General Mathematics focuses on mathematical skills and techniques, which have direct application to everyday activity. The course content is written in five areas of study, with an emphasis on application of specific skills and on tasks that involve integrating mathematical skills and techniques across a range of familiar and unfamiliar situations. These tasks may draw from more than one area of study, and encourage transfer of knowledge across the entire course, as well as linking with study in other Stage 6 subjects.

The course is constructed on the assumption that students have achieved the outcomes in the core of the Standard Mathematics course for the School Certificate, along with the recommended options: Trigonometry and Further Algebra.

The course is designed to support TAFE and other vocational courses. It provides an appropriate mathematical background for students who do not wish to pursue the formal study of mathematics at tertiary level, while giving a strong foundation for university study in the areas of business, humanities, nursing and paramedical sciences.

Aims:

a. to see mathematics as an important tool in the solution of problems;

b. to develop the mathematical skills, operation skills and communication skills of the students:

c. to provide opportunities for students to see the contribution that mathematics has made to the development of society.

Course Content

Preliminary Course	HSC Course
Financial mathematics	Financial mathematics
Data Analysis	Data analysis
Measurement	Measurement
Probability	Probability
Algebraic modeling	Algebraic modeling

Mathematics

Senior Course Description

Preamble

Mathematics is intended to give students who have demonstrated general competence in the skills of Stage 5 Mathematics, an understanding of and competence in some further aspects of mathematics, which are applicable to the real world. It 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 of Mathematics Extension 2 course.

Aims:

a. to give an understanding of important Mathematical ideas such as function, variable, limits;

b. to introduce students to Mathematical techniques relevant to the real world;

c. to understand the need to prove results and to appreciate the role of deductive reasoning;

d. to apply the techniques of Mathematical reasoning to problems drawn from the field of science, industrial arts and commerce.

Course Content

Preliminary Course	HSC Course
Basic arithmetic and algebra	Coordinate methods in geometry
Real functions	Applications of geometrical properties
Trigonometric ratios	Geometrical applications of differentiation
Linear functions	Integration
The quadratic polynomial and the parabola	Trigonometric functions
Plane geometry	Logarithmic and exponential functions
Tangent to a curve and derivative of a function	Applications of calculus to the physical world
	Probability
	Series and series applications

Mathematics Extension 1

Senior Course Description

Preamble

Mathematics Extension 1 is intended for students who have demonstrated a mastery of the skills of Stage 5 Mathematics and who are interested in the study of further skills and ideas in mathematics. The course is intended to give these students a thorough understanding of and competence in aspects of mathematics, including many which are applicable to the real world. It has general educational merit and is also useful for concurrent studies of science, industrial arts and commerce. The course is a recommend minimum basis for further studies in mathematics as a major discipline at a tertiary level and for the study of mathematics in support of the physical and engineering sciences. Although the Mathematics Extension 1 course is sufficient for these purposes, students of outstanding mathematical ability should consider undertaking the Mathematics Extension 2 course.

Aims:

a. to appreciate the role of deductive reasoning;

b. to develop the ability to construct thorough proofs;

c. to enhance the Mathematical skills required for further studies in a Mathematical field in tertiary studies;

d. to emphasize the use of precise language;

e. to be able to use the techniques learned to solve complex and intuitive problems in a Mathematical context.

Course Content

Preliminary Course	HSC Course
Other inequalities	Methods of integration
Further geometry	Primitive of sin²x and cos²x
Further trigonometry	Equation dN = k (N – P) dt
Angles between two lines	Velocity and acceleration as a function of x
Internal and external division of lines into given ratios	Projectile motion
Parametric representation	Simple harmonic motion
Permutations and combinations	Inverse functions and inverse trigonometric functions
Polynomials	Induction
Harder applications of the Preliminary Mathematics course	Binomial theorem
	Further probability
	Iterative methods of numerical estimation of the roots of a polynomial equation
	Harder applications of HSC Mathematics topics

Mathematics Extension 2

Senior Course Description

Preamble

Mathematics Extension 2 is designed for students with a special interest in mathematics who have shown that they possess special aptitude for the subject.

The course offers a suitable preparation for study of mathematics at a tertiary level, as well as a deeper and more extensive treatment of certain topics than is offered in other Mathematics courses. It represents a distinctly high level in school mathematics involving the development of considerable manipulative skill and a high degree of understanding of the fundamental ideas of algebra and calculus. These topics are treated in some depth. Thus, the course provides a sufficient basis for a wide range of useful applications of mathematics as well as an adequate foundation for the further study of the subject.

Aims:

a. to present Mathematics as a living art which is intellectually exciting, aesthetically satisfying and relevant to a great variety of practical situations;

b. to present a challenge to students of the highest mathematical ability;

c. to study useful and important Mathematical ideas and techniques appropriate to the level of ability;

d. to develop an understanding of these ideas and to apply them to the study and solution of a wide variety of problems;

e. to provide a background necessary for further study in Mathematics in tertiary studies.