Study design and exam specifications

Compiled 15 September 2026. Written for students targeting a study score of 45+, and for the people building study material for them.

Every substantive claim below is tagged with its source. Where the published source is itself ambiguous, incomplete, or silent, that is stated explicitly rather than papered over. Nothing here is inferred key knowledge.

---

0. Sources, and what they can and cannot tell you

0.1 Corpus data-quality notes — read these before trusting any number

• Four corpus text files are empty (16–32 bytes, header only) and could not be used: Documents_exams_mathematics_2024_2024MM1-w.txt, Documents_exams_mathematics_2024_2024MM2-w.txt, 2025-05_2025-NHT-mathsmethods1.txt, 2025-05_2025-NHT-mathsmethods2.txt. The 2024 November papers were reconstructed from the 2024 reports and assessment guides instead.
• 2011 is unusable. Both 2011 reports were OCR'd from degraded PDFs; question labels are duplicated and mark distributions are missing for roughly half the paper. Every table in §10 excludes 2011. Do not quote 2011 statistics from this corpus.
• 2008 and 2009 Exam 2 are partially extracted. Only 8 of 22 multiple-choice questions were recovered for 2008 and 17 of 22 for 2009. The Section 2 data for both years is complete. Paper-level percentages for those two years are therefore computed over 66 and 75 marks respectively, not 80.
• 2022 and 2024 Exam 2 each total 79 marks in [QJSON], not 80 — one mark is missing from the extraction in each. The effect on a paper mean is under 1%.
• NHT papers carry no state statistics. The NHT (Northern Hemisphere Timetable) cohort is small enough that VCAA publishes answers but not mark distributions. [QJSON] therefore has pct: null for every 2024 NHT and 2025 NHT entry. NHT papers are still valuable as content evidence — they are set by the same panel to the same specifications — but they can tell you nothing about difficulty.
• VCAA stopped publishing paper means and cohort sizes after 2011. The 2006–2011 assessment reports state the cohort size, the paper mean, the median, and the percentage of students scoring 90%+. From 2012 the reports give only per-question mark distributions. Every paper mean in §10 for 2012 onwards is reconstructed from those per-question distributions. §10.2 validates that reconstruction against the four years where VCAA published a figure; the method is accurate to within about 0.7 of a mark on a 40-mark paper and 0.7 of a mark on an 80-mark paper.

---

1. The shape of the course

1.1 What Units 3 and 4 are

[SD], verbatim:

"Mathematical Methods Units 3 and 4 extend the introductory study of simple elementary functions of a single real variable, to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. Units 3 and 4 consist of the areas of study 'Algebra, number and structure', 'Data analysis, probability and statistics', 'Calculus', and 'Functions, relations and graphs', which must be covered in progression from Unit 3 to Unit 4, with an appropriate selection of content for each of Unit 3 and Unit 4. Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2, and will be drawn on, as applicable, in the development of related content from the areas of study, and key knowledge and key skills for the outcomes of Mathematical Methods Units 3 and 4."

Note the phrase "which must be covered in progression from Unit 3 to Unit 4". There is no module choice and no optional content in Mathematical Methods. All four areas of study are compulsory and all of them are examinable in both papers.

One phrase that appeared in the 2016–2022 design has been dropped: [OLDSD] said "Mathematical Methods Units 3 and 4 are completely prescribed and extend the introductory study…". The 2023 design removes "completely prescribed". In practice nothing changed — the course is still fully prescribed — but the wording change matters if you are reading old advice.

1.2 The Unit 3 / Unit 4 split

This is the part of the study design most often misquoted. [SD] does not prescribe the split. It says what a split "would typically" look like:

"For Unit 3 a selection of content would typically include the areas of study 'Functions, relations and graphs' and 'Algebra, number and structure', applications of derivatives and differentiation, and identifying and analysing key features of the functions and their graphs from the 'Calculus' area of study. For Unit 4, a corresponding selection of content would typically consist of remaining content from 'Functions, relations and graphs', 'Algebra, number and structure' and 'Calculus' areas of study, and the study of random variables, discrete and continuous probability distributions, and the distribution of sample proportions from the 'Data analysis, probability and statistics' area of study. For Unit 4, the content from the 'Calculus' area of study would be likely to include the treatment of anti-differentiation, integration, the relation between integration and the area of regions specified by lines or curves described by the rules of functions, and simple applications of this content, including to probability distributions of continuous random variables."

