# HSC Course descriptions – Mathematics

- Preliminary Mathematics General (BDC)/HSC Mathematics General 2 (BDC) Pathway
- Preliminary Mathematics General (BDC)/HSC Mathematics General 1 (CEC) Pathway
- Mathematics
- Mathematics Extension 1
- Mathematics Extension 2

## Preliminary Mathematics General (BDC*)/HSC Mathematics General 2 (BDC*) Pathway

Course Nos:

- 11235 Preliminary Mathematics General
- 15235 HSC Mathematics General 2

2 units Preliminary (Board Developed Course*)

2 units HSC (Board Developed Course*)

### Prerequisites:

The Preliminary Mathematics General course has been constructed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus (2002) up to, and including, the content and outcomes of Stage 5.1. For students who intend to study the HSC Mathematics General 2 course, it is recommended that they study at least some of the Stage 5.2 content of the *Mathematics Years 7–10 Syllabus (2002),* particularly the *Patterns and Algebra topics and Trigonometry*, if not all of the content.

### Exclusions:

Students may not study any other Stage 6 preliminary mathematics course in conjunction with the Preliminary Mathematics General course, or any other Stage 6 HSC mathematics course in conjunction with the HSC Mathematics General 2 course.

### Course Description

The Preliminary Mathematics General course and the HSC Mathematics General 2 course are designed to promote the development of knowledge, skills and understanding in areas of mathematics that have direct application to the broad range of human activity. The Preliminary Mathematics General course content is written in five Strands and two Focus Studies. The HSC Mathematics General 2 course content is written in the same five Strands and includes a further two Focus Studies. As well as introducing some new mathematical content, the Focus Studies give students the opportunity to apply and develop, in contemporary contexts, the knowledge, skills and understanding initially developed in the study of the Strands.

The Preliminary Mathematics General course is the same preliminary course that forms part of the Preliminary Mathematics General/HSC Mathematics General 1 pathway. The Preliminary Mathematics General/HSC Mathematics General 2 pathway provides students with the opportunity to develop an understanding of and competence in further aspects of mathematics for a range of concurrent HSC studies, such as in the life sciences, the humanities and business studies. The pathway also provides a strong foundation for students entering the workforce and/or undertaking further training, and for university courses in the humanities, nursing and paramedical sciences.

### Main Topics Covered

Preliminary Mathematics General Course

- Strand: Financial Mathematics
- Strand: Data and Statistics
- Strand: Measurement
- Strand: Probability
- Strand: Algebra and Modelling
- Focus Study: Mathematics and Communication
- Focus Study: Mathematics and Driving

HSC Mathematics General 2 Course

- Strand: Financial Mathematics
- Strand: Data and Statistics
- Strand: Measurement
- Strand: Probability
- Strand: Algebra and Modelling
- Focus Study: Mathematics and Health
- Focus Study: Mathematics and Resources

*BDC – Board Developed Course (HSC BDCs are examined at the HSC)

**CEC – Content Endorsed Course (HSC CECs are not examined at the HSC)

## Preliminary Mathematics General (BDC*)/HSC Mathematics General 1 (CEC**) Pathway

**Course Nos:**

- 11235 Preliminary Mathematics General
- 30120 HSC Mathematics General 1

2 units Preliminary (Board Developed Course*)

2 units HSC (Content Endorsed Course**)

### Prerequisites:

The Preliminary Mathematics General course has been constructed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus (2002) up to, and including, the content and outcomes of Stage 5.1.

### Exclusions:

Students may **not** study any other Stage 6 preliminary mathematics course in conjunction with the Preliminary Mathematics General course, or any other Stage 6 HSC mathematics course in conjunction with the HSC Mathematics General 1 course.

### Course Description

The Preliminary Mathematics General course and the HSC Mathematics General 1 (Content Endorsed) course (CEC) are designed to promote the development of knowledge, skills and understanding in areas of mathematics that have direct application to the broad range of human activity. The Preliminary Mathematics General course content is written in five Strands and two Focus Studies. The HSC Mathematics General 1 course content is written in the same five Strands and includes a further four Focus Studies. As well as introducing some new mathematical content, the Focus Studies give students the opportunity to apply and develop, in contemporary contexts, the knowledge, skills and understanding initially developed in the study of the Strands.

The Preliminary Mathematics General course is the same preliminary course that forms part of the Preliminary Mathematics General/HSC Mathematics General 2 pathway. The Preliminary Mathematics General/HSC Mathematics General 1 pathway provides students with the opportunity to develop an understanding of and competence in further aspects of mathematics for concurrent HSC studies, such as in vocational education and training courses, other practically oriented courses, and some humanities courses. It also provides an appropriate mathematical background for students entering the workforce and/or undertaking further training.

Note: As for other Content Endorsed Courses, the HSC Mathematics General 1 course will be subject to internal assessment only, and not formal examination at the HSC. Also, the two units of study for the HSC Mathematics General 1 course cannot be counted in the 10 units required for the calculation of an ATAR.

### Main Topics Covered

Preliminary Mathematics General Course

- Strand: Financial Mathematics
- Strand: Data and Statistics
- Strand: Measurement
- Strand: Probability
- Strand: Algebra and Modelling
- Focus Study: Mathematics and Communication
- Focus Study: Mathematics and Driving

HSC Mathematics General 1 Course

- Strand: Financial Mathematics
- Strand: Data and Statistics
- Strand: Measurement
- Strand: Probability
- Strand: Algebra and Modelling
- Focus Study: Mathematics and Design
- Focus Study: Mathematics and Household Finance
- Focus Study: Mathematics and the Human Body
- Focus Study: Mathematics and Personal Resource Usage

*BDC – Board Developed Course (HSC BDCs are examined at the HSC)

**CEC – Content Endorsed Course (HSC CECs are not examined at the HSC)

## 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 sin
^{2}*x*and cos^{2}*x* - 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