Australian Mathematics courses by State and Territory
The senior secondary Australian Curriculum for Mathematics has been organised into four units, with the last two units designed to be cognitively more challenging than the first two. Each unit is designed to be taught in about half a ‘school year’ (approximately 50–60 hours duration including assessment and examinations). The units have also been designed so that they may be studied singly, in pairs over the course of a year, or as four units taken over two years.
State and territory curriculum authorities are responsible for the structure and organisation of the senior secondary curriculum implemented in their jurisdiction. They decide how the Australian Curriculum content and achievement standards are integrated into their courses. They continue to be responsible for assessment, certification and quality assurance in accordance with its respective legislation and the policy framework of its state government and Board (ACARA, 2020).
Essential Mathematics
 Seeks to prepare students for employment or further training.
 Focuses on using mathematics for problem solving and informed decisionmaking.
Unit 1  Unit 2  Unit 3  Unit 4 
Calculations, percentages and rates Measurement Algebra Graphs 
Representing and comparing data Percentages Rates and ratios Time and motion 
Measurement Scales, plans and models Graphs Data collection 
Probability and relative frequencies Earth geometry and time zones Loans and compound interest 
General Mathematics
 Students explore a wide range of geometrical problems in areas such as measurement, scaling, triangulation and navigation.
 Focuses on problemsolving using discrete mathematics in contexts such as financial modelling, network analysis, route and project planning, decision making, and growth and decay.
 Provides opportunities for students to develop systematic strategies for answering statistical questions.
Unit 1  Unit 2  Unit 3  Unit 4 
Consumer arithmetic Algebra and matrices Shape and measurement 
Univariate data analysis and the statistical investigation process Applications of trigonometry Linear equations and their graphs 
Bivariate data analysis Growth and decay in sequences Graphs and networks 
Time series analysis Loans, investments and annuities Networks and decision mathematics 
Mathematical Methods
 Focuses on developing understanding of the role of calculus, including the use of functions, their derivatives and integrals, in modelling physical processes.
 Students develop the ability to describe and analyse phenomena involving uncertainty and variation through their study of statistics.
Unit 1  Unit 2  Unit 3  Unit 4 
Functions and graphs Trigonometric functions Counting and probability 
Exponential functions Arithmetic and geometric sequences and series Introduction to differential calculus 
Further differentiation and applications Integrals Discrete random variables 
The logarithmic function Continuous random variables and the normal distribution Interval estimates for proportions 
Specialist Mathematics
 Specialist Mathematics is taken in conjunction with, and builds on the study of functions and calculus in, Mathematical Methods.
 Provides opportunities to develop rigorous mathematical arguments and proofs and use mathematical models more extensively.
 Extends understanding of probability and statistics and introduces the topics of vectors, complex numbers and matrices.
Unit 1  Unit 2  Unit 3  Unit 4 
Combinatorics Vectors in the plane Geometry 
Trigonometry Matrices Real and complex numbers 
Complex numbers Functions and sketching graphs Vectors in three dimensions 
Integration and applications of integration Rates of change and differential equations Statistical inference 
Source: https://www.australiancurriculum.edu.au/seniorsecondarycurriculum/mathematics/
The senior secondary curriculum is managed by the Board of Senior Secondary Studies in the ACT.
Essential Mathematics
 Based on AC: Essential Mathematics.
 Focuses on using mathematics for problem solving and informed decisionmaking.
Mathematical Methods
 Based on AC: Mathematical Methods
 The discrete random variables and the logarithmic function topics have switched places between Units 3 and 4.
Specialist Mathematics
 Based on AC: Specialist Mathematics.
Mathematical Applications
 Based on AC: General Mathematics.
Source: http://www.bsss.act.edu.au/curriculum/australian_curriculum
Mathematics Standard 1 and 2
 A basic mathematics course containing precalculus concepts and heavily based on practical mathematics used in everyday life.
Mathematics Standard 1 Topics (Year 11)  Mathematics Standard 2 Topics (Year 12) 
Algebra
Measurement
Financial Mathematics
Statistical Analysis

