Which VCE Specialist Mathematics past paper do students score lowest on?

The 2021 Paper 2, averaging 51.5% across 3,885 marked attempts on AusGrader. The 2024 Paper 2 is the highest on 62.5%.

Which VCE Specialist Mathematics dot points give the best return on revision time?

4.3.2 (4.6 marks at risk per 100), 3.1.2 (3.3 marks at risk per 100) and 4.1.7 (3.0 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 Specialist Mathematics figure based on?

19,387 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 Specialist Mathematics hardest topics

Across 19,387 marked attempts on AusGrader, VCE Specialist Mathematics students average 58.9% on questions taken from board external papers. The lowest average of any command verb is evaluate on 39.0%, and the verb that costs the most marks is show, which carries 9.9% of the paper against 1.6% for evaluate. 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 13 papers, 11 dot points and 16 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the VCE Specialist Mathematics study design from any board's external papers, which is why the sample is larger than the 21 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 Specialist Mathematics performance stats, which count every attempt.

Score by past paper

Year	Paper	Average	Attempts
2025	Paper 2	61.5%	4,014
2024	Paper 2	62.5%	3,486
2022	Paper 2	57.4%	2,658
2021	Paper 2	51.5%	3,885
2020	Paper 2	60.3%	3,271

The lowest average belongs to the 2021 Paper 2 on 51.5% from 3,885 attempts, and the highest to the 2024 Paper 2 on 62.5% from 3,486 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
Short answer	58.1%	1,342
Multiple choice	59.1%	18,045

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Calculus	37.7%	58.9%	7,161	15.5
Space and measurement	25.2%	61.2%	5,433	9.8
Algebra, number and structure	13.4%	56.8%	2,804	5.8
Data analysis, probability and statistics	12.3%	53.0%	1,759	5.8
Functions, relations and graphs	9.3%	56.2%	1,729	4.1
Discrete mathematics	2.1%	66.4%	812	0.7

Calculus tops the list on 15.5 marks at risk per 100 paper marks, 5.7 ahead of Space and measurement.

The same cut at subtopic level

Subtopic	Share of marks	Average	Attempts	Marks at risk
Differential calculus and integral calculus	21.0%	57.0%	2,909	9.0
Complex numbers	13.4%	56.8%	2,804	5.8
Kinematics: rectilinear motion	10.3%	53.6%	1,922	4.8
Vector calculus	11.1%	58.3%	1,018	4.6
Vectors	8.5%	61.8%	3,997	3.3
Differential equations	6.4%	65.6%	2,399	2.2
Distribution of linear combinations of random variables	4.2%	47.7%	1,004	2.2
Vector and Cartesian equations	5.6%	62.2%	1,112	2.1
Hypothesis testing for a population mean with a sample drawn from a normal distribution of known variance, or for a large sample	4.3%	69.8%	205	1.3
Confidence intervals for the population mean	2.2%	58.1%	269	0.9
Logic and proof	2.1%	66.4%	812	0.7
Distribution of the sample mean	1.5%	53.5%	285	0.7

The same cut at dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
4.3.2	application of differentiation, anti-differentiation and solution of differential equations to rectilinear motion of a single particle, including the different derivative forms for acceleration $a=\frac{d^2x}{dt^2}=\frac{dv}{dt}=v\frac{dv}{dx}=\frac{d}{dx}\left(\frac{1}{2}v^2\right)$	9.4%	50.9%	1,518	4.6
3.1.2	the $n$ th roots of unity and other complex numbers and their location in the complex plane	8.0%	58.8%	1,618	3.3
4.1.7	application of integration, areas of regions bounded by curves, arc lengths for parametrically determined curves, surface area of solids of revolution, volumes of solids of revolution of a region about either coordinate axis	7.1%	57.3%	1,330	3.0
5.3.3	differentiation and anti-differentiation of a vector function with respect to time and applying vector calculus to motion in a plane and in three dimensions	6.1%	60.5%	931	2.4
2.0.2	graphs of rational functions of low degree, their asymptotic behaviour, and the nature and location of stationary points and points of inflection	5.3%	60.2%	1,064	2.1
4.1.4	applications of chain rule to related rates of change and implicit differentiation; for example, implicit differentiation of the relations $x^2 + y^2 = 9$ , $3xy^2 = x + y$ and $x\sin(y) + x^2\cos(y) = 1$	3.4%	40.3%	304	2.0
4.1.3	second derivatives, use of notations $f''(x)$ and $\frac{d^2y}{dx^2}$ , and their application to the analysis of graphs of functions, including points of inflection and concavity	3.2%	43.6%	441	1.8
3.1.1	De Moivre’s theorem, proof for integral powers, powers and roots of complex numbers in polar form, and their geometric representation and interpretation	3.1%	42.2%	664	1.8
4.1.5	techniques of anti-differentiation and for the evaluation of definite integrals anti-differentiation of $\frac{1}{x}$ to obtain $\log_e\\|x\\|$ ; anti-differentiation of $\frac{1}{\sqrt{a^2-x^2}}$ and $\frac{a}{a^2+x^2}$ for $a>0$ by recognition that they are derivatives of corresponding inverse circular functions; use of the substitution $u=g(x)$ to anti-differentiate expressions; use of the trigonometric identities $\sin^2(ax)=\frac{1}{2}(1-\cos(2ax))$ and $\cos^2(ax)=\frac{1}{2}(1+\cos(2ax))$ in anti-differentiation techniques; anti-differentiation using partial fractions of rational functions; integration by parts	5.3%	66.6%	825	1.8
5.3.1	position vector as a function of time and sketching the corresponding path given the function, including circles, ellipses and hyperbolas in Cartesian or parametric forms	3.3%	54.2%	270	1.5
6.1.2	for $n$ independent random variables $X_1, X_2, \ldots, X_n$ and real numbers $a_1, a_2, \ldots, a_n$ $E(a_1X_1+a_2X_2+\cdots+a_nX_n)=a_1E(X_1)+a_2E(X_2)+\cdots+a_nE(X_n)$ ; $\mathrm{Var}(a_1X_1+a_2X_2+\cdots+a_nX_n)=a_1^2\mathrm{Var}(X_1)+a_2^2\mathrm{Var}(X_2)+\cdots+a_n^2\mathrm{Var}(X_n)$	2.6%	48.4%	1,003	1.3
5.1.5	scalar (dot) product of two vectors, deduction of dot product for the $\mathbf{i}$ , $\mathbf{j}$ and $\mathbf{k}$ vector system and its use to find scalar resolute and vector resolute	3.1%	60.9%	2,120	1.2
2.0.3	graphs of simple quotient functions, their asymptotic behaviour, and the nature and location of stationary points and points of inflection	2.4%	58.7%	1,040	1.0

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
show	9.9%	72.0%	90	2.8
evaluate	1.6%	39.0%	57	1.0
prove	1.5%	56.9%	90	0.7
determine	1.5%	57.1%	584	0.6
state	1.6%	76.8%	51	0.4

Evaluate has the lowest average on the page at 39.0%, and it is not where the marks go. Show averages 72.0% but carries 9.9% of the paper against 1.6%, so it puts 2.8 marks per 100 at risk against 1.0. Each verb above is practised in the VCE Specialist Mathematics 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 Space and measurement 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 Specialist Mathematics most tested topics.

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