Which topic carries the most marks in the VCE Mathematical Methods external exam?

Calculus carries 32.3% of the marks across the 19 VCAA papers from 2020 to 2025, ahead of Algebra, number and structure on 23.7%.

How are marks split between question types in the VCE Mathematical Methods exam?

Short answer carries 82.8% of the marks and multiple choice carries 17.2% of the marks, measured across 19 papers and 1161 marks from 2020 to 2025.

Has the topic balance changed in recent VCE Mathematical Methods papers?

Yes. Calculus moved down 4.1 percentage points between the 2020 to 2022 and 2023 to 2025 papers.

How many past papers is this VCE Mathematical Methods analysis based on?

19 VCAA external papers from 2020 to 2025, covering 324 questions and 1161 marks. 1.6% of those marks carry no dot-point mapping and sit outside the percentages.

VCE Mathematical Methods most tested topics

Across the 19 VCAA Mathematical Methods external papers from 2020 to 2025, Calculus leads on 32.3% and Data analysis, probability and statistics trails on 21.7%, with the rest between them. At dot-point level 4.2 carries 9.0% of paper marks, and zero of the 26 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 98.4% of marks that map to a study design dot point.

Computed from 19 VCAA Mathematical Methods external papers, 2020 to 2025: 324 questions, 780 question parts and 1161 marks.

Unit, topic and dot-point shares below are of the 1142 marks that map to a dot point, so each of those tables adds to 100%. 333 of the 780 parts are assessed against more than one dot point, and their 560 marks are divided evenly between the dot points they cover.

What these papers are

Year	Paper	Questions	Marks
2025	Paper 1	9	40
2025	Paper 1 (NHT)	8	42
2025	Paper 2	24	80
2025	Paper 2 (NHT)	25	80
2024	Paper 1	8	40
2024	Paper 2	25	80
2024	Paper 2 (NHT)	25	80
2023	Paper 1	9	40
2023	Paper 1 (NHT)	8	40
2023	Paper 2	25	80
2023	Paper 2 (NHT)	25	80
2022	Paper 1	8	40
2022	Paper 1 (NHT)	8	40
2022	Paper 2	25	79
2022	Paper 2 (NHT)	25	80
2021	Paper 1	9	40
2021	Paper 2	25	80
2020	Paper 1	8	40
2020	Paper 2	25	80

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Calculus	32.3%	19 of 19	6 of 6
Algebra, number and structure	23.7%	19 of 19	6 of 6
Functions, relations and graphs	22.3%	19 of 19	6 of 6
Data analysis, probability and statistics	21.7%	19 of 19	6 of 6

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
4.2	discrete random variables specification of probability distributions for discrete random variables using graphs, tables and probability mass functions; calculation and interpretation of mean, $\mu$ , variance, $\sigma^2$ , and standard deviation of a discrete random variable and their use; Bernoulli trials and the binomial distribution, $\mathrm{Bi}(n,p)$ , as an example of a probability distribution for a discrete random variable; effect of variation in the value(s) of defining parameters on the graph of a given probability mass function for a discrete random variable; calculation of probabilities for specific values of a random variable and intervals defined in terms of a random variable, including conditional probability	Data analysis, probability and statistics	9.0%	18 of 19
4.3	continuous random variables construction of probability density functions from non-negative functions of a real variable; specification of probability distributions for continuous random variables using probability density functions; calculation and interpretation of mean, $\mu$ , variance, $\sigma^2$ , and standard deviation of a continuous random variable and their use; standard normal distribution, $N(0,1)$ , and transformed normal distributions, $N(\mu,\sigma^2)$ , as examples of a probability distribution for a continuous random variable; effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable; calculation of probabilities for intervals defined in terms of a random variable, including conditional probability (the cumulative distribution function may be used but is not required)	Data analysis, probability and statistics	8.6%	15 of 19
2.4	solution of equations of the form $f(x)=g(x)$ over a specified interval, where $f$ and $g$ are functions of the type specified in the ‘Functions, relations and graphs’ area of study, by graphical, numerical and algebraic methods, as applicable	Algebra, number and structure	7.1%	19 of 19
3.3	derivatives of $f(x)\pm g(x)$ , $f(x)\times g(x)$ , $\frac{f(x)}{g(x)}$ and $(f\circ g)(x)$ where $f$ and $g$ are polynomial functions, exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions	Calculus	6.3%	19 of 19
3.10	application of integration to problems involving finding a function from a known rate of change given a boundary condition, calculation of the area of a region under a curve and simple cases of areas between curves, average value of a function and other situations	Calculus	6.3%	18 of 19
1.6	modelling of practical situations using polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions	Functions, relations and graphs	6.1%	12 of 19
2.2	functions and their inverses, including conditions for the existence of an inverse function, and use of inverse functions to solve equations involving exponential, logarithmic, circular and power functions	Algebra, number and structure	6.1%	19 of 19
1.3	transformation from $y=f(x)$ to $y=A f(n(x+b))+c$ , where $A,n,b,$ and $c\in\mathbb{R}$ , $A\neq 0$ , $n\neq 0$ , and $f$ is one of the functions specified above, and the inverse transformation	Functions, relations and graphs	5.0%	19 of 19
3.4	application of differentiation to graph sketching and identification of key features of graphs, including stationary points and points of inflection, and intervals over which a function is strictly increasing or strictly decreasing	Calculus	4.8%	16 of 19
1.2	graphs of the following functions: power functions, $y=x^n$ , $n\in\mathbb{Q}$ ; exponential functions, $y=a^x$ , $a\in\mathbb{R}^+$ , in particular $y=e^x$ ; logarithmic functions, $y=\log_e(x)$ and $y=\log_{10}(x)$ ; and circular functions, $y=\sin(x)$ , $y=\cos(x)$ and $y=\tan(x)$ and their key features	Functions, relations and graphs	4.6%	19 of 19
3.5	identification of local maximum/minimum values over an interval and application to solving optimisation problems in context, including identification of interval endpoint maximum and minimum values	Calculus	4.4%	17 of 19
2.5	solution of literal equations and general solution of equations involving a single parameter	Algebra, number and structure	4.1%	16 of 19

These 12 dot points carry 72.4% of the paper marks between them. Another 14 assessed dot points share the rest, and 0 of the 26 externally assessable dot points have not been assessed in any of these 19 papers. Content that has not appeared is still examinable.

What has moved between papers

Comparing the 2020 to 2022 papers with the 2023 to 2025 papers, one topic has moved by more than 3.0 percentage points.

Topic	2020 to 2022 share	2023 to 2025 share	Movement
Calculus	34.7%	30.6%	down 4.1 points

How the papers are built

Short answer carries 82.8% of the marks across these 19 papers.

Question type	Share of marks	Marks	Parts
Short answer	82.8%	961	580
Multiple choice	17.2%	200	200

Verb	Share of marks	Marks	Parts
show	5.4%	63	42
state	5.2%	60	54
determine	4.3%	50	26
sketch	3.4%	39	15
solve	2.3%	27	10
evaluate	1.9%	22	11
calculate	1.1%	13	7
label	0.9%	11	5

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: Calculus, Algebra, number and structure, Functions, relations and graphs and Data analysis, probability and statistics. For how students actually score on this content, read VCE Mathematical Methods hardest topics, and for the full question bank start at VCE Mathematical Methods.

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.

VCE Mathematical Methods most tested topics

What these papers are

Marks by topic

Marks by dot point

What has moved between papers

How the papers are built

What these percentages do not tell you

Where to practise

Frequently asked questions

Sources

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VCE Mathematical Methods Hardest Topics: Where Students Lose the Most Marks

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