DfE statement A6 · Algebra
Identities, equivalence and algebraic proof
Identities, equivalence and algebraic proof is content statement A6 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs." (statement A6). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "and proofs". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Testing one or two numbers and calling the result proved. A proof must hold for every value, which means working algebraically.
- Using the same letter for two different quantities: if 2n is your even number, the next even number is 2n + 2, not 2n + 1 and not 2m.
- Writing = between lines that are not equal, so the chain of reasoning says something untrue even if the final answer is right.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is identities, equivalence and algebraic proof on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "and proofs" — are Higher only; the rest is Foundation content.
Can I use a calculator for identities, equivalence and algebraic proof?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Testing one or two numbers and calling the result proved. A proof must hold for every value, which means working algebraically.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Algebra at Foundation or at Higher.