Mathematics

Prerequisite:  Nil

Note: Students studying Year 10 Mathematics Foundations are encouraged to discuss the selection of this course with their classroom teacher.

The Mathematics Essential (General) course 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.

In Year 11 students will study Units 1 & 2 followed by Units 3 & 4 in Year 12.

Unit 1 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. Unit 2 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. These topics are all delivered in contexts that are relevant to students and the real world. Possible contexts are Earning and managing money, Transport, Independent living and Nutrition and health.

 

Prerequisite: 

  • Year 10 Intermediate B Mathematics: B Grade, or
  • Year 10 Intermediate A Mathematics: C Grade, or
  • Year 10 Advanced Mathematics: All Grades

This course 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 statistical 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.

Students will study Units 1 and 2 in year 11 followed by Units 3 and 4 in year 12. Students must achieve a passing mark at the conclusion of year 11 in order to continue in this course in year 12.

Students start with ‘Consumer arithmetic’ which 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. ‘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.

Prerequisite:

  • Year 10 Intermediate A Mathematics: A Grade, or
  • Year 10 Advanced Mathematics: C Grade

This course 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 Methods 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 sciences. In summary, this course is designed for students whose future pathways may involve mathematics and statistics and their applications in a range of disciplines at the tertiary level.

Students will study Units 1 and 2 in year 11 followed by Units 3 and 4 in year 12. Students must achieve a passing mark at the conclusion of year 11 in order to continue in this course in year 12.

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. 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.

Prerequisite:

  • Year 10 Advanced Mathematics: B Grade

This course 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. Mathematics Specialist contains topics in functions and calculus that build on and deepen the ideas presented in the Mathematics Methods course, as well as demonstrate their application in many areas. The Mathematics Specialist course also extends understanding and knowledge of statistics and introduces the topics of vectors, complex numbers and matrices. Mathematics Specialist is the only (ATAR) mathematics course that should not be taken as a stand-alone course and it is recommended to be studied in conjunction with the Mathematics Methods (ATAR) course as preparation for entry to specialised university courses such as engineering, physical sciences and mathematics.

The three topics in Unit 1 complement the content of the Mathematics Methods (ATAR) course. The proficiency strand of Reasoning, from the Year 7–10 curriculum, is continued explicitly in the topic Geometry through a discussion of developing mathematical arguments. 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. These three topics considerably broaden students’ mathematical experience and therefore begin an awakening to the breadth and utility of the subject. They also enable students to increase their mathematical flexibility and versatility.

In Unit 2, Matrices provide new perspectives for working with two-dimensional space and Real and complex numbers provides a continuation of the study of numbers. The topic Trigonometry contains techniques that are used in other topics in both this unit and Units 3 and 4. The technique of proof by the principle of mathematical induction is introduced in this unit. All topics develop students’ ability to construct mathematical arguments and formulate mathematics proofs.

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