Study design and exam specifications

Compiled 13 September 2026. Every major claim below is tagged with its source. Nothing in this document is inferred key knowledge — where a dot point is ambiguous or truncated in the published source itself, that is stated explicitly.

---

0. Sources used

Corpus data-quality note. Four corpus text files are empty (32 bytes, header only) and could not be used: Documents_exams_mathematics_2024_2024GeneralMaths1-w.txt, Documents_exams_mathematics_2024_2024GeneralMaths2-w.txt, 2025-05_2025-NHT-generalmaths1.txt, 2025-05_2025-NHT-generalmaths2.txt. The 2024 exams were reconstructed from 2024genmaths1-markguideresponses.txt and the 2024 reports instead. Two assessment-guide files (2025-06_2025NHT-GeneralMath1-assessment-guide.txt, 2026-06_2026-NHT-GeneralMaths1-assessment-guide_0.txt) are ~550 bytes and contain only the answer key header.

---

1. Units 3 & 4 structure

1.1 The two Areas of Study, and the four content areas

[SD] states verbatim:

"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."

So there are formally two Areas of Study, subdivided into four content areas. The exam specification [SPEC] uses the four content areas as its organising unit, not the two Areas of Study.

Sources: structure [SD]; weightings [SPEC].

All four content areas are compulsory. There is no module choice. This is the single biggest structural change from Further Mathematics (see §8).

1.2 Assumed knowledge

[SD]:

"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."

1.3 Assessment weighting

SAC structure [SD]: - Unit 3 (60 marks): an Application task (guided investigation of a given data set with several variables, 4–6 hours over 1–2 weeks; three components of increasing complexity — data plots incl. smoothed plots; summary statistics incl. seasonal indices; modelling of linear associations/trends incl. data transformation) + Modelling or problem-solving task 1, which "is to relate to Recursion and financial modelling" (2–3 hours over 1 week). Marks: Outcome 1 = 15 (10 AT + 5 MPST1), Outcome 2 = 30 (20 + 10), Outcome 3 = 15 (10 + 5). - Unit 4 (40 marks): Modelling or problem-solving tasks 2 and 3; "One of the modelling or problem-solving tasks is to relate to Matrices and the other modelling or problem-solving task is to relate to Networks and decision mathematics." Each 2–3 hours over 1 week. Marks: Outcome 1 = 10 (5 + 5), Outcome 2 = 20 (10 + 10), Outcome 3 = 10 (5 + 5).

---

2. Area of Study 1 — Data analysis, probability and statistics (Unit 3)

[SD] topic overview:

"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."

The content is given under four sub-topic headings. All dot points below are verbatim from [SD].

2.1 Investigating data distributions

This topic includes:
- types of data
- representation, display and description of the distributions of categorical variables: data tables, two-way frequency tables and their associated segmented bar charts
- representation, display and description of the distributions of numerical variables: dot plots, stem plots, histograms; the use of a logarithmic (base 10) scale to display data ranging over several orders of magnitude and their interpretation in terms of powers of ten
- use of the distribution(s) of one or more categorical or numerical variables to answer statistical questions
- summary of the distributions of numerical variables; the five-number summary and boxplots (including the use of the lower fence (Q1 – 1.5 × IQR) and upper fence (Q3 + 1.5 × IQR) to identify and display possible outliers); the sample mean and standard deviation and their use in comparing data distributions in terms of centre and spread
- the normal model for bell-shaped distributions and the use of the 68–95–99.7% rule to estimate percentages and to give meaning to the standard deviation; standardised values (z-scores) and their use in comparing data values across distributions.

2.2 Investigating association between two variables

This topic includes:
- response and explanatory variables and their role in investigating associations between variables
- contingency (two-way) frequency tables, their associated bar charts (including percentage segmented bar charts) and their use in identifying and describing associations between two categorical variables
- back-to-back stem plots, parallel dot plots and boxplots and their use in identifying and describing associations between a numerical variable and a categorical variable
- scatterplots and their use in identifying and qualitatively describing the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)
- answering statistical questions that require a knowledge of the associations between pairs of variables
- Pearson correlation coefficient, r, and its calculation and interpretation
- cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect.

