Units 3 and 4
Mathematical Methods Units 3 and 4 cover the areas of study ‘Functions and graphs’, ‘Algebra’, ‘Calculus’ and ‘Probability and statistics’ and extend the introductory study of simple elementary functions of a single real variable from Units 1 and 2 to include combinations of these functions and related graphs, algebra and calculus. Courses based on these units should be implemented so that there is a balanced and progressive development of skills and knowledge from each of the four areas of study, and connections between them, in practical and theoretical contexts. In Unit 3 the focus is on the study of transformed and combined functions, related graphs and algebra and differentiation of these functions. In Unit 4 the focus is on anti-differentiation and integration and the study of random variables, probability distributions and their application to simple statistical inference with proportions.
In undertaking these units, students learn to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs and differentiation, anti-differentiation and integration with and without the use of technology. They should develop their facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout the units as applicable.