Algebra
Measurement
Financial Mathematics
Statistical Analysis
Networks

Mathematics Advanced
 An advanced level calculusbased course with detailed study in probability and statistics, trigonometry, curve sketching, and applications of calculus. It is the highest level nonextension mathematics course.
Mathematics Advanced (Year 11)  Mathematics Advanced (Year 12) 
Functions
Trigonometric Functions
Calculus
Exponential and Logarithmic Functions
Statistical Analysis

Functions
Trigonometric Functions
Calculus
Financial Mathematics
Statistical Analysis

Mathematics Extension 1
 A more advanced course building on concepts in calculus, trigonometry, polynomials, basic combinatorics, vectors, and further statistics.
 Must be studied concurrently with Mathematics Advanced.
Mathematics Extension 1 (Year 11)  Mathematics Extension 1 (Year 12) 
Functions
Trigonometric Functions
Calculus
Combinatorics

Proof
Vectors
Trigonometric Functions
Calculus
Statistical Analysis

Mathematics Extension 2
 A highly advanced mathematics course containing an introduction to complex numbers, advanced calculus, motion, and further work with vectors.
 Must be studied concurrently with Mathematics Advanced & Mathematics Extension 1.
Mathematics Extension 2 (Year 12) 
Proof
Vectors
Complex Numbers
Calculus
Mechanics

Mathematics Life Skills
Mathematics Life Skills 
Number and Modelling (Algebra)
Measurement
Financial Mathematics
Statistics and Probability (Statistical Analysis)
Plans, Maps and Networks (Networks)

Visit NSW Education Standards
Mathematics (Stage 1)
 Provides a variety of contexts in algebra and geometry for incorporating mathematical arguments and problemsolving.
Topics 1 – 6  Topics 7 – 12 


 As a guide, Topics 1 to 6 prepare students for the study of Stage 2 Mathematical Methods and Topics 7 to 12 prepare students for the study of Stage 2 Specialist Mathematics.
General Mathematics (Stage 1 and 2)
 In Stage 1 students extend their mathematical skills through problemsolving and mathematical modelling in everyday contexts. There is an emphasis on consolidating computational and algebraic skills and expanding students’ ability to reason and analyse mathematically.
 In Stage 2 students develop a strong understanding of the process of mathematical modelling and its application to problem‑solving in everyday contexts.
Topics (Stage 1)  Topics (Stage 2) 

Students study five topics from the list above. 
Essential Mathematics (Stage 1 and 2)
 Essential Mathematics extends students’ mathematical skills in ways that apply to practical problemsolving in everyday and workplace contexts.
 In Stage 1 there is an emphasis on extending students’ computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways.
 In Stage 2 a problembased approach is used to develop mathematical skills and the associated key ideas.
Topics (Stage 1)  Topics (Stage 2) 

Students study five topics from the list above. 
Mathematical Methods (Stage 2)
 Enables students to explore, describe, and explain aspects of the world around them by using calculus and statistics to model practical situations.
Topics (Stage 2) 

Specialist Mathematics (Stage 2)
 Extends students’ mathematical experience in the areas of complex numbers and vectors. The study of functions, differential equations, and dynamic systems provides opportunities to analyse the consequences of more complex laws of interaction.
 Specialist Mathematics provides different scenarios for incorporating mathematical arguments, proofs, and problemsolving.
Topics (Stage 2) 

Mathematics (Stage 1)
 Provides a variety of contexts in algebra and geometry for incorporating mathematical arguments and problemsolving.
Topics 1 – 6  Topics 7 – 12 


 As a guide, Topics 1 to 6 prepare students for the study of Stage 2 Mathematical Methods and Topics 7 to 12 prepare students for the study of Stage 2 Specialist Mathematics.
General Mathematics (Stage 1 and 2)
 In Stage 1 students extend their mathematical skills through problemsolving and mathematical modelling in everyday contexts. There is an emphasis on consolidating computational and algebraic skills and expanding students’ ability to reason and analyse mathematically.
 In Stage 2 students develop a strong understanding of the process of mathematical modelling and its application to problem‑solving in everyday contexts.
Topics (Stage 1)  Topics (Stage 2) 