2.3 Investigating and modelling linear associations

This topic includes:
- least squares line of best fit y = a + bx, where x represents the explanatory variable, and y represents the response variable; the determination of the coefficients a and b using technology, and the formulas b = r·(s_y/s_x) and a = ȳ − b·x̄
- modelling linear association between two numerical variables, including the:
- identification of the explanatory and response variables
- use of the least squares method to fit a linear model to the data
- interpretation of the slope and intercepts of the least squares line in the context of the situation being modelled, including:
- use of the rule of the fitted line to make predictions being aware of the limitations of extrapolation
- use of the coefficient of determination, r², to assess the strength of the association in terms of explained variation
- use of residual analysis to check quality of fit
- data transformation and its use in transforming some forms of non-linear data to linearity using a square, logarithmic (base 10) or reciprocal transformation (applied to one axis only)
- interpretation and use of the equation of the least squares line fitted to the transformed data to make predictions.

2.4 Investigating and modelling time series data

This topic includes:
- qualitative features of time series plots; recognition of features such as trend (long-term direction), seasonality (systematic, calendar related movements) and irregular fluctuations (unsystematic, short-term fluctuations); possible outliers and their sources, including one-off real-world events, and signs of structural change such as a discontinuity in the time series
- numerical smoothing of time series data using moving means with consideration of the number of terms required (using centring when appropriate) to help identify trends in time series plot with large fluctuations
- graphical smoothing of time series plots using moving medians (involving an odd number of points only) to help identify long-term trends in time series with large fluctuations
- seasonal adjustment including the use and interpretation of seasonal indices and their calculation using seasonal and yearly means
- modelling trend by fitting a least squares line to a time series with time as the explanatory variable (data de-seasonalised where necessary), and the use of the model to make forecasts (with re-seasonalisation where necessary) including consideration of the possible limitations of fitting a linear model and the limitations of extending into the future.

---

3. Area of Study 2 — Discrete mathematics

3.1 Recursion and financial modelling (Unit 3)

[SD] topic overview:

"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."

Five sub-topic headings. All verbatim from [SD].

Depreciation of assets

This topic includes:
- use of a first-order linear recurrence relation of the form: u₀ = a, u_{n+1} = R·u_n + d where a, R and d are constants to generate the terms of a sequence
- use of a recurrence relation to model and compare (numerically and graphically) flat rate, unit cost and reducing balance depreciation of the value of an asset with time, including the use of a recurrence relation to determine the depreciating value of an asset after n depreciation periods for the initial sequence
- use of the rules for the future value of an asset after n depreciation periods for flat rate, unit cost and reducing balance depreciation and their application.

Compound interest investments and loans

This topic includes:
- the concepts of simple and compound interest
- use of a recurrence relation to model and analyse (numerically and graphically) a compound interest investment or loan, including the use of a recurrence relation to determine the value of the compound interest loan or investment after n compounding period for an initial sequence from first principles
- the difference between nominal and effective interest rates and the use of effective interest rates to compare investment returns and the cost of loans when interest is paid or charged, for example, daily, monthly, quarterly
- the future value of a compound interest investment or loan after n compounding periods and its use to solve practical problems.

Reducing balance loans

This topic includes:
- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) the amortisation of a reducing balance loan, including the use of a recurrence relation to determine the value of the loan or investment after n payments for an initial sequence from first principles
- use of a table to investigate and analyse the amortisation of a reducing balance loan on a step-by-step basis, the payment made, the amount of interest paid, the reduction in the principal and the balance of the loan
- use of technology with financial modelling functionality to solve problems involving reducing balance loans, such as repaying a personal loan or a mortgage, including the impact of a change in interest rate on repayment amount, time to repay the loan, total interest paid and the total cost of the loan.

Annuities and perpetuities

This topic includes:
- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) the amortisation of an annuity, including the use of a recurrence relation to determine the value of the annuity after n payments for an initial sequence from first principles
- use of a table to investigate and analyse the amortisation of an annuity on a step-by-step basis, the payment made, the interest earned, the reduction in the principal and the balance of the annuity
- use of technology to solve problems involving annuities including determining the amount to be invested in an annuity to provide a regular income paid, for example, monthly, quarterly
- simple perpetuity as a special case of an annuity that lasts indefinitely.

Compound interest investment with periodic and equal additions to the principal

This topic includes:
- use of a first-order linear recurrence relation to model and analyse (numerically and graphically) annuity investment, including the use of a recurrence relation to determine the value of the investment after n payments have been made for an initial sequence from first principles
- use of a table to investigate and analyse the growth of an annuity investment on a step-by-step basis after each payment is made, the payment made, the interest earned and the balance of the investment
- use of technology with financial modelling functionality to solve problems involving annuity investments, including determining the future value of an investment after a number of compounding periods, the number of compounding periods for the investment to exceed a given value and the interest rate or payment amount needed for an investment to exceed a given value in a given time.

