Mathematics

Year 7
Learning mathematics creates opportunities for and enriches student perspectives of the world. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals on which mathematical specialties and professional applications of mathematics are built.

Mathematics has its own value and beauty and this course aims to instil in students an appreciation of the elegance and power of mathematical reasoning. Mathematical ideas have evolved across all cultures over thousands of years, and are constantly developing. Digital technologies are facilitating this expansion of ideas and providing access to new tools for continuing mathematical exploration and invention. This course focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Year 8
The Mathematics course at Somerville House will provide students with the opportunity to:

• become confident, creative users and communicators of mathematics, who are able to investigate, represent, interpret situations and construct meaningful conclusions in a variety of contexts.
• develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in the strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability.
• recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study.

Year 9
Students will investigate a variety of mathematical and life-related contexts. They will use these contexts to develop the mathematical tools and mathematical models needed to make informed conjectures and generate meaningful solutions to problems. Students will develop techniques for collecting data from a variety of sources and use the mathematical tools to generate a meaningful analysis of that data. Students will investigate linear and non-linear relations and apply them to real life contexts. They will learn how to communicate their understanding using mathematical and natural language.

Mathematics 1 focuses on the core Year 10 Mathematics concepts detailed in the Australian Curriculum Strands- Number and Algebra, Measurement and Space, and Probability and Statistics.

The course develops the knowledge, skills and processes required for a study of General Mathematics in Years 11 and 12. This course will require students to use their mathematics to solve problems, develop mathematical models and use them to make predictions. It caters for those students who have experienced difficulty with the harder and more abstract concepts studied in Year 9 (for example, algebraic facility) or who do not require advanced mathematics in Years 11 and 12 for courses beyond Year 12.

Students who study Mathematics 1 in Year 10 will study the General Mathematics syllabus in Years 11 and 12 and will not be able to study Mathematical Methods or Specialist Mathematics.

Mathematics 2 focuses on the core and the advanced Year 10 Mathematics concepts detailed in the Australian Curriculum Strands - Number and Algebra, Measurement and Space, and Probability and Statistics.

This course develops the knowledge, skills and processes required for the courses of study Mathematical Methods or Mathematical Methods and Specialist Mathematics. This course is for students who enjoy mathematical challenges and who are wishing to use their understanding of mathematics to solve problems, to develop mathematical models and to evaluate the accuracy of their conclusions. Students are required to have a good understanding of algebraic concepts and be able to apply them fluently.

In general, students who study Mathematics 2 in Year 10 will select from one of the following courses of study, Mathematical Methods or Mathematical Methods and Specialist Mathematics in Years 11 and 12.

To study either of the courses, Mathematical Methods or Mathematical Methods and Specialist Mathematics in Year 11, students must have satisfied the following prerequisites:

1. Studied a full year of Mathematics 2 (or equivalent) and
2. Obtained a year rating of at least B-.

Students who are uncertain about their choice of Mathematics subject should seek advice from their class teacher or Mr Redmond, Head of Mathematics.

General Mathematics is designed for students who want to extend their mathematical skills beyond Year 10 but whose future studies or employment pathways do not require calculus. It incorporates a practical approach that equips learners for their needs as future citizens. Students will learn to ask appropriate questions, map out pathways, reason about complex solutions, set up models and communicate in different forms. They will experience the relevance of mathematics to their daily lives, communities and cultural backgrounds. They will develop the ability to understand, analyse and take action regarding social issues in their world. When students gain skill and self-assurance, when they understand the content and when they evaluate their success by using and transferring their knowledge, they develop a mathematical mindset.

The major domains of mathematics in General Mathematics are Number and algebra, Measurement and geometry, Statistics and Networks and matrices, building on the content of the P–10 Australian Curriculum. Learning reinforces prior knowledge and further develops key mathematical ideas, including rates and percentages, concepts from financial mathematics, linear and non-linear expressions, sequences, the use of matrices and networks to model and solve authentic problems, the use of trigonometry to find solutions to practical problems, and the exploration of real-world phenomena in statistics. 

Topics studied:

In Unit 1, students will develop mathematical understandings and skills to solve problems relating to the topics:

• Topic 1: Consumer arithmetic
• Topic 2: Shape and measurement
• Topic 3: Linear equations and their graphs.

In Unit 2, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: Applications of trigonometry
• Topic 2: Algebra and matrices
• Topic 3: Univariate data analysis.

In Unit 3, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: Bivariate data analysis
• Topic 2: Time series analysis
• Topic 3: Growth and decay in sequences
• Topic 4: Earth geometry and time zones.

In Unit 4, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: Loans, investments and annuities
• Topic 2: Graphs and networks
• Topic 3: Networks and decision mathematics.

Essential Mathematics’ major domains are Number, Data, Location and time, Measurement and Finance. Essential Mathematics benefits students because they develop skills that go beyond the traditional ideas of numeracy.

Students develop their conceptual understanding when they undertake tasks that require them to connect mathematical concepts, operations and relations. They learn to recognise definitions, rules and facts from everyday mathematics and data, and to calculate using appropriate mathematical processes.