So the typical split is:

Two consequences that matter for exam preparation:

1. The exams do not respect the split. [SPEC] says both examinations "will cover all areas of study". There is no Unit 3 section and no Unit 4 section in either paper. A Section B question routinely moves from a Unit 3 graphing task into a Unit 4 integration task inside the same question — see 2023 Exam 2 Section B Question 3, which sketches h(x) = 2ˣ − x², finds its point of inflection, identifies where it is strictly decreasing, and then applies Newton's method, all in one 12-mark question.
2. Statistics is the one area you can be confident sits entirely in Unit 4. It is also the area most likely to be taught last and revised least. Section 10 shows that statistics questions produce some of the widest mark spreads in Exam 2.

[SD] adds a requirement about progression that schools must honour and that shapes SAC design:

"The selection of content from the areas of study should be constructed so that there is a development in the complexity and sophistication of problem types and mathematical processes used (modelling, transformations, graph sketching and equation solving) in application to contexts related to these areas of study. There should be a clear progression of skills and knowledge from Unit 3 to Unit 4 in an area of study."

1.3 Assumed knowledge

[SD]:

"In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algorithms, algebraic manipulation, equations, graphs, differentiation, anti-differentiation, integration and inference, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable."

Two words in that paragraph are new in 2023 relative to [OLDSD]: "algorithms" and "geometric constructions". The 2016–2022 version of the same sentence read "…sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation, and integration and inference…" — no algorithms. The insertion of "algorithms" into the assumed-knowledge paragraph is the first signal of the computational-thinking strand that runs through Outcome 2 and Outcome 3 in the current design.

Assumed knowledge is genuinely examinable. The 2007 Exam 1 report [RPT] makes this explicit:

"Students need also to be reminded that material from Units 1 and 2 of the study can be drawn on; Question 6, which related to basic probability, was an example of this. Question 11b. on conditional probability was another example and this area is often seen in either examination 1 or 2 questions."

Conditional probability, index and logarithm laws, exact circular-function values, and the null factor law are all Units 1–2 material that reappears every year without being flagged.

1.4 Assessment weighting

[SD] and [SPEC] agree:

[SPEC], verbatim: "Examination 1 will contribute 20 per cent to the study score. Examination 2 will contribute 40 per cent to the study score."

This is a change from the 2016–2022 design, where [OLDSD] set SAC at 17% per unit (34% total), Examination 1 at 22% and Examination 2 at 44%. The externally assessed share therefore fell from 66% to 60% in 2023.

Exam 2 is worth exactly twice Exam 1. A mark on Exam 2 is worth half a mark on Exam 1 in study-score terms only because Exam 2 has twice as many marks (80 vs 40) for twice the weight — so, per raw mark, the two papers are worth the same. What differs is the total: 40 marks of technology-free work carries 20% of your score, and 80 marks of technology-active work carries 40%.

1.5 School-assessed Coursework structure

[SD] prescribes the SAC forms exactly.

Unit 3 — 50 marks, one task:

"Application task. A function and calculus-based mathematical investigation of a practical or theoretical context involving content from two or more areas of study, with the following three components of increasing complexity:
- introduction of the context through specific cases or examples
- consideration of general features of the context
- variation or further specification of assumption or conditions involved in the context to focus on a particular feature or aspect related to the context.

The application task is to be of 4–6 hours' duration over a period of 1–2 weeks."

Marks: Outcome 1 = 15, Outcome 2 = 20, Outcome 3 = 15.

Unit 4 — 50 marks, two tasks:

"One of the modelling or problem-solving tasks is to address the Data analysis, probability and statistics area of study. Each modelling or problem-solving task is to be of 2–3 hours' duration over a period of 1 week."

Marks: Outcome 1 = 15, Outcome 2 = 20, Outcome 3 = 15.

Note that both units carry the same 50 marks and the same 20% weighting, and that in both units Outcome 2 carries the largest share (20 of 50). That is the investigative/modelling outcome. It is also the outcome [SPEC] says Examination 2 emphasises. If you are aiming at 45+, the Outcome 2 marks in a SAC and the Section B marks in Exam 2 reward the same thing: formulating a problem, choosing a method, and communicating the reasoning.

---

2. Area of Study 1 — Functions, relations and graphs

2.1 What the study design says

[SD] topic overview, verbatim:

"In this area of study students cover transformations of the plane and the behaviour of some elementary functions of a single real variable, including key features of their graphs such as axis intercepts, stationary points, points of inflection, domain (including maximal, implied or natural domain), co-domain and range, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is to be explored in a variety of modelling contexts and theoretical investigations."

