Course: General Mathematics
Course No: 15230
2 units for each of Preliminary and HSC
Board Developed Course
Prerequisites:For students who intend to study the General Mathematics course, it is recommended that they study at least some of the Stage 5.2 content of Mathematics Years 7–10 Syllabus, particularly the Patterns and Algebra topics and Trigonometry, if not all of the content.
Exclusions:Students may not study any other Stage 6 Mathematics course in conjunction with General Mathematics.
Course Description
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 fully prescribed, and 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.
Main Topics Covered
Preliminary Course
- Financial Mathematics
- Data Analysis
- Measurement
- Probability
- Algebraic Modelling
HSC Course
- Financial Mathematics
- Data Analysis
- Measurement
- Probability
- Algebraic Modelling
Course: Mathematics
Course No: 15240
2 units for each of Preliminary and HSC
Board Developed Course
Prerequisites: For students who intend to study the Mathematics course, it is recommended that they study the topics Real Numbers, Algebraic Techniques and Coordinate Geometry as well as at least some of Trigonometry and Deductive Geometry from Stage 5.3 (identified by §) of Mathematics Years 7–10 Syllabus, if not all of the content.
Exclusions:General Mathematics
Course Description
The course 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 or both the Mathematics Extension 1 and Mathematics Extension 2 courses.
Main Topics Covered
Preliminary Course
- Basic arithmetic and algebra
- Real functions
- Trigonometric ratios
- Linear functions
- The quadratic polynomial and the parabola
- Plane geometry – geometrical properties
- Tangent to a curve and derivative of a function
HSC Course
- Coordinate methods in geometry
- Applications of geometrical properties
- Geometrical applications of differentiation
- Integration
- Trigonometric functions
- Logarithmic and exponential functions
- Applications of calculus to the physical world
- Probability
- Series and series applications
Course: Mathematics Extension 1
Course No: 15250
1 unit in each of Preliminary (Preliminary Mathematics Extension) and HSC
Board Developed Course
Prerequisites: For students who intend to study the Mathematics Extension 1 course, it is recommended that they study the Stage 5.3 optional topics (identified by #) Curve Sketching and Polynomials, Functions and Logarithms, and Circle Geometry of Mathematics Years 7–10 Syllabus.
Exclusions:General Mathematics
Course Description
The content of this course and its depth of treatment indicate that it is intended for students who have demonstrated a mastery of the skills of Stage 5 Mathematics and 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 recommended 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 course is sufficient for these purposes, students of outstanding mathematical ability should consider undertaking the Mathematics Extension 2 course.
Main Topics Covered
Preliminary Course
- Other inequalities
- Further geometry
- Further trigonometry
- Angles between two lines
- Internal and external division of lines into given ratios
- Parametric representation
- Permutations and combinations
- Polynomials
- Harder applications of the Mathematics Preliminary course topics
HSC Course
- Methods of integration
- Primitive of sin2x and cos2x
- Equation
- Velocity and acceleration as a function of x
- Projectile motion
- Simple harmonic motion
- Inverse functions and inverse trigonometric functions
- Induction
- Binomial theorem
- Further probability
- Iterative methods for numerical estimation of the roots of a polynomial equation
- Harder applications of Mathematics HSC course topics
Course: Mathematics Extension 2
Course No: 15260
1 unit for the HSC
Board Developed Course
The course is designed for students with a special interest in mathematics who have shown that they possess special aptitude for the subject.
Exclusions:General Mathematics
Course Description
The course offers a suitable preparation for study of mathematics at 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.
Main Topics Covered
- Graphs
- Complex Numbers
- Conics
- Integration
- Volumes
- Mechanics
- Polynomials
- Harder Mathematics Extension 1 topics