VCE General Mathematics Units 1 & 2

General Mathematics provides for different combinations of student interests and preparation for study of VCE Mathematics at the Unit 3 and 4 level. The six Areas of Study for General Mathematics Unit 1 and Unit 2 are listed below. In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations and graphs with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.

Units 1 and 2, suits a range of students. The content is selected from the six areas of study using the following rules:

• for each unit, content covers four or more topics in their entirety, selected from at least three different areas of study
• courses intended as preparation for study at the Units 3 and 4 level should include a selection of topics from areas of study that provide a suitable background for these studies
• topics can also be selected from those available for Specialist Mathematics Units 1 and 2
• content covered from an area of study provides a clear progression in knowledge and skills from Unit 1 to Unit 2.

AREAS OF STUDY

Area of study 1: Algebra and structure

In this area of study students cover representation and manipulation of linear relations and equations, including simultaneous linear equations, and their applications in a range of contexts.

Area of study 2: Arithmetic and number

In this area of study students cover mental, by-hand and technology assisted computation with rational numbers, practical arithmetic and financial arithmetic, including estimation, order of magnitude and accuracy.

Area of study 3: Discrete mathematics

In this area of study students cover matrices, graphs and networks, and number patterns and recursion, and their use to model practical situations and solve a range of related problems.

Area of study 4: Geometry, measurement and trigonometry

In this area of study students cover shape, measurement and trigonometry and their application to formulating and solving two- and three-dimensional problems involving length, angle, area and surface area, volume and capacity, and similarity and the application of linear scale factors to measurement.

Area of study 5: Graphs of linear and non-linear relations

In this area study students cover continuous models involving linear and non-linear relations and their graphs, linear inequalities and programming, and variation.

Area of study 6: Statistics

In this area of study students cover representing, analysing and comparing data distributions and investigating relationships between two numerical variables, including an introduction to correlation.

Outcomes

For each unit the student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass all of the selected areas of study for each unit. For each of Unit 1 and Unit 2, the outcomes apply to the content from the areas of study selected for that unit.

Outcome 1

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

For example: Linear relations and equations

Key knowledge

• The forms of linear relations and equations including literal linear equations
• The rules of linear functions and tables of values
• The forms of simultaneous linear equations in two variables and their solutions

Key skills

• Solve linear equations including literal linear equations
• Construct tables of values from a given formula
• Solve algebraically and/or graphically, simultaneous linear equations in two variables
• Solve word problems that involve the setting up and solving of a linear equation or a pair of simultaneous linear equations

Outcome 2

On completion of each unit the student should be able to select and apply mathematical facts, concepts, models and techniques from the topics covered in the unit to investigate and analyse extended application problems in a range of contexts.

Outcome 3

On completion of this unit the student should be able to 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 whether the student has demonstrated the set of outcomes specified for the unit. Teachers should use a variety of learning activities and assessment tasks that provide a range of opportunities for students to demonstrate the key knowledge and key skills in the outcomes.

The areas of study, including the key knowledge and key skills listed for the outcomes, are used for course design and the development of learning activities and assessment tasks. Assessment is part of the regular teaching and learning program, completed mainly in class and within a limited timeframe.

Assessment tasks include components with and without the use of technology and include
• Assignments
• Tests
• Summary  or review notes
• Modeling tasks
• Problem solving
• Mathematical investigation

Pathway

• VCE Further Mathematics (Units 3 and 4)