Courses for Mathematics

### Year 11 Mathematics Foundation – F1MAT & F2MAT

#### Unit 1

Students must be in OLNA Category 1 or 2 to enrol in this Unit

This unit provides students with the mathematical knowledge, understanding and skills to solve problems relating to addition and subtraction, length, mass, capacity and time, and involving the extraction of information from, and the interpretation of, various simple forms of data representation used in everyday contexts. The number formats for the unit are whole numbers and money.

Unit Cost: $55.00 (textbook included)

#### Unit 2

Students must be in OLNA Category 1 or 2 to enrol in this Unit

This unit provides students with the mathematical knowledge, understanding and skills relating to fractions and decimals, solving problems relating to multiplication and division, perimeter, area and volume and qualitative probability from everyday contexts. The number formats for this unit are whole numbers, money, fractions and decimals.

Unit Cost: $55.00 (textbook included)

### Year 11 Mathematics Essentials – G1MAE & G2MAE

**Unit 1**

Prerequisites:

Students must have at least a C grade in Year 10 number and algebra. Students must have sat the OLNA and be Category 3 to enrol in this Unit.

This unit provides you with the mathematical skills and understanding 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, you will use the mathematical thinking process. The number formats for the unit are whole numbers, decimals, common fractions, common percentages, square and cubic numbers written with powers.

**Unit Cost: $55 (Textbooks included)**

**Unit 2**

Prerequisites:

Students must have at least a C grade in Year 10 number and algebra.

Students must have sat the OLNA and be Category 3 to enrol in this Unit.

This unit provides you with the mathematical skills and understanding to solve problems related to representing and comparing data, percentages, rates and ratios and time and motion. You will further develop the use of the mathematical thinking process and apply the statistical investigation process. The number formats for the unit are whole numbers, decimals, fractions and percentages, rates and ratios.

**Unit Cost: $55 (Textbooks included)**

### Year 11 ATAR Mathematics Applications – A1MAA & A2MAA

**Unit 1**

Prerequisites:

Students must have sat the OLNA and be Category 3 to enrol in this Unit

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 includes the use of spread sheets. ‘Algebra and matrices’ continues the 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 the knowledge and skills of students 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.

**Unit Cost: $60* (Textbook included)**

***ATAR courses require the purchase **

**of a Classpad Calculator: $240**

**Unit 2**

Prerequisites:

Students must have sat the OLNA and be Category 3 to enrol in this Unit

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’ develop students’ ability to organise and summarise univariate data in the context of conducting a statistical investigation. ‘Linear equations and their graphs’ use 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 your 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.

**Unit Cost: $60* (Textbook included)**

***ATAR courses require the purchase **

**of a Classpad Calculator: $240**

### Year 11 ATAR Mathematics Methods – A1MAM & A2MAM

**Unit 1**

Prerequisites: Successful completion equivalent Year 10 and Year 10a Mathematics.

Students must have sat the OLNA and be Category 3 to enrol in this Unit.

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.

**Unit Cost: $60 (Textbook included)**

***ATAR courses require the purchase of a Classpad Calculator: $240**

**Unit 2**

Prerequisites: Successful completion equivalent Year 10 and Year 10a Mathematics. Students must have sat the OLNA and be Category 3 to enrol in this Unit.

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’. These concepts are reinforced numerically, by calculating difference quotients both geometrically as slopes of chords and tangents, and algebraically. Calculus is developed to study the derivatives of polynomial functions, with simple application of the derivative to curve sketching, the calculation of slopes and equations of tangents, the determination of instantaneous velocities and the solution of optimisation problems. The unit concludes with a brief consideration of anti-differentiation.

**Unit Cost: $60 (Textbook included)**

***ATAR courses require the purchase of a Classpad Calculator: $240**

### Year 11 ATAR Mathematics Methods – A1MAM & A2MAM

**Unit 1**

Prerequisites:

1. Successful completion equivalent Year 10 mathematics is strongly advised (or complete appropriate placement test).

2. Student has sat the OLNA and attained Category 3

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.

Unit Cost: $60.00 (Textbook included)

ATAR courses require the purchase of a Classpad Calculator – $230.00

**Unit 2**

Prerequisites:

1. Successful completion equivalent Year 10 mathematics is strongly advised (or complete appropriate placement test).

2. Student has sat the OLNA and attained Category 3

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’. These concepts are reinforced numerically, by calculating difference quotients both geometrically as slopes of chords and tangents, and algebraically. Calculus is developed to study the derivatives of polynomial functions, with simple application of the derivative to curve sketching, the calculation of slopes and equations of tangents, the determination of instantaneous velocities and the solution of optimisation problems. The unit concludes with a brief consideration of anti-differentiation.

Unit Cost: $60.00 (Textbook included)

ATAR courses require the purchase of a Classpad Calculator – $230.00

### Year 12 Mathematics Foundation – FTMAT

Prerequisites: Successful completion of Mathematics Foundation Units 1&2.

