Proof Techniques

 Proof is the language of higher mathematics — and a significant part of both HSC Maths Extension 1 and Extension 2. NESA expects clear, logical arguments: direct proof, proof by contradiction, proof by contrapositive, and mathematical induction.

Proof methods you must know

• Direct proof — assume P, derive Q step by step
• Proof by contradiction — assume ¬Q, derive a contradiction
• Proof by contrapositive — prove ¬Q → ¬P instead of P → Q
• Mathematical induction — base case, inductive assumption, inductive step
• Combinatorial proof — counting arguments (Extension 2)

Proof booklets

HSC Proofs on Vu's Maths Hub covers proof structure, rigour, and strategies with proof by contradiction examples for Extension 1 and 2.

For induction specifically: HSC Induction — HSC mathematical induction proofs for divisibility, inequalities, and summations.

Proof in context

Proof skills appear in HSC Combinatorics, HSC Inequalities, and HSC Polynomials. Harder proof questions: HSC Last Resorts.

Free NESA-aligned HSC Maths booklets — your tutoring alternative for NSW Year 12 proof revision at vumaths.com.