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Goulburn High School

Goulburn High School

Justice and Tenacity

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15240                                                                                      MATHEMATICS

Course:  Mathematics                                                 Category:  A

2 units for each of Preliminary and HSC       

Board developed Course

Prerequisites:    The course is presented on the assumption that students have achieved a Grade "A10" or "A9" for Mathematics in the School Certificate

Course Description: The course is intended to give students who have demonstrated 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 Extension I or Extension II courses..

Main Topics Covered:


Preliminary Course

·         Basic arithmetic and algebra

·         Real functions

·         Trigonometric ratios

·         Linear functions

·         The quadratic polynomial and the parabola

·         Plane geometry

·         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

Assessment:  HSC Course only


External Assessment

Internal Assessment

A single written examination paper of three hours duration, consisting of ten questions of equal value.


No more than the equivalent of two questions will be based on the Preliminary course.  Questions from the Preliminary course will be short and represent a minor part of a total question.  Marks can be awarded for demonstration of knowledge and skills from the Preliminary course (or earlier) when required for questions on the HSC course.  That is, questions based on the Preliminary course can be asked when they lead in to questions based on topics from the HSC course.  Marks from these lead-in questions will not be counted in the two-question allowance from the Preliminary course.


Board-approved calculators, geometrical instruments and approved geometrical templates may be used.


The objectives of the course are grouped into two components, Component A and Component B, for assessment purposes.  Component A (80%) is primarily concerned with the student's knowledge, understanding and skills developed in each Content Area listed in the syllabus.  Component B (20%) is primarily concerned with the student's reasoning, interpretative, explanatory and communicative abilities.  A number of tasks will be used to determine a student's school-based assessment and any one task may contribute to measuring attainment in both components.


Once the assessment of the HSC course has commenced, some Preliminary course work can be included in assessment tasks for Mathematics.  No more than 20% of the assessment is to be based on the Preliminary course.