# Senior Mathematics

Mathematics provides students with access to important mathematical ideas, knowledge, and skills that they will draw on in their personal and work lives. The curriculum also provides students, as life-long learners, with the basis on which further study and research in mathematics and applications in many other fields are built.

Number, measurement and geometry, statistics and probability are common aspects of most people’s mathematical experience in everyday personal, study and work situations. Equally important are the essential roles that algebra, functions and relations, logic, mathematical structure and working mathematically play in people’s understanding of the natural and human worlds, and the interaction between them.

The curriculum ensures that the links between the various components of mathematics, as well as the relationship between mathematics and other disciplines, are made clear. Mathematics is composed of multiple but interrelated and interdependent concepts and structures which students apply beyond the mathematics classroom.

The Mathematics curriculum aims to ensure that students:

- develop useful mathematical and numeracy skills for everyday life, work, and as active and critical citizens in a technological world
- see connections and apply mathematical concepts, skills, and processes to pose and solve problems in mathematics and in other disciplines and contexts
- acquire specialist knowledge and skills in mathematics that provide for further study in the discipline

**Understanding Senior Mathematics Pathway Options**

- Students at Year 10 who plan on a VCE pathway should be completing Core or Advanced Maths. Applied Maths is a VCE VM Numeracy Pathway option only.
- Students who are working at 9.5 in the Number and Algebra strand in Year 9 Maths are eligible to pursue Advanced Maths at Year 10.
- Students are advised to continue with Maths through their VCE. They should select a Maths that matches their pathway and that is attainable for them. There are 4 VCE Maths options:
- Foundation Maths Units 1-4
- General Maths Units 1-4
- Math Methods Units 1-4
- Specialist Maths Units 1-4

- Students who are planning on a VCE (Vocational Major) Pathway may enrol in Applied Maths. This version of Year 10 Maths is designed to prepare them for the VCE Vocational Major Numeracy subject in Year 11. Students should only take on this option if they know that they do not require a higher level of Maths. Some trades do require a VCE level maths, those students should be selecting Core or Advanced Maths at Year 10.

## Year 10 - Core Mathematics

**Overview**

Year 10 Mathematics students will continue to develop and consolidate their F – 10 Mathematics Curriculum knowledge and skills in a variety of mathematical concepts from the Mathematics 2.0 Victorian Curriculum.

Students will be introduced to the Level 10 Mathematics curriculum and will develop an understanding of mathematical concepts and fluency with processes and be able to reason, pose and solve problems in Number, Algebra, Measurement, Space, Statistics and Probability.

The Year 10 Mathematics course focuses on consolidating and enhancing students’ skills in all areas of mathematics in order to best prepare them for the VCE study of Mathematics.

Units / Topics | Types of Assessment |
---|---|

Number systems and algebra. | Test (technology free and technology allowed components) |

Linear equations and relationships, including inequalities. | Application and Modelling Tasks (technology allowed) |

Functions and relations, including non-linear relationships such as circles. | Semester Examination (technology free and technology allowed components) |

Quadratic relationships and functions, both algebraically and graphically. | |

Exponential relationships and functions, including applications of growth and decay. | |

Trigonometry and measurement, including volume and surface area of different shapes. | |

Probability, including conditional probability and independent events. |

**Future Directions**

Satisfactory completion of this subject will provide a sound foundation for students to proceed to Unit 1 & 2 General Mathematics and/or Unit 1 & 2 Foundation Mathematics.

## Year 10 - Advanced Mathematics (Year 10 Core Program)

**Overview**

Students will extend their existing knowledge of their F – 10 Mathematics Curriculum by completing an in-depth exploration of the Mathematics 2.0 Victorian Curriculum 10A content.

Students will develop a sophisticated understanding of mathematical concepts and fluency with processes and be able to reason, pose and solve problems in Number, Algebra, Measurement, Space, Statistics and Probability.

This subject will allow for consolidation and deepening of knowledge as well as provide a foundation for technology use to mathematics required for the VCE study of Mathematics via the use of a CAS calculator.

