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NSW Syllabuses

Mathematics Advanced Stage 6 Course Description

Course No: TBC

2 units Year 11 (Preliminary) Board Developed Course.
2 units Year 12 (HSC) Board Developed Course.

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.

Exclusions:

Students may not study the Mathematics Standard Year 11 course in conjunction with the Mathematics Advanced Year 11 course, or either the Mathematics Standard 1 Year 12 course or the Mathematics Standard 2 Year 12 course in conjunction with the Mathematics Advanced Year 12 course.

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

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.

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 are:

Year 11

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

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