Mathematics Advanced (Year 11 and Year 12)

The Mathematics Advanced course is a calculus-based course focused on developing student awareness of mathematics as a unique and powerful way of viewing the world to investigate order, relation, pattern, uncertainty and generality.

All students studying the Mathematics Advanced course will sit for an HSC examination.

The study of Mathematics Advanced in Stage 6 enables students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely. It provides opportunities for students to consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling and use these models to solve problems related to their present and future needs.

It provides opportunities for students to develop ways of thinking in which problems are explored through observation, reflection and reasoning. It provides a basis for further studies in disciplines in which mathematics and the skills that constitute thinking mathematically have an important role. It provides an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in a range of disciplines at the tertiary level.

Due to the difficulty of the course, it is strongly recommended that students who are interested in completing the Advanced course also elect to complete the Extension 1 Preliminary course.

Prerequisites: The Mathematics Advanced Year 11 course has been developed on the assumption that students have studied the content and achieved reasonable success with the outcomes of the 5.3 content in Year 9 and 10.

Content: The Mathematics Advanced Year 11 course content is comprised of five Topics, with the Topics divided into Subtopics. The Mathematics Advanced Year 12 course content includes four of the same Topics and the Topic of Financial Mathematics in place of the Topic of Exponential and Logarithmic Functions. The Topics and Subtopics (in brackets) are:

Year 11:

•  Topic: Functions (Working with Functions)
•  Topic: Trigonometric Functions (Trigonometry and Measure of Angles and Trigonometric Functions and Identities )
•  Topic: Calculus (Introduction to Differentiation)
•  Topic: Exponential and Logarithmic Functions (Logarithms and Exponentials)
•  Topic: Statistical Analysis (Probability and Discrete Probability Distributions)

Year 12:

•  Topic: Functions (Graphing Techniques)
•  Topic: Trigonmetric Functions (Trigonometric Functions and graphs)
•  Topic: Calculus (Differential Calculus, the second derivative and Integral Calculus)
•  Topic: Financial Mathematics (Modeling Financial Situations)
•  Topic: Statistical Analysis (Descriptive Statistics and Bivariate Data Analysis, Random Variables)