# VCE Mathematics

### General Mathematics Units 1 – 4

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams, networks and geometric constructions, algorithms, algebraic manipulation, equations and graphs, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically.

### Mathematical Methods Units 1 – 4

Mathematical Methods Units 1 and 2 offer an introductory exploration of simple elementary functions of a single real variable, algebra, calculus, probability, and statistics, as well as their applications in various practical and theoretical contexts. These units serve as preparation for Mathematical Methods Units 3 and 4, which build on this foundation and expand the study to include combinations of these functions and their applications in more advanced contexts.

Unit 1 focuses on the study of simple algebraic functions and covers the areas of study 'Functions, relations and graphs', 'Algebra, number and structure', 'Calculus', and 'Data analysis, probability and statistics.' By the end of Unit 1, students should have covered the content outlined in each area of study, except for 'Algebra, number and structure,' which continues into Unit 2. The content should be presented in a balanced and progressive manner, with connections between and across the areas of study being developed consistently throughout both Units 1 and 2.

Units 3 and 4 consist of the areas of study 'Algebra, number and structure', 'Data analysis, probability and statistics', 'Calculus', and 'Functions, relations and graphs', and must be covered in progression from Unit 3 to Unit 4. The selection of content for each unit should be appropriate and build on the assumed knowledge and skills from Units 1 and 2.

The assumed knowledge and skills from Units 1 and 2 will be drawn on, as applicable, in the development of related content from the areas of study, and key knowledge and skills for the outcomes of Mathematical Methods Units 3 and 4. For example, Unit 3 would typically cover 'Functions, relations and graphs' and 'Algebra, number and structure', as well as applications of derivatives and differentiation, and identifying and analysing key features of the functions and their graphs from the 'Calculus' area of study. Unit 4 would typically cover remaining content from 'Functions, relations and graphs', 'Algebra, number and structure', and 'Calculus', as well as the study of random variables, discrete and continuous probability distributions, and the distribution of sample proportions from the 'Data analysis, probability and statistics' area of study. The content from the 'Calculus' area of study in Unit 4 would likely include the treatment of anti-differentiation, integration, and the relation between integration and the area of regions specified by lines or curves described by the rules of functions, as well as simple applications of this content, including to probability distributions of continuous random variables.

VCE Mathematical Methods is a highly demanding and sought-after subject and serves as a prerequisite for entry into top-ranked university courses. Therefore, it is essential for students who wish to pursue higher studies in mathematics to have a solid foundation in Mathematical Methods Units 1 and 2.

### Specialist Mathematics Units 1 – 4

Specialist Mathematics Units 1–4 provide for the study of various mathematical structures, reasoning and proof. The areas of study in Units 3 and 4 extend content from Mathematical Methods Units 3 and 4 to include rational and other quotient functions as well as other advanced mathematics topics such as logic and proof, complex numbers, vectors, differential equations, kinematics, and statistical inference. They also provide background for advanced studies in mathematics and other STEM fields. Study of Specialist Mathematics Units 3 and 4 assumes concurrent study or previous completion of Mathematical Methods
Units 3 and 4.

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists, tables and vectors, diagrams and geometric constructions, algorithms, algebraic manipulation, equations, graphs, differentiation, anti-differentiation and integration and inference, with and without the use of technology. They should have 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 each unit as applicable.