Mathematics 

Contact:       Mr Ross Barnett, Head of Mathematics

Mathematics Applications: ATAR

Mathematics Methods: ATAR

Mathematics Specialist: ATAR

Mathematics Essential: General

Mathematics Preliminary: General

Great Southern Grammar offers five mathematics courses, two General and three ATAR.  Each course is organised into four units. Unit 1 and Unit 2 are taken in Year Eleven and Unit 3 and Unit 4 in Year Twelve.  The Western Australian Certificate of Education (WACE) examination for each of the three ATAR courses is based on Unit 3 and Unit 4 only.  The courses are differentiated, each focusing on a pathway that will meet the learning needs of a particular group of senior secondary students. 

ATAR Course Combinations: It is possible, and in one case essential, to select more than one ATAR mathematics course at GSG.  If you select Specialist, you must also select Methods as the Specialist course relies on knowledge taught in the Methods course. It is possible to select both Methods and Applications and have both scores contribute to forming a resultant ATAR.  This course pairing is suitable for students who need Methods as a prerequisite to a university course but believe that sitting Applications will help them form a higher ATAR.  Alternatively, Methods and Applications may be selected as a stand-alone course.

Description of Mathematics courses offered at GSG

Mathematics Applications: ATAR

Prerequisites: Students require a B grade in Year Ten Mathematics

Mathematics Applications is an ATAR course, which focuses on the use of mathematics to solve problems in contexts that involve financial modelling, geometric and trigonometric analysis, graphical and network analysis, and growth and decay in sequences. It also provides opportunities for students to develop systematic strategies based on the statistical investigation process for answering questions that involve analysing univariate and bivariate data, including time series data. 

Year Eleven Course Outline

Unit 1: 

• Consumer arithmetic

• Algebra and matrices

• Shape and Measurement

‘Consumer arithmetic’ reviews the concepts of rate and percentage change in the context of earning and managing money, and provides a context for the use of spreadsheets. ‘Algebra and matrices’ continues the Year 7–10 study of algebra and introduces the new topic of matrices. The emphasis of this topic is the symbolic representation and manipulation of information from real-life contexts using algebra and matrices. ‘Shape and measurement’ extends the knowledge and skills students developed in the Year 7–10 curriculum with the concept of similarity and associated calculations involving simple and compound geometric shapes. The emphasis in this topic is on applying these skills in a range of practical contexts, including those involving three-dimensional shapes.

Unit 2:

• Univariate data analysis and the statistical investigation process

• Applications of trigonometry

• Linear equations and their graphs

Univariate data analysis and the statistical investigation process develop students’ ability to organise and summarise univariate data in the context of conducting a statistical investigation. Applications of trigonometry extends students’ knowledge of trigonometry to solve practical problems involving non-right-angled triangles in both two and three dimensions, including problems involving the use of angles of elevation and depression and bearings in navigation. Linear equations and their graphs uses linear equations and straight-line graphs, as well as linear-piece-wise and step graphs, to model, and analyse practical situations.

Assessment for the Mathematics Applications: ATAR course in Year Eleven

Year Twelve Course Outline

Prerequisites: Students require a C grade in Year Eleven Mathematics Applications

Unit 3:

• Bivariate data analysis

• Growth and decay in sequences

• Graphs and networks

Bivariate data analysis introduces students to some methods for identifying, analysing and describing associations between pairs of variables, including using the least-squares method as a tool for modelling and analysing linear associations. The content is to be taught within the framework of the statistical investigation process.

Growth and decay in sequences employs recursion to generate sequences that can be used to model and investigate patterns of growth and decay in discrete situations. These sequences find application in a wide range of practical situations, including modelling the growth of a compound interest investment, the growth of a bacterial population, or the decrease in the value of a car over time. Sequences are also essential to understanding the patterns of growth and decay in loans and investments that are studied in detail in Unit 4. 

Graphs and networks introduces students to the language of graphs and the way in which graphs, represented as a collection of points and interconnecting lines, can be used to analyse everyday situations, such as a rail or social network. 

Unit 4:

• Time series analysis

• Loans, investments and annuities

• Network and decision mathematics

Time series analysis continues students’ study of statistics by introducing them to the concepts and techniques of time series analysis.  The content is taught within the framework of the statistical investigation process.

Loans, investments and annuities aims to provide students with sufficient knowledge of financial mathematics to solve practical problems associated with taking out or refinancing a mortgage and making investments.