3.2 Matrices (Unit 4)

[SD] topic overview:

"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."

Matrices and their applications

This topic includes:
- matrix arithmetic: the order of a matrix, types of matrices (row, column, square, diagonal, symmetric, triangular, zero, binary and identity), the transpose of a matrix, and elementary matrix operations (sum, difference, multiplication of a scalar, product and power)
- inverse of a matrix, its determinant, and the condition for a matrix to have an inverse
- use of matrices to represent numerical information presented in tabular form, and the use of a rule for the a_ij th element of a matrix to construct the matrix
- binary and permutation matrices, and their properties and applications
- communication and dominance matrices and their use in analysing communication systems and ranking players in round-robin tournaments.

Transition matrices

This topic includes:
- use of the matrix recurrence relation: S₀ = initial state matrix, S_{n+1} = T·S_n or S_{n+1} = L·S_n where T is a transition matrix, L is a Leslie matrix, and S_n is a column state matrix, to generate a sequence of state matrices (assuming the next state only relies on the current state)
- informal identification of the equilibrium state matrix in the case of regular transition matrices (no noticeable change from one state matrix to the next state matrix)
- use of transition diagrams, their associated transition matrices and state matrices to model the transitions between states in discrete dynamical situations and their application to model and analyse practical situations such as the modelling and analysis of an insect population comprising eggs, juveniles and adults
- use of the matrix recurrence relation S₀ = initial state matrix, S_{n+1} = T·S_n + B to extend modelling to populations that include culling and restocking.

Note — Leslie matrices are new content. The Leslie matrix (S_{n+1} = L·S_n) does not appear anywhere in the 2016–2022 Further Mathematics Matrices module [OLDSD], nor on any Further Mathematics formula sheet [FM]. It appears in the 2023+ area of study and on the 2023+ formula sheet [FS].

3.3 Networks and decision mathematics (Unit 4)

[SD] topic overview:

"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."

Six sub-topic headings. All verbatim from [SD].

Graphs and networks

• the concepts, conventions and terminology of graphs including planar graphs and Euler's rule, and directed (digraphs) and networks
• use of matrices to represent graphs, digraphs and networks and their application.

Exploring and travelling problems

• the concepts, conventions and notations of walks, trails, paths, cycles and circuits
• Eulerian trails and Eulerian circuits: the conditions for a graph to have a Eulerian trail or a Eulerian circuit, properties and applications
• Hamiltonian paths and cycles: properties and applications.

Trees and minimum connector problems

• trees and spanning trees
• minimum spanning trees in a weighed connected graph and their determination by inspection or by Prim's algorithm
• use of minimal spanning trees to solve minimal connector problems.

(“weighed” is a typo present in the published study design; it means "weighted".)

Flow problems

• use of networks to model flow problems: capacity, sinks and sources
• solution of small-scale network flow problems by inspection and the use of the 'maximum-flow minimum-cut' theorem to aid the solution of larger scale problems.

Shortest path problems

• determination of the shortest path between two specified vertices in a graph, digraph or network by inspection
• Dijkstra's algorithm and its use to determine the shortest path between a given vertex and each of the other vertices in a weighted graph or network.

Matching problems

• use of a bipartite graph and its tabular or matrix form to represent a matching problem
• determination of the optimum assignment(s) of people or machines to tasks by inspection or by use of the Hungarian algorithm for larger scale problems.

Scheduling problems and critical path analysis

• construction of an activity network from a precedence table (or equivalent) including the use of dummy activities where necessary
• use of forward and backward scanning to determine the earliest starting times (EST) and latest starting times (LST) for each activity
• use of earliest starting times and latest starting times to identify the critical path in the network and determine the float times for non-critical activities
• use of crashing to reduce the completion time of the project or task being modelled.

---

4. Outcomes 1, 2 and 3

[SD]:

"For each unit the student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass all of the areas of study for each unit. For each of Unit 3 and Unit 4 the outcomes as a set apply to the content from the areas of study covered in that unit."

The same three outcomes apply to both Unit 3 and Unit 4; only the content they range over changes.

Each outcome adds: "To achieve this outcome the student will draw on key knowledge and key skills outlined in all the areas of study."

