Specialist Mathematics Units 1 and 2 provide a course of study for students who wish to undertake an in-depth study of mathematics, with an emphasis on concepts, skills and processes related to mathematical structure, modelling, problem solving and reasoning. This study has a focus on interest in the discipline of mathematics in its own right and investigation of a broad range of applications, as well as development of a sound background for further studies in mathematics and mathematics related fields.

Areas of Study

1 - Algebra and Structure

• Logic and algebra

• Transformations, trigonometry and matrices

2 - Arithmetic and Number

• Principles of counting

• Number systems and recursion

3 - Discrete Mathematics

• Graph theory

4 - Geometry, measurement and trigonometry

• Geometry in the plane and proof

• Vectors in the plane

5 - Graphs of linear and non-linear relations

• Kinematics

• Non-linear relations and functions

6 - Statistics

• Simulation, sampling and sampling distributions

Outcomes

1. On completion of this unit the student should be able to define and explain key concepts in relation to the topics from the selected areas of study, and apply a range of related mathematical routines and procedures.

2. On completion of each unit the student should be able to apply mathematical processes in non-routine contexts, and analyse and discuss these applications of mathematics in at least three areas of study.

3. On completion of this unit the student should be able to use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in at least three areas of study

Assessment

The award of satisfactory completion for a unit is based on the set of outcomes specified for the unit.

Demonstration of achievement of Outcome 1 should be based on the student’s performance on a selection of the following assessment tasks:

• topic tests & semester examinations

• assignments

• summary or review notes.

Demonstration of achievement of Outcome 2 should be based on the student’s performance on a selection of the following assessment tasks:

• modelling tasks

• problem-solving tasks

• mathematical investigations.

Demonstration of achievement of Outcome 3 is based on the student’s performance on aspects of tasks completed in demonstrating achievement of Outcomes 1 and 2 that incorporate opportunity for the effective and appropriate use of technology.

Specialist Mathematics Units 3 and 4 consists of the areas of study: ‘Functions and Graphs’, ‘Algebra’, ‘Calculus’, ‘Vectors’, ‘Mechanics’ and ‘Probability and Statistics’. The development of course content will highlight mathematical structure, reasoning and applications across a range of modelling contexts with an appropriate content for each of Unit 3 and Unit 4. The content for Unit 3 and Unit 4 will provide a balanced and progressive development of knowledge and skills with appropriate connections among the areas of study being developed.

Areas of Study

1 - Functions and Graphs

• inverse circular functions, reciprocal functions, rational functions and other simple quotient functions, the absolute value function, graphical representation of these functions, and the analysis of key features of their graphs including intercepts, asymptotic behaviour and the nature and location of stationary points, points of inflection, periodicity, and symmetry.

2 - Algebra

• the expression of simple rational functions as a sum of partial fractions; the arithmetic and algebra of complex numbers, including polar form; points and curves in the complex plane; introduction to factorisation of polynomial functions over the complex field; and an informal treatment of the fundamental theorem of algebra.

3 - Calculus

• advanced calculus techniques for analytic and numeric differentiation and integration of a range of functions, and combinations of functions; and their application in a variety of theoretical and practical situations, including curve sketching, evaluation of arc length, area and volume, differential equations and kinematics.

4 - Vectors

• the arithmetic and algebra of vectors, linear dependence and independence of a set of vectors, proof of geometric results using vectors, vector representation of curves in the plane and vector kinematics in one and two dimensions.

5 - Mechanics

• cover an introduction to Newtonian mechanics, for both constant and variable acceleration.

6 - Probability and Statistics

• statistical inference related to the definition and distribution of sample means, simulations and confidence interval.

Outcomes

1. On completion of each unit the student should be able to define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures.

2. Apply mathematical processes, with an emphasis on general cases, in non-routine, contexts and analyse and discuss these applications of mathematics.

3. Select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Assessment

The award of satisfactory completion for a unit is based on the set of outcomes specified for the unit. This includes

• topic tests & semester examinations

• assignments

• summary or review notes

The student’s level of achievement for Units 3 and 4 will be determined by School-assessed Coursework (SACs). The SACs are

• Unit 3

  • Application Task

• Unit 4

  • Problem Solving or Modelling Task 1

  • Problem Solving or Modelling Task 2