Networks and decision mathematics uses networks to model and aid decision making in practical situations.

Assessment for the Mathematics Applications: ATAR course in Year Twelve

Mathematics Methods: ATAR

Prerequisites:   Students require an A or B grade in 10A Mathematics.  Students with a B grade may be accepted into Mathematics Methods following an interview with the Head of Mathematics.

Mathematics Methods is an ATAR course that focuses on the use of calculus and statistical analysis. The study of calculus provides a basis for understanding rates of change in the physical world, and includes the use of functions, their derivatives and integrals, in modelling physical processes. The study of statistics develops students’ ability to describe and analyse phenomena that involve uncertainty and variation.

Year Eleven Course Outline

Unit 1:

• Functions and graphs

• Trigonometric functions

• Counting and probability

Simple relationships between variable quantities are reviewed, and these are used to introduce the key concepts of a function and its graph. The study of probability and statistics begins in this unit with a review of the fundamentals of probability, and the introduction of the concepts of conditional probability and independence. The study of the trigonometric functions begins with a consideration of the unit circle using degrees and the trigonometry of triangles and its application. Radian measure is introduced, and the graphs of the trigonometric functions are examined and their applications in a wide range of settings are explored.

Unit 2:

• Exponential functions

• Arithmetic and geometric sequences and series

• Introduction to differential calculus

Exponential functions are introduced and their properties and graphs examined. Arithmetic and geometric sequences and their applications are introduced and their recursive definitions applied. Rates and average rates of change are introduced and this is followed by the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically (by calculating difference quotients), geometrically (as slopes of chords and tangents), and algebraically. This first calculus topic concludes with derivatives of polynomial functions, using simple applications of the derivative to sketch curves, calculate slopes and equations of tangents, determine instantaneous velocities, and solve optimisation problems.

Assessment for the Mathematics Methods: ATAR course in Year Eleven

Year Twelve Course Outline

Prerequisites: Students require a C grade in Year Eleven Mathematics Methods

Unit 3:

• Further differentiation and applications

• Integrals

• Discrete random variables

The study of calculus continues by introducing the derivatives of exponential and trigonometric functions and their applications, as well as some basic differentiation techniques and the concept of a second derivative, its meaning and applications. The aim is to demonstrate to students the beauty and power of calculus and the breadth of its applications. The unit includes integration, both as a process that reverses differentiation and as a way of calculating areas. The fundamental theorem of calculus as a link between differentiation and integration is emphasised.  Discrete random variables are introduced, together with their uses in modelling random processes involving chance and variation. The purpose here is to develop a framework for statistical inference.

Unit 4:

• The logarithmic function

• Continuous random variables and the normal distribution

• Interval estimates for proportions

The logarithmic function and its derivative are studied. Continuous random variables are introduced and their applications examined. Probabilities associated with continuous distributions are calculated using definite integrals. In this unit, students are introduced to one of the most important parts of statistics, namely, statistical inference, where the goal is to estimate an unknown parameter associated with a population using a sample of that population. In this unit, inference is restricted to estimating proportions in two-outcome populations. Students will already be familiar with many examples of these types of populations.

Assessment for the Mathematics Methods: ATAR course in Year Twelve

Mathematics Specialist: ATAR 

Prerequisites:   Students require an A or B grade in 10A Mathematics.  Students with a B grade may be accepted into Mathematics Specialist following an interview with the Head of Mathematics.

Mathematics Specialist is an ATAR course that provides opportunities beyond those presented in the Mathematics Methods: ATAR course, to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively. The Mathematics Specialist: ATAR course contains topics in functions and calculus that build on and deepen the ideas presented in the Mathematics Methods: ATAR course, as well as demonstrate their application in many areas. This course also extends understanding and knowledge of statistics and introduces the topics of vectors, complex numbers and matrices. The Mathematics Specialist: ATAR course is the only ATAR mathematics course that cannot be taken as a stand-alone course.

Year Eleven Course Outline

Unit 1:

• Geometry

• Combinatorics

• Vectors in the plane

This topic also provides the opportunity to summarise and extend students’ studies in Euclidean Geometry, knowledge which is of great benefit in the later study of topics such as vectors and complex numbers. The topic Combinatorics provides techniques that are very useful in many areas of mathematics, including probability and algebra. The topic Vectors in the plane provides new perspectives on working with two-dimensional space and serves as an introduction to techniques which can be extended to three-dimensional space in Unit 3. 