Students study five topics from the list above. 
Essential Mathematics (Stage 1 and 2)
 Essential Mathematics extends students’ mathematical skills in ways that apply to practical problemsolving in everyday and workplace contexts.
 In Stage 1 there is an emphasis on extending students’ computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways.
 In Stage 2 a problembased approach is used to develop mathematical skills and the associated key ideas.
Topics (Stage 1)  Topics (Stage 2) 

Students study five topics from the list above. 
Mathematical Methods (Stage 2)
 Enables students to explore, describe, and explain aspects of the world around them by using calculus and statistics to model practical situations.
Topics (Stage 2) 

Specialist Mathematics (Stage 2)
 Extends students’ mathematical experience in the areas of complex numbers and vectors. The study of functions, differential equations, and dynamic systems provides opportunities to analyse the consequences of more complex laws of interaction.
 Specialist Mathematics provides different scenarios for incorporating mathematical arguments, proofs, and problemsolving.
Topics (Stage 2) 

Mathematics A
 Maths A is suitable for students who either struggled with mathematics in Year 10, or who do not require a knowledge of abstract mathematics in the future.
 There are fewer algebraic concepts in this subject, which is designed to help students develop an appreciation of the value of Mathematics and how mathematical concepts may be applied to a variety of life situations.
 The Mathematics A course is divided into four semesters.
Semester 1 (Year 11)  Semester 2 (Year 11)  Semester 3 (Year 12)  Semester 4 (Year 12) 




Mathematics B
 Maths B is considerably more theoretical than Maths A, requiring advanced algebra skills to successfully complete.
 Maths B is a prerequisite for any tertiary course which deals with or uses math and/or science.
 In some schools, Maths B can be studied at the same time as either Maths A or Maths C, but not both.
 The course is divided into four semesters.
Semester 1 (Year 11)  Semester 2 (Year 11)  Semester 3 (Year 12)  Semester 4 (Year 12) 




Mathematics C
 Maths C extends the topics taught in Maths B, and covers additional puremaths topics (including complex numbers, matrices, vectors, further calculus and number theory).
 Maths C must be studied in conjunction with Maths B.
 Maths C can be a prerequisite to tertiary courses with a heavy maths/science basis.
 The course is divided into four semesters.
Semester 1 (Year 11)  Semester 2 (Year 11)  Semester 3 (Year 12)  Semester 4 (Year 12) 




Foundation Mathematics
 Focuses on very basic practical maths skills and only runs at a Unit 1 + 2 level.
 These students generally would not undertake Unit 3 and 4 studies in VCE Mathematics.
Areas of Study
 Space, shape and design
 Patterns and number
 Data
 Measurement
General Mathematics
 General Mathematics Units 1 and 2 provide for a range of courses of study involving noncalculus based topics for a broad range of students
 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.
Areas of Study
 Algebra and structure
 Arithmetic and number
 Computation and practical arithmetic
 Financial arithmetic
 Discrete mathematics
 Matrices
 Graphs and networks
 Number patterns and recursion
 Geometry, measurement and trigonometry
 Shape and measurement
 Applications of trigonometry
 Graphs of linear and nonlinear relationships
 Linear graphs and models
 Inequalities and linear programming
 Variation
 Statistics
 Investigating and comparing data distributions
 Investigating relationships between two numerical variables
Further Mathematics
 Further Mathematics Units 3 and 4 are designed to be widely accessible and is considered to be the secondleast demanding of the four maths subjects taken by Victorian students.
 They provide general preparation for employment or further study, in particular where data analysis, recursion and number patterns are important.
 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.
Areas of Study – Unit 3
 Data analysis
 Investigating data distributions
 Investigating associations between two variables
 Investigating and modelling linear associations
 Investigating and modelling time series data
 Recursion and financial modelling
 Depreciation of assets
 Compound interest investments and loans
 Reducing balance loans
 Annuities and petpetuities
 Compound interest investment with periodic and equal additions
Mathematical Methods
 Mathematical Methods is the most common noncompulsory prerequisite for tertiary study in Victoria.
 Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions, algebra, calculus, probability and statistics and their applications.
 Mathematical Methods Units 3 and 4 extend the study of simple elementary functions to include combinations of these functions, algebra, calculus, probability and statistics.
Unit 1  Unit 2  Unit 3  Unit 4  