That last clause changed in 2023. [OLDSD] read "The behaviour of these functions and their graphs is to be linked to applications in practical situations." The 2023 wording — "explored in a variety of modelling contexts and theoretical investigations" — licenses the abstract, parameter-driven questions that have dominated the hardest multiple-choice items since 2023.

The content dot points, verbatim from [SD] (equations recovered from the embedded objects):

This area of study includes:
- graphs of polynomial functions and their key features
- graphs of the following functions: power functions, y = xⁿ, n ∈ Q; exponential functions, y = aˣ, a ∈ R, in particular y = eˣ; logarithmic functions, y = logₑ(x) and y = log₁₀(x); and circular functions, y = sin(x), y = cos(x) and y = tan(x) and their key features
- transformation from y = f(x) to y = A f(n(x + b)) + c, where A, n, b and c ∈ R, A, n ≠ 0, and f is one of the functions specified above, and the inverse transformation
- the relation between the graph of an original function and the graph of a corresponding transformed function (including families of transformed functions for a single transformation parameter)
- graphs of sum, difference, product and composite functions involving functions of the types specified above (not including composite functions that result in reciprocal or quotient functions)
- modelling of practical situations using polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions.

2.2 The constraints hiding in that list

Four boundary conditions in that list are load-bearing and are where students lose marks:

1. n ∈ Q for power functions. Rational exponents, so x^(1/3), x^(−2), x^(3/2) are all in. Irrational exponents are not.
2. A, n ≠ 0. The transformation parameters for dilation and reflection cannot be zero; b and c can be.
3. "not including composite functions that result in reciprocal or quotient functions." You can be asked for f(g(x)) where the result is, say, logₑ(x² + 1). You cannot be asked for a composite that produces 1/(x² + 1). Note that this restriction applies to composites only. Quotients themselves are explicitly in scope for differentiation — the quotient rule is in the Calculus area of study and on the formula sheet. The restriction is about what a composite may evaluate to, not about what functions exist.
4. "simple piecewise (hybrid) functions." Hybrid functions are in. They appear most often as probability density functions — see [SAMP] Exam 2 sample multiple-choice Question 4, a two-piece hybrid pdf where you must solve Pr(X ≤ a) = 5/8.

2.3 What this looks like in the exams

The transformation form y = A f(n(x + b)) + c is the single most reliable annual appearance in the subject, and it is also where the state most reliably fails. 2024 Exam 1 Question 5b asked students to describe a sequence of transformations; [QJSON] records 2% of the state earning full marks on a 2-mark part. The report [RPT]:

"This question was not responded to well. Many students were able to list one transformation, usually the dilation; however, frequently the incorrect axis or direction was specified. Students are urged to use the correct language when referring to transformations."

and, in the general comments:

"Students need to use correct mathematical language when describing transformations of graphs and students are encouraged to follow the study design for the correct expression of these descriptions. For dilations, students should be familiar with both 'parallel to an axis' and 'from an axis' descriptions."

2025 Exam 2 multiple-choice Question 20 is the same content in reverse: given f(x) = aˣ and g(x) = a²ˣ², identify which of four sequences of transformations does not produce g from f. Sum/difference/product/composite graphs turn up as sketching tasks — 2023 Exam 2 Section B Question 3 is built around h(x) = 2ˣ − x², a difference of an exponential and a polynomial.

---

3. Area of Study 2 — Algebra, number and structure

3.1 What the study design says

[SD] overview, verbatim:

"In this area of study students cover the algebra of functions, including composition of functions, inverse functions and the solution of equations. They also study the identification of appropriate solution processes for solving equations, and systems of simultaneous equations, presented in various forms. Students also cover recognition of equations and systems of equations that are solvable using inverse operations or factorisation, and the use of graphical and numerical approaches for problems involving equations where exact value solutions are not required, or which are not solvable by other methods. This content is to be incorporated as applicable to the other areas of study."

Content dot points, verbatim:

This area of study includes:
- solution of polynomial equations with real coefficients of degree n having up to n real solutions, including numerical solutions
- 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
- composition of functions, where f composite g, f ∘ g, is defined by (f ∘ g)(x) = f(g(x)) given rg ⊆ df
- 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
- solution of literal equations and general solution of equations involving a single parameter
- solution of simple systems of simultaneous linear equations, including consideration of cases where no solution or an infinite number of possible solutions exist (geometric interpretation only required for two equations in two variables).

3.2 What changed here in 2023 — and it is a lot

This is the area of study that was rewritten most aggressively.

