## Mathematics

The Cecil Andrews College Mathematics Learning Area takes major, although not sole, responsibility for the development of students’ numeracy. It aims to foster students’ mathematical interests, talents and creative development through an interesting and challenging curriculum in an environment that supports the pursuit of growth. With a focus on assisting each student to do their best, we deliver regular tutoring for students at all stages.

Our Mathematics Teachers are skilled in assisting students with a range of interests and abilities to understand and apply the full range of mathematical concepts. Our programs are designed to:

- Encourage students to develop an interest and a liking for Mathematics.
- Provide a challenging curriculum that fosters appropriate academic and creative development.
- Illustrate to students the applications of Mathematics in their personal and work lives.
- Develop student initiative in problem solving.

We aim for students to read, write and speak Mathematics in a variety of contexts and forms so that they can understand and convey mathematical ideas, and continue to use and learn Mathematics autonomously outside the school environment.

At Cecil Andrews College Mathematics we see parents as partners because we know that true success in this discipline can only occur with parental support. All Mathematics teachers encourage and welcome constructive and timely communication and can be contacted through Connect.

**Lower school – Years 7, 8, 9 and 10**

Students in lower school are grouped into an Academic Extension course or a General course. Placement in the Academic Extension course is determined by the previous years results, as well as NAPLAN data and teacher recommendations.

All courses follow the West Australian curriculum, which covers the following three strands:

- Number and Algebra
- Measurement and Geometry
- Statistics and Probability

**Senior School – Years 11 and 12**

Students in Years 11 and 12 make selections according to their preferred pathway – ATAR or General, from the following subjects:

- Mathematics Foundation (General)
- Mathematics Essential (General)
- Mathematics Applications (ATAR)
- Mathematics Methods (ATAR)

#### GENERAL MATHEMATICS FOUNDATION (YEAR 11)

**Code:**

FEMAT (F1MAT, F2MAT)

**External Exam:**

A common assessment task will be delivered in semester one of year 12, under examination conditions, that will contribute to the marks in this course.

**Pathway:**

Year 11 – F1MAT, F2MAT

**Pre-requisites:**

Yet to achieve the WACE standard for numeracy.

**Other Information:**

Mathematics Foundation is a course which 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. This course provides the opportunity for students to prepare for post-school options of employment and further training.

**Content:**

**Unit 1 – F1MAT**

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, such as shopping and debits and credits. Teachers are encouraged to apply the content of this unit in contexts which are meaningful and of interest to their students. The number formats for the unit are whole numbers and money.

**Unit 2 – F2MAT**

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, such as sports scores, recipes and pay. Teachers are encouraged to apply the content of this unit in contexts which are meaningful and of interest to their students. The number formats for this unit are whole numbers, money, fractions and decimals.

#### ATAR MATHEMATICS METHODS (YEAR 11)

**Code:**

AEMAM (A1MAM, A2MAM)

**External Exam:**

Yes (if studied in Year 12)

**Pathway:**

Year 11 – A1MAM, A2MAM / Year 12 – A3MAM, A4MAM

A or B grade in Year 10 Mathematics

**Other Information:**

This course requires a considerable work ethic and commitment to homework. Mathematics Methods is an ATAR course which 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.

Mathematics Method provides a foundation for further studies in disciplines in which mathematics and statistics have important roles. It is also advantageous for further studies in the health and social science. In summary, this course is designed for students whose future pathway may involve mathematics and statistics and their application in a range of disciplines at the tertiary (university) level.

**Content:**

The Year 11 syllabus is divided into two units, each of one semester duration, which are typically delivered as a pair. The notional time for each unit is 55 class contact hours.

**Unit 1 – A1MAM**

Contains the three topics:

- Functions and graphs
- Trigonometric functions
- Counting and probability

Unit 1 begins with a review of the basic algebraic concepts and techniques required for a successful introduction to the study of functions and calculus. 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 – A2MAM**

Contains the three topics:

- Exponential functions
- Arithmetic and geometric sequences and series
- Introduction to differential calculus

In Unit 2, 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.

