# Mathematics Methods ATAR

### What is ATAR Mathematics Methods all about?

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 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.

### Who should select these units in Year 11?

Students wanting to select Mathematics Methods will need to have successfully passed the Online Literacy and Numeracy Assessment (OLNA) in Year 10 or prequalified by achieving Band 8 or higher in the Year 9 NAPLAN.

Recommended that students have achieved an A or high B grade in Year 10 Mathematics.

You should select this course

• You want to use Mathematics Methods as a University entrance course.
• Mathematical Methods is a prerequisite for a course you wish to study at university
• If your future pathways may involve mathematics and statistics and their applications in a range of disciplines at the tertiary level.

### Pathway

Year 12 – Mathematics Methods – ATAR

Course Code ATMAM

### Areas of Study

Unit 1

Involves key concepts of a function and its graph. It includes the study of probability and statistics with the introduction of conditional probability and independence. Students will examine the study of trigonometric functions beginning with the unit circle and the trigonometry of triangles and its applications, degrees and radians.

Unit 2

Introduces exponential functions and their properties and graphs. Arithmetic and geometric sequences are examined with recursive definitions applied. Rates and average rates of change are introduced followed by the concept of derivative as as instantaneous rate of change. This first calculus topic concludes with derivatives of polynomial functions, sketching and calculating slopes and equations of tangents, determine velocities and solve optimisation problems.

To provide for different learning styles a variety of assessment tasks are used. For each course of study tasks are selected from:

• Response (tests)
• Investigations
• Examinations

### What is ATAR Mathematics Methods all about?

The major themes of the Mathematics Methods ATAR course are calculus and statistics. 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.

### Who should select these units in Year 12?

It is recommended that students studying Unit 3 and Unit 4 have successfully completed Mathematics Methods Unit 1 and Unit 2. An understanding of the Year 11 content is assumed knowledge for students in Year 12.

You should select this course if

• You want to use Mathematics Methods as a University entrance course.
• Mathematical Methods is a prerequisite for a course you wish to study at university
• Your future pathways may involve mathematics and statistics and their applications in a range of disciplines at the tertiary level.

### Areas of Study

Unit 3

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

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.

To provide for different learning styles a variety of assessment tasks are used. For each course of study tasks are selected from:

• Response (tests)
• Investigations
• Examinations