← Maths Extension 1 syllabus

NSWMaths Extension 1

Proof (ME-P1)

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we use mathematical induction to prove divisibility statements?

Prove divisibility statements involving an integer parameter $n$ using mathematical induction
A focused answer to the HSC Maths Extension 1 dot point on induction proofs of divisibility. The standard four-part structure, the trick of writing $k + 1$ expressions in terms of the $k$ case plus a divisible chunk, and worked examples.
8 min answer →

How do we use induction to prove general statements involving a recursion, a formula or a property?

Apply mathematical induction to prove general statements about a recursive sequence, a property of a formula, or a recursive procedure
A focused answer to the HSC Maths Extension 1 dot point on induction for general (non-series, non-divisibility, non-inequality) statements. Closed-form for a recurrence, properties preserved by an iterative process, and worked examples.
7 min answer →

How do we use induction to prove an inequality holds for every positive integer?

Prove inequalities involving an integer parameter $n$ using mathematical induction
A focused answer to the HSC Maths Extension 1 dot point on induction for inequalities. The standard structure, the trick of strengthening one side to match the hypothesis, and worked examples including $2^n > n^2$ and $n! > 2^n$ .
7 min answer →

How do we use mathematical induction to prove identities involving sums of a sequence?

Prove identities for sums of series using the principle of mathematical induction
A focused answer to the HSC Maths Extension 1 dot point on induction proofs of series identities. The base case, induction hypothesis, induction step, and conclusion, applied to sums of integers, squares, cubes and geometric-like patterns, with worked examples.
8 min answer →