4.1 Outcome 1 — key knowledge and key skills, by area of study

Area of Study 1 — Data analysis, probability and statistics

Key knowledge (verbatim, [SD]):

• types of data: categorical (nominal and ordinal) and numerical (discrete and continuous)
• frequency tables, bar charts including segmented bar charts, histograms, stem plots, dot plots, and their application in the context of displaying and describing distributions
• logarithmic (base 10) scales, and their purpose and application
• the five-number summary and boxplots (including the designation and display of possible outliers)
• mean x̄ and sample standard deviation s = √( Σ(x − x̄)² / (n − 1) )
• the normal model and the 68–95–99.7% rule, and standardised values (z-scores)
• response and explanatory variables
• two-way frequency tables, segmented bar charts, back-to-back stem plots, parallel boxplots, and scatterplots, and their application in the context of identifying and describing associations
• correlation coefficient, r, its interpretation, the issue of correlation and cause and effect
• coefficient of determination, its interpretation
• least squares line and its use in modelling linear associations
• data transformation and its purpose
• time series data and its analysis

Key skills (verbatim, [SD]):

• construct frequency tables and bar charts and use them to describe and interpret the distributions of categorical variables
• answer statistical questions that require a knowledge of the distribution(s) of one or more categorical variables
• construct stem and dot plots, boxplots, histograms and appropriate summary statistics and use them to describe and interpret the distributions of numerical variables
• answer statistical questions that require a knowledge of the distribution(s) of one or more numerical variables
• solve problems using z-scores and the 68–95–99.7% rule
• construct two-way tables and use them to identify and describe associations between two categorical variables
• construct parallel boxplots and use them to identify and describe associations between a numerical variable and a categorical variable
• construct scatterplots and use them to identify and describe associations between two numerical variables
• calculate the correlation coefficient, r, and interpret it in the context of the data
• answer statistical questions that require a knowledge of the associations between pairs of variables
• determine the equation of the least squares line giving the coefficients correct to a required number of decimal places or significant figures as specified, and distinguish between correlation and causation
• use the least squares line of best fit to model and analyse the linear association between two numerical variables and interpret the model in the context of the association being modelled
• calculate the coefficient of determination, r², and interpret in the context of the association being modelled and use the model to make predictions, being aware of the problem of extrapolation
• construct a residual analysis to test the assumption of linearity and, in the case of clear non-linearity, transform the data to achieve linearity and repeat the modelling process using the transformed data
• identify key qualitative features of a time series plot including trend (using smoothing if necessary), seasonality, irregular fluctuations and outliers, and interpret these in the context of the data
• calculate, interpret and apply seasonal indices
• model linear trends using the least squares line of best fit, interpret the model in the context of the trend being modelled, use the model to make forecasts with consideration of the limitations of extending forecasts too far into the future

Area of Study 2 — Discrete mathematics: Recursion and financial modelling

Key knowledge (verbatim, [SD]):

• the use of first-order linear recurrence relations to model growth and decay problems in financial contexts
• the use of first-order linear recurrence relations to model flat rate and unit cost, and reduce balance depreciation of an asset over time, including the rule for the future value of the asset after n depreciation periods
• the concepts of financial mathematics including simple and compound interest, nominal and effective interest rates, the present and future value of an investment, loan or asset, amortisation of a reducing balance loan or annuity and amortisation tables
• the use of first-order linear recurrence relations to model compound interest investments and loans, and the flat rate, unit cost and reducing balance methods for depreciating assets, reducing balance loans, annuities, perpetuities and annuity investments

(“reduce balance” is a typo present in the published study design; it means "reducing balance".)

Key skills (verbatim, [SD]):

• model and analyse growth and decay in financial contexts using a first-order linear recurrence relation of the form: u₀ = a, u_{n+1} = R·u_n + d where a, R and d are constants
• demonstrate the use of a recurrence relation to determine the depreciating value of an asset or the future value of an investment or a loan after n time periods for the initial sequence
• use a rule for the future value of a compound interest investment or loan, or a depreciating asset, to solve practical problems
• use a table to investigate and analyse on a step-by-step basis the amortisation of a reducing balance loan or an annuity, and interpret amortisation tables
• use technology with financial mathematics capabilities, to solve practical problems associated with compound interest investments and loans, reducing balance loans, annuities and perpetuities, and annuity investments

Area of Study 2 — Discrete mathematics: Matrices

Key knowledge (verbatim, [SD], version 1.1):