#### ATAR MATHEMATICS METHODS (YEAR 12)

**Code:**

AEMAM (A3MAM, A4MAM)

**External Exam:**

Yes

**Pathway:**

Year 11 – A1MAM, A2MAM / Year 12 – A3MAM, A4MAM

**Prerequisites:**

C grade or better in Year 11 Mathematics Method

**Other Information:**

**Content:**

**Unit 3 – A3MAM**

Contains the 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. 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 – A4 MAM**

Contains the 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. Students will already be familiar with many examples of these types of populations.

#### ATAR MATHEMATICS APPLICATION (YEAR 11)

**Code:**

AEMAA (A1MAA, A2MAA)

**External Exam:**

Yes (if studied in Year 12)

**Pathway:**

Year 11 – A1MAA, A2MAa / Year 12 – A3MAA, A4MAA

**Prerequisites:**

A or B grade in Year 10 Mathematics

**Other Information:**

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.

The Mathematics Applications ATAR course is designed for students who want to extend their mathematical skills beyond Year 10 level, but whose future studies or employment pathways do not require knowledge of calculus. The course is designed for students who have a wide range of educational and employment aspirations, including continuing their studies at university or TAFE.

**Content:**

The Year 11 syllabus is divided into two units, each of one semester duration, which are typically delivered as a pair. The notional time for each unit is 55 class contact hours.

**Unit 1 – A1MAA**

Contains the three topics:

- 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 spread sheets. ‘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 – A2MAA**

Contains the three topics:

- 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’ use linear equations and straight-line graphs, as well as linear-piece-wise and step graphs, to model and analyse practical situations.

#### ATAR MATHEMATICS APPLICATION (YEAR 12)

**Code:**

ATMAA (A3MAA, A4MAA)

**External Exam:**

Yes (if studied in Year 12)

**Pathway:**

Year 11 – A1MAA, A2MAA / Year 12 – A3MAA, A4MAA

**Prerequisites:**

C grade or better in Year 11 Mathematics Application

**Other Information:**

**Content:**

**Unit 3 – A3MAA**

Contains the 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 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 – A4MAA**

Contains the 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. The content is to be 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.

#### GENERAL MATHEMATICS ESSENTIAL (YEAR 11)

**Code:**

GEMAE (G1MAE, G2MAE)

**External Exam:**

A common assessment task will be delivered in semester one of year 12, under examination conditions that will contribute to the marks in this course.

**Pathway:**

Year 11 – G1MAE, G2MAE / Year 12 – G3MAE, G4MAE

**Prerequisites:**

Nil

**Other Information:**

Mathematics Essential is a General course which 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.

**Content:**

**Unit 1 – G1MAE**

This unit provides students 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, students use the mathematical thinking process. This process should be explicitly taught in conjunction with the unit content. Teachers are advised to apply the content of the four topics in this unit: Basic calculations, percentages and rates; Algebra; Measurement; and Graphs, 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.

It is assumed that an extensive range of technological applications and techniques will to be used in teaching this unit. The ability to choose when or 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 whole numbers, decimals, common fractions, common percentages, square and cubic numbers written with powers.

**Unit 2 – G2MAE**

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 statistical investigation process should be explicitly taught in conjunction with the statistical content within this unit. Teachers are advised to apply the content of the four topics in this unit: Representing and comparing data; Percentages; Rates and ratios; and Time and motion, in a context which is meaningful and of interest to their students. Possible contexts for this unit are Transport and Independent living.

It is assumed that students will be taught this course with an extensive range of technological applications and techniques. The ability to be able to choose when or when not to use some form of technology and to be able to work flexibly with technology are important skills.

The number formats for the unit are whole numbers, decimals, fractions and percentages, rates and ratios.

#### GENERAL MATHEMATICS ESSENTIAL (YEAR 12)

**Code:**

GTMAE (G3MAE, G4MAE)

**External Exam:**

**Pathway:**

Year 11 – G1MAE, G2MAE / Year 12 – G3MAE, G4MAE

**Prerequisites:**

Nil

**Other Information:**

A common assessment task will be delivered in semester one of year 12, under examination conditions that will contribute to the marks in this course.

**Content:**

**Unit 3 – G3MAE**

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.

**Unit 4 – G4MAE**

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.

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 and numbers expressed with integer powers.