11–12Mathematics Advanced 11–12 Syllabus

Implementation from 2026

Expand for detailed implementation advice

Content

Year 11

Year 12

Teaching advice

Examples

Differential calculus

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
MAV-12-04
selects and applies differentiation methods to solve problems

Differential calculus

Differentiation with exponential functions

Apply the rules of differentiation to find the derivative of $f (x) = k e^{ax}$ , where $k$ and $a$ are constants
Use the chain rule to prove $\frac{d}{dx} (e^{ax + b}) = a e^{ax + b}$ , where $a$ and $b$ are constants and $a \neq 0$
Prove and use the formula $\frac{d}{dx} (a^{x}) = (\ln a) a^{x}$ , where $a$ is a constant and $a > 0$
Use the chain rule to differentiate functions of the form $e^{f (x)}$

Differentiation with logarithmic functions

Use chain rule on the identity $e^{\ln x} = x$ to prove the formula $\frac{d}{dx} (\ln x) = \frac{1}{x}$ for the derivative of the natural logarithm function where $x > 0$
Prove and use the formula $\frac{d}{dx} (\log_{a} x) = \frac{1}{x \ln a}$ , where $a$ is a constant and $a > 0$
Use the chain rule to differentiate functions of the form $\ln f (x)$

Differentiation with trigonometric functions

Determine the formulas $\frac{d}{dx} (\sin x) = \cos x$ and $\frac{d}{dx} (\cos x) = - \sin x$ informally by using the graphs of $y = \sin x$ and $y = \cos x$ and verify with graphing applications
Use the rules of differentiation to show that $\frac{d}{dx} (\tan x) = \sec^{2} x$
Use the rules of differentiation to find the derivatives of $cosec x$ , $\sec x$ and $\cot x$
Use the chain rule to differentiate functions of the form $\sin f (x)$ , $\cos f (x)$ and $\tan f (x)$

Using derivatives

Apply the product, quotient and chain rules to differentiate functions of the form
$f (x) g (x)$ , $\frac{f (x)}{g (x)}$ or $f (g (x))$ , where $f (x)$ and $g (x)$ are any of the functions within the scope of the Mathematics Advanced course
Solve problems involving equations of tangents and normals to curves involving any of the functions within the scope of the Mathematics Advanced course

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