HSC Year 12 Mathematics Advanced Online Courses

1.1 Transformations
1.2 Inequalities

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15 Lessons
2.1 Trigonometric Graphs
2.2 Trigonometric Equations
2.3 Trigonometric Models

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19 Lessons
3.1 Differentiation
3.2 Application of Differentiation
3.3 Integration
3.4 Application of Integration

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36 Lessons
4.1 Annuity
4.2 Arithmetic Sequences and Series
4.3 Geometric Sequences and Series
4.4 Financial Mathematics

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21 Lessons
5.1 Descriptive Statistics
5.2 Exploring Data
5.3 Bivariate Data
5.4 Normal Distribution

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37 Lessons


The topic of Functions involves the use of both algebraic and graphical conventions and terminology to describe, interpret and model relationships of and between changing quantities. Knowledge of functions enables students to discover, recognise and generalise connections between algebraic and graphical representations of the same expression and to describe interactions between dependent and independent variables. The study of functions is important in developing students’ ability to find and recognise connections and patterns, to communicate concisely and precisely, and to use algebraic techniques and manipulations to describe and solve problems and predict future outcomes in finance and economics and weather.

Trigonometric Functions

The topic of Trigonometric Functions involves the study of periodic functions in geometric, algebraic, numerical and graphical representations. A knowledge of trigonometric functions enables solving practical problems involving the manipulation of trigonometric expressions to model the behaviour of naturally occurring periodic phenomena such as waves and signals and to predict future outcomes. Studying trigonometric functions is important in developing students’ understanding of periodic functions. Utilising the properties of periodic functions, mathematical models have been developed that describe the behaviour of many naturally occurring periodic phenomena, such as vibrations or waves, as well as oscillatory behaviour found in pendulums, electric currents and radio signals.


The topic of Calculus involves studying how things change and provides a framework for developing quantitative models of change and deducing their consequences. It involves developing two key aspects of calculus, differentiation and integration. The study of calculus is important in developing students’ capacity to operate with and model situations involving change, using algebraic and graphical techniques to describe and solve problems and predict outcomes in fields such as biomathematics, economics, engineering and the construction industry.

Financial Mathematics

Financial Mathematics involves sequences and series and their application to financial situations. Knowledge of financial mathematics enables analysis and interpretation of different financial situations, calculating the best options for the circumstances, and solving financial problems. The study of financial mathematics is important in developing students’ ability to make informed financial decisions, be aware of such decisions’ consequences, and manage personal financial resources prudently.

Statistical Analysis

Statistical Analysis involves the exploration, display, analysis and interpretation of data to identify and communicate key information. Knowledge of statistical analysis enables careful interpretation of situations and an awareness of the contributing factors when presented with information by third parties, including its possible misrepresentation. The study of statistical analysis is important in developing students’ ability to recognise, describe and apply statistical techniques to analyse current situations or predict future outcomes. It also develops an awareness of how conclusions drawn from data can be used to inform decisions made by groups such as scientific investigators, business people and policy-makers.

source – NSW Education Standards Authority