General Mathematics Units 1 and 2 cater for a range of student interests, provide preparation for the study of VCE General Mathematics at the Units 3 and 4 level and contain assumed knowledge and skills for these units. The areas of study for Unit 1 of General Mathematics are ‘Data analysis, probability and statistics’, ‘Algebra, number and structure’, ‘Functions, relations and graphs’ and ‘Discrete mathematics’.

Areas of Study

1 - Data analysis, probability & statistics

In Unit 1, students cover types of data, display and description of the distribution of data, summary statistics for centre and spread, and the comparison of sets of data.

In Unit 2, students cover association between two numerical variables, scatterplots, and lines of good fit by eye and their interpretation.

2 - Algebra, number and structure

Students cover the concept of a sequence and its representation by rule, table and graph, arithmetic or geometric sequences as examples of sequences generated by first-order linear recurrence relations, and simple financial and other applications of these sequences. This is a Unit 1 only AOS. 

3 - Functions, relations and graphs

In Unit 1, students cover linear function and relations, their graphs, modelling with linear functions, solving linear equations and simultaneous linear equations, line segment and step graphs and their applications.

In Unit 2, students cover direct and inverse variation, transformations to linearity and modelling of some non-linear data.

4 - Discrete mathematics

In Unit 1, students cover the concept of matrices and matrix operations to model and solve a range of practical problems, including population growth and decay.

In Unit 2,  students cover the use of graphs and networks to model and solve a range of practical problems, including connectedness, shortest path and minimum spanning trees.

5 - Space and measurement

In this area of study students cover units of measurement, accuracy, computations with formulas for different measures, similarity and scale in two and three dimensions, and their practical applications involving simple and composite shapes and objects, trigonometry, problems involving navigation and Pythagoras’ theorem and their applications in the plane. This is a Unit 2 only AOS.

Outcomes

The student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass all of the areas of study for the unit.

1. On completion of this 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. On completion of this unit the student should be able to apply mathematical processes in non-routine contexts, including situations with some open-ended aspects requiring investigative, modelling or problem-solving techniques or approaches, and analyse and discuss these applications of mathematics.

3. On completion of this unit the student should be able to apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring investigative, modelling or problem-solving techniques or approaches.

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.

General Mathematics Units 3 and 4 focus on real-life application of mathematics and consist of the areas of study ‘Data analysis, probability and statistics’ and ‘Discrete mathematics’.

Unit 3 comprises Data analysis and Recursion and financial modelling, and Unit 4 comprises Matrices and Networks and decision mathematics.

Areas of Study

1 - Data analysis

Students cover data types, representation and distribution of data, location, spread, association, correlation and causation, response and explanatory variables, linear regression, data transformation and goodness of fit, times series, seasonality, smoothing and prediction.

2 - Recursion and financial modelling

Students cover the use of first-order linear recurrence relations and the time value of money (TVM) to model and analyse a range of financial situations, and using technology to solve related problems involving interest, appreciation and depreciation, loans, annuities and perpetuities.

3 - Matrices

Students cover the definition of matrices, different types of matrices, matrix operations, transition matrices and the use of first-order linear matrix recurrence relations to model a range of situations and solve related problems.

4 - Networks and decision mathematics

Students cover the definition and representation of different kinds of undirected and directed graphs, Eulerian trails, Eulerian circuits, bridges, Hamiltonian paths and cycles, and the use of networks to model and solve problems involving travel, connection, flow, matching, allocation and scheduling.

Outcomes

The student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass Area of Study 1 (core modules) and Areas of Study 2 (applications - 2 selected modules)  

1. On completion of this unit the student should be able to define and explain key concepts and apply related mathematical techniques and models as specified in Area of Study 1  &  2 in routine contexts. 

2. On completion of this unit the student should be able to select and apply the mathematical concepts, models and techniques as specified in Area of Study 1 & 2 in a range of contexts of increasing complexity. 

3. On completion of this unit the student should be able to 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

• Data Analysis: Application Task (40%)

• Recursion and Financial Modelling: Problem Solving or Modelling Task (20%)

• Matrices: Problem Solving or Modelling Task (20%)

• Networks: Problem Solving or Modelling Task (20%)