**Unit 3**

This unit provides you with the mathematical knowledge, understanding and skills relating to percentages and the link to fractions and decimals, and the solving of problems relating to the four operations using whole number, fractions and decimals. Location, time and temperature, and shape and its relationship to design, are also covered in this unit.

**Unit 4**

This unit provides you with the mathematical knowledge, understanding and skills relating to rates and ratios, and the connection between statistics and probability. The collection of mathematical concepts and thinking processes encountered in this and previous units culminates in the solving of comprehensive real life problems encountered in personal, workplace and community contexts.

(Textbooks included) Unit Pair Cost: $110.00

### Year 12 Mathematics Essentials – GTMAE

Prerequisites: Successful Completion of Mathematics Essential Units 1&2.Students must have sat the OLNA and be Category 3 to enrol in this Unit.

Unit 3: This unit provides you with the mathematical skills and understanding to solve problems related to measurement, scales, plans and models, drawing and interpreting graphs and data collection. You will use the mathematical thinking process and apply the statistical investigation process. You will also 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 you. 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.

Unit 4: This unit provides you with the mathematical skills and understanding to solve problems related to probability, earth geometry and time zones, loans and compound interest. You will use the mathematical thinking process and apply the statistical investigation process to solve problems involving probability. You will also 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 you. Possible contexts for this unit are Finance, and Travel. The number formats for the unit are positive and negative numbers, decimals, fractions, percentages, rates, ratios and numbers expressed with integer powers.

**Unit Pair Cost: $110 (Textbooks included)**

### Year 12 ATAR Mathematics Applications – ATMAA

Prerequisites:

Successful completion of Mathematics Applications Units 1&2.

Students must have sat the OLNA and be Category 3 to enrol in this Unit.

Unit 3: This unit has three topics: ‘Bivariate data analysis’, ‘Growth and decay in sequences’, and ‘Graphs and networks’. ‘Bivariate data analysis’ introduces you 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. 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 you 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.

Unit 4: This unit has three topics: ‘Time series analysis’, ‘Loans, investments and annuities’, and ‘Networks and decision mathematics’. ‘Time series analysis’ continues your study of statistics by introducing you to the concepts and techniques of time series analysis. The content is to be taught within the framework of the statistical investigation process. ‘Loans investments and annuities’ aims to provide you 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.

**Unit Pair Cost: $120* (Textbooks included)**

***ATAR courses require the purchase **

**of a Classpad Calculator: $240**

### Year 12 ATAR Mathematics Methods – ATMAM

Prerequisites: Successful Completion of Mathematics Methods Units 1&2.Students must have sat the OLNA and be Category 3 to enrol in this Unit.

Unit 3: The study of calculus continues with the derivatives of exponential and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. It concludes with 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. In statistics, discrete random variables are introduced, together with their uses in modelling random processes involving chance and variation. This supports the development of a framework for statistical inference.

Unit 4: The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts. The study of statistical inference in this unit is the culmination of earlier work on probability and random variables. Statistical inference is one of the most important parts of statistics, in which the goal is to estimate an unknown parameter associated with a population using a sample of data drawn from that population. In the Mathematics Methods ATAR course, statistical inference is restricted to estimating proportions in two-outcome populations.

**Unit Pair Cost: $120 (Textbooks included)**

***ATAR courses require the purchase of a Classpad Calculator: $240**

### Year 12 ATAR Mathematics Specialist – ATMAS

Specialist Mathematics should be studied in conjunction with units from Mathematics. This course is for students who are proficient mathematicians and interested in pursuing a career that requires advanced mathematics.

Mathematics Specialist: ATAR Units 3&4 (ATMAS)

(Co-requisite: Mathematics: Methods Units 3&4)

Prerequisites: Successful Completion of Mathematics Specialist Units 1&2.

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 your knowledge of calculus from the Mathematics Methods ATAR course. Cartesian and vector equations, together with equations of planes, enables you to solve geometric problems and to solve problems involving motion in three-dimensional space.

The Cartesian form of complex numbers was introduced in Unit 2, and the study of complex numbers is now extended to the polar form.

The study of functions and techniques of graph sketching, begun in the Mathematics Methods ATAR course, is extended and applied in sketching graphs and solving problems involving integration.

Unit 4 of the Mathematics Specialist ATAR course contains three topics: Integration and applications of integration, Rates of change and differential equations and Statistical inference.

In Unit 4, the study of differentiation and integration of functions continues, and the calculus techniques developed in this and previous topics are applied to simple differential equations, in particular in biology and kinematics. These topics demonstrate the real-world applications of the mathematics learned throughout the Mathematics Specialist ATAR course.

In this unit, all of your previous experience working with probability and statistics is drawn together in the study of statistical inference for the distribution of sample means and confidence intervals for sample means.

**Unit Pair Cost: $120 (Textbooks included)**

***ATAR courses require the purchase of a Classpad Calculator: $240**