Square
Rewrite a quadratic in completed-square form and use it to solve and sketch. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.
What you need to know
The concepts examiners test on completing the square, and what each one is really asking.
Where marks get lost
The exam technique that separates a correct method from a correct answer.
- Forgetting to subtract the square of the halved number, so the expression is no longer equal to the original
- Reading the turning point of (x + 3)² - 8 as (3, -8) rather than (-3, -8)
- Not factorising out the leading coefficient first when it is not 1
- Losing the plus-or-minus when square-rooting to solve
Completing the Square questions students ask
Is Completing the Square on the Foundation paper?
No — Completing the Square is a Higher tier topic, so it appears on Higher papers only.
What should I know before starting Completing the Square?
It builds on Quadratics and Expanding brackets and Surds. If those feel shaky, practise them first — Completing the Square questions assume them.
What is the most common mistake in Completing the Square?
Forgetting to subtract the square of the halved number, so the expression is no longer equal to the original.
Which exam boards cover Completing the Square?
All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.