Mathematics

General Mathematics Description

General Mathematics is designed for those students who want to extend their mathematical skills beyond Year 10. It provides a course of study for students who either intend to study General Mathematics Units 3 and 4. The areas of study are all related to using Mathematics and its applications in students’ personal, work and civic lives and provide the fundamentals on which professional applications of Mathematics are built. Digital technologies, including the CAS calculator, are used extensively to enhance students’ learning in each topic.

Areas of Study

• Investigating and comparing data distributions

• Algebra, number and structure

• Linear functions, graphs, equations and models

• Matrices

• Investigating relationships between two numerical variables

• Graphs and Networks

• Variation

• Space, measurement and applications of trigonometry

Learning Outcomes

On completion of this unit students should be able to:

• Define and explain key concepts as specified in the selected areas of study, and apply a range of related mathematical routines and procedures.

• Select and apply mathematical facts, concepts, models and techniques to investigate and analyse extended application problems in a range of contexts.

• Select and 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 decision that the student has demonstrated achievement of the learning outcomes above. This decision will be based on student completion of work requirements as specified in the Work Requirements document, which is provided to students at the commencement of each unit.

Students will also complete tests, tasks and the end of unit examinations on the following topics:

• Computation and practical arithmetic

• Investigating and comparing data distributions

• Graphs and networks

• Linear graphs and models

• Linear relations and equations

• Investigating relationships between two numerical variables

• Matrices

• Number patterns and recursion

Pathways

• Units 3 and 4 General Mathematics

Entry into Units 3 and 4 General Mathematics is dependent on successfully completing Units 1 and 2 General Mathematics and teacher recommendation.

Mathematical Methods

Description

Mathematical Methods is a course designed for students who can apply more abstract ideas in Mathematics. It is a prerequisite course of study for students who intend to study Units 3 and 4 Mathematical Methods. Students will study techniques, routines and processes involving irrational and real arithmetic, algebraic manipulation, equation solving, graph sketching, and differentiation and integration with and without the use of technology. Students are expected to be familiar with quadratic functions, algebra and graphs, and basic concepts of probability as well as being able to use relevant mental and by-hand approaches. Digital technologies, including the CAS calculator, are used extensively to enhance students’ learning in each topic.

Areas of Study

• Functions, relations and graphs

• Algebra, number and structure

• Calculus

• Data analysis, probability and statistics

Learning Outcomes

On completion of this unit students 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.

• Apply mathematical processes in non-routine contexts, including situations requiring problem-solving, modelling or investigative techniques or approaches, and analysis and discuss these applications of Mathematics.

• 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 decision that the student has demonstrated achievement of the learning outcomes above. This decision will be based on student completion of work requirements as specified in the Course Outline document, which is provided to students at the commencement of each unit.

Students will also complete tests and the end of unit examinations on the following topics:

• Polynomials

• Gallery of Graphs

• Relations and Functions

• Circular Functions

• Rates of change and introductory to calculus

• Applications of calculus

• Logarithms and exponentials

• Integration techniques

• Probability

• Pseudocode and Algorithms

Pathways

• Units 3 and 4 Mathematical Methods

• Units 3 and 4 General Mathematics

Specialist Mathematics

Description

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, reasoning and proof. This study has a focus on interest in the discipline of mathematics 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.

Mathematical Methods Units 1 and 2 and Specialist Mathematics Units 1 and 2, taken in conjunction, provide a comprehensive preparation for Specialist Mathematics Units 3 and 4. Study of Specialist Mathematics Units 3 and 4 also assumes concurrent study or previous completion of Mathematical Methods Units 3 and 4.

Areas of Study

• Algebra, number and structure

• Discrete mathematics

• Data analysis, probability and statistics

• Space and measurement

• Functions, relations and graphs

Learning Outcomes

On completion of this unit students 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.

• Apply mathematical processes in non-routine contexts, and analyse and discuss these applications of Mathematics.

• Use technology to 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 decision that the student has demonstrated achievement of the learning outcomes above. This decision will be based on student completion of work requirements as specified in the Work Requirements document, which is provided to students at the commencement of each unit.

Students will also complete tests and the end of unit examinations on the following topics:

• Proof and number

• Graph theory

• Logic and algorithms

• Pseudocode

• Sequences and series

• Combinatorics

• Matrices

• Simulation, sampling and sampling distributions

• Trigonometry

• Transformations

• Vectors in the plane

• Complex numbers

• Functions, relations and graphs

Pathways

• Units 3 and 4 Specialist Mathematics (alongside Units 3 and 4 Mathematical Methods)

• Units 3 and 4 Mathematical Methods

• Units 3 and 4 General Mathematics

Entry into Units 3 and 4 Specialist Mathematics is dependent on successfully completing Mathematical Methods 1 & 2 in conjunction with Specialist Mathematics 1 & 2, and teacher recommendation.