Units / Topics | Types of Assessment |
---|---|

Number systems. | Test (technology free and technology allowed components) |

Indices, exponentials, and logarithms. | Application and Modelling Tasks (technology allowed) |

Linear and quadratic relationships | Semester Examination (technology free and technology allowed components) |

Polynomial relationships, including higher order polynomials. | |

Functions and relations, including non-linear relationships. | |

Trigonometry and measurement. | |

Probability |

**Future Directions**

Satisfactory completion of this subject will provide a sound foundation for students to proceed to Unit 1 & 2 Mathematical Methods and Unit 1 & 2 Specialist Mathematics.

## VCE Units 1 & 2 - Foundation Mathematics

### Overview

Foundation Mathematics Units 1 and 2 provide students with the mathematical knowledge, skills, and understanding to solve problems in real contexts for a range of workplace, personal, further learning, and community settings relevant to contemporary society.

### Unit 1: Foundation Mathematics

Students consolidate mathematical foundations, further develop their knowledge and capability to plan and conduct activities independently and collaboratively, communicate their mathematical ideas, and acquire mathematical knowledge to make informed decisions in their lives.

*Areas of Study (for both units)*

- Algebra, number, and structure
- Data analysis, probability, and statistics
- Discrete mathematics
- Space and measurement

### Unit 2: Foundation Mathematics

Students extend their depth in the application of mathematics to solve practical problems from contexts present in students’ familiar situations.

*Outcomes (for both units) *

- Students should be able to use and apply a range of mathematical concepts, skills, and procedures to solve practical problems
- Students can apply mathematical processes in open-ended aspects requiring investigative, modelling, or problem-solving techniques
- Students can apply computational thinking and use technology to produce results and carry out analysis

### Forms of Assessment

- Chapter questions
- Tests
- Problem-solving tasks
- Mathematical investigations
- Semester exams

### Prerequisites and Corequisites

Students are expected to have satisfied the work requirements of Year 10 Mathematics.

### Future Directions

Students will be able to undertake VCE Units 3 and 4 Foundation Mathematics.

### Link to Study Design

VCE Foundation Mathematics 2023 - 2027 Study Design## VCE Units 1 & 2 - General Mathematics

### Overview

General Mathematics Units 1 and 2 cater for a range of student interests and provides preparation for the study of VCE General Mathematics at the Units 3 and 4 level. In Units 1 and 2, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, matrices, diagrams and geometric constructions, algebraic manipulation, recurrence relations, and equations and graphs.

### Unit 1: General Mathematics

Students study content that includes percentages and ratios, comparing data distributions, linear relations and modelling, sequences and finance, and matrices.

*Areas of Study (for both units) *

- Data analysis, probability, and statistics
- Algebra, number and structure
- Functions, relations and graphs
- Discrete mathematics

### Unit 2: General Mathematics

Students extend their study to include investigating relationships between two numerical variables, variation, graphs and networks, measurement, and trigonometry.

*Outcomes (for both units)*

- Students can define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures
- Students can apply mathematical processes in non-routine practical 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
- Students can apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in practical situations requiring investigative, modelling or problem-solving techniques or approaches

### Forms of Assessment

- Chapter questions
- Formatives
- Modelling and problem-solving tasks
- SACs
- Mathematical investigations
- Semester exams

### Prerequisites and Corequisites

Students are expected to have satisfied the work requirements of Year 10 Mathematics.

### Future Directions

Students will be able to undertake VCE Units 3 and 4 General Mathematics.

### Link to Study Design

VCE General Mathematics 2023 - 2027 Study Design## VCE Units 1 & 2 - Mathematical Methods

### Overview

Units 1 & 2 Mathematical Methods comprises of a study of Functions and Graphs, Algebra, Probability and Calculus. These areas of study are explored in both units of Mathematical Methods, with a balanced and progressive development of skills from Unit 1 to Unit 2.

### Unit 1

Students study simple algebraic functions and their graphs, focusing mainly on polynomials and other common function types. Students develop skills and knowledge in creating, solving, and graphing various equations, and apply these skills to real world contexts.

*Areas of Study (for both units)*

- Functions and graphs
- Algebra
- Calculus
- Probability and statistics

### Unit 2

Students expand on their study of basic and common functions and graphs through the introduction of transcendental functions. They are introduced to more complex calculus and explore the study of probability. Students develop skills and knowledge in these topics by applying these skills to real world contexts.

### Forms of Assessment

Students will be assessed on their content knowledge, use of technology (CAS calculator) and ability to apply their knowledge and skills to modelling and problem-solving contexts, including real world applications.

