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. 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, use algebraic techniques and manipulations to describe and solve problems and 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. A knowledge of trigonometric functions enables the solving of 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. The study of 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 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 two key aspects of calculus, namely 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 construction industry.
The topic of Financial Mathematics involves sequences and series and their application to financial situations. Knowledge of financial mathematics enables analysis and interpretation of different financial situations, the calculation of the best options for the circumstances, and the solving of financial problems. The study of financial mathematics is important in developing students’ ability to make informed financial decisions, to be aware of the consequences of such decisions, and to manage personal financial resources prudently.
The topic of 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 in order 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