Proof
The nature of proof, including induction extended to stronger forms, and the standards a proof must meet.
- The Nature of Proof
- Further Proof by Mathematical Induction
- Strong Induction
NSW Mathematics Extension 2 Stage 6 syllabus strand structure, expressed in Dux teaching language.
Dux tracks each dot point separately, so “I did Mathematics Extension 2” becomes a list of specific things you can already do and specific things you have never been asked. Open a module for all of its dot points, written out.
The nature of proof, including induction extended to stronger forms, and the standards a proof must meet.
Vectors in three dimensions, equations of lines and planes, and vector methods applied to geometric proof.
Arithmetic, geometric representation, De Moivre's theorem, polynomials over the complex numbers, and loci.
Rates of change, first order differential equations, and motion described by a differential relationship.
Substitution, integration by parts, partial fractions, recurrence relations and the applications of the definite integral.
Motion under forces, resisted projectile motion, and simple harmonic motion, derived from Newton's second law.
A Mathematics Extension 2 paper is not one question type repeated. Each command word asks for a different shape of answer, and each is worth a different number of marks.
| Command word | Question type | Marks |
|---|---|---|
| analyse | Problem solving | 3–5 |
| analyse | Calculation | 3–5 |
| calculate | Multiple choice | 1 |
| calculate | Calculation | 2–4 |
| explain | Short answer | 2–4 |
| identify | Multiple choice | 1 |
| justify | Calculation | 4–6 |
| justify | Short answer | 3–5 |
| justify | Problem solving | 4–6 |
| solve | Calculation | 3–5 |
| solve | Problem solving | 4–6 |
HSC Mathematics Extension 2 - Trial Paper Shape — 100 marks, 180 minutes. Practice papers in Dux are assembled to this shape rather than invented, so the timing is training too.
Diagnostic first, then questions written in the shape this course uses. Written answers come back marked against the bands, not just scored.