Unit 2:

• Trigonometry

• Matrices

• Real and complex numbers

The topic Trigonometry contains techniques that are used in other topics in both this unit and Units 3 and 4. All topics develop students’ ability to construct mathematical arguments. The technique of proof by the principle of mathematical induction is introduced in this unit. 

Assessment for the Mathematics Specialist: ATAR course in Year Eleven

Year Twelve Course Outline

Prerequisites: Students require a C grade in Year Eleven Mathematics Specialist

Unit 3:

• Complex numbers

• Functions and sketching graphs

• Vectors in three dimensions

Unit 3 of the Mathematics Specialist ATAR course contains three topics: Complex numbers, Functions and sketching graphs and Vectors in three dimensions. The study of vectors was introduced in Unit 1 with a focus on vectors in two-dimensional space. In this unit, three-dimensional vectors are studied and vector equations and vector calculus are introduced, with the latter extending students’ knowledge of calculus from the Mathematics Methods ATAR course. Cartesian and vector equations, together with equations of planes, enables students to solve geometric problems and to solve problems involving motion in three-dimensional space.  The Cartesian form of complex numbers that was introduced in Unit 2 and the study of complex numbers is now extended to the polar form.

Unit 4:

• Integration and applications of integration

• Rates of change and differential equations

• Statistical inference

In this unit, the study of differentiation and integration of functions is continued, and the techniques developed from this and previous topics in calculus are applied to the area of simple differential equations, in particular in biology and kinematics. These topics serve to demonstrate the applicability of the mathematics learnt throughout this course. Also in this unit, all of the students’ previous experience in statistics is drawn together in the study of the distribution of sample means.  This is a topic that demonstrates the utility and power of statistics.

Assessment for the Mathematics Specialist: ATAR course in Year Twelve

Mathematics Preliminary: General

Prerequisites: Nil

Mathematics Preliminary is a General course that 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.  Grades are not assigned for these units. Student achievement is recorded as ‘completed’ or ‘not completed’. This course provides the opportunity for students to prepare for post-school options of employment and further training.

Mathematics Essential: General

Prerequisites: D grade or better in Year Ten Mathematics

Mathematics Essential is a General course that focuses on using mathematics effectively, efficiently and critically to make informed decisions.  It provides 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. This course provides the opportunity for students to prepare for post-school options of employment and further training. 

Year Eleven Course Outline

Unit 1: 

• Basic calculations 

• Percentages and rates

• Using formulas for practical purposes

• Measurement

• Graphs

This unit provides students with the mathematical skills and understanding to solve problems relating to calculations, the use of formulas to find an unknown quantity, applications of measurement and the use and interpretation of graphs.  Teachers are advised to apply the content of all topics in contexts, which are meaningful, and of interest to their students. Possible contexts for this unit are Earning and managing money and Nutrition and health.

Unit 2: 

• Representing and comparing data

• Percentages

• Rates and ratios

• Time and motion

This unit provides students with the mathematical skills and understanding to solve problems related to representing and comparing data, percentages, rates and ratios, and time and motion. Teachers are advised to apply the content of all topics in contexts which are meaningful and of interest to the students. Possible contexts for this unit to achieve this goal are Transport and Independent living.

Assessment for the Mathematics Essential: General course in Year Eleven

Year Twelve Course Outline

Unit 3: 

• Measurement

• Scales, plans and models

• Graphs in practical situations

• Data collection

This unit provides students with the mathematical skills and understanding to solve problems related to measurement, scales, plans and models, drawing and interpreting graphs and data collection. Students use the mathematical thinking process and apply the statistical investigation process. Teachers are encouraged to apply the content of the four topics in this unit: Measurement; Scales, plans and models; Graphs in practical situations; and Data collection, in a context which is meaningful and of interest to the students. A variety of approaches could be used to achieve this purpose. Possible contexts for this unit are Construction and design, and Medicine.

Unit 4: 

• Probability and relative frequencies

• Earth geometry and time zones

• Loans and compound interest

This unit provides students with the mathematical skills and understanding to solve problems related to probability, earth geometry and time zones, loans and compound interest. Students use the mathematical thinking process and apply the statistical investigation process to solve problems involving probability. Teachers are advised to apply the content of the three topics in this unit: Probability and relative frequencies; Earth geometry and time zones; and Loans and compound interest, in a context which is meaningful and of interest to the students. Possible contexts for this unit are Finance, and Travel.

Assessment for the Mathematics Essential: General course in Year Twelve