Removed in 2023. [OLDSD] contained a dot point that no longer exists:

"use of simple functional relations such as f(x + k) = f(x), f(xⁿ) = n f(x), f(x) + f(−x) = 0, f(xy) = f(x)f(y), to characterise properties of functions including periodicity and symmetry, and to specify algebraic equivalence, including the exponent and logarithm laws"

and a matching Outcome 1 key-knowledge point, "functional relations that describe properties, symmetry and equivalence". Both are gone from the 2023 design. Functional-relation questions were a recurring multiple-choice type — [PAPERS] 2015 Exam 2 Question 18 is the canonical example: "For which one of the following functions is the equation f(x + y) − f(x − y) = 4 f(x) f(y) true for all x ∈ R and y ∈ R?" That question type is no longer in scope. If you are drilling pre-2023 multiple choice, skip these.

Also removed: "review of algebra of polynomials, equating coefficients". Equating coefficients survives in practice as a technique — you still need it to solve, say, a "show that" question about a cubic — but it is no longer a named dot point.

Added in 2023: "including numerical solutions" on the polynomial dot point. This is the hook that brings Newton's method into the course (the algorithm itself is named in the Outcome 1 key skills; see §6.1).

Retained, and now examined much harder: simultaneous linear equations with no solution or infinitely many solutions. This dot point existed in [OLDSD] too, but it was rarely examined before 2023. Since 2023 it has become a fixture. [SAMP] Exam 1 sample Question 4 is exactly this — "Find the values of a and b for which the simultaneous equations have no solutions" — and [SAMP] Exam 2 sample multiple-choice Question 1 goes further, asking for the general solution of a 3-variable, 2-equation system in parameter form (x = k, y = ½(k − 3), z = k − 7), which is beyond what the pre-2023 exams ever asked. In the live papers, 2025 Exam 2 multiple-choice Question 4 asks for the values of k for which kx − 3y = k + 2, 2x + (2k − 1)y = 6 + 2k has no real solutions.

Note the parenthesis in the dot point: "geometric interpretation only required for two equations in two variables". You can be asked to interpret a 2×2 system as two lines that are parallel or coincident. You cannot be asked to interpret a 3-variable system as planes.

---

4. Area of Study 3 — Calculus

4.1 What the study design says

[SD] overview, verbatim:

"In this area of study students cover graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations."

Content dot points, verbatim:

This area of study includes:
- deducing the graph of the derivative function from the graph of a given function and deducing the graph of an anti-derivative function from the graph of a given function
- derivatives of xⁿ for n ∈ Q, eˣ, logₑ(x), sin(x), cos(x) and tan(x)
- derivatives of f(x) ± g(x), f(x) × g(x), f(x)/g(x) and (f ∘ g)(x) where f and g are polynomial functions exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions
- 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
- 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
- anti-derivatives of polynomial functions and functions of the form f(ax + b) where f is xⁿ, for n ∈ Q, eˣ, sin(x), cos(x) and linear combinations of these
- informal consideration of the definite integral as a limiting value of a sum involving quantities such as area under a curve and approximation of definite integrals using the trapezium rule
- anti-differentiation by recognition that F′(x) = f(x) implies ∫f(x) dx = F(x) + c and informal treatment of the fundamental theorem of calculus, ∫ₐᵇ f(x) dx = F(b) − F(a)
- properties of anti-derivatives and definite integrals
- 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.

(The grammar in the third dot point — "polynomial functions exponential, circular, logarithmic or power functions" — is VCAA's, not a transcription error. The published document is missing a comma.)

4.2 What changed in 2023

Points of inflection were put back. [OLDSD] carried an explicit exclusion in its corresponding dot point:

"…identification of intervals over which a function is constant, stationary, strictly increasing or strictly decreasing, identification of the maximum rate of increase or decrease in a given application context (consideration of the second derivative is not required), identification of local maximum/minimum values over an interval and application to solving problems…"

The 2023 dot point instead reads "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". The exclusion clause is gone and inflection points are named.

The 2023 Exam 2 report [RPT] confirms this was understood as a genuine addition:

"This is the first year of the new study design and most students were able to respond effectively to the questions involving the introduced concepts, such as Newton's method in Questions 3f. and 3g. and the point of inflection in Question 3d."

The corpus bears this out: searching the paper texts for "point of inflection" finds hits in 2009, 2010 and 2014 (the MM(CAS) era, which did include it), then nothing across 2016–2022, then 2023, 2024 NHT, 2025 and the sample questions. The topic left the course in 2016 and returned in 2023.