Each topic studied will be assessed via either a topic test or investigation task and there will be two exams at the end of each unit (technology free and technology allowed).

### Prerequisites and Corequisites

Students intending to undertake Mathematical Methods Units 1 & 2 require a very sound background in Mathematics from the Year 10 Advanced Mathematics program.

### Future Directions

Students who successfully complete Mathematical Methods Units 1 & 2 will be able to undertake Mathematical Methods Units 3 & 4, as well as Specialist Maths Units 3 & 4.

### Link to Study Design

VCE Mathematical Methods 2023 - 2027 Study Design## VCE Units 1 & 2 - Specialist Mathematics

### Overview

Specialist Mathematics is a course designed to challenge students, complement, and consolidate material covered in Mathematical Methods 1 & 2. This study should prepare them for the more demanding Unit 3 & 4 Specialist Mathematics course at Year 12. Students who undertake Specialist Mathematics Units 1 & 2 will benefit from the consolidation of skills also required in Mathematical Methods Units 1 & 2.

### Unit 1

At the end of Unit 1 students are expected to have covered the material in the areas of study: ‘Algebra, number and structure’ and ‘Discrete mathematics’. Concepts from these areas of study will be further developed and used in Unit 2, as well as in Units 3 and 4.

*Areas of Study:*

- Algebra, number, and structure
- Discrete mathematics

### Unit 2

At the end of Unit 2 students are expected to have covered the material in the areas of studies: ‘Data analysis, probability and statistics’, ‘Space and measurement’, ‘Algebra, number and structure’ and ‘Functions, relations and graphs.’

*Areas of Study:*

- Data analysis, probability, and statistics
- Space and measurement
- Algebra, number, and structure
- Functions, relations, and graphs

### Forms of Assessment

- All topics will be assessed using a test, application task, or Mathematical investigation
- Examination: Technology and Non-Technology Examinations

### Prerequisites and Corequisites

- Students intending to undertake Specialist Mathematics Units 1 & 2 require a very sound background in Mathematics from Year 10 Advanced Mathematics.
- The study of Mathematical Methods Units 1 & 2 is assumed as a co-requisite.

### Future Directions

Students who successfully complete Specialist Mathematics Units 1 & 2 will be able to undertake Specialist Maths Units 3 & 4.

### Link to Study Design

VCE Specialist Mathematics 2023 - 2027 Study Design## VCE Units 3 & 4 - Foundation Mathematics

### Overview

Foundation Mathematics Units 3 and 4 provide students with the mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning, community, and global settings relevant to contemporary society.

### Unit 3: Foundation Mathematics

Students study content that includes number operations, equations and formulas including interpolation and extrapolation, ratio and variation, accuracy in measurement, perimeter, area, surface area, volume, capacity, scales, views of objects, floor plans, symmetry, transformations, and projections.

*Areas of Study (for both units)*

- Algebra, number, and structure
- Data analysis, probability, and statistics
- Discrete mathematics
- Space and measurement

### Unit 4: Foundation Mathematics

Students extend their study to include data calculations, analysing data, investing money, and borrowing money, financial risk, running a business, paying tax and super, finances from a global perspective.

*Outcomes (for both units)*

- Students can define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures to solve practical problems from a range of everyday and real-life contexts
- Students can apply mathematical processes in non-routine practical 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
- Students can apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in practical situations requiring investigative, modelling or problem-solving techniques or approaches

### Forms of Assessment

- Mathematical investigations
- End of year examination

### Prerequisites and Corequisites

Assumed knowledge and skills for Foundation Mathematics Units 3 and 4 are contained in Foundation Mathematics Units 1 and 2 and will be drawn on in the development of related content from the areas of study, and key knowledge and key skills for the outcomes.

### Link to Study Design

VCE Foundation Mathematics 2023 - 2027 Study Design## VCE Unit 3 & 4 - General Mathematics

### Overview

General Mathematics Units 3 and 4 consists of two areas of study per unit which combine and extend the topics covered in Units 1 and 2 General Mathematics. Students will develop their knowledge of data analysis, financial mathematics, and some applications of both matrices and networks.

### Unit 3: General Mathematics

Students study content that includes investigating data distributions, association between two variables, investigating and modelling linear associations and time series data, as well as depreciation of assets, compound interest investments and loans, reducing balance loans, annuities and perpetuities and annuity investments.