• the order of a matrix, types of matrices (row, column, square, diagonal, symmetric, triangular, zero, binary, permutation and identity), the transpose of a matrix, and elementary matrix operations (sum, difference, multiplication of a scalar, product and power)
• the inverse of a matrix and the condition for a matrix to have an inverse, including determinant
• for transition matrices, assuming the next state only relies on the current state with a fixed population
• communication and dominance matrices and their application
• transition diagrams and transition matrices and regular transition matrices and their identification

⚠️ Verification note — two of these bullets are incomplete in the published document itself. In both the official DOCX and the official PDF of version 1.1, bullet 2 ends at the bare word "determinant" with nothing following it, and bullet 3 begins with a lower-case "for transition matrices…" with no preceding symbol. I confirmed by (a) inspecting the DOCX XML for embedded equation objects (there are none in these two paragraphs) and (b) rendering PDF page 91 as an image (the only image on that page is the footer logo). The obvious intent is det A in bullet 2 and S_{n+1} = T·S_n in bullet 3 — matching the corresponding formulas on the formula sheet — but VCAA has not printed them, so I am not asserting them as study-design text. These two bullets are exactly the ones changed by amendment 1.1 ("Update to key knowledge for Matrices in Units 3 and 4 General Mathematics (page 91)", November 2022, [SD] amendment history).

Key skills (verbatim, [SD]):

• use matrix recurrence relations to generate a sequence of state matrices, including an informal identification of the equilibrium or steady state matrix in the case of regular state matrices
• construct a transition matrix from a transition diagram or a written description and vice versa
• construct a transition matrix to model the transitions in a population with an equilibrium state
• use matrix recurrence relations to model populations with culling and restocking

Area of Study 2 — Discrete mathematics: Networks and decision mathematics

Key knowledge (verbatim, [SD]):

• the conventions, terminology, properties and types of graphs; edge, face, loop, vertex, the degree of a vertex, isomorphic and connected graphs, and the adjacency matrix, and Euler's formula for planar graphs and its application
• the exploring and travelling problem, walks, trails, paths, Eulerian trails and circuits, and Hamiltonian paths and cycles
• the minimum connector problem, trees, spanning trees and minimum spanning trees and Prim's algorithm
• the flow problem, and the minimum cut/maximum flow theorem
• the shortest path problem and Dijkstra's algorithm
• the matching problem and the Hungarian algorithm
• the scheduling problem and critical path analysis

Key skills (verbatim, [SD]):

• construct graphs, digraphs and networks and their matrix equivalents to model and analyse practical situations
• recognise the exploring and travelling problem and to solve it by utilising the concepts of walks, trails, paths, Eulerian trails and circuits, and Hamiltonian paths and cycles
• recognise the minimum connector problem and solve it by utilising the properties of trees, spanning trees and by determining a minimum spanning tree by inspection or using Prim's algorithm for larger scale problems
• recognise the flow problem, use networks to model flow problems and determine the minimum flow problem by inspection, or by using the minimum cut/maximum flow theorem for larger scale problems
• recognise the shortest path problem and solve it by inspection or using Dijkstra's algorithm for larger scale problems
• recognise the matching problem and solve it by inspection or using the Hungarian algorithm for larger scale problems
• recognise the scheduling problem and solve it by using critical path analysis

4.2 Outcome 2 — key knowledge and key skills

Outcome 2 has a single combined list (not split by area of study).

Key knowledge (verbatim, [SD]):

• the facts, concepts and techniques associated with data analysis, recursion and financial modelling, matrices and networks and decision mathematics
• standard models studied in data analysis, recursion and financial modelling, matrices, and networks and decision mathematics, and their areas of application
• general formulation of the concepts, techniques and models studied in data analysis, recursion and financial modelling, matrices, and networks and decision mathematics
• assumptions and conditions underlying the use of the concepts, techniques and models associated with data analysis, recursion and financial modelling, matrices, and networks and decision mathematics

Key skills (verbatim, [SD]):

• identify, recall and select facts, concepts, models and techniques needed to investigate and analyse statistical features of a data set with several variables that can include time series data
• select and implement standard financial models to investigate and analyse a financial or mathematically equivalent non-financial situation that requires the use of increasingly sophisticated models to complete the analysis
• identify, recall and select the mathematical concepts, models and techniques needed to solve an extended problem or conduct an investigation in a variety of contexts related to matrices and networks and decision mathematics
• interpret and report the results of a statistical investigation or of completing a modelling or problem-solving task in terms of the context under consideration, including discussing the assumptions in application of these models

4.3 Outcome 3 — key knowledge and key skills

Key knowledge (verbatim, [SD]):

