VCE | MATHEMATICAL METHODS

Mathematical Methods Units 1–4 provide for the study of simple elementary functions, transformations and combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts.

YEAR 11

MATHEMATICAL METHODS (Units 1 & 2)

This subject provides an introductory study of simple functions of a real variable, alongside algebra, calculus and probability and their applications in a variety of practical and theoretical contexts. It is also designed as preparation for Mathematical Methods Units 3 and 4, as well as Specialist Mathematics Units 3 and 4 and contains assumed knowledge and skills for these units.

Areas of Study

• Functions, relations and graphs (mathematical notation, interpretation of the features of graphs of functions, polynomial and power functions)

• Algebra (use of the laws of algebra to simplify expressions, transforming graphs of functions, solutions of linear, simultaneous, quadratic and polynomial functions in real life situations)

• Calculus (rates of change, gradients, tangents and normal, maximal and minimal problems, antidifferentiation)

• Probability (simulating probability situations and determining likelihood of outcomes, permutations and combinations)

• Circular functions (graphs, solutions, applications of trigonometric functions, graphing and solving exponential and logarithmic functions)

Students develop the ability to carry out relevant mental and by-hand approaches to complete a range of mathematical process and routines. Efficient use of available technology is a focus when dealing with larger scale application problems. Modelling and problem solving tasks undertaken in this subject have both theoretical and practical applications, with open -ended investigations requiring exploration and communication of results.

They also provide background for further study in, for example, science, technology, engineering and mathematics (STEM), humanities, economics and medicine.

YEAR 12

MATHEMATICAL METHODS (Units 3 & 4)

This subject extends the study of simple functions to include combinations of functions, inverse functions, calculus, probability and statistics, and the applications of these topics to a variety of theoretical and practical contexts.

Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2, and these will be drawn on, as applicable, in the development of related content from the areas of study. There will be a clear progression of skills from Unit 3 to Unit 4 across the year’s studies.

Areas of Study

• Functions, relations and graphs (graph a wide variety of functions and apply transformations, find inverse and composite functions)

• Algebra (solve equations – linear, polynomial and systems of simultaneous equations)

• Calculus (derivative functions and their graphs, including circular functions, limitations, continuity and differentiability, maximum and minimum values, integration and its use to find the area under a graph)

• Probability (random variables, using probability functions to describe the distribution of probabilities, sample proportions and confidence intervals)

• Computational thinking (pseudocode and algorithms to describe the process of solving mathematical problems)

On completion of these units, students should be able to apply mathematical processes in non-routine contexts, including situations with some open-ended aspects requiring investigative, modelling or problem-solving techniques or approaches, and analyse and discuss these applications of mathematics.