Learning pack · IGCSE handout

Proof

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Mathematical proof needs clear statements, defined starting points, and reasons — algebra identities and geometric angle chains are typical IGCSE proofs.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 51_proof_handout.pdf · 51_proof_handout_answers.pdf

Full topic summary

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

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.

🎬 Topic videos

Fool-Proof Test for Primes - Numberphile
Numberphile · 4 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Golden Proof - Numberphile
Numberphile · 5 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
When a complicated proof simplifies everything
Stand-up Maths · 6 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
An ingenious & unexpected proof of the Binomial Theorem (1 of 2: Prologue)
Eddie Woo · 7 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
The Cosine Rule (1 of 3: Proof of the Formula)
Eddie Woo · 13 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Concurrence of Medians (1 of 2: Proof via similar triangles)
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

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Browse the hub Learning Packs & Summary, or open the compact Proof summary.