### Mathematics Methods (ATAR)

**Course Code: **AEMAM/ATMAM**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.

The major themes of the Mathematics Methods (ATAR) course are calculus and statistics. They include, as

necessary prerequisites, studies of algebra, functions and their graphs, and probability. They are developed

systematically, with increasing levels of sophistication and complexity. Calculus is essential for developing an

understanding of the physical world because many of the laws of science are relationships involving rates of

change. Statistics is used to describe and analyse phenomena involving uncertainty and variation. For these

reasons, this course 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.

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.

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

curriculum continue to be applicable and should be inherent in students’ learning of this course. 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 in skills, such as

calculating derivatives and integrals, or solving quadratic equations, and frees up working memory for more

complex aspects of problem solving. The ability to transfer skills to solve problems based on a wide range of

applications is a vital part of this course. Because both calculus and statistics are widely applicable as models

of the world around us, there is ample opportunity for problem-solving throughout the course.

#### Unit One

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 Two

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 Three

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 Four

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.

#### 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