The topic Functions involves the use of both algebraic and graphical conventions and terminology to describe, interpret and model relationships of and between changing quantities. This topic provides the means to more fully understand the behaviour of functions, extending to include inequalities, absolute values and inverse functions. Knowledge of functions enables students to discover connections between algebraic and graphical representations, determine solutions to equations and model theoretical or real-life situations involving algebra. The study of functions is important in developing students’ ability to find, recognise and use connections, to communicate concisely and precisely, to use algebraic techniques and manipulations to describe and solve problems, and to predict future outcomes in areas such as finance, economics and weather.
The topic of Trigonometric Functions involves the study of periodic functions in geometric, algebraic, numerical and graphical representations. It extends to exploration and understanding of inverse trigonometric functions over restricted domains and their behaviour in both algebraic and graphical form. A knowledge of trigonometric functions enables the solving of problems involving inverse trigonometric functions and the modelling of the behaviour of naturally occurring periodic phenomena such as waves and signals to solve problems and predict future outcomes. The study of the graphs of trigonometric functions is important in developing students’ understanding of the connections between algebraic and graphical representations and how this can be applied to solve problems from theoretical or real-life scenarios and situations.
The topic of Calculus involves the study of how things change and provides a framework for developing quantitative models of change and deducing their consequences. It involves the development of the connections between rates of change and related rates of change, the derivatives of functions and the manipulative skills necessary for the effective use of differential calculus. The study of calculus is important in developing students’ knowledge and understanding of related rates of change and developing the capacity to operate with and model situations involving change, using algebraic and graphical techniques to describe and solve problems and predict outcomes with relevance to, for example, the physical, natural and medical sciences, commerce and the construction industry.
The topic of Combinatorics involves counting and ordering as well as exploring arrangements, patterns, symmetry and other methods to generalise and predict outcomes. The consideration of the expansion of \( (x+y)^n \), where \( n \) is a positive integer, draws together aspects of number theory and probability theory. A knowledge of combinatorics is useful when considering situations and solving problems involving counting, sorting and arranging. Efficient counting methods have many applications and are used in the study of probability. The study of combinatorics is important in developing students’ ability to generalise situations, explore patterns and ensure the consideration of all outcomes in situations such as the placement of people or objects, setting-up of surveys, jury or committee selection and design.
source – NSW Education Standards Authority