Mathematics Advanced

2 units for each of Year 11 & Year 12 

Board Developed Category A

Exclusions: Students may not study the Mathematics Advanced course in conjunction with the Mathematics Standard 1 or the Mathematics Standard 2 course.

Course Costs: $10.00 (plus $15.00 online access)

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.

The Mathematics Extension 1 Year 11 course includes the Mathematics Advanced Year 11 course. The Mathematics Extension 1 Year 12 course includes the Mathematics Advanced Year 12 course.

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
• 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
• provides opportunities for students to develop ways of thinking in which problems are explored through observation, reflection and reasoning
• provides a basis for further studies in disciplines in which mathematics and the skills that constitute thinking mathematically have an important role
• 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.

The Mathematics Advanced Year 11 course content comprises five Topics, with the Topics divided into Subtopics.

Topic: Functions
Working with Functions

Topic: Trigonometric Functions
Trigonometry and Measure of Angles
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

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.

Topic: Functions
Graphing Techniques

Topic: Trigonometric Functions
Trigonometric Functions and Graphs

Topic: Calculus
Differential Calculus
The Second Derivative
Integral Calculus

Topic: Financial Mathematics
Modelling Financial Situations

Topic: Statistical Analysis
Descriptive Statistics and Bivariate Data Analysis
Random Variables

Particular Course Requirements: NIL

Prerequisites: The Mathematics Advanced Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus and in particular, the content and outcomes of all substrands of Stage 5.1 and Stage 5.2, the following substrands of Stage 5.3:

• Algebraic techniques
• Surds and indices
• Equations
• Linear relationships
• Trigonometry and Pythagoras’ theorem
• Single variable data analysis
• and at least some of the content from the following substrands of Stage 5.3:
• Non-linear relationships
• Properties of Geometrical Shapes.