Specialist Mathematics (Units 1 and 2)
 Specialist Mathematics is considered the most advanced high school mathematics subject in Victoria.
 Specialist Mathematics integrates already learnt concepts of calculus into other fields of mathematics, thus giving Specialist Mathematics a far more practical orientation than standard mathematical subjects.
 Specialist Mathematics Units 1 and 2 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.
Areas of Study – Prescribed
 Arithmetic and number
 Number systems and recursion
 Geometry, measurement and trigonometry
 Geometry in the plane and proof
 Vectors in the plane
 Graphs of linear and nonlinear relations
 Graphs of nonlinear relations
Areas of Study – Optional
 Algebra and structure
 Logic and algebra
 Transformations, trigonometry and matrices
 Arithmetic and number
 Principles of counting
 Discrete mathematics
 Graph theory
 Graphs of linear and nonlinear relations
 Kinematics
 Statistics
 Simulation, sampling and sampling distributions
Specialist Mathematics (Units 3 and 4)
 Specialist Mathematics Units 3 and 4 are designed to be taken in conjunction with or following 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.
Areas of Study – Prescribed
 Functions and graphs
 Algebra
 Rational functions
 Complex numbers
 Calculus
 Differential and integral calculus
 Differential equations
 Kinematics: rectilinear motion
 Vectors
 Vectors
 Vector calculus
 Mechanics
 Probability and statistics
 Linear combinations of random variables
 Sample means
 Confidence intervals for means
 Hypothesis testing
Sources:
Mathematics Specialist
 Based on AC: Specialist Mathematics.
 Should be studied in conjunction with the Mathematics Methods course, on which it builds.
Mathematics Methods
 Based on AC: Mathematical Methods.
 May be studied in conjunction with the Mathematics Specialist course.
Mathematics Applications
 Based on AC: General Mathematics.
Mathematics Essential
 Based on AC: Essential Mathematics.
 Focuses on using mathematics effectively, efficiently and critically to make informed decisions.
Unit 1  Unit 2  Unit 3  Unit 4 




Mathematics Foundation
 Focuses on building the capacity, confidence and disposition to use mathematics to meet the numeracy standard for the WACE.
 It provides students with the knowledge, skills and understanding to solve problems across a range of contexts including personal, community and workplace/employment.
Unit 1  Unit 2  Unit 3  Unit 4 
1.1: Whole numbers and money
1.2: Addition and subtraction with whole numbers and money 1.3: Length, mass and capacity 1.4: Time 1.5: Data, graphs and tables

2.1: Understanding fractions and decimals
2.2: Multiplication and division with whole numbers and money 2.3: Metric relationships 2.4: Perimeter, area and volume 2.5: The probability of everyday events

3.1: The four operations: whole numbers and money
3.2: Percentages linked with fractions and decimals 3.3: The four operations: fractions and decimals 3.4: Location, time and temperature 3.5: Space and design 
4.1: Rates and ratios
4.2: Statistics and probability 4.3: Application of the Mathematical Thinking Process

Mathematics Preliminary
 Focuses on the practical application of knowledge, skills and understandings to a range of environments that will be accessed by students with special education needs.
1 Whole number 
2 Addition and subtraction of whole numbers 
3. Money 
4. Addition and subtraction of money 
5. Multiplication and division 
6. Multiplication and division of money 
7. Time 
8. Measurement 
9. Location 
10. Shape and transformation 
11. Chance and data 
Sources:
 https://seniorsecondary.scsa.wa.edu.au/syllabusandsupportmaterials/mathematics
 Australian Curriculum, Assessment and Reporting Authority. (2020). Overview of the senior secondary Australian Curriculum. Retrieved from https://www.australiancurriculum.edu.au/seniorsecondarycurriculum/mathematics/overviewoftheseniorsecondaryaustraliancurriculum/