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GCSE Mathematics · key term
A logically connected sequence of true mathematical statements that establishes a result in every case covered by the claim.
Used by AQA, Edexcel and OCR
Specification A6 · Paper 1, Paper 2, Paper 3
Revise: Equations vs IdentitiesAt Higher tier, you must be able to construct formal algebraic proofs. A proof begins by representing every relevant number generally, proceeds through valid algebra and ends by explaining why the final form establishes the result.
Specification A6, G6 · Paper 1, Paper 2, Paper 3
A logically connected sequence of mathematical statements that establishes that a claim is always true.
Revise: Equations and ProofA proof requires valid algebra that works generally.
A logical argument that establishes a statement for every case covered by its conditions, using known facts and justified steps.
Specification 9.03a, 9.04a · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
A logical sequence of justified mathematical steps establishing that a statement must be true.
Revise: Vector OperationsA diagram is a guide to the routes; the vector argument is the proof.
A statement whose conclusion follows logically from given information and established geometrical facts.
To justify an identity, simplify or expand one side until it becomes exactly the other side. Testing a few values is not a proof.
In a proof about parity, state that the letters represent integers. Without this, forms such as and do not necessarily represent even and odd integers.
End an algebraic proof by linking its final form to the claim, for example: “This is a multiple of 3, so the result is divisible by 3.”
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