11–12Mathematics Extension 1 11–12 Syllabus

Implementation from 2026

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Content

Year 11

Teaching advice

Examples

Further trigonometry

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
ME1-11-03
solves problems in three dimensions using trigonometry and simplifies expressions, proves results and solves problems involving compound angles using trigonometric identities

Further trigonometry

Trigonometry in three dimensions

Interpret information about a 3-dimensional context given in diagrammatical form
Interpret information about a 3-dimensional context given in written form
Apply trigonometry to solve problems in three dimensions where a diagram is given

Further trigonometric identities

Derive the sum and difference expansions for the trigonometric functions $\sin (A \pm B) = \sin A \cos B \pm \cos A \sin B$ , $\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B$ and $\tan (A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$
Use sum and difference expansion formulas to solve problems and prove results
Derive the double angle formulas $\sin 2 A = 2 \sin A \cos A$ , $\cos 2 A = \cos^{2} A - \sin^{2} A = 2 \cos^{2} A - 1 = 1 - 2 {s i n}^{2} A$ and $\tan 2 A = \frac{2 \tan A}{1 - {t a n}^{2} A}$
Use the double angle formulas to solve problems and prove results

Further trigonometric equations

Solve trigonometric equations involving factorisation and/or substitution of trigonometric identities over restricted domains
Examine the representations of $a \cos x + b \sin x$ as $R \cos (x \pm α)$ or $R \sin (x \pm α)$ with and without graphing applications, where $a \neq 0$ and $b \neq 0$
Apply the representations of $a \cos x + b \sin x$ as $R \cos (x \pm α)$ or $R \sin (x \pm α)$ to graph functions, solve equations of the form $a \cos x + b \sin x = c$ over restricted domains, and model and solve related problems
Interpret solutions of trigonometric equations graphically with and without graphing applications
Model and solve practical problems using trigonometric equations and analyse their solutions in a variety of contexts

Related files

Year 12