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## Mathematics

## Overview

Many students and parents are concerned about completing Mathematics during the VCE, and about which specific Mathematics subjects they should complete. Hopefully, this information will make this decision simpler.

Firstly, the best advice that can be given to prospective Senior School students is to complete the highest level of Mathematics you are capable of. There is simply no question that by completing Mathematics at VCE many career options open up for students, ranging from some pre-apprenticeship TAFE courses through to Medicine and Law qualifications. Specific courses do have pre-requisite Mathematics subjects required and students should ensure that they inform themselves of what will be required for their intended future courses by consulting the relevant VICTER Guide.

Secondly, students do not have to complete VCE Mathematics. It is certainly in their best interests to finish at least a Unit 1 & 2 in a Mathematics of the students’ choice, but it is not mandatory.

Finally, students intending to study Mathematic subjects at Year 12 will need to select the appropriate prerequisite Mathematics Units in Year 11 to allow them to enter their selections the following year.

Hopefully, the following descriptions, in order of difficulty, will make these required selections clearer.

### General Mathematics Units 1 and 2

General Mathematics provides for different combinations of student interests and preparation for study of VCE Mathematics at the Unit 3 and 4 level. 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 and geometric constructions, 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, and in related assessment, is to be incorporated throughout each unit as applicable.

- Area of study 1: Algebra and structure
- Area of study 2: Arithmetic and number
- Area of study 3: Discrete mathematics
- Area of study 4: Geometry, measurement and trigonometry
- Area of study 5: Graphs of linear and non-linear relations
- Area of study 6: Statistics

### Mathematical Methods Units 1 and 2

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.

In undertaking this unit, students are expected to be able 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 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 the unit as applicable. Students should be familiar with quadratic and exponential functions, algebra and graphs and basic concepts of probability.

- Area of study 1: Functions and graphs
- Area of study 2: Algebra
- Area of study 3: Calculus
- Area of study 4: Probability and statistics

### Specialist Mathematics Units 1 and 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.

Mathematical Methods Units 1 and 2 and Specialist Mathematics Units 1 and 2, taken in conjunction, provide a comprehensive preparation for Specialist Mathematics Units 3 and 4. Students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations and graphs with and without the use of technology.

- Area of study 1: Algebra and structure
- Area of study 2: Arithmetic and number
- Area of study 3: Discrete mathematics
- Area of study 4: Geometry, measurement and trigonometry
- Area of study 5: Graphs of linear and non-linear relations
- Area of study 6: Statistics

## Year 12 Mathematics

Pre-requisites for entering a Year 12 Mathematics

- Further Maths 3 & 4 - Requires General Maths Units 1 & 2.
- Maths Methods 3 & 4 – Maths Methods 1 & 2, essential.
- Specialist Maths 3 & 4 – Both Maths methods 1 & 2 and specialist Maths 1 & 2 recommended.

### Further Mathematics Units 3 and 4

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’.

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 and geometric constructions, algebraic manipulation, equations, and graphs.

They should have a 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, and in related assessment, is to be incorporated throughout each unit as applicable.

- Area of study 1: Data analysis, Recursion and financial modelling
- Area of study 2: Matrices, Networks and decision mathematics, Geometry and measurement, Graphs and relations

### Mathematical Methods Units 3 & 4

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.

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.

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 and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation, 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.

- Area of study 1: Functions and graphs
- Area of study 2: Algebra
- Area of study 3: Calculus
- Area of study 4: Probability and statistics

### Specialist Mathematics Units 3 & 4

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

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists and tables, diagrams and geometric constructions, 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.

- Area of study 1: Functions and graphs
- Area of study 2: Algebra
- Area of study 3: Calculus
- Area of study 4: Vectors
- Area of study 5: Mechanics
- Area of study 6: Probability and statistics

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