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VCE · VCE Units 3 & 4 · official past papers

VCE Specialist Mathematics past exams 2016–2025, by year and topic

The official VCAA exams, marking guides and examiner reports we index, organised by topic and subtopic and labelled with the study design it was written under. Open the official paper, work the question in your own workspace, or bring a tutor into it live.

Index last synced 19 August 2026.

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ATARMAxxing indexes 20 official VCAA Specialist Mathematics papers from 2016 to 2025, with 15 questions mapped to 6 areas of study. Every paper opens on the VCAA website.

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SD 2016–2022 · 2016–2022SD 2023–current · 2023–present

VCE Specialist Mathematics exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016. Open the official VCAA papers, with marking guidance where available.

Year	Study design	Official paper(s)	Marking guidance
2025 VCE Specialist Mathematics exam	SD 2023–current	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2024 VCE Specialist Mathematics exam	SD 2023–current	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2023 VCE Specialist Mathematics exam	SD 2023–current	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2022 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2021 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2020 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2019 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2018 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2017 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2016 VCE Specialist Mathematics exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗

20 official papers across 10 years (2016–2025), 10 with marking guidance, published by VCAA. These span more than one study design; the most recent is SD 2023–current. Earlier papers may cover material that has since changed.

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Discrete mathematics · 1 mapped question

Logic and proof

2025SD 2023–currentExam 1 Q74 marksProving a closed-form summation identity by mathematical induction.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Logic and proof: conjectures, connectives, quantifiers, examples and counter-examples · Proof techniques: direct proof, proof by cases, proof by contradiction, proof by contrapositive · Proof by mathematical induction — question-level mapping in progress; the year table above links every official paper.

Functions, relations and graphs · 2 mapped questions

Rational functions and graphs of rational/quotient functions

2025SD 2023–currentExam 1 Q96 marksSimplifying a rational function algebraically, finding a value making a piecewise extension continuous at a point, and sketching the resulting graph with labelled asymptotes.Official paper ↗Marking guidance ↗Check tutors for this question →

Graphs of rational functions of low degree

2025SD 2023–currentExam 2 Section B Q110 marksSketching a cubic-over-quadratic rational function with labelled features, computing a solid-of-revolution volume from it, and analysing how a parameter affects stationary points and asymptotes in a related family of curves.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Rational functions and expression as sums of partial fractions · Graphs of rational functions of low degree: asymptotic behaviour, stationary points, points of inflection · Graphs of simple quotient functions and their key features — question-level mapping in progress; the year table above links every official paper.

Algebra, number and structure · 2 mapped questions

Complex numbers

2025SD 2023–currentExam 1 Q85 marksPlotting a complex number and its conjugate on an Argand diagram, then factorising and fully solving a quadratic complex polynomial given one known root.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2023–currentExam 2 Section B Q210 marksSketching complex-number loci on the Argand plane, algebraically converting one locus to Cartesian form, finding intersection points of two loci, and computing a circular segment area involving those points.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Complex numbers: Cartesian and polar (cis) form, De Moivre's theorem · Roots of unity and roots of complex numbers, geometric representation · Factorisation of polynomials over C and the fundamental theorem of algebra · Solving polynomial equations over C, conjugate root theorem — question-level mapping in progress; the year table above links every official paper.

Calculus · 4 mapped questions

Differential calculus and integral calculus

2025SD 2023–currentExam 1 Q14 marksFinding the tangent line to an implicitly defined exponential curve at a given point.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2023–currentExam 1 Q64 marksComputing the volume of a solid of revolution generated by rotating a region under an inverse-tangent-type curve about the x-axis, expressed in exact form.Official paper ↗Marking guidance ↗Check tutors for this question →

Kinematics: rectilinear motion

2025SD 2023–currentExam 1 Q35 marksDeriving a displacement expression from a velocity function via integration, finding initial acceleration, and solving for an unknown parameter using a second particle's relative position.Official paper ↗Marking guidance ↗Check tutors for this question →

Differential equations

2025SD 2023–currentExam 2 Section B Q310 marksModelling a mixing-tank salt-concentration problem as a differential equation, approximating a solution with Euler's method, solving the equation analytically by separation of variables, and finding a long-run/threshold value.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Differential calculus: derivatives of inverse circular functions, second derivatives, concavity, implicit differentiation, related rates · Integral calculus: anti-differentiation techniques, partial fractions, integration by parts, substitution · Applications of integration: area, arc length, volumes and surface areas of solids of revolution · Differential equations: formulation, logistic equation, direction fields, separation of variables, Euler's method · Kinematics: rectilinear motion using velocity-time graphs, differentiation, anti-differentiation and differential equations — question-level mapping in progress; the year table above links every official paper.

Space and measurement · 4 mapped questions

Vector and Cartesian equations

2025SD 2023–currentExam 1 Q23 marksDetermining the point of intersection of two skew/non-parallel 3D vector lines given their point-direction forms.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2023–currentExam 2 Section B Q510 marksFinding the intersection point of three planes, the line of intersection of two of them, the shortest distance from a point to a plane, and unknown constants for a parallel-plane family at a specified distance.Official paper ↗Marking guidance ↗Check tutors for this question →

Vector calculus

2025SD 2023–currentExam 1 Q54 marksFinding unknown parameters in two particles' vector position functions given a collision condition, a perpendicular-velocities condition, and an equal-acceleration-magnitude condition.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2023–currentExam 2 Section B Q410 marksAnalysing a particle's vector-valued position function to find its starting point, direction, return time, a speed expression via calculus, maximum speed, and the arc length traced over a given interval.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Vectors: addition, scalar multiplication, linear dependence/independence, dot product, cross product · Vector proofs of geometric results · Vector and Cartesian equations of lines and planes · Vector calculus: position vectors as functions of time, motion in two and three dimensions — question-level mapping in progress; the year table above links every official paper.

Data analysis, probability and statistics · 2 mapped questions

Distribution of the sample mean

2025SD 2023–currentExam 1 Q45 marksUsing integration to establish the expected value of a continuous random variable (waiting time), then finding a probability for a sample mean using the normal approximation.Official paper ↗Marking guidance ↗Check tutors for this question →

Distribution of the sample mean / Hypothesis testing for a population mean

2025SD 2023–currentExam 2 Section B Q610 marksDetermining the sampling distribution of a sample mean for a normally distributed quantity and using it for further inferential calculations.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Distribution of linear combinations of random variables · Confidence intervals for the population mean · Hypothesis testing for a population mean — question-level mapping in progress; the year table above links every official paper.

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