### Mathematics Specialist (ATAR)

**Course Code: **AEMAS/ATMAS**Domain: **Maths**Timetable: **Semester 1 and 2**Length of Course: **2 Years

### Unit Information

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring, it has

evolved in highly sophisticated and elegant ways to become the language now used to describe much of the

modern world. Statistics are concerned with collecting, analysing, modelling and interpreting data in order

to investigate and understand real world phenomena and solve problems in context. Together, mathematics

and statistics provide a framework for thinking and a means of communication that is powerful, logical,

concise and precise.

Both mathematics and statistics are widely applicable as models of the world around us and there is ample

opportunity for problem-solving throughout the Mathematics Specialist (ATAR) course. There is also a sound

logical basis to this subject, and in mastering the course, students will develop logical reasoning skills to a

high level.

The Mathematics Specialist (ATAR) course provides opportunities, beyond those presented in the

Mathematics Methods (ATAR) course, to develop rigorous mathematical arguments and proofs and to use

mathematical and statistical models more extensively. Topics are developed systematically and lay the

foundations for future studies in quantitative subjects in a coherent and structured fashion. Students of the

Mathematics Specialist (ATAR) course will be able to appreciate the true nature of mathematics, its beauty

and its functionality.

**The Mathematics Specialist (ATAR) course has been designed to be taken in conjunction with theMathematical Methods (ATAR) course.** The subject contains topics in functions, calculus, probability and

statistics that build on and deepen the ideas presented in the Mathematical Methods (ATAR) course and

demonstrate their application in many areas. Vectors, complex numbers and matrices are introduced. The

Mathematics Specialist (ATAR) course is designed for students with a strong interest in mathematics, including

those intending to study mathematics, statistics, all sciences and associated fields, economics or engineering

at university.

For all content areas of the Mathematics Specialist (ATAR) course, the proficiency strands of the Year 7–10

curriculum continue to be applicable and should be inherent in students’ learning of the subject. These

strands are Understanding, Fluency, Problem-solving and Reasoning and they are both essential and

mutually reinforcing. For all content areas, practice allows students to achieve fluency of skills, such as

finding the scalar product of two vectors, or finding the area of a region contained between curves, freeing

up working memory for more complex aspects of problem-solving. In the Mathematics Specialist (ATAR)

course, the formal explanation of reasoning through mathematical proof takes on an important role and the

ability to present the solution of any problem in a logical and clear manner is of paramount importance. The

ability to transfer skills learned to solve one class of problem, for example, integration, to solve another class

of problem, such as in biology, kinematics or statistics, is a vital part of mathematics learning in this subject.

#### Unit One

Unit 1 of the Mathematics Specialist (ATAR) course contains three topics: Combinatorics, Vectors in the plane,

and Geometry that complement the content of the Mathematical Methods (ATAR) course. The proficiency

strand, Reasoning, of the Year 7–10 curriculum is continued explicitly in Geometry through a discussion of

developing mathematical arguments. While these ideas are illustrated through deductive Euclidean

geometry in this topic, they recur throughout all topics in the Mathematics Specialist (ATAR) course.

Geometry also provides the opportunity to summarise and extend students’ studies in Euclidean Geometry.

An understanding of this topic is of great benefit in the study of later topics in the course, including vectors

and complex numbers.

Vectors in the plane provides new perspectives for working with two-dimensional space and serves as an

introduction to techniques that will be extended to three-dimensional space in Unit 3.

Combinatorics provides techniques that are useful in many areas of mathematics, including probability and

algebra. All topics develop students’ ability to construct mathematical arguments.

The three topics considerably broaden students’ mathematical experience and therefore begin an

awakening to the breadth and utility of the course. They also enable students to increase their mathematical

flexibility and versatility.

#### Unit Two

Unit 2 of the Mathematics Specialist (ATAR) course contains three topics: Trigonometry, Matrices, and Real

and complex numbers.

Trigonometry contains techniques that are used in other topics in both this unit and Unit 3. Real and

complex numbers provides a continuation of students’ study of numbers, and the study of complex numbers

is continued in Unit 3. This topic also contains a section on proof by mathematical induction. The study of

Matrices is undertaken, including applications to linear transformations of the plane.

#### Unit Three

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 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 Four

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 the students’ 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.

#### Pathway Information

### Tertiary

### Workforce

Students undertaking this course may wish to consider tertiary studies in:

- Bachelor of Science
- Bachelor of Commerce

This course suits direct workforce entry into the following:

- Insurance Agent
- Laboratory Worker

#### Additional Information

**Estimated Charges: **$50 per year