11–12Mathematics Advanced 11–12 Syllabus (2024)

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Implementation from 2026

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Year 11

Teaching advice

Examples

Trigonometry and measure of angles

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-11-04
applies trigonometry to solve problems involving geometric shapes

Trigonometry and measure of angles

Trigonometry with acute angles

Use Pythagoras’ theorem to find the exact sine, cosine and tangent ratios for angles of $30 °$ , $45 °$ and $60 °$
Apply trigonometry to solve problems involving right-angled triangles in two dimensions, Loading and Loading , and Loading and Loading

Trigonometry with angles of any magnitude

Represent angles of any Loading using rays from the origin in the Loading and describe how one ray represents Loading many angles
Develop the definitions $\cos θ = \frac{x}{r}$ , $\sin θ = \frac{y}{r}$ and $\tan θ = \frac{y}{x}$ , where $(x, y)$ is a point on the circle of radius $r$ , centred at the origin, and $θ$ is the angle between the positive $x$ -axis and the radius drawn to this point
Use the definitions $\cos θ = \frac{x}{r}$ , $\sin θ = \frac{y}{r}$ and $\tan θ = \frac{y}{x}$ to evaluate $\sin θ$ , $\cos θ$ and $\tan θ$ where $θ$ is a multiple of $90 °$ , and identify the values of $θ$ for which these ratios are undefined
Extend and apply the definitions $\cos θ = \frac{x}{r}$ , $\sin θ = \frac{y}{r}$ and $\tan θ = \frac{y}{x}$ for angles of any magnitude
Identify the related angle of an angle of any magnitude, excluding multiples of $90 °$ , as the acute angle between the ray and the $x$ -axis and obtain the values of the trigonometric functions of an angle of any magnitude from the trigonometric functions of the related angle
Develop and use the trigonometric ratios for angles that can be written in the form $θ = 180 ° \pm A$ , and $θ = 360 ° - A$ , where $0 ° < A < 90 °$
Establish and use the results $\cos (- θ) = \cos θ$ , $\sin (- θ) = - \sin θ$ and $\tan (- θ) = - \tan θ$
Examine the proof of the sine rule $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ , cosine rule $c^{2} = a^{2} + b^{2} - 2 ab \cos C$ and the area of a triangle formula $A = \frac{1}{2} ab \sin C$ for a given triangle $ABC$
Use graphing applications or geometric construction to examine the Loading , in which there are two possible solutions for an angle, and the condition for it to arise
Apply the sine rule, cosine rule and formula for the area of a triangle to solve problems where angles are measured in Loading , or degrees and Loading

Radians

Recognise that both ratios $\frac{arc length}{circumference}$ and $\frac{area of sector}{area of circle}$ are equal to $\frac{θ}{one revolution}$ where $θ$ is the angle at the centre of a circle subtended by the arc
Define the angle size of $θ$ in radian measure as the ratio $\frac{arc length}{radius of a circle}$
Explain why $360 ° = 2 π$ radians and $1 radian = \frac{180}{π} degrees$
Convert between degrees and radians and find the exact sine, cosine and tangent ratios for integer multiples of $\frac{π}{6}$ and $\frac{π}{4}$
Graph $y = s i n x$ , $y = c o s x$ and $y = t a n x$ over domains given in degrees or radians, showing intercepts with the $x$ -axis and $y$ -axis and any asymptotes, determine their domains and ranges, and period and amplitude where appropriate, and whether each is even or odd or neither
Establish and use the formula $l = rθ$ for the length $l$ of arc subtending an angle $θ$ in radians at the centre of a circle of radius $r$
Prove and use the formula $A = \frac{1}{2} r^{2} θ$ for the area of a sector with angle $θ$ in radians at the centre of a circle of radius $r$
Solve problems involving Loading and areas of major and minor sectors and Loading

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Year 12

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11–12Mathematics Advanced 11–12 Syllabus (2024)

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