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.

### Units of Study

### Units 1 and 2: Foundation Mathematics

**This subject leads to VCAL Senior Numeracy in Year 12. It is suitable for students who may wish to go on to TAFE or take up an apprenticeship**.

Foundation Mathematics provides for the continuing mathematical development of students entering VCE and who do not necessarily intend to undertake Unit 3 and 4 studies in VCE Mathematics in the following year. Students completing this course would need to undertake additional targeted mathematical study in order to attempt Further Mathematics Units 3 and 4.

In Foundation Mathematics there is a strong emphasis on the use of mathematics in practical contexts encountered in everyday life in the community, at work and at study. The areas of study for Units 1 and 2 of Foundation Mathematics are ‘Space, shape and design’, ‘Patterns and number’, ‘Data’ and ‘Measurement’.

### Units 1 and 2: General Mathematics

**This subject leads into Further Mathematics Unit 3 and 4.**

General Mathematics provides for different combinations of student interests and preparation for study of VCE Mathematics at the Unit 3 and 4 level. The areas of study for General Mathematics Unit 1 and Unit 2 are ‘Algebra and structure’, ‘Arithmetic and number’, ‘Discrete mathematics’, ‘Geometry, measurement and trigonometry’, ‘Graphs of linear and non-linear relations’ and ‘Statistics’.

### Unit 1 and 2: Mathematical Methods

**This subject leads to Units 3 & 4 Mathematical Methods and Specialist Mathematics Units 3 & 4. It is strongly recommended that Specialist Mathematics Units 1 and 2 should be studied in conjunction with this subject.**

Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions of a single real variable, 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 contain assumed knowledge and skills for these units.

### Unit 1 and 2: Specialist Mathematics

**This subject leads to Units 3 & 4 Mathematical Methods and Specialist Mathematics only when taken in conjunction with Mathematical Methods Units 1 & 2.**

Specialist Mathematics Units 1 and 2 provide a course of study for students who wish to undertake an in-depth study of mathematics, with an emphasis on concepts, skills and processes related to mathematical structure, modelling, problem solving and reasoning. This study has a focus on interest in the discipline of mathematics in its own right and investigation of a broad range of applications, as well as development of a sound background for further studies in mathematics and mathematics related fields.

### Units 3 & 4: Further Mathematics

Further Mathematics consists of two areas of study, a compulsory Core area of study to be completed in Unit 3 and an Applications area of study to be completed in Unit 4. The Core comprises ‘Data analysis’ and ‘Recursion and financial modelling’. The Applications comprises two modules to be completed in their entirety, from a selection of four possible modules: ‘Matrices’, ‘Networks and decision mathematics’, ‘Geometry and measurement’ and ‘Graphs and relations’. ‘Data analysis’ comprises 40 per cent of the content to be covered, ‘Recursion and financial modelling’ comprises 20 per cent of the content to be covered, and each selected module comprises 20 per cent of the content to be covered. Assumed knowledge and skills for the Core are contained in the General Mathematics Units 1 and 2 course.

### Units 3 & 4: Mathematical Methods

**This subject may be taken alone or in conjunction with either Units 3 and 4 Specialist Mathematics or Further Mathematics.**

Mathematical Methods Units 3 and 4 are completely prescribed and extend the introductory study of simple elementary functions of a single real variable, to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. Units 3 and 4 consist of the areas of study ‘Functions and graphs’, ‘Calculus’, ‘Algebra’ and ‘Probability and statistics’, which must be covered in progression from Unit 3 to Unit 4, with an appropriate selection of content for each of Unit 3 and Unit 4. Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2, and 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 Unit 3 a selection of content would typically include the areas of study ‘Functions and graphs’ and ‘Algebra’, and applications of derivatives and differentiation, and identifying and analysing key features of the functions and their graphs from the ‘Calculus’ area of study.

For Unit 4, this selection would typically consist of remaining content from the areas of study: ‘Functions and graphs’, ‘Calculus’ and ‘Algebra’, and the study of random variables and discrete and continuous probability distributions and the distribution of sample proportions. For Unit 4, the content from the ‘Calculus’ area of study would be likely to include the treatment of anti-differentiation, integration, the relation between integration and the area of regions specified by lines or curves described by the rules of functions, and simple applications of this content.

### Units 3 & 4: Specialist Mathematics

**This subject must be taken in conjunction with Mathematical Methods Units 3 and 4.**

Specialist Mathematics Units 3 and 4 consist of the areas of study: ‘Functions and graphs’, ‘Algebra’, ‘Calculus’, ‘Vectors’, ‘Mechanics’ and ‘Probability and statistics’.

Specialist Mathematics Units 3 and 4 assumes familiarity with the key knowledge and skills from Mathematical Methods Units 1 and 2, the key knowledge and skills from Specialist Mathematics Units 1 and 2 topics 'Number systems and recursion' and 'Geometry in the plane and proof', and concurrent or previous study of Mathematical Methods Units 3 and 4.

In Unit 3 a study of Specialist Mathematics would typically include content from ‘Functions and graphs’ and a selection of material from the ‘Algebra’, ‘Calculus’ and ‘Vectors’ areas of study. In Unit 4 this selection would typically consist of the remaining content from the ‘Algebra’, ‘Calculus’, and ‘Vectors’ areas of study and the content from the ‘Mechanics’ and ‘Probability and statistics’ areas of study.

Specialist Mathematics is intended for those with strong interests in mathematics and those who wish to undertake further study in mathematics and related disciplines.

##### Example pathways

- Accountant
- Architect
- Chemist
- Engineer
- Education
- Economist
- Finance/Banking
- Physicist
- Optometrist
- Statistician

**This is a guide only, please see the careers team for pathway planning advice.**

**VCAA Study Designs**

##### Entry

There are no prerequisites for entry to Units 1, 2 and 3; however, students undertaking Mathematical Methods Units 1 and 2 or Specialist Mathematics Units 1 and 2 are assumed to have a sound background in number, algebra, function, geometry, probability and statistics. Some additional preparatory work will be needed for any student who is undertaking Mathematical Methods Unit 2 without completing Mathematical Methods Unit 1.

Students must undertake Unit 3 prior to undertaking Unit 4.

Enrolment in Specialist Mathematics Units 3 and 4 assumes a current enrolment in, or previous completion of, Mathematical Methods Units 3 and 4.

There are no restrictions on the number of mathematics units students may obtain credit towards satisfactory completion of the VCE.

##### Unit 3 and 4 Assessment

Percentage contributions to the study score in VCE Mathematics are as follows:

**Further Mathematics**

- Unit 3 school-assessed coursework: 20 per cent
- Unit 4 school-assessed coursework: 14 per cent
- Units 3 and 4 examination 1: 33 per cent
- Units 3 and 4 examination 2: 33 per cent

**Mathematical Methods**

- Unit 3 school-assessed coursework: 17 per cent
- Unit 4 school-assessed coursework: 17 per cent
- Units 3 and 4 examination 1: 22 per cent
- Units 3 and 4 examination 2: 44 per cent

**Specialist Mathematics**

- Unit 3 school-assessed coursework: 17 per cent
- Unit 4 school-assessed coursework: 17 per cent
- Units 3 and 4 examination 1: 22 per cent
- Units 3 and 4 examination 2: 44 per cent

Examination 1 for Mathematical Methods Units 3 and 4 and Examination 1 for Specialist Mathematics Units 3 and 4 are technology free examinations.