Which topic carries the most marks in the VCE General Mathematics external exam?

Data analysis, probability and statistics carries 40.0% of the marks across the 9 VCAA papers from 2023 to 2025, ahead of Discrete mathematics on 20.0%.

How are marks split between question types in the VCE General Mathematics exam?

Short answer carries 65.2% of the marks and multiple choice carries 34.8% of the marks, measured across 9 papers and 460 marks from 2023 to 2025.

Has the topic balance changed in recent VCE General Mathematics papers?

No. Comparing the 2023 papers with the 2025 papers, the largest movement in any topic's share was 0.0 percentage points, which is too small to plan revision around.

How many past papers is this VCE General Mathematics analysis based on?

9 VCAA external papers from 2023 to 2025, covering 239 questions and 460 marks. 0.0% of those marks carry no dot-point mapping and sit outside the percentages.

VCE General Mathematics most tested topics

Across the nine VCAA General Mathematics external papers from 2023 to 2025, Data analysis, probability and statistics carries 40.0% of the marks against 20.0% for Networks and decision mathematics, so the paper rewards Data analysis, probability and statistics more than any other topic. At dot-point level 3.1.1.5 carries 7.3% of paper marks, and two of the 67 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 100.0% of marks that map to a study design dot point.

Computed from 9 VCAA General Mathematics external papers, 2023 to 2025: 239 questions, 427 question parts and 460 marks.

Unit, topic and dot-point shares below are of the 460 marks that map to a dot point, so each of those tables adds to 100%. 88 of the 427 parts are assessed against more than one dot point, and their 97 marks are divided evenly between the dot points they cover.

What these papers are

Year	Paper	Questions	Marks
2025	Paper 1	40	40
2025	Paper 1 (NHT)	40	40
2025	Paper 2	18	60
2025	Paper 2 (NHT)	16	60
2024	Paper 1	40	40
2024	Paper 2	15	60
2024	Paper 2 (NHT)	16	60
2023	Paper 1	40	40
2023	Paper 2	14	60

Marks by unit

Unit	Share of marks
Unit 3: Data analysis and Recursion and financial modelling	60.0%
Unit 4: Matrices and Networks and decision mathematics	40.0%

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Data analysis, probability and statistics	40.0%	9 of 9	3 of 3
Discrete mathematics	20.0%	9 of 9	3 of 3
Matrices	20.0%	9 of 9	3 of 3
Networks and decision mathematics	20.0%	9 of 9	3 of 3

Marks by subtopic

Each topic above breaks into the subtopics below, in the same order.

Subtopic	Share of marks	Papers
Investigating data distributions	15.3%	9 of 9
Investigating and modelling linear associations	12.6%	9 of 9
Investigating and modelling time series data	6.5%	9 of 9
Investigating association between two variables	5.5%	9 of 9
Reducing balance loans	7.4%	8 of 9
Depreciation of assets	5.9%	9 of 9
Annuities and perpetuities	3.7%	7 of 9
Compound interest investments and loans	2.6%	8 of 9
Compound interest investment with periodic and equal additions to the principal	0.4%	2 of 9
Matrices and their applications	12.5%	9 of 9
Transition matrices	7.5%	9 of 9
Scheduling problems and critical path analysis	6.3%	9 of 9
Graphs and networks	4.1%	8 of 9
Exploring and travelling problems	3.7%	8 of 9
Flow problems	2.2%	5 of 9
Matching problems	1.7%	5 of 9
Trees and minimum connector problems	1.1%	5 of 9
Shortest path problems	0.9%	4 of 9

Marks by dot point

Dot-point numbers and wording are VCAA's own. Where a dot point is written as a list, its items run together here separated by semicolons.