• the role of computational thinking (abstraction, decomposition, pattern and algorithm) in problem-solving, and its application to mathematical investigation
• the difference between exact numerical and approximate numerical answers when using technology to perform computation, and rounding to a given number of decimal places or significant figures
• domain and range requirements for specification of graphs of models and relations, when using technology
• the role of parameters in specifying general forms of models and equations
• the relation between numerical, graphical and symbolic forms of information about models and equations, and the corresponding features of those models and equations
• the similarities and differences between formal mathematical expressions and their representation by technology
• the appropriate functionality of technology for a variety of mathematical contexts

Key skills (verbatim, [SD]):

• use computational thinking, algorithms, models and simulations to solve problems related to a given context
• distinguish between exact and approximate presentations of mathematical results produced by technology, and interpret these results to a specified degree of accuracy in terms of a given number of decimal places or significant figures
• use technology to carry out numerical, graphical and symbolic computation as applicable
• produce results, using a technology, which identify examples or counter-examples for propositions
• produce tables of values, families of graphs and collections of other results using technology, which support general analysis in investigative, modelling and problem-solving contexts
• use appropriate domain and range specifications to illustrate key features of graphs
• identify the relation between numerical, graphical and symbolic forms of information about models and equations, and the corresponding features of those models and equations
• specify the similarities and differences between formal mathematical expressions and their representation by technology
• select an appropriate functionality of technology in a variety of mathematical contexts, related to data analysis, recurrence relations and financial modelling, and provide a rationale for these selections
• apply suitable constraints and conditions, as applicable, to carry out required computations
• relate the results from a particular technology application to the nature of a particular mathematical task (investigative, modelling or problem-solving) and verify these results
• specify the process used to develop a solution to a problem using technology and communicate the key stages of mathematical reasoning (formulation, solution, interpretation) used in this process

---

5. Examination 1 specification

All rows from [SPEC] (Version 3, March 2025) unless otherwise noted.

5.1 Exact question breakdown by content area

[SPEC], verbatim:

"The examination will be divided into four content areas: data analysis, recursion and financial modelling, matrices, and networks and decision mathematics. The examination will consist of 40 multiple-choice questions worth 1 mark each. Of these 40 questions, 16 will be allocated to data analysis, 8 will be allocated to recursion and financial modelling, 8 will be allocated to matrices, and 8 will be allocated to networks and decision mathematics."

The question numbering has been identical every year 2023–2025 [RPT23] [RPT24] [RPT25]:

Each report states it in exactly this form, e.g. [RPT25]: "The examination comprised 40 multiple-choice questions covering all areas of study. Questions 1–16: Data analysis / Questions 17–24: Recursion and financial modelling / Questions 25–32: Matrices / Questions 33–40: Networks and decision mathematics".

5.2 ⚠️ The 5-option → 4-option change (2024)

This is not stated in the specification document (which never mentions the number of options), but is unambiguous in the papers and reports:

Practical consequence for students: the 2023 GM Exam 1, the 2023 sample Exam 1, and every Further Mathematics Exam 1 (2006–2023) have five options. Current papers have four. Distractor-elimination strategy differs, and the "guess" baseline moves from 20% to 25%.

---

6. Examination 2 specification

All rows from [SPEC] unless noted.

6.1 Marks per content area

[SPEC], verbatim:

"The examination will be divided into four content areas: data analysis, recursion and financial modelling, matrices, and networks and decision mathematics. … 24 marks will be allocated to data analysis, 12 marks will be allocated to recursion and financial modelling, 12 marks will be allocated to matrices, and 12 marks will be allocated to networks and decision mathematics."

[RPT24] (Exam 2 report) restates this as: "Students were required to attempt four compulsory sections: Data analysis (24 marks) / Recursion and financial modelling (12 marks) / Matrices (12 marks) / Networks and decision mathematics (12 marks)."

The four content areas appear as plain headings in the paper — they are not labelled "Section A / Section B". (Contrast with Further Mathematics, which did use Section A / Section B.) Verified in [PAPERS] for 2023, 2025 and 2026 NHT.

Worked example — 2025 Exam 2 [PAPERS]:

6.2 Standing instructions in Exam 2 (worth memorising)

From the Instructions page of the paper [PAPERS], unchanged 2023–2025:

• Answer all questions in the spaces provided.
• Write your responses in English.
• In all questions where a numerical answer is required, you should only round your answer when instructed to do so.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.

