Which VCE Mathematical Methods past paper do students score lowest on?

The 2023 Paper 2, averaging 48.1% across 4,263 marked attempts on AusGrader. The 2023 Paper 2 (NHT) is the highest on 72.7%.

Which VCE Mathematical Methods dot points give the best return on revision time?

4.2 (3.6 marks at risk per 100), 4.3 (3.1 marks at risk per 100) and 2.4 (2.9 marks at risk per 100). Marks at risk combines a dot point's share of paper marks with the marks students drop on it, so it ranks by recoverable marks and not by score alone.

How many attempts is each VCE Mathematical Methods figure based on?

31,503 marked attempts overall, with the per-row count shown in every table. Any cut below 50 attempts is withheld instead of published.

Do these averages show how the VCAA cohort performed?

No. They are AusGrader users' marked attempts, a self-selected group practising when they chose to and often without exam timing. They corroborate what VCAA publishes about this subject and do not replace it.

VCE Mathematical Methods hardest topics

Across 31,503 marked attempts on AusGrader, VCE Mathematical Methods students average 59.6% on questions taken from board external papers. The lowest average of any command verb is solve on 41.7%, and the verb that costs the most marks is determine, which carries 4.3% of the paper against 2.3% for solve. These are self-selected users practising when they chose to, not the VCAA cohort under exam conditions.

How to read these numbers

The figures are AusGrader users' marked attempts, not VCAA results. They corroborate what the board publishes about this subject and do not stand in for it.
Any cut with fewer than 50 attempts is withheld, which on this page is 6 papers, 1 dot point and 18 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the VCE Mathematical Methods study design from any board's external papers, which is why the sample is larger than the 19 VCAA papers alone. The paper table below is the exception and uses VCAA papers only.
Internal assessment and school-uploaded exams are excluded throughout, so these averages differ from the ones on VCE Mathematical Methods performance stats, which count every attempt.

Score by past paper

Year	Paper	Average	Attempts
2025	Paper 1	55.3%	139
2025	Paper 2	53.9%	3,822
2024	Paper 1	69.9%	90
2024	Paper 2	57.2%	3,821
2023	Paper 1	63.4%	95
2023	Paper 2	48.1%	4,263
2023	Paper 2 (NHT)	72.7%	50
2022	Paper 1	63.1%	60
2022	Paper 2	62.6%	4,260
2022	Paper 2 (NHT)	68.9%	112
2021	Paper 1	64.3%	117
2021	Paper 2	62.8%	3,379
2020	Paper 2	52.4%	4,255

The lowest average belongs to the 2023 Paper 2 on 48.1% from 4,263 attempts, and the highest to the 2023 Paper 2 (NHT) on 72.7% from 50 attempts. A paper's average reflects both how hard it was and who chose to sit it, so treat the spread as a guide to which papers make demanding practice.

Score by question type

Question type	Average	Attempts
Multiple choice	58.4%	26,514
Short answer	62.4%	4,989

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Calculus	32.3%	58.6%	11,826	13.4
Algebra, number and structure	23.7%	56.7%	6,624	10.3
Functions, relations and graphs	22.3%	59.0%	8,999	9.1
Data analysis, probability and statistics	21.7%	63.0%	8,294	8.0

Calculus tops the list on 13.4 marks at risk per 100 paper marks, 3.1 ahead of Algebra, number and structure.

The same cut at dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
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	9.0%	60.0%	3,634	3.6
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)	8.6%	63.6%	3,245	3.1
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	7.1%	58.7%	1,553	2.9
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	6.1%	55.2%	1,542	2.7
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	6.3%	58.6%	1,584	2.6
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	6.3%	61.0%	3,362	2.5
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	4.8%	52.4%	1,831	2.3
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	4.4%	48.9%	1,884	2.3
2.5	solution of literal equations and general solution of equations involving a single parameter	4.1%	46.4%	926	2.2
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	6.1%	65.0%	1,781	2.1
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	5.0%	57.5%	3,270	2.1
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	4.6%	64.2%	4,072	1.6

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
determine	4.3%	61.0%	2,093	1.7
state	5.2%	67.6%	255	1.7
solve	2.3%	41.7%	55	1.3
show	5.4%	75.4%	119	1.3
sketch	3.4%	62.6%	56	1.3
evaluate	1.9%	53.3%	163	0.9
express	0.8%	64.6%	75	0.3
calculate	1.1%	77.3%	204	0.3

Solve has the lowest average on the page at 41.7%, and it is not where the marks go. Determine averages 61.0% but carries 4.3% of the paper against 2.3%, so it puts 1.7 marks per 100 at risk against 1.3. Each verb above is practised in the VCE Mathematical Methods question bank, where the marking criteria show what VCAA expects the answer to do.

What this does not measure

Where to practise

Work the priority list from the top: Calculus and Algebra, number and structure first, then the dot points above. Each topic page holds real VCAA questions with marking criteria attached. For what the papers actually cover, read VCE Mathematical Methods most tested topics.

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 hardest topics

How to read these numbers

Score by past paper

Score by question type

The priority list: heavy topics with low scores

The same cut at dot-point level

Which command verbs cost the most marks

What this does not measure

Where to practise

Frequently asked questions

Sources

Keep reading

VCE Mathematical Methods Most Tested Topics: What the VCAA Exams Cover

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