*Areas of Study*

- Data analysis
- Recursion and financial modelling

### Unit 4: General Mathematics

Students study content that includes matrices and their applications, transition matrices, graphs and networks, exploring and travelling problems, trees and minimum connector problems, flow, shortest path and matching problems.

*Areas of Study*

- Matrices
- Networks and decision mathematics

*Outcomes (for both units)*

- Students can define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures
- Students can apply mathematical processes in non-routine practical 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

- Students can apply computational thinking and use numerical, graphical, symbolic, and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in practical situations requiring investigative, modelling or problem-solving techniques or approaches

### Forms of Assessment

- Application task
- Modelling tasks
- Two end of year examinations

### Prerequisites and Corequisites

It is an advantage to have completed Units 1 and 2 General Mathematics

### Link to Study Design

VCE General Mathematics 2023 - 2027 Study Design## VCE Units 3 & 4 - Mathematical Methods

### Overview

Units 3 & 4 Mathematical Methods extend the introductory study from Units 1 & 2 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.

### Unit 3

Students study a selection of content that includes various common functions and their graphs, and the use of algebra to solve and analyse these. They also investigate the applications of derivatives and differentiation to identify and analyse key features of the functions.

*Areas of Study*

- Functions and graphs
- Algebra
- Calculus (differential)

### Unit 4

Students extend their study of Calculus to include anti-differentiation and integration and apply that knowledge to a range of contexts involving the content studied in Unit 3. They also study random variables, discrete and continuous probability distributions, and sample proportions.

*Areas of Study*

- Calculus (integral)
- Probability and statistics

### Forms of Assessment

Students undertake one Application Task in Unit 3. This is a function and calculus-based mathematical investigation of a practical or theoretical context involving content from two or more areas of study and is 4–6 hours duration over a period of 1–2 weeks.

Students undertake two Problem Solving or Modelling Tasks in Unit 4. Both tasks are 2-3 hours duration over a period of 1 week and one of the modelling tasks must focus on Probability and Statistics, the other can be a combination of any of the other areas of study.

Students then sit 2 exams at the end of the year that covers all content studied from Units 1 – 4. Exam 1 is a technology free exam of 1 hour duration. Exam 2 is a technology allowed exam of 2 hours duration.

### Prerequisites and Corequisites

Students need to have successfully completed Mathematical Methods Units 1 & 2.

### Link to Study Design

VCE Mathematical Methods 2023 - 2027 Study Design## VCE Units 3 & 4 - Specialist Mathematics

### Overview

Specialist Mathematics is a course designed to extend students’ mathematical knowledge and skills. This subject provides a pathway for students intending to pursue careers in Science, Mathematics or Engineering. Students who undertake Specialist Mathematics Units 3 & 4 will benefit from the consolidation of skills also required in Mathematical Methods Units 3 & 4.

### Unit 3

For Unit 3 a selection would typically include content from the ‘Discrete mathematics’, ‘Functions, relations and graphs’, ‘Algebra, number and structure’, ‘Space and measurement’ and ‘Calculus’ areas of study.

*Areas of Study*

- Discrete mathematics
- Functions, relations, and graphs
- Algebra, number, and structure
- Calculus
- Space and measurement
- Data analysis, probability, and statistics

### Unit 4

In Unit 4 the corresponding selection of content would typically consist of the remaining content from the ‘Discrete mathematics’, ‘Calculus’, and ‘Space and measurement’ areas of study and the content from the ‘Data analysis, probability and statistics’ area of study.

### Forms of Assessment

- Unit 3 Application Task
- Unit 4 Analysis Task (Calculus)
- Unit 4 Analysis Task (Data analysis, probability, and statistics)
- Examination 1 – November (1 hour) Technology Free: Short answer and extended-type questions
- Examination 2 – November (2 hours): Technology Allowed: Multiple choice and extended-type questions

### Prerequisites and Corequisites

- Prerequisite entry to Specialist Mathematics Units 3 & 4 is the satisfactory completion of Mathematical Methods Units 1 & 2 and Specialist Mathematics Units 1 & 2.
- Enrolment in Specialist Mathematics Units 3 & 4 assumes a current enrolment in, or previous completion of, Mathematical Methods Units 3 & 4.