[RPT24] adds assessor-level advice: bring a ruler (often needed in Data analysis to draw straight lines); write in a dark colour because scanned images are used for assessing; extra information in a response must be correct or the mark can be lost.

---

7. The formula sheet — complete contents

[FS]. The formula sheet is identical for Examination 1 and Examination 2 [SPEC]. It is 4 pages (cover + 2 content pages + back). Students may keep it.

There are exactly 11 formulas.

Data analysis (5 formulas)

Recursion and financial modelling (2 formulas)

Matrices (4 formulas)

Networks and decision mathematics (1 formula)

7.1 What is NOT on the formula sheet

This is the high-value list for students: every item below is examinable key knowledge or key skill under [SD], but is not supplied.

Data analysis - The sample standard deviation formula s = √(Σ(x − x̄)²/(n − 1)) — explicitly named in Outcome 1 key knowledge but not on the sheet. - The mean formula. - The 68–95–99.7% rule percentages and the z-values they correspond to (±1, ±2, ±3 standard deviations). - The Pearson correlation coefficient r computation formula. - The coefficient of determination relationship r² (you must know to square r, and to convert to a percentage). - The rearranged de-seasonalising rule: deseasonalised figure = actual figure ÷ seasonal index (derivable from the given seasonal index formula, but not printed in that direction). - That seasonal indices for m seasons sum to m (e.g. 4 for quarters, 12 for months). - Moving mean / centred moving mean / moving median procedures. - Percentage-change and "increase/decrease by k%" conversions (e.g. ×0.57 ⇒ a 43% reduction — tested in 2025 Q16 [RPT25]). - Interpretation templates for slope, intercept, r, r², and residual plots.

Recursion and financial modelling - The compound interest future value rule V_n = V₀ · Rⁿ (or A = P(1 + r/100)ⁿ). - The flat rate depreciation rule, the unit cost depreciation rule, and the reducing balance depreciation rule. - The simple interest rule I = Prt. - R = 1 + r/(100 × compounds per year) — the conversion from an annual nominal rate to a per-period multiplier. - Any annuity / amortisation closed-form formula. (Intentional: the study design expects the TVM/finance solver on CAS.) - Amortisation table column relationships (interest = balance × r; principal reduction = payment − interest). - The perpetuity condition payment = interest per period.

Matrices - Rules for when a matrix product is defined and what order the product has. - Transpose, identity, permutation and binary matrix properties. - The dominance matrix construction (one-step + two-step, i.e. A + A²) and ranking procedure. - Communication-matrix interpretation of powers (number of n-step links). - How to find the steady/equilibrium state (Sₙ for large n). - The structure and meaning of a Leslie matrix (birth rates in row 1, survival rates on the subdiagonal) — only the recurrence S_{n+1} = L·S_n is given. - Determinants and inverses of matrices larger than 2 × 2 (only the 2 × 2 case is on the sheet).

Networks and decision mathematics - Conditions for an Eulerian trail (exactly 2 odd-degree vertices) and an Eulerian circuit (all vertices even degree). - The degree-sum / handshake relationship (sum of degrees = 2e). - Definitions/properties of Hamiltonian paths and cycles. - Prim's algorithm, Dijkstra's algorithm, the Hungarian algorithm — all procedures, none given. - The maximum-flow minimum-cut theorem statement and cut-capacity counting rules. - Critical path analysis: forward/backward scanning, float time = LST − EST, the crashing procedure. - The number of edges in a spanning tree of an n-vertex graph (n − 1). - Adjacency matrix conventions (including loops counting as 1 in a directed graph vs 2 in an undirected one).

Implication for the bound reference. Because so much is missing from the sheet, the bound reference is doing real work in this subject. A student's notes should carry the depreciation rules, the compound-interest rule, dominance/communication matrix procedures, the four network algorithms, Eulerian/Hamiltonian conditions, and interpretation sentence templates.

---

8. Old Further Mathematics (to 2022) vs new General Mathematics (2023+)

8.1 Three eras of the subject

Sources: 2006/2015 structure tables and module contents pages [FM] (Documents_exams_mathematics_2006furmath1-w.txt, ...2015furmath1-w.txt, ...2015furmath2-w.txt); 2016/2022 structure tables [FM] (...2016furmath1-w.txt, ...2022furmath1-w.txt, ...2022furmath2-w.txt) and [OLDSD]; 2023+ [SPEC].

