# MATHEMATICS

## General Mathematics

Unit 1: Semester 1

This unit is designed to have practical significance for the students. It involves the study of statistics, covering the collection, analysis and presentation of univariate data and an introduction to bivariate statistics; linear relationships and formulae covering graphical representation of linear functions, substitution of equations and simultaneous linear equations; and the study of matrices, including their use to store information and operations of matrices.
On completion of this unit students should be able to: define and explain key concepts 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; and use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

ASSESSMENT
1. Coursework including assignments, tests, problem-solving and modelling tasks (34%)
2. Examination 1 (calculator active and open book) (33%)
3. Examination 2 (calculator active and open book) (33%)

Unit 2: Semester 2

This unit is designed to have practical significance for the students. It involves the study of geometry covering mensuration, similar figures and Pythagoras’ theorem; number patterns and recursion covering arithmetic, geometric and Fibonacci sequences; financial arithmetic; and Decision mathematics and networks; number functions including logarithms, rounding, significant figures and basic percentage change.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework including assignments, tests, problem-solving and modelling tasks (34%)
2. Examination 1 (calculator active and open book) (33%)
3. Examination 2 (calculator active and open book) (33%)

## Further Mathematics

#### Unit 3: Semester 1

The prescribed material for this unit covers the majority of the core section of the course including: The prescribed material for this unit is drawn largely from the core data analysis covering univariate and bivariate data and the study of time series; recursion and financial modelling covering depreciation of assets; compound interest investments and loans; reducing balance loans, annuities and perpetuities.
On completion of this unit students should be able to: define and explain key concepts 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.

#### Unit 4: Semester 2

This unit consists of the continued study of two modules selected from six available optional modules. At Geelong Grammar School, all classes study the modules, matrices and networks and decision mathematics. The study of core material from Unit 3 is revisited.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework – Unit 3 (60% of 34%)
2. Coursework – Unit 4 (40 of 34%)
3. Examination 1 (33%)
4. Examination 2 (33%)

Mathematical Methods (CAS)

Unit 1: Semester 1

This unit involves the study of functions and graphs covering co-ordinate geometry, polynomial functions, power functions, the concept of a function and domain and range; algebra covering remainder and factor theorems; probability covering simple and compound events, conditional probability and independence and an introduction to probability distributions.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework including assignments, tests, problem-solving and modelling tasks (34%)
2. Examination 1 (calculator free) (22%)
3. Examination 2 (calculator active and open book) (44%)

#### Unit 2: Semester 2

This unit involves the study of functions and graphs, covering trigonometric functions and their relationships, exponential and logarithmic functions and their applications; algebra covering work on exponential and logarithmic functions; rates of change and calculus covering rates of change, gradient of a tangent, differentiation rules, application of differentiation and anti-differentiation.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework including assignments, tests, problem-solving and modelling tasks (34%)
2. Examination 1 (calculator free) (22%)
3. Examination 2 (calculator active and open book) (44%)

#### Unit 3: Semester 1

This unit follows directly on from Mathematical Methods (CAS) Units 1 and 2 and assumes knowledge normally acquired in Unit 2. Prescribed material includes polynomials; functions and graphs; trigonometric, exponential and logarithmic functions; calculus and applications of differential calculus.
On completion of this unit students should be able to: define and explain key concepts 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.

#### Unit 4: Semester 2

This unit involves the study of applications of differential calculus; probability covering discrete random variables emphasising the binominal distribution, continuous random variables emphasising the normal distribution and statistical inference, including sample proportions, simulations and confidence intervals.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework – Unit 3 (17%)
2. Coursework – Unit 4 (17%)
2. Examination 1 (22%)
3. Examination 2 (44%)

## Specialist Mathematics

#### Unit 1: Semester 1

This unit involves the study of: arithmetic and number, including number systems, sequences and series, proof by inductions, absolute value and complex numbers; geometry, measurement and trigonometry, including proof, congruence, use of the sine and cosine rules and circle theorems.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework including assignments, tests, problem solving and modelling tasks (34%)
2. Examination 1 (calculator free) (22%)
3. Examination 2 (calculator active and open book) (44%)

#### Unit 2: Semester 2

This unit involves the study of: vectors in the plane including vector algebra, geometric proof, scalar product and applications; graphs of linear and non-linear relations including circular functions, cartesian, polar and parametric forms of relations in the plane and kinematics.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework including assignments, tests, problem-solving and modelling tasks (34%)
2. Examination 1 (calculator free) (22%)
3. Examination 2 (calculator active and open book) (44%)

## Specialist Mathematics

#### Unit 3: Semester 1

This unit involves the study of prescribed material covering: complex numbers, vectors, trigonometry, coordinate geometry and integral calculus covering techniques and applications. This work involves extending and developing the material from Mathematical Methods Unit 3. To be enrolled in Specialist Mathematics, students need to have completed or concurrently be studying Mathematical Methods (CAS) Units 3 and 4.
On completion of this unit students should be able to: define and explain key concepts 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.

#### Unit 4: Semester 2

Prescribed material for this unit is drawn largely from Unit 3 where the study of integral calculus is extended to differential equations, kinematics and vector calculus, the study of mechanics and the study of probability and statistics including sample means, confidence intervals and Hypothesis testing. Mathematical Methods Units 3 and 4 contain required material for Specialist Mathematics Unit 4.
On completion of this unit students should be able to: define and explain key concepts 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
1. Coursework – Unit 3 (17%)
2. Coursework – Unit 4 (17%)
3. Examination 1 (22%)
4. Examination 2 (44%)

## MATHEMATICS PATHWAY AT GGS

Group 5 - Mathematics HL
Year 11 and 12 - IB

Group 5 - Mathematical Studies
Year 11 and 12 - IB

Group 5 - Mathematics SL
Year 11 and 12 - IB

Mathematics
Year 10

Mathematics
Timbertop - Year 9

Mathematics
Years 5 to 8