HSC inequalities Extension 2 is a topic where knowing the right technique makes the difference between a one-line proof and a dead end. AM-GM, Cauchy-Schwarz, and clever algebraic manipulation appear regularly in Extension 2 exams and in harder past paper questions.
Essential inequality tools
- AM-GM inequality — arithmetic mean ≥ geometric mean for non-negative reals
- Cauchy-Schwarz inequality — (Σaᵢbᵢ)² ≤ (Σaᵢ²)(Σbᵢ²)
- Triangle inequality for complex numbers and vectors
- Proof techniques for inequalities — substitution, homogenisation, convexity arguments
- Connection to induction — proving inequalities by mathematical induction
Inequalities booklet
HSC Inequalities on Vu's Maths Hub covers common techniques, classic results, and worked examples for Extension 2 preparation.
Related revision
- HSC Induction — inequality proofs by induction
- HSC Proofs — proof structure and rigour
- HSC Last Resorts — creative approaches to hard inequality problems
Extension 2 worked solutions, free HSC Maths revision notes — vumaths.com.
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