HSC mathematical induction is one of the most distinctive Extension 1 topics — and one of the most feared. Students must prove statements about natural numbers using a base case, an inductive assumption, and an inductive step. Get the structure wrong and you lose marks even if the maths is correct.
What induction questions look like
Extension 1 induction problems typically involve:
- Proving divisibility (e.g. "show that 7n − 1 is divisible by 6")
- Proving inequalities (e.g. "show that 2n > n² for n ≥ 5")
- Proving summation formulas (e.g. sums of squares or cubes)
- Strong induction variants for harder questions
Dedicated induction booklet
The HSC Induction booklet on Vu's Maths Hub walks through patterns, inequalities, and divisibility proofs with full worked examples — exactly the kind of HSC mathematical induction proofs NESA assesses.
Pair it with HSC Proofs for broader proof techniques including direct proof and proof by contradiction.
Related Extension 1 topics
Induction connects to HSC Sequences (summation and series) and HSC Polynomials Extension 1 (algebraic manipulation in inductive steps).
Free Extension 1 worked solutions, NESA-aligned revision, and past paper practice — all at vumaths.com.
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