## Unit description of WACE Maths Specialist Unit 4 Year 12 ATAR Course

WACE Maths Specialist Unit 4 Year 12 ATAR Course contains three topics:

- Integration and applications of integration,
- Rates of change and differential equations and
- Statistical inference.

In WACE Maths Specialist Unit 4 Year 12 ATAR Course, 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 WACE Maths Specialist Unit 4 Year 12 ATAR Course, 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.

Access to technology to support the computational aspects of these topics is assumed.

## Learning outcomes of WACE Maths Specialist Unit 4 Year 12 ATAR Course

By the end of this unit, students:

- understand the concepts and techniques in applications of calculus and statistical inference
- apply reasoning skills and solve problems in applications of calculus and statistical inference
- communicate their arguments and strategies when solving problems
- construct proofs of results
- interpret mathematical and statistical information and ascertain the reasonableness of their solutions to problems.

*referred from Mathematics Specialist ATAR Course Year 12 Syllabus Western Australia School Curriculum and Standards Authority 1 January 2015*

#### Differentiation of Trigonometric Functions

- Differentiation of Sine Function : Chain Rule
- Differentiation of Sine Function : Product Rule
- Differentiation of Sine Function : Quotient Rule
- Differentiation of Cosine Function : Chain Rule
- Differentiation of Cosine Function : Product Rule
- Differentiation of Cosine Function : Quotient Rule
- Differentiation of Tangent Function

#### Integration of Trigonometric Functions

- Standard Integral of Cosine
- Standard Integral of Sine
- Standard Integral of Tangent
- Integrations by Derivatives
- Trigonometric Functions
- Exponential and Logarithmic Functions
- Substitutions
- Double Angles
- Tangents and Secants
- Sine Functions
- Cosine Functions
- Sine and Cosine Functions
- Tangent Functions
- Secant Functions
- Cosecant Functions
- Cotangent Functions