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

Calculus carries 37.7% of the marks across the 21 VCAA papers from 2020 to 2025, ahead of Space and measurement on 25.2%.

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

Short answer carries 83.9% of the marks and multiple choice carries 16.1% of the marks, measured across 21 papers and 1227 marks from 2020 to 2025.

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

Yes. Calculus moved down 7.1 percentage points, Space and measurement moved up 3.2 percentage points and Discrete mathematics moved up 4.0 percentage points between the 2020 to 2022 and 2023 to 2025 papers.

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

21 VCAA external papers from 2020 to 2025, covering 363 questions and 1227 marks. 6.3% of those marks carry no dot-point mapping and sit outside the percentages.

VCE Specialist Mathematics most tested topics

Across the 21 VCAA Specialist Mathematics external papers from 2020 to 2025, Calculus carries 37.7% of the marks against 2.1% for Discrete mathematics, so the paper rewards Calculus more than any other topic. At dot-point level 4.3.2 carries 9.4% of paper marks, and two of the 53 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 93.7% of marks that map to a study design dot point.

Computed from 21 VCAA Specialist Mathematics external papers, 2020 to 2025: 363 questions, 761 question parts and 1227 marks.

Unit, topic and dot-point shares below are of the 1150 marks that map to a dot point, so each of those tables adds to 100%. 235 of the 761 parts are assessed against more than one dot point, and their 398 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)	9	40
2025	Paper 2	26	80
2025	Paper 2 (NHT)	26	75
2024	Paper 1	10	40
2024	Paper 1 (NHT)	10	40
2024	Paper 2	26	80
2024	Paper 2 (NHT)	26	79
2023	Paper 1	10	40
2023	Paper 1 (NHT)	10	40
2023	Paper 2 (NHT)	26	80
2022	Paper 1	10	38
2022	Paper 1 (NHT)	10	40
2022	Paper 2	24	75
2022	Paper 2 (NHT)	26	80
2021	Paper 1	9	40
2021	Paper 1 (NHT)	10	40
2021	Paper 2	26	80
2021	Paper 2 (NHT)	26	80
2020	Paper 1	9	40
2020	Paper 2	25	80

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Calculus	37.7%	21 of 21	6 of 6
Space and measurement	25.2%	20 of 21	6 of 6
Algebra, number and structure	13.4%	20 of 21	6 of 6
Data analysis, probability and statistics	12.3%	19 of 21	5 of 6
Functions, relations and graphs	9.3%	17 of 21	6 of 6
Discrete mathematics	2.1%	9 of 21	3 of 6

Marks by subtopic

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

Subtopic	Share of marks	Papers
Differential calculus and integral calculus	21.0%	21 of 21
Kinematics: rectilinear motion	10.3%	20 of 21
Differential equations	6.4%	17 of 21
Vector calculus	11.1%	16 of 21
Vectors	8.5%	19 of 21
Vector and Cartesian equations	5.6%	16 of 21
Complex numbers	13.4%	20 of 21
Hypothesis testing for a population mean with a sample drawn from a normal distribution of known variance, or for a large sample	4.3%	10 of 21
Distribution of linear combinations of random variables	4.2%	15 of 21
Confidence intervals for the population mean	2.2%	12 of 21
Distribution of the sample mean	1.5%	10 of 21
Logic and proof	2.1%	9 of 21

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
4.3.2	application of differentiation, anti-differentiation and solution of differential equations to rectilinear motion of a single particle, including the different derivative forms for acceleration $a=\frac{d^2x}{dt^2}=\frac{dv}{dt}=v\frac{dv}{dx}=\frac{d}{dx}\left(\frac{1}{2}v^2\right)$	Calculus	9.4%	20 of 21
3.1.2	the $n$ th roots of unity and other complex numbers and their location in the complex plane	Algebra, number and structure	8.0%	15 of 21
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	Calculus	7.1%	21 of 21
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	Space and measurement	6.1%	15 of 21
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	Calculus	5.3%	19 of 21
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	Functions, relations and graphs	5.3%	15 of 21
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 $x\sin(y) + x^2\cos(y) = 1$	Calculus	3.4%	15 of 21
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	Space and measurement	3.3%	13 of 21
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	Calculus	3.2%	11 of 21
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	Algebra, number and structure	3.1%	12 of 21
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	Space and measurement	3.1%	16 of 21
4.2.4	solution of simple differential equations of the form $\frac{dy}{dx}=f(x)$ , $\frac{dy}{dx}=g(y)$ and in general differential equations of the form $\frac{dy}{dx}=f(x)g(y)$ using separation of variables and differential equations of the form $\frac{d^2y}{dx^2}=f(x)$	Calculus	2.7%	15 of 21

These 12 dot points carry 60.0% of the paper marks between them. Another 39 assessed dot points share the rest, and 2 of the 53 externally assessable dot points have not been assessed in any of these 21 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, three topics have moved by more than 3.0 percentage points.

Topic	2020 to 2022 share	2023 to 2025 share	Movement
Calculus	41.5%	34.4%	down 7.1 points
Space and measurement	23.5%	26.7%	up 3.2 points
Discrete mathematics	0.0%	4.0%	up 4.0 points

How the papers are built

Short answer carries 83.9% of the marks across these 21 papers.

Question type	Share of marks	Marks	Parts
Short answer	83.9%	1029	563
Multiple choice	16.1%	198	198

Verb	Share of marks	Marks	Parts
show	9.9%	122	71
sketch	6.7%	82	40
solve	2.9%	35	12
express	2.6%	32	21
label	2.6%	32	16
evaluate	1.6%	20	6
state	1.6%	20	14
prove	1.5%	19	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, Space and measurement, Algebra, number and structure, Data analysis, probability and statistics, Functions, relations and graphs and Discrete mathematics. For how students actually score on this content, read VCE Specialist Mathematics hardest topics, and for the full question bank start at VCE Specialist 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.

VCE Specialist Mathematics most tested topics

What these papers are

Marks by topic

Marks by subtopic

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 Specialist Mathematics Hardest Topics: Where Students Lose the Most Marks

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