An important open question. The 2023 design names points of inflection but never mentions the second derivative, and [FS] contains no second-derivative notation. Whether VCAA expects f''(x) = 0 as a method, or expects inflection points to be found graphically / by technology, is not stated anywhere in [SD] or [SPEC]. The evidence from the papers is that inflection points have only ever been asked in Exam 2, where technology answers them: 2023 Exam 2 Question 3d asked for "the coordinates of the point of inflection for h, correct to two decimal places" — a numeric, calculator-friendly answer. Treat a technology-free second-derivative question as possible but unevidenced. I could not find a VCAA statement resolving it.

"Approximation to the area under a curve using rectangles" became "using the trapezium rule". The [OLDSD] Outcome 1 key knowledge said "the concept of approximation to the area under a curve using rectangles"; the 2023 version says "using the trapezium rule". The matching key skill changed from "evaluate rectangular area approximations to the area under a curve" to "evaluate approximations to the area under a curve using the trapezium rule". The trapezium rule formula was added to [FS] at the same time.

Searching the paper texts for the exact phrase "trapezium rule" (as opposed to "area of a trapezium", which is on every formula sheet ever printed) returns hits in exactly five documents: 2023 Exam 1, 2023 Exam 2, 2024 NHT Exam 1, 2024 NHT Exam 2, 2025 Exam 2, and the Exam 2 sample questions. Zero hits before 2023. [SAMP] Exam 1 sample Question 5c is the archetype — four trapeziums of equal width approximating the area under f(x) = 2 − x² from x = −1 to x = 1, by hand.

"Distance travelled in a straight line" was dropped. [OLDSD] listed it twice, in the "limiting value of a sum" dot point and in the integration-applications dot point. Neither mention survives into 2023. Kinematics language ("velocity", "displacement", "distance travelled") has not been the frame of a Methods integration question since. Average value of a function — which sat alongside it in the same 2016–2022 dot point — was retained and is examined most years.

Average value versus average rate of change is the confusion VCAA now flags almost annually. 2023 Exam 2 report: "Some students had difficulty understanding some of the concepts, such as the difference between average value of a function and average rate of change (Questions 2b. and 2c.)." 2024 Exam 2 report: "Some students found the average value when the average rate of change was required. This occurred in Question 2b." [SAMP] Exam 1 sample Question 5 deliberately puts both in the same question, parts a and b.

Note that neither formula is on the formula sheet. You must know that the average value of f over [a, b] is (1/(b−a))∫ₐᵇ f(x)dx and that the average rate of change is (f(b) − f(a))/(b − a).

---

5. Area of Study 4 — Data analysis, probability and statistics

5.1 What the study design says

[SD] overview, verbatim:

"In this area of study students cover discrete and continuous random variables, their representation using tables, probability functions (specified by rule and defining parameters as appropriate); the calculation and interpretation of central measures and measures of spread; and statistical inference for sample proportions. The focus is on understanding the notion of a random variable, related parameters, properties and application and interpretation in context for a given probability distribution."

Content dot points, verbatim:

This area of study includes:
- random variables, including the concept of a random variable as a real function defined on a sample space and examples of discrete and continuous random variables
- discrete random variables:
- specification of probability distributions for discrete random variables using graphs, tables and probability mass functions
- calculation and interpretation of mean, μ, variance, σ², and standard deviation of a discrete random variable and their use
- Bernoulli trials and the binomial distribution, 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
- 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, μ, variance, σ², and standard deviation of a continuous random variable and their use
- standard normal distribution, N(0, 1), and transformed normal distributions, N(μ, σ²), 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)
- statistical inference, including definition and distribution of sample proportions, simulations and confidence intervals:
- distinction between a population parameter and a sample statistic and the use of the sample statistic to estimate the population parameter
- simulation of random sampling, for a variety of values of p and a range of sample sizes, to illustrate the distribution of P̂ and variations in confidence intervals between samples
- concept of the sample proportion P̂ = X/n as a random variable whose value varies between samples, where X is a binomial random variable which is associated with the number of items that have a particular characteristic and n is the sample size
- approximate normality of the distribution of P̂ for large samples and, for such a situation, the mean p (the population proportion) and standard deviation, √(p(1 − p)/n)
- determination and interpretation of, from a large sample, an approximate confidence interval (p̂ − z√(p̂(1 − p̂)/n), p̂ + z√(p̂(1 − p̂)/n)), for a population proportion where z is the appropriate quantile for the standard normal distribution, in particular the 95% confidence interval as an example of such an interval where z ≈ 1.96 (the term standard error may be used but is not required).

