## Scope of VCE Maths

VCE Maths is the study of function and pattern in number, logic, space and structure, and of randomness, chance, variability and uncertainty in data and events. It is both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and precise. Mathematics also provides a means by which people can understand and manage human and natural aspects of the world and inter-relationships between these. Essential mathematical activities include: conjecturing, hypothesising and problem posing; estimating, calculating and computing; abstracting, proving, refuting and inferring; applying, investigating, modelling and problem solving.

## Rationale

This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the interests, needs, dispositions and aspirations of a wide range of students, and introduces them to key aspects of the discipline. It is also designed to promote students’ awareness of the importance of mathematics in everyday life in a technological society, and to develop confidence and the disposition to make effective use of mathematical concepts, processes and skills in practical and theoretical contexts.

## Aims

This study enables students to:

- develop mathematical concepts, knowledge and skills
- apply mathematics to analyse, investigate and model a variety of contexts and
- solve practical and theoretical problems in situations that range from well-defined and familiar to open-ended and unfamiliar
- use technology effectively as a tool for working mathematically.

## Structure

The study of VCE Maths is made up of the following units:

- Foundation Mathematics Units 1 and 2
- General Mathematics Units 1 and 2
- Mathematical Methods Units 1 and 2
- Specialist Mathematics Units 1 and 2
- Further Mathematics Units 3 and 4
- Mathematical Methods Units 3 and 4
- Specialist Mathematics Units 3 and 4

Each unit deals with specific content contained in areas of study and is designed to enable students to achieve a set of three outcomes for that unit. Each outcome is described in terms of key knowledge and key skills. A glossary defining mathematical terms and notations used across Units 1 to 4 in the VCE Maths Study Design is included in a companion document Advice for teachers.

#### Foundation Mathematics Units 1 and 2

are completely prescribed and provide for the continuing mathematical development of students entering VCE. In general, these students would not intend to undertake Unit 3 and 4 studies in VCE Maths in the following year. However, students who do well in these units and undertake some supplementary study of selected topics could proceed to Further Mathematics Units 3 and 4.

#### General Mathematics Units 1 and 2

provide for a range of courses of study involving non-calculus based topics for a broad range of students and may be implemented in various ways to reflect student interests in, and applications of, mathematics. They incorporate topics that provide preparation for various combinations of studies at Units 3 and 4 and cover assumed knowledge and skills for those units.

#### Mathematical Methods Units 1 and 2

are completely prescribed and provide an introductory study of simple elementary functions, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. They are designed as preparation for Mathematical Methods Units 3 and 4 and cover assumed knowledge and skills for those units.

#### Specialist Mathematics Units 1 and 2

comprise a combination of prescribed and selected non-calculus based topics and provide courses of study for students interested in advanced study of mathematics, with a focus on mathematical structure and reasoning. They incorporate topics that, in conjunction with Mathematical Methods Units 1 and 2, provide preparation for Specialist Mathematics Units 3 and 4 and cover assumed knowledge and skills for those units.

#### Further Mathematics Units 3 and 4

are designed to be widely accessible and comprise a combination of non-calculus based content from a prescribed core and a selection of two from four possible modules across a range of application contexts. They provide general preparation for employment or further study, in particular where data analysis, recursion and number patterns are important. The assumed knowledge and skills for the Further Mathematics Units 3 and 4 prescribed core are covered in specified topics from General Mathematics Units 1 and 2. Students who have done only Mathematical Methods Units 1 and 2 will also have had access to assumed knowledge and skills to undertake Further Mathematics but may also need to undertake some supplementary study of statistics content.

#### Mathematical Methods Units 3 and 4

are completely prescribed and extend the study of simple elementary functions to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. They also provide background for further study in, for example, science, humanities, economics and medicine.

#### Specialist Mathematics Units 3 and 4

are designed to be taken in conjunction with Mathematical Methods Units 3 and 4, or following previous completion of Mathematical Methods Units 3 and 4. The areas of study 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 complex numbers, vectors, differential equations, mechanics and statistical inference. Study of Specialist Mathematics Units 3 and 4 assumes concurrent study or previous completion of Mathematical Methods Units 3 and 4.

*VCE Mathematics Study Design 2016-2018*