GCSE & iGCSE Algebraic Proof worksheet

Algebraic proof worksheet for GCSE and iGCSE maths: counterexamples, writing even, odd and consecutive numbers in algebra, and formal proofs.

A complete algebraic proof worksheet for Pearson Edexcel GCSE (1MA1) and International GCSE (4MA1), written so one resource works for both tiers. Every section is clearly labelled Foundation or Higher, and questions get harder as you go.

What’s covered — Foundation

Disproving a statement with a counterexample
Explaining why examples do not prove a statement
Writing consecutive, even and odd numbers in algebra
Using algebra to show a statement is always true

What’s covered — Higher (grades 6 to 9)

Formal proofs using 2m and 2n + 1
Proofs about multiples
Proving identities
Prove or disprove questions

How it’s structured

A. Worked examples & Your turn — a model solution beside a matching question to try
B. Fluency — core skills
C. Reasoning — explain it
D. Problem solving — unfamiliar, multi-step questions
E. Exam practice — exam-style questions with mark allocations

123 marks across Sections B to E (61 Foundation, 62 Higher), with a progress tracker on the front page so students can record their score per section. Why examples do not constitute a proof is addressed head on, since that misconception is what stops students starting these questions at all.

How to use it

Works as a full lesson, homework, a cover lesson or targeted intervention. Because each tier is labelled, you can set the Foundation sections to one group and the Higher sections to another from the same print.

What’s included

13-page worksheet (PDF, printable, with answer spaces)
6-page full worked solutions (PDF) — complete method for every question, not just final answers
No calculator

Specification

Pearson Edexcel GCSE Mathematics (1MA1) and International GCSE Mathematics (4MA1), Algebra. All questions are original.