5.2 Boundaries that matter

• "the cumulative distribution function may be used but is not required." You will never be required to construct a cdf, but you may use one. Median and quartiles of a continuous random variable are found by solving ∫₋∞^m f(x)dx = 0.5.
• Median is no longer named. [OLDSD] listed "calculation and interpretation of mean (μ), median, variance (σ²) and standard deviation of a continuous… random variable". The 2023 dot point drops "median". Median questions have still appeared since — they are reachable through "calculation of probabilities for intervals defined in terms of a random variable" — but the word no longer appears in the study design. Treat median as in scope but de-emphasised.
• Only the binomial and the normal are named as distributions. Discrete distributions given by an arbitrary table or probability mass function are in scope (the first discrete dot point says so), but the only named discrete family is Bi(n, p) and the only named continuous family is the normal. There is no Poisson, no geometric, no exponential-by-name in Methods.
• Sample means are not in the course. Statistical inference in Methods is about sample proportions only. The distribution of sample means belongs to Specialist Mathematics.
• Simulation is explicitly in the content. "simulation of random sampling, for a variety of values of p and a range of sample sizes, to illustrate the distribution of P̂ and variations in confidence intervals between samples". In practice this is assessed in SACs, and in Exam 2 as a reasoning question about what happens to the width of a confidence interval as n changes.

5.3 When statistics entered the course

Sample proportions and confidence intervals are a 2016 addition. Searching [PAPERS] for "confidence interval" returns no hit before the 2016 papers; the same is true for "sample proportion". Neither concept exists in any 2006–2015 MM(CAS) paper, and the 2006–2015 formula sheet has no sample-proportion block. For anyone working through the archive: every statistics question in a 2006–2015 paper is discrete/continuous random variables and normal distributions only. There is nothing on inference.

Conversely, the binomial distribution formula, the binomial coefficient, and the binomial mean and variance were added to the formula sheet only in 2023 (see §7.5). From 2006 to 2022 students had to memorise Pr(X = x) = ⁿCₓ pˣ(1−p)ⁿ⁻ˣ, μ = np and σ² = np(1−p). If you are using a pre-2023 paper as timed practice, remember that you now get those three for free.

[PAPERS] 2025 Exam 2 multiple-choice Question 8 is a clean example of the current inference style: given an approximate 95% confidence interval of (0.248, 0.552) for a proportion, find n. It requires you to read the interval's half-width, recognise p̂ as the midpoint, and invert the formula on the sheet.

---

6. The three outcomes

[SD], verbatim:

"For each unit the student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass all of the areas of study for each unit. For each of Unit 3 and Unit 4 the outcomes as a set apply to the content from the areas of study covered in that unit."

The outcomes are what the exams are actually built against. [SPEC] maps them to the papers explicitly: Examination 1 assesses Outcome 1 only; Examination 2 assesses all three, with an emphasis on Outcome 2.

6.1 Outcome 1 — concepts, routines and procedures

[SD], verbatim:

"On completion of this unit the student should be able to define and explain key concepts as specified in the content from the areas of study and apply a range of related mathematical routines and procedures.

To achieve this outcome the student will draw on key knowledge and key skills outlined in all the areas of study."

Key knowledge, verbatim:

• the key features and properties of a function or relation and its graph and of families of functions and relations and their graphs
• the effect of transformations on the graphs of a function or relation
• representations of points and transformations of the plane
• the concepts of domain, maximal domain, range and asymptotic behaviour of functions
• the concept of an inverse function, connection between domain and range of the original function and its inverse relation and the conditions for existence of an inverse function, including the form of the graph of the inverse function for specified functions
• the concept of combined functions, and the connection between domain and range of the functions involved and the domain and range of the combined functions
• the features which enable the recognition of general forms of possible models for data presented in graphical or tabular form
• exponent laws and logarithm laws
• analytical, graphical and numerical approaches to solving equations and the nature of corresponding solutions (real, exact or approximate) and the effect of domain restrictions
• features which link the graph of a function to the graph of the corresponding gradient function or its numerical values, the tangent to a curve at a given point and how the sign and magnitude of the derivative of a function can be used to describe key features of the function and its derivative function
• the sum, difference, chain, product and quotient rules for differentiation
• the properties of anti-derivatives and definite integrals
• the concept of approximation to the area under a curve using the trapezium rule, the ideas underlying the fundamental theorem of calculus and the relationship between the definite integral and area
• the concepts of a random variable (discrete and continuous), Bernoulli trials and probability distributions, the parameters used to define a distribution and properties of probability distributions and their graphs
• the conditions under which a Bernoulli trial or a probability distribution may be selected to suitably model various situations
• the definition of sample proportion as a random variable and key features of the distribution of sample proportions
• the concept of confidence intervals for proportions, variation in confidence intervals between samples and confidence intervals for estimates

