11–12Mathematics Extension 2 11–12 Syllabus (2024)

Record of changes

Implementation from 2026

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Overview Rationale Aim Outcomes Content Assessment Glossary Teaching and learning support

Content

Year 12

Teaching advice

Examples

Further integration

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
ME2-12-04
selects and uses techniques of integration to solve problems

Further integration

Derive the identities for trigonometric products as sums and differences for $\cos A \cos B = \frac{1}{2} (\cos (A - B) + \cos (A + B)]$ , $\sin A \sin B = \frac{1}{2} (\cos (A - B) - \cos (A + B)]$ , $\sin A \cos B = \frac{1}{2} (\sin (A + B) + \sin (A - B)]$ and $\cos A \sin B = \frac{1}{2} (\sin (A + B) - \sin (A - B)]$
Use the identities for trigonometric products as sums and differences to solve problems and prove results
Solve trigonometric equations by applying the formulas for trigonometric products as sums and differences for $\cos A \cos B$ , $\sin A \sin B$ and $\sin A \cos B$ over restricted domains
Use identities relating the trigonometric products as sums and differences to solve problems involving integrals of the form $\int \sin (mx) \cos (nx) dx$ , $\int \sin (mx) \sin (nx) dx$ or $\int \cos (mx) \cos (nx) dx$
Derive the expressions $\sin A = \frac{2 t}{1 + t^{2}}$ , $\cos A = \frac{1 - t^{2}}{1 + t^{2}}$ and $\tan A = \frac{2 t}{1 - t^{2}}$ where $t = \tan \frac{A}{2}$ (the $t$ -formulas) and use them to solve trigonometric equations over restricted domains
Find Loading and evaluate definite integrals using the method of Loading by substitution, where the Loading may or may not be given
Decompose rational Loading whose Loading can be expressed as a product of Loading Loading factors, distinct irreducible quadratic factors and perfect square factors into Loading
Integrate rational functions whose denominators can be expressed as a product of distinct linear factors, distinct irreducible quadratic factors and perfect square factors, using partial fraction decomposition
Integrate rational functions by completing the square on a quadratic denominator
Integrate rational functions where the degree of the Loading is not less than the degree of the denominator
Integrate functions by changing an Loading into an appropriate form using algebraic manipulation
Derive the method for Loading
Find indefinite integrals and evaluate definite integrals using the method of integration by parts, including problems where more than one application is required
Derive and use Loading involving integration by parts
Solve theoretical problems involving multiple techniques of integration
Solve practical problems involving multiple techniques of integration

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