Functions
Inverse functions, parametric representation and polynomials, including the graphing skills Extension 1 assumes and extends.
- Inverse Functions
- Parametric Representation
- Polynomial Functions
NSW Mathematics Extension 1 Stage 6 syllabus strand structure, expressed in Dux teaching language.
Dux tracks each dot point separately, so “I did Mathematics Extension 1” 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.
Inverse functions, parametric representation and polynomials, including the graphing skills Extension 1 assumes and extends.
Inverse trigonometric functions, further identities and trigonometric equations, treated graphically and algebraically.
Rates of change, exponential and logarithmic calculus, integration techniques, and applications to the physical world.
Discrete and continuous probability distributions, and the sampling ideas that make an estimate meaningful.
Vector algebra and geometry in two dimensions, leading to projectile motion as a vector application.
Mathematical induction and the binomial theorem, plus the counting techniques that Extension 1 questions assume fluently.
A Mathematics Extension 1 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 | Calculation | 3–5 |
| calculate | Calculation | 2–4 |
| calculate | Multiple choice | 1 |
| explain | Short answer | 2–4 |
| identify | Multiple choice | 1 |
| justify | Short answer | 4–6 |
| justify | Calculation | 4–6 |
| justify | Problem solving | 4–6 |
| solve | Short answer | 3–5 |
| solve | Problem solving | 4–6 |
| solve | Calculation | 3–5 |
HSC Mathematics Extension 1 - Trial Paper Shape — 70 marks, 120 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.