Topic summary · IGCSE handout

Proof summary

Mathematical proof needs clear statements, defined starting points, and reasons — algebra identities and geometric angle chains are typical IGCSE proofs.

Open Learning Sheet — Proof Download Proof answers PDF

Files: 51_proof_handout.pdf · 51_proof_handout_answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Identity proof: start from one side and reach the other (or show both equal a third expression).
Geometric proof: state equal angles/lines with theorem names.
Counter-examples disprove universal claims quickly.

Worked example 1 — Odd + odd

Prove the sum of two odds is even.

Working

(2k+1)+(2m+1)=2(k+m+1)

Algebraic parity.

Worked example 2 — Consecutive product

Show $n(n+1)$ is even.

Working

\text{one of }n,n+1\text{ is even}

Consecutive integers.

Worked example 3 — Square difference

Expand $(n+1)^2-n^2$ .

Working

2n+1

Next odd number.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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