Dot point	Content	Topic	Share of marks	Papers
3.1.1.5	summary of the distributions of numerical variables; the five-number summary and boxplots (including the use of the lower fence ( $Q_1 - 1.5 \times IQR$ ) and upper fence ( $Q_3 + 1.5 \times IQR$ ) 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	Data analysis, probability and statistics	7.3%	9 of 9
3.1.3.3	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, $r^2$ , to assess the strength of the association in terms of explained variation; use of residual analysis to check quality of fit	Data analysis, probability and statistics	6.2%	8 of 9
4.1.1.1	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)	Matrices	5.8%	9 of 9
3.2.3.3	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	Discrete mathematics	4.1%	8 of 9
4.1.2.1	use of the matrix recurrence relation: $S_0$ = initial state matrix, $S_{n+1} = TS_n$ or $S_{n+1} = LS_n$ 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)	Matrices	3.0%	8 of 9
4.2.1.1	the concepts, conventions and terminology of graphs including planar graphs and Euler’s rule, and directed (digraphs) and networks	Networks and decision mathematics	3.0%	8 of 9
3.1.1.6	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	Data analysis, probability and statistics	2.8%	9 of 9
3.1.3.1	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 $b = r\frac{s_y}{s_x}$ and $a = \bar{y} - b\bar{x}$	Data analysis, probability and statistics	2.6%	9 of 9
3.1.4.4	seasonal adjustment including the use and interpretation of seasonal indices and their calculation using seasonal and yearly means	Data analysis, probability and statistics	2.6%	7 of 9
4.1.1.5	communication and dominance matrices and their use in analysing communication systems and ranking players in round-robin tournaments	Matrices	2.5%	6 of 9
4.1.2.3	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	Matrices	2.4%	8 of 9
3.1.3.2	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	Data analysis, probability and statistics	2.3%	8 of 9
3.2.1.3	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	Discrete mathematics	2.3%	7 of 9
3.2.1.2	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	Discrete mathematics	2.2%	7 of 9
4.2.2.3	Hamiltonian paths and cycles: properties and applications	Networks and decision mathematics	2.1%	7 of 9
3.2.3.1	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	Discrete mathematics	2.1%	6 of 9
4.1.1.3	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	Matrices	2.0%	7 of 9
4.2.7.3	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	Networks and decision mathematics	2.0%	7 of 9
3.1.1.4	use of the distribution(s) of one or more categorical or numerical variables to answer statistical questions	Data analysis, probability and statistics	1.7%	5 of 9
3.1.2.2	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	Data analysis, probability and statistics	1.7%	4 of 9

These 20 dot points carry 60.7% of the paper marks between them. Another 45 assessed dot points share the rest, and 2 of the 67 externally assessable dot points have not been assessed in any of these 9 papers. Content that has not appeared is still examinable.

What has moved between papers

No topic's share moved by more than 3.0 percentage points between the 2023 papers and the 2025 papers. The largest movement was 0.0 points, which is inside the range two papers a year produce by chance, so nothing here is a trend to revise around.

How the papers are built

Short answer carries 65.2% of the marks across these 9 papers.

Question type	Share of marks	Marks	Parts
Short answer	65.2%	300	267
Multiple choice	34.8%	160	160

Verb	Share of marks	Marks	Parts
determine	12.0%	55	45
write	4.6%	21	19
calculate	3.5%	16	14
explain	2.8%	13	11
show	2.6%	12	8
draw	1.7%	8	8
identify	1.7%	8	7
describe	1.5%	7	6

What these percentages do not tell you

Where to practise

Every topic above links to its own page of real VCAA questions with marking criteria and average scores attached: Data analysis, probability and statistics, Discrete mathematics, Matrices and Networks and decision mathematics. For how students actually score on this content, read VCE General Mathematics hardest topics, and for the full question bank start at VCE General Mathematics.

Syllabus and assessment material referenced in this guide is reproduced by permission, © VCAA. See our VCAA licensing notice. The VCAA does not endorse or make any warranties regarding this study resource. VCE® is a registered trademark of the VCAA.