General Mathematics
Unit 3-4
General Mathematics Units 3–4 provide for the study of non-calculus and discrete mathematics topics. They are designed to be widely accessible and provide preparation for general employment, business or further study, in particular where data analysis, recursion and financial modelling, networks and matrices are important. Students who have done only Mathematical Methods Units 1 and 2 will have had access to assumed key knowledge and key skills for General Mathematics Units 3 and 4 but may also need to undertake some supplementary study.
Entry
General Mathematics Unit 3 and 4 can be taken on its own or with Mathematical Methods Units 3 and 4. General Mathematics Unit 3 and 4 assumes successful completion of General Mathematics Units 1 and 2.
Subject Overview
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.
Assumed knowledge and skills for General Mathematics Units 3 and 4 are contained in General Mathematics Units 1 and 2, and will be drawn on, as applicable, in the development of related content from the areas of study, and key knowledge and key skills for the outcomes of General Mathematics Units 3 and 4.
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, networks, algorithms, algebraic manipulation, recurrence relations, equations and graphs. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic statistical and financial functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
Data analysis covers 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.
Recursion and financial modelling covers 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.
Matrices 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.
Networks and decision mathematics covers 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.
Assumed knowledge and skills are contained in the General Mathematics Units 1 and 2 topics: ‘Computation and practical arithmetic’, ‘Investigating and comparing data distributions’, ‘Investigating relationships between two numerical variables’, ‘Linear graphs and modelling’, ‘Linear relations and equations’, and ‘Number patterns and recursion’. For each module there are related topics in General Mathematics Units 1 and 2.
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. They should have a 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.
Assessment
Satisfactory completion
The award of satisfactory completion for a unit is based on a decision that the student has demonstrated achievement of the set of outcomes specified for the unit. This decision will be based on the teacher’s assessment of the student’s performance on assessment tasks designated for the unit. Students are also required to meet the minimum work requirements for each unit as well as the TC VCE minimum attendance requirement of 80 per cent.
A non-satisfactory outcome for Unit 3 or Unit 4 implies that the student will not receive a study score for this subject.
Assessment
The Victorian Curriculum and Assessment Authority will supervise the assessment of all students undertaking Units 3 and 4. In the study of VCE Mathematics, students’ level of achievement will be determined by School-assessed Coursework (SACs) and two end-of-year examinations.
Unit 3 School-assessed Coursework: 24 %
Unit 4 School-assessed Coursework: 16 %
Examination 1: 30 %
Examination 2: 30 %
School-based assessment
Demonstration of achievement of Outcomes 1, 2 and 3 are based on the student’s performance on a selection of the following assessment tasks:
Formative tests, application tasks and SACs
Successful completion of minimum work requirements
External assessment
Examination 1:
Description
This examination comprises multiple-choice questions covering all areas of study. The examination is designed to assess students’ knowledge of mathematical concepts, models and techniques and their ability to reason, interpret and apply this knowledge in a range of contexts.
Conditions
The examination will be one and a half hours in duration and student access to an approved technology with numerical, graphical, symbolic, financial and statistical functionality will be assumed. One bound reference - text (which may be annotated) or lecture pad - may be brought into the examination. VCAA examination rules will apply.
Contribution to final assessment
The examination will contribute 30 %.
Examination 2:
Description
This examination comprises written response questions covering all areas of study. The examination will be designed to assess students’ ability to select and apply mathematical facts, concepts, models and techniques to solve extended application problems in a range of contexts.
Conditions
The examination will be one and a half hours in duration and student access to an approved technology with numerical, graphical, symbolic, financial and statistical functionality will be assumed. One bound reference - text (which may be annotated) or lecture pad - may be brought into the examination. VCAA examination rules will apply.
Contribution to final assessment
The examination will contribute 30 %
EXPECTATIONS
As part of General Mathematics, students are expected to complete all formative assessments, coursework and a reference book in order to receive an S. Students are also expected to bring a CAS calculator, pens and/or pencils, their notes book and a device or textbook.