Key skills, verbatim:

• identify key features and properties of the graph of a function or relation and draw the graphs of specified functions and relations, clearly identifying their key features and properties, including any vertical or horizontal asymptotes
• describe the effect of transformations on the graphs of a function or relation
• find the rule of an inverse function and give its domain and range
• find the rule of a composite function and give its domain and range
• sketch by hand graphs of polynomial functions up to degree 4; simple power functions, y = xⁿ where n ∈ N, y = aˣ, (using key points (−1, 1/a), (0, 1) and (1, a)); logₑ(x); log₁₀(x); and simple transformations of these
• apply a range of analytical, graphical and numerical processes (including the algorithm for Newton's method), as appropriate, to obtain general and specific solutions (exact or approximate) to equations (including literal equations) over a given domain and be able to verify solutions to a particular equation or equations over a given domain
• solve by hand equations of the form sin(ax + b) = c, cos(ax + b) = c and tan(ax + b) = c with exact value solutions over a given interval
• apply algebraic, logarithmic and circular function properties to the simplification of expressions and the solution of equations
• evaluate derivatives of basic, transformed and combined functions and apply differentiation to curve sketching and related optimisation problems
• find derivatives of polynomial functions and power functions, functions of the form f(ax + b) where f is xⁿ, for n ∈ Q, sine, cosine; tangent, eˣ, or logₑ(x) and simple linear combinations of these, using pattern recognition, or by hand
• apply the product, chain and quotient rules for differentiation to simple combinations of functions by hand
• find derivatives of basic and more complicated functions and apply differentiation to curve sketching and optimisation problems
• find anti-derivatives of polynomial functions and power functions, functions of the form f(ax + b) where f is xⁿ, for n ∈ Q, eˣ, sine or cosine, and simple linear combinations of these, using pattern recognition, or by hand
• evaluate approximations to the area under a curve using the trapezium rule, find and verify anti-derivatives of specified functions and evaluate definite integrals
• apply definite integrals to the evaluation of the area under a curve and between curves over a specified interval
• analyse a probability mass function or probability density function and the shape of its graph in terms of the defining parameters for the probability distribution and the mean and variance of the probability distribution
• calculate and interpret the probabilities of various events associated with a given probability distribution, by hand in cases where simple arithmetic computations can be carried out
• apply probability distributions to modelling and solving related problems
• simulate repeated random sampling and interpret the results, for a variety of population proportions and a range of sample sizes, to illustrate the distribution of sample proportions and variations in confidence intervals
• calculate sample proportions and approximate confidence intervals for population proportions

Three things in that list decide what Exam 1 can ask, and they are the most under-read text in the whole study design.

1. The by-hand sketching list is closed and explicit. "polynomial functions up to degree 4; simple power functions, y = xⁿ where n ∈ N, y = aˣ (using key points (−1, 1/a), (0, 1) and (1, a)); logₑ(x); log₁₀(x); and simple transformations of these". Note n ∈ N here — the by-hand power functions are the natural-exponent ones, even though the course content covers n ∈ Q. This y = xⁿ, n ∈ N clause is new in 2023; [OLDSD]'s corresponding key skill did not name it. Also note what is absent: sin, cos and tan are not on the by-hand sketching list, yet circular graphs are sketched by hand in Exam 1 most years. The list is best read as a floor, not a ceiling.
2. The by-hand equation-solving list is closed and explicit. "solve by hand equations of the form sin(ax + b) = c, cos(ax + b) = c and tan(ax + b) = c with exact value solutions over a given interval." That is the technology-free trigonometric guarantee. c will be an exact value.
3. "including the algorithm for Newton's method". This single parenthesis is the entire study-design authority for Newton's method. It sits in a key skill, not in an area-of-study dot point, which is why it is easy to miss.

There is one more sentence worth isolating: "calculate and interpret the probabilities of various events associated with a given probability distribution, by hand in cases where simple arithmetic computations can be carried out". That is VCAA telling you the shape of every technology-free probability question: the arithmetic will be simple, the fractions will be manageable, and the answer will be exact.

One key-knowledge point is a ghost. "representations of points and transformations of the plane" is what remains of the 2016–2022 point "the matrix representation of points and transformations of the plane". The word "matrix" was deleted in 2023, and the accompanying 2016–2022 key skill — "apply matrices to transformations of functions and their graphs" — was deleted entirely with no replacement. See §9.4 for the exam evidence that matrix transformations have genuinely left the exams.