8.2 What was removed, what became compulsory

Removed entirely from the 2023+ design:

Became compulsory: Matrices and Networks and decision mathematics. Under Further Mathematics these were two of four optional modules; from 2023 every student sits both.

New content in 2023+: - Leslie matrices — S_{n+1} = L·S_n, with a dedicated line on the formula sheet. Not in [OLDSD], not on any FM formula sheet [FM]. - Computational thinking is elevated into Outcome 3 key knowledge ("abstraction, decomposition, pattern and algorithm") [SD].

Notation and emphasis changes:

Formula sheet diff. Old FM sheet [FM] vs new GM sheet [FS]:

Everything on the current sheet other than the Leslie line appeared on the 2016–2022 FM sheet in the same wording.

8.3 Which past papers are still relevant practice — the mapping

This is the practically important table. Further Mathematics 2016–2022 (and 2017–2023 NHT) papers map one-for-one onto the current exam structure — the current General Mathematics exam is, in effect, the old FM Core plus Modules 1 and 2, with the module choice removed.

Exam 1 (multiple choice)

Mark accounting: the old FM Core Section A was 24 questions split 16/8 — exactly the current Data analysis/Recursion split. Each old module was 8 questions — exactly the current Matrices and Networks blocks. Verified against the 2022 and 2016 papers [FM].

Exam 2 (written response)

Pre-2016 Further Mathematics papers (2006–2015)

Lower value, but not worthless:

General Mathematics papers (fully aligned)

---

9. Residual uncertainties / things I could not verify

1. The two truncated Matrices key-knowledge bullets (§4.1). Confirmed truncated in the published v1.1 DOCX and PDF; the intended symbols (det A, S_{n+1} = T·S_n) are not printed. I did not obtain version 1.0 of the study design to see what the November 2022 amendment replaced.
2. The number of multiple-choice options is not specified anywhere in [SPEC] Version 3. The A–D format is evidenced only by the papers, the reports' answer tables, and the sample answer sheet. If a definitive VCAA Bulletin notice announcing the change exists, I did not locate it.
3. Earlier versions of the examination specifications (Versions 1 and 2) were not retrieved — only Version 3 (March 2025) is published on the VCAA page. The 16/8/8/8 and 24/12/12/12 splits were already in force for the 2023 exam [RPT23], so these weightings appear unchanged across versions, but I cannot confirm that from a primary Version 1 document.
4. Number of questions in Exam 2 is genuinely unconstrained by the specification; the 14–18 range quoted is observed, not prescribed.
5. Four corpus text files are empty (listed in §0) — 2024 GM1/GM2 and 2025 NHT GM1/GM2. Their content was inferred from the corresponding reports and marking guides, not read directly.

---

10. Quick-reference summary card

VCE GENERAL MATHEMATICS UNITS 3 & 4  (2023–2027)

Unit 3: Data analysis + Recursion and financial modelling     SAC 24%
Unit 4: Matrices + Networks and decision mathematics          SAC 16%
Exam 1: 30%     Exam 2: 30%

EXAM 1 — Multiple-Choice Question Book
  15 min reading + 1 h 30 min writing
  40 questions, 4 options (A–D), 1 mark each, no penalty for wrong answers
  Q1–16  Data analysis                      (16 marks)
  Q17–24 Recursion and financial modelling  (8 marks)
  Q25–32 Matrices                           (8 marks)
  Q33–40 Networks and decision mathematics  (8 marks)
  Total 40 marks. Formula sheet supplied.

EXAM 2 — Question and Answer Book
  15 min reading + 1 h 30 min writing
  Short-answer and extended-answer, multi-stage; ~14–18 questions
  Data analysis                      24 marks
  Recursion and financial modelling  12 marks
  Matrices                           12 marks
  Networks and decision mathematics  12 marks
  Total 60 marks. Same formula sheet.

BOTH EXAMS
  1 approved CAS technology + 1 scientific calculator
  1 bound reference (may be annotated; no foldouts)
  Basic stationery. All questions compulsory.

FORMULA SHEET — 11 formulas only
  DA:  z-score; boxplot fences; least squares (b = r·sy/sx, a = ȳ − b·x̄);
       residual = actual − predicted; seasonal index = actual / deseasonalised
  RFM: u₀ = a, u_{n+1} = R·u_n + d;  r_eff = [(1 + r/100n)ⁿ − 1] × 100%
  MAT: det of 2×2; inverse of 2×2;  S_{n+1} = T·S_n + B;  S_{n+1} = L·S_n
  NET: v + f = e + 2