Mathematics Advanced
ALL STUDENTS MUST COMPLETE 2 UNITS OF MATHEMATICS IN YEAR 11
Course Type: Board Developed Course
Units: 2
Prerequisites:
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 Mathematics Years 7–10 Syllabus and in particular, the content and outcomes of all substrands of Stage 5.1 and Stage 5.2, and 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.
Exclusions: Mathematics Standard
Course description
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 course provides students with the opportunity to develop ways of thinking in which problems are explored through observation, reflection and reasoning.
This course is intended for students who have demonstrated a high degree of competence in the skills of Stage 5 Mathematics.
It is a sufficient basis for further studies in mathematics as a minor discipline at tertiary level in support of courses such as the life sciences or commerce.
All students studying the Mathematics Advanced course will sit for an HSC examination.
What students learn
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.
Year 11 Course
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
Year 12 Course
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