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VCE · VCE Units 3 & 4 · official past papers

Mathematical Methods — past papers by topic

Every official VCAA exam and examiner report 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.

Papers and examiner reports open on the official VCAA website — they stay official and up to date. Question descriptions below are our own; we never republish exam content. Prefer to be walked through it? Book a tutor →

Mathematical Methods (CAS) SD 2006–2015 · 2006–2015SD 2016–2022 · 2016–2022SD 2023–2027 (current) · 2023–2027

Official papers & examiner reports, year by year

YearStudy designOfficial paper(s)Examiner report
2025SD 2023–2027 (current)Exam 1 ↗ · Exam 2 ↗ · Exam 1 Assessment Guide ↗ · Exam 2 Assessment Guide ↗Report ↗
2024SD 2023–2027 (current)Exam 1 ↗ · Exam 2 ↗Report ↗
2023SD 2023–2027 (current)Exam 1 ↗ · Exam 2 ↗Report ↗
2022SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2021SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2020SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2019SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2018SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2017SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2016SD 2016–2022Exam 1 ↗ · Exam 2 ↗Report ↗
2015Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗
2014Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗
2013Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗
2012Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗
2011Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗
2010Mathematical Methods (CAS) SD 2006–2015Exam 1 ↗ · Exam 2 ↗Report ↗

All data was verified directly against official VCAA sources (vcaa.vic.edu.au) using WebFetch on the live index page and curl HTTP checks (status 200 + correct content-type: application/pdf or the Word MIME type) on every URL listed above. Two full 2024 exam PDFs were read in full (Exam 1: 8 questions/40 marks; Exam 2: Section A 20 MCQ/20 marks + Section B 5 questions/60 marks) to produce the questions[] entries — every desc is an original one-line paraphrase, never copied question text. URL pattern notes: (1) years 2006-2024 resolve at https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/{year}/{filename} — the shorter/legacy form https://www.vcaa.vic.edu.au/Documents/exams/mathematics/... returns HTTP 200 but is actually a client-side JS app shell (not the PDF), so it was NOT used; (2) 2025 files resolve under a date-stamped folder, e.g. https://www.vcaa.vic.edu.au/sites/default/files/2025-11/... ; both patterns were confirmed live via curl. Study design eras: current SD is confirmed directly from the official docx (https://www.vcaa.vic.edu.au/Documents/vce/mathematics/2023MathematicsSD.docx, downloaded and parsed) as "Units 1-4: 1 January 2023 - 31 December 2027." The 2016-2022 era boundary is corroborated by multiple independent sources (VCAA-hosted PDF mirrors, study-notes sites) describing "Accreditation Period 2016-2022" for the prior Mathematics Study Design; VCAA's own past-exams page confirms 2016 as the first year the subject dropped the "(CAS)" suffix and filename convention (2015 and earlier use "mmcas1/mmcas2" filenames; 2016 onward use "MM1/MM2"), which is used here as the practical era boundary for badging. This pre-2016 era boundary (2006-2015) is inferred from the filename/branding change and is the least independently corroborated element — flagged as the main assumption in this dataset. Topics[] and their subtopics are extracted essentially verbatim from the official Units 3 and 4 Areas of Study text in the current (2023-2027) study design docx — wording condensed for list format but drawn directly from the source, not invented. Coverage: years[] spans 2010-2025 (16 years) as the "most recent ~10" requirement, but I extended back further (through 2006) since VCAA's own index page listed papers that far back and all resolved live; only 2010-2025 are included in years[] to match the "most recent ~10" instruction while the sdEras[] correctly spans the full history back to 2006 for badging older years if the caller wants to extend the list later (2006-2009 papers were all verified live at the same URL pattern and can be added on request). Gaps/anomalies: no VCAA notation was found describing 2020 as "cancelled" — Victorian VCE written exams that year were delayed (started 9 Nov instead of the normal late-Oct date) but ran as normal, confirmed via an independent web search of Victorian government sources; this is noted in the 2020 year entry rather than treated as a missing-paper gap. No NHT (Northern Hemisphere Timetable) exam papers exist for Mathematical Methods on the VCAA site — NHT is only offered for a small set of language/other subjects, so none were fabricated. No sample/specimen exam was included in years[] since it is not a genuine annual sitting, though the page does host "Sample questions for written examination 1/2" separately from the current specifications.

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Functions, relations and graphs · 18 mapped questions

Graphs of polynomial functions and their key features

Graphs of power, exponential, logarithmic and circular functions and their key features

Transformations of the plane applied to these functions and their inverse transformations

Relation between the graph of an original function and a transformed function, including families of transformed functions

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Graphs of sum, difference, product and composite functions of the specified function types

Modelling practical situations using polynomial, power, circular, exponential and logarithmic functions and simple piecewise (hybrid) functions

Algebra, number and structure · 16 mapped questions

Solution of polynomial equations with real coefficients of degree n, including numerical solutions

Functions and their inverses, including conditions for existence of an inverse function

Composition of functions

Solution of equations f(x) = g(x) over a specified interval by graphical, numerical and algebraic methods

Solution of literal equations and general solution of equations involving a single parameter

Solution of simple systems of simultaneous linear equations, including no-solution and infinite-solution cases

Calculus · 30 mapped questions

Graphical treatment of limits, continuity and differentiability

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Derivatives of polynomial, power, exponential, logarithmic and circular functions, and of sums, products, quotients and composites of these

Application of differentiation to graph sketching, key features and optimisation problems

Anti-derivatives of polynomial and other standard functions

Definite integrals, the trapezium rule, and the fundamental theorem of calculus

Application of integration to area under/between curves, average value of a function, and rates of change problems

Data analysis, probability and statistics · 20 mapped questions

Discrete random variables: probability mass functions, mean, variance and standard deviation

Bernoulli trials and the binomial distribution

Continuous random variables: probability density functions, mean, variance and standard deviation

The normal distribution, including standard and transformed normal distributions

Statistical inference: sample proportions, distribution of sample proportions and simulation

Approximate confidence intervals for a population proportion, including the 95% confidence interval

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