Objective Students: develop knowledge, skills and understanding about efficient strategies for pattern recognition, generalisation and modelling techniques Year 11 outcomes A student: Year 12 outcomes A student: MA11-1 uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems MA12-1 uses detailed algebraic and graphical techniques to critically construct, model and evaluate arguments in a range of familiar and unfamiliar contexts MA12-2 models and solves problems and makes informed decisions about financial situations using mathematical reasoning and techniques MA12-3 applies calculus techniques to model and solve problems Objective Students: develop the ability to use mathematical concepts and skills and apply complex techniques to the modelling and solution of problems in algebra and functions, measurement, financial mathematics, calculus, data and statistics and probability Year 11 outcomes A student: Year 12 outcomes A student: MA11-2 uses the concepts of functions and relations to model, analyse and solve practical problems MA12-4 applies the concepts and techniques of arithmetic and geometric sequences and series in the solution of problems MA11-3 uses the concepts and techniques of trigonometry in the solution of equations and problems involving geometric shapes MA12-5 applies the concepts and techniques of periodic functions in the solution of problems involving trigonometric graphs MA11-4 uses the concepts and techniques of periodic functions in the solutions of trigonometric equations or proof of trigonometric identities
A knowledge of functions enables students to discover, recognise and generalise connections between algebraic and graphical representations of the same expression and to describe interactions through the use of both dependent and independent variables. The study of functions is important in developing students’ ability to find connections and patterns, 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, data analysis, marketing and weather. Subtopics MA-F1 Working with Functions Functions MA-F1 Working with Functions Outcomes A student: uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems MA11-1 uses the concepts of functions and relations to model, analyse and solve practical problems MA11-2 uses appropriate technology to investigate, organise, model and interpret information in a range of contexts MA11-8 provides reasoning to support conclusions which are appropriate to the context MA11-9 Subtopic Focus The principal focus of this subtopic is to introduce students to the concept of a function and develop their knowledge of functions and their respective graphs. Function notation is introduced, which is essential for describing the ideas of calculus. Students develop their use of mathematical language to describe functions, their properties and respective graphs while applying this knowledge to everyday problems and applications. In business and economics, for example revenue depends on the number of items sold, and expressing this relationship as a function allows the investigation of changes in revenue as sales change. Within this subtopic, schools have the opportunity to identify areas of Stage 5 content which may need to be reviewed to meet the needs of students. Content F1.1: Algebraic techniques Students: use index laws and surds solve quadratic equations using the quadratic formula and by completing the square (ACMMM008)