Students interpret and use mathematics to make informed predictions and decisions about personal and financial priorities. This is achieved through an emphasis on estimation, problem-solving and reasoning,
which develops students into thinking citizens.

Essential Mathematics is not a General subject, however, it can contribute to QCE eligiblity and the results
can contribute to the ATAR. 

By the conclusion of the course of study, students will be able to:

• select, recall and use facts, rules, definitions and procedures drawn from Number, Data, Location and time, Measurement and Finance
• comprehend mathematical concepts and techniques drawn from Number, Data, Location and time, Measurement and Finance
• communicate using mathematical, statistical and everyday language and conventions
• evaluate the reasonableness of solutions
• justify procedures and decisions by explaining mathematical reasoning
• solve problems by applying mathematical concepts and techniques drawn from Number, Data, Location and time, Measurement and Finance.

Topics studied:

• Unit 1: Number, data and graphs
• Unit 2: Money, travel and data
• Unit 3: Measurement, scales and data
• Unit 4: Graphs, chance and loans

Students who undertake Mathematical Methods will see the connections between mathematics and other areas of the curriculum and apply their mathematical skills to real-world problems, becoming critical thinkers, innovators and problem-solvers. Through solving problems and developing models, they will appreciate that mathematics and statistics are dynamic tools that are critically important in the 21st century.

The major domains of mathematics in Mathematical Methods are Algebra, Functions, relations and their graphs, Calculus and Statistics. Topics are developed systematically, with increasing levels of sophistication, complexity and connection, and build on algebra, functions and their graphs, and probability from the P–10 Australian Curriculum. Calculus is essential for developing an understanding of the physical world. The domain Statistics is used to describe and analyse phenomena involving uncertainty and variation. Both are the basis for developing effective models of the world and solving complex and abstract mathematical problems. The ability to translate written, numerical, algebraic, symbolic and graphical information from one representation to another is a vital part of learning in Mathematical Methods.

In Unit 1, students will develop mathematical understandings and skills to solve problems relating to the topics:

• Topic 1: Functions and graphs
• Topic 2: Arithmetic and geometric sequences 1
• Topic 3: Counting and probability
• Topic 4: Exponential and logarithmic functions 1
• Topic 5: Arithmetic and geometric sequences and series 2.

Continued enrolment in Mathematical Methods:

Students offered provisional enrolment in Mathematical Methods at the end of Year 10 will have their continued enrolment in Mathematical Methods evaluated at the end of Unit 1. Students not meeting the minimum standard required to continue their study of the Mathematical Methods course will have their enrolment evaluated at the end of Unit 1.

In Unit 2, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: Exponential functions
• Topic 2: The logarithmic function 1
• Topic 3: Trigonometric functions 1
• Topic 4: Differential calculus and applications
• Topic 5: Discrete random variables 1.

In Unit 3, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: The logarithmic function 2
• Topic 2: Further differentiation and applications 2
• Topic 3: Integrals.

In Unit 4, students will develop mathematical understandings and skills to solve problems relating to:

• Topic 1: Further differentiation and application 3
• Topic 2: Trigonometric functions 2
• Topic 3: Discrete random variables 2
• Topic 4: Continuous random variables and the normal distribution
• Topic 5: Interval estimates for proportions.

Students who undertake Specialist Mathematics will develop confidence in their mathematical knowledge and ability, and gain a positive view of themselves as mathematics learners. They will gain an appreciation of the true nature of mathematics, its beauty and its power.

The major domains of mathematical knowledge in Specialist Mathematics are Vectors and matrices, Real and complex numbers, Trigonometry, Statistics and Calculus. Topics are developed systematically, with increasing levels of sophistication, complexity and connection, building on functions, calculus, statistics from Mathematical Methods, while vectors, complex numbers and matrices are introduced. Functions and calculus are essential for creating models of the physical world. Statistics are used to describe and analyse phenomena involving probability, uncertainty and variation. Matrices, complex numbers and vectors are essential tools for explaining abstract or complex relationships that occur in scientific and technological endeavours.

In Unit 1, students will develop the mathematical understandings and skills to solve problems relating to the topics:

• Topic 1: Combinatorics
• Topic 2: Vectors in a plane
• Topic 3: Introduction to proof.

Continued enrolment in Specialist Mathematics:

Students offered provisional enrolment in Specialist Mathematics at the end of Year 10 will have their continued enrolment in Specialist Mathematics evaluated at the end of Unit 1. Students not meeting the minimum standards required to continue their study of the Specialist Mathematics course will have their enrolment evaluated at the end of Unit 1.

In Unit 2, students will develop the mathematical understandings and skills to solve problems relating to:

• Topic 1: Complex numbers 1
• Topic 2: Trigonometry and functions
• Topic 3: Matrices.

In Unit 3, students will develop the mathematical understandings and skills to solve problems relating to:

• Topic 1: Proof by mathematical induction
• Topic 2: Vectors and matrices
• Topic 3: Complex numbers 2.

In Unit 4, students will develop the mathematical understandings and skills to solve problems relating to:

• Topic 1: Integration and applications of integration
• Topic 2: Rates of change and differential equations
• Topic 3: Statistical inference.