Algebraic Proof | 40 Worked Examples | Edexcel GCSE Higher Maths

40 fully worked algebraic proof questions for Edexcel GCSE Higher Maths (1MA1), building from simple expand-and-simplify identities up to full formal proofs with mark-scheme annotations on every line.

What’s inside:
Easy: Representing even numbers as 2n, odd numbers as 2n+1, and consecutive integers as n, n+1, n+2, then expanding and simplifying basic algebraic identities.
Medium: Proving that sums of consecutive integers or odd numbers are multiples of a given number, proving the product of consecutive integers is even, and using differences of two squares.
Hard: Multi-step proofs involving differences of squares that are multiples of 8 or 12, proving n squared plus n is always even, and completing the square to prove an expression is always positive.

Every question includes a full worked solution with step-by-step reasoning, annotated mark-scheme points (M1, A1, B1), and a clear concluding sentence explaining why the algebra proves the statement, not just what the algebra says. The 10 hardest questions include extra explanatory notes on why general algebraic representations (2n, n and n+1, and so on) prove a result for every integer rather than just one example, plus common pitfalls to avoid.

Ideal for Year 10/11 students studying Edexcel GCSE Higher (1MA1) working towards grades 5-9, and for tutors or teachers wanting a ready-made resource covering the full algebraic proof topic with model answers included.