11–12Mathematics Extension 1 11–12 Syllabus

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Implementation from 2026

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Overview Rationale Aim Outcomes Content Assessment Glossary Teaching and learning support

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Year 11

Teaching advice

Examples

Further work with functions

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
ME1-11-01
solves problems involving inequalities, functions and their inverses, graphical relationships between functions, and parametric equations

Further work with functions

Graphical relationships

Examine the relationship between the graph of $y = f (x)$ and the graph of $y = \frac{1}{f (x)}$ using graphing applications, and graph $y = \frac{1}{f (x)}$ given $y = f (x)$ in algebraic or graphical form, identifying any vertical and horizontal asymptotes of $y = f (x)$ and $y = \frac{1}{f (x)}$
Graph $y = \sec x$ , $y = cosec x$ and $y = \cot x$ in both radians and degrees, identifying key properties including asymptotes, period, domain, range and symmetry, and compare each graph with the graph of its reciprocal
Examine the relationship between the graph of $y = f (x)$ and the graphs of $y = | f (x) |$ and $y = f (| x |)$ using graphing applications, and graph $y = | f (x) |$ and $y = f (| x |)$ given $y = f (x)$ in algebraic or graphical form
Examine the relationship between the graphs of $y = f (x)$ and $y = g (x)$ and the graphs of $y = f (x) + g (x)$ and $y = f (x) - g (x)$ using graphing applications, and graph $y = f (x) + g (x)$ and $y = f (x) - g (x)$ given $y = f (x)$ and $y = g (x)$ in algebraic or graphical form
Determine the domains and ranges of the sum and difference of functions where possible, and, if appropriate, verify them using a graphing application
Apply knowledge of graphical relationships to solve problems involving graphs of functions, justifying conclusions in the context of the problem where appropriate

Inverse functions

Describe a function as one-to-one if every element in the range of the function corresponds to exactly one element of the domain
Establish that the reflection of a point in the line $y = x$ reverses the coordinates of the point
Define an inverse function $f^{- 1}$ informally as a function that reverses or undoes the effect of the function $f$
Recognise that inverse functions exist for one-to-one functions
Determine the equation for the inverse function $f^{- 1} (x)$ of a given one-to-one function $y = f (x)$ by interchanging the variables $x$ and $y$ in $y = f (x)$
Compare the graphs of a function and its inverse function using graphing applications, and recognise that the two graphs are reflections of each other in the line $y = x$
Establish that the domain of $f^{- 1} (x)$ is the range of $f (x)$ , and the range of $f^{- 1} (x)$ is the domain of $f (x)$ , and use this relationship to solve problems
Graph the inverse function of a given one-to-one function
Explain that the reflection in the line $y = x$ exchanges horizontal and vertical lines and recognise that the horizontal line test can therefore be applied to the graph of $y = f (x)$ to determine whether its reflection in the line $y = x$ is a function
Apply restrictions to the domain of a function, if it is not one-to-one, to obtain an inverse function
Define formally $f^{- 1} (x)$ to be the inverse function of $f (x)$ if the relationships $f (f^{- 1} (x)) = x$ and $f^{- 1} (f (x)) = x$ hold, and use this definition to solve problems
Solve problems based on the relationship between a function and its inverse function using algebraic and graphical techniques, including determining the points of intersection of a function and its inverse, where they exist

Parametric form of a function or relation

Recognise that a curve may be represented by two parametric equations that give $x$ and $y$ as functions of a parameter and that the curve may also have a Cartesian equation in $x$ and $y$
Express linear and quadratic functions and circles in parametric form
Convert linear and quadratic functions and circles from parametric form to Cartesian form
Graph linear and quadratic functions and circles expressed in parametric form

Inequalities

Solve cubic inequalities where the cubic is expressed as a product of linear factors
Solve inequalities involving rational expressions with variables in the denominator
Solve absolute value inequalities of the form $| ax + b | \geq k$ , $|ax + b| \leq k$ , $|ax + b| < k$ , $|ax + b| > k$ , where $a$ , $b$ and $k$ are constants, using algebraic and graphical methods or the characterisation of $|x|$ as the distance of $x$ from the origin

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Year 12

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11–12Mathematics Extension 1 11–12 Syllabus

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