Advanced Mathematics

Course Description:

The Advanced course places a considerable emphasis on the more abstract concepts that are contained in the areas of algebra, functions and calculus.

The course is intended to give students who have demonstrated some competence in the 5.3 pathway at Year 10, and therefore attained an A or B grade in that course, an understanding of and competence in some further aspects of mathematics which are applicable to the real world. It is essential that students have developed the mathematical thinking skills required for an A or B grade at Stage 5, as students will be required to employ these problem-solving skills throughout the study of the Advanced course.

Advanced Mathematics has general educational merit and is also useful for concurrent studies in science and commerce. The course 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. Students who require substantial mathematics at a tertiary level, supporting the physical sciences, computer science or engineering, should undertake the Mathematics Extension 1 course or both the Mathematics Extension 1 and Mathematics Extension 2 course.

The Mathematics Advanced course is the first basic part of a continuum of Mathematics that provides opportunities for students to study at progressively higher levels and to acquire knowledge, skills and understanding in relation to concepts within the area of mathematics that have applications in an increasing number of contexts. The concepts and techniques of differential and integral calculus form a strong basis of the course, and are developed and used in a range of applications and in increasing complexity.

Students who choose to undertake the Extension Mathematics course will study the Advanced Mathematics course concurrently.

Main Topics Covered

The topics that are studied in the HSC Advanced Course are:

Functions

• Graphing Techniques

Trigonometric Functions

• Trigonometric Functions & Graphs

Calculus

• Differential Calculus

• Differentiation of trigonometric, exponential and logarithmic functions

• Rules of differentiation

• Applications of Differentiation

• The first and second derivatives

• Applications of the derivative

• Integral Calculus

• The anti-derivative

• Areas and the definite integral

Financial Mathematics

• Modelling Financial Situations

• Modelling investments and loans

• Arithmetic Sequences and Series

• Geometric Sequences and Series

• Financial applications of sequences and series

Statistical Analysis

• Descriptive Statistics & Bivariate Data Analysis

• Data (grouped and ungrouped) and summary statistics

• Bivariate Data Analysis

• Random Variables

• Continuous Random Variables

• The Normal Distribution

The textbook that is used at Marian Catholic College is the Pearson Publication: New Senior Mathematics Advanced Years 11 & 12.

• Demonstration Text