Topic explanation
Proof & Reasoning is part of the Algebra strand in GCSE Maths. Structure deductive steps, use known facts, and avoid circular reasoning in GCSE proof questions.
Exam papers from AQA, Edexcel, OCR assess fluency (short questions) and reasoning (multi-mark). Practise reading command words (“show that”, “hence”, “give your answer in the form…”) before you rearrange algebra or interpret a result.
Key formulas & rules
- Expanding: single bracket, double brackets, watch signs on every term
- Factorising: HCF first, then pairs/quadratics; difference of two squares a² − b²
- Rearranging: inverse operations in reverse order; keep equality balanced
Common mistakes
- Arithmetic and sign errors when simplifying expressions involving proof & reasoning.
- Not answering in the required form (fraction vs decimal, surd vs rounded).
- Missing a final sentence that interprets the result in context when the question is applied.
Exam tips
- Underline key words in the question: “exact”, “integer”, “give reasons”.
- Estimate or use inverse operations to sanity-check answers when a calculator is allowed.
- Use StudyVector practice filtered to “Algebraic Notation & Simplifying” to drill exam-style questions on this skill.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
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