Course map
Functions
- LessonPractice
Working with functions
Year 11: Working with functions- Manipulate indices and surds, solve quadratics and use the discriminant
- Use function notation, domain, range, odd and even functions
- Work with linear, quadratic, cubic, reciprocal, absolute value and piecewise functions, circles and semicircles
- Model direct and inverse variation
- LessonPractice
Graph transformations and modelling
Year 11 and Year 12: Graph transformations; Further graph transformations and modelling- Apply translations, reflections and dilations and find the new function rule
- Transform trigonometric graphs: amplitude, period, phase and vertical shifts
- Choose, fit and use functions to model a situation
Trigonometric functions
- LessonPractice
Trigonometry, radians and identities
Year 11: Trigonometry and measure of angles; Trigonometric identities and equations- Solve triangles with the sine and cosine rules, including the ambiguous case and bearings
- Use the unit circle, exact values and radians, arcs and sectors
- Prove identities and solve trigonometric equations in a given domain
Calculus
- LessonPractice
Introduction to differentiation
Year 11: Introduction to differentiation- Find average and instantaneous rates of change
- Differentiate from first principles and with the power, product, quotient and chain rules
- Find tangents and normals and interpret the derivative as a rate of change
- LessonPractice
Differential calculus
Year 12: Differential calculus- Differentiate exponential, logarithmic and trigonometric functions
- Combine the product, quotient and chain rules on any function in the course
- LessonPractice
Integral calculus
Year 12: Integral calculus- Find primitives and indefinite integrals of the course's functions
- Evaluate definite integrals and use the fundamental theorem of calculus
- Find areas between curves and estimate integrals with the trapezoidal rule
- LessonPractice
Applications of calculus
Year 12: Applications of calculus- Find stationary points and points of inflection and sketch curves
- Solve optimisation problems
- Solve rates of change and motion problems
Exponential and logarithmic functions
Statistical analysis
- LessonPractice
Probability and data
Year 11: Probability and data- Use set notation, Venn diagrams, arrays and tree diagrams
- Find conditional probabilities and test for independence
- Organise data and use relative frequency to estimate probability
- LessonPractice
Random variables
Year 12: Random variables- Find the expected value and variance of discrete random variables
- Use probability density and cumulative distribution functions
- Use the normal distribution, the empirical rule and z-scores
Sequences and series
Financial mathematics
The HSC examination
NSW HSC Mathematics Advanced, Year 11 and Year 12. The HSC examines Year 11 and Year 12 content. School-based assessment is set by your school, so it is described in a lesson rather than practised here.