Mathematics

1. Combinatorics 
2. Vectors in the plane 
3. Geometry 

1. Trigonometry 
2. Matrices 
3. Real and complex numbers. 

1. Complex numbers 
2. Functions and sketching graphs 
3. Vectors in three dimensions 

1. Integration and applications of integration 
2. rates of change and differential equations 
3. Statistical inference 

This unit begins with a review of the basic algebraic concepts and techniques required for a successful introduction to the study of calculus. The basic trigonometric functions are then introduced. 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 inferential statistics begins in this unit with a review of the fundamentals of probability and the introduction of the concepts of counting, conditional probability and independence. Access to technology to support the computational and graphical aspects of these topics is assumed. 

The algebra section of this unit focuses on exponentials. Their graphs are examined and their applications in a wide range of settings are explored. Arithmetic and geometric sequences are introduced and their applications are studied. 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’. 

This unit contains three topics: 

• 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. 

This unit contains three topics: 

• 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. 

This unit has three topics: consumer arithmetic, algebra and matrices, and shape and measurement. 

Consumer arithmetic reviews the concepts of rate and percentage change in the context of earning and managing money and provides a fertile ground for the use of spread sheets. 

Algebra and matrices continues the Year 7 – 10 curriculum study of algebra and introduces the 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 builds on and extends the knowledge and skills students developed in the Year 7 – 10 curriculum with the concept of similarity and associated calculations involving simple geometric shapes. The emphasis in this topic is on applying these skills in a range of practical contexts, including those involving three-dimensional shapes. 

This unit has three topics: univariate data analysis and the statistical process, linear equations and their graphs, and applications of trigonometry. 

Univariate data analysis and the statistical process develops students’ ability to organise and summarise univariate data in the context of conducting a statistical investigation. 

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. 

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. 

This unit has three topics: 

• 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 the use of the least-squares method as a tool for modelling and analysing linear associations. Content is 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 ways in which graphs, represented as a collection of points and interconnecting lines, can be used to model and analyse everyday situations, such as a rail or social network. 

This unit has three topics: 

• Time series analysis 

• Loans, investments and annuities 
• Networks and decision mathematics. 

Time series analysis continues students’ study of statistics by introducing them to the concepts and techniques of time series analysis. It is a requirement that students are 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. 

This unit provides students with the mathematical skills and understandings to solve problems relating to calculations, applications of measurement, the use of formulas to find an unknown quantity and the interpretation of graphs. Throughout this unit, students use the mathematical thinking process. 

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. Students further develop the use of the mathematical thinking process and apply the statistical investigation process. The investigation process should be explicitly taught in conjunction with the statistical content within this unit. 

This unit includes the following four topics: 

• 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. 

It is assumed that an extensive range of technological applications and techniques will be used in teaching this unit. The ability to choose when, and when not, to use some form of technology, and the ability to work flexibly with technology, are important skills. 

The number formats for the unit are positive and negative numbers, decimals, fractions, percentages, rates, ratios, square and cubic numbers written with powers and square roots. 

This unit includes the following three topics: 

• 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. 

An extensive range of technological applications and techniques are used in teaching these units. The ability to choose when, and when not, to use some form of technology, and the ability to work flexibly with technology, are important skills.