Senior Secondary 2026 Pathways Information

General Mathematics

Units 1 -4

Rationale

This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the interests, needs, dispositions and aspirations of a wide range of students, and introduces them to key aspects of the discipline. It is also designed to promote students’ awareness of the importance of mathematics in everyday life in a technological society, and to develop confidence and the disposition to make effective use of mathematical concepts, processes and skills in practical and theoretical contexts.

Entry

There are no prerequisites for entry to Units 1, 2 and 3. Students must undertake Unit 3 prior to undertaking Unit 4. Units 1 to 4 are designed to a standard equivalent to the final two years of secondary education. All VCE studies are benchmarked against comparable national and international curriculum.

Assessment

Satisfactory completion

The award of satisfactory completion for a unit is based on the teacher’s decision that the student has demonstrated achievement of the set of outcomes specified for the unit. Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks. Teachers must develop courses that provide appropriate opportunities for students to demonstrate satisfactory achievement of outcomes. The decision about satisfactory completion of a unit is distinct from the assessment of levels of achievement. Schools will report a student’s result for each unit to the VCAA as S (Satisfactory) or N (Not Satisfactory).

Levels of achievement

Units 1 and 2

Procedures for the assessment of levels of achievement in Units 1 and 2 are a matter for school decision. Assessment of levels of achievement for these units will not be reported to the VCAA. Schools may choose to report levels of achievement using grades, descriptive statements or other indicators.

Units 3 and 4

Unit 3 School-assessed Coursework: 24 per cent

Unit 4 School-assessed Coursework: 16 per cent

Units 3 and 4 Examination 1: 30 per cent

Units 3 and 4 Examination 2: 30 per cent.

Study Design Mathematics

Click on the link to take you to the VCAA site.

Outcome 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.

Outcome 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.

Outcome 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.

General Mathematics - Units 1 & 2

General Mathematics Units 1 and 2

Caters for a range of student interests, provides preparation for the study of VCE General Mathematics at the Units 3 and 4 level and contains 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’.

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists, tables and matrices, diagrams and geometric constructions, algorithms, algebraic manipulation, recurrence relations, 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.

Resources

Mathematical investigation

This comprises one to two weeks of investigation into one or two practical or theoretical contexts or scenarios based on content from areas of study and application of key knowledge and key skills for the outcomes.

Investigation is to be incorporated in the development of concepts, skills and processes for the unit, and can be used to assess the outcomes.

There are three components to mathematical investigation:

Formulation

Exploration

Communication

Area of Study 1 - Unit 1

Data analysis, probability and statistics

Investigating and comparing data distributions

In this area of study, 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.

Area of Study 2 - Unit 1

Algebra, number and structure

Arithmetic and geometric sequences, first-order linear recurrence relations and financial mathematics

In this area of study 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.

Area of Study 3 - Unit 1

Functions, relations and graphs

Linear functions, graphs, equations and models

In this area of study, 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.

Area of Study 4 - Unit 1

Discrete mathematics

Matrices

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

Area of Study 1 - Unit 2

Data analysis, probability and statistics

Investigating and comparing data distributions

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

Area of Study 2 - Unit 2

Discrete mathematics

Graphs and networks

In this area of study 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.

Area of Study 3 - Unit 2

Functions, relations and graphs

Variation

In this area of study students cover direct and inverse variation, transformations to linearity and modelling of some non-linear data.

Area of Study 4 - Unit 2

Space and measurement

Space, measurement and applications of trigonometry

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.

General Mathematics - Units 3 & 4

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.

Resources

Area of Study 1 - Unit 3

Data analysis, probability and statistics

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.

Area of Study 2 - Unit 3

Discrete mathematics

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.

Area of Study 2 - Unit 4

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.

Area of Study 2 - Unit 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.

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