6.2 Outcome 2 — non-routine contexts, modelling, investigation

[SD], verbatim:

"On completion of this unit the student should be able to apply mathematical processes in non-routine contexts, including situations with some open-ended aspects requiring investigative, modelling or problem-solving techniques or approaches, and analyse and discuss these applications of mathematics.

To achieve this outcome the student will draw on key knowledge and key skills outlined in all the areas of study."

Key knowledge, verbatim:

• key mathematical content from one or more areas of study related to a given context
• specific and general formulations of concepts used to derive results for analysis within a given context
• the role of examples, counter-examples and general cases in working mathematically
• key elements of algorithm design, including sequencing, decision-making and repetition, and representations of the ordered steps for an algorithm including through the use of pseudocode
• inferences from analysis and their use to draw valid conclusions related to a given context

Key skills, verbatim:

• specify the relevance of key mathematical content from one or more areas of study to the investigation of various questions in a given context
• identify important information, variables, constraints and other key features to the investigation of various questions in a given context
• develop mathematical formulations of specific and general cases used to derive results for analysis within a given context
• use algorithms, patterns, models and simulation to solve problems related to a given context
• use a variety of techniques to verify results
• make inferences from analysis and use these to draw valid conclusions related to a given context
• communicate results and conclusions using both mathematical expression and everyday language, in particular, the interpretation of mathematics with respect to the context

The algorithm/pseudocode dot point is new in 2023 and has no equivalent in [OLDSD]. It is the only place in the study design where pseudocode is named. Read it carefully: "key elements of algorithm design, including sequencing, decision-making and repetition, and representations of the ordered steps for an algorithm including through the use of pseudocode". Sequencing = statements in order; decision-making = If … Then … Else; repetition = While … Do … EndWhile. Those three constructs are the complete grammar VCAA has committed to.

Two more skills were added in 2023 and neither is cosmetic: "identify important information, variables, constraints and other key features" (new), and "use algorithms, patterns, models and simulation to solve problems" (the 2016–2022 version had no algorithms and no "identify important information" skill at all).

6.3 Outcome 3 — computational thinking and technology

[SD], verbatim:

"On completion of this unit the student should be able to apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring investigative, modelling or problem-solving techniques or approaches."

Compare [OLDSD]: "…should be able to select and appropriately use numerical, graphical symbolic and statistical functionalities of technology…". The 2023 outcome statement leads with "apply computational thinking". That is the headline change.

Key knowledge, verbatim:

• the role of computational thinking (abstraction, decomposition, pattern and algorithm) in problem-solving, and its application to mathematical investigation
• exact and approximate specification of mathematical information such as numerical data, graphical forms and general or specific forms of solutions of equations produced by use of technology
• domain and range requirements for specification of graphs of functions and relations when using technology
• the role of parameters in specifying general forms of functions and equations
• the relation between numerical, graphical and symbolic forms of information about functions and equations and the corresponding features of those functions and equations
• the similarities and differences between formal mathematical expressions and their representation by technology
• the purpose and effect of sequencing, decision-making and repetition statements on relevant functionalities of technology, and their role in the design of algorithms and simulations
• the appropriate functionality of technology for a variety of mathematical contexts

Key skills, verbatim:

• use computational thinking, algorithms, models and simulations to solve problems related to a given context
• distinguish between exact and approximate presentations of mathematical results produced by technology, and interpret these results to a specified degree of accuracy
• use technology to carry out numerical, graphical and symbolic computation as applicable
• produce results, using technology, which identify examples or counter-examples for propositions
• produce tables of values, families of graphs and collections of other results using technology, which support general analysis in investigative, modelling and problem-solving contexts
• use appropriate domain and range specifications to illustrate key features of graphs of functions and relations
• identify the relation between numerical, graphical and symbolic forms of information about functions and equations, and the corresponding features of those functions and equations
• specify the similarities and differences between formal mathematical expressions and their representation by technology, in particular, equivalent forms of symbolic expressions
• select an appropriate functionality of technology in a variety of mathematical contexts and provide a rationale for these selections
• design and implement simulations and algorithms using appropriate functionalities of technology
• apply suitable constraints and conditions, as applicable, to carry out required computations
• relate the results from a particular technology application to the nature of a particular mathematical task (investigative, modelling, or problem-solving) and verify these results
• specify the process used to develop a solution to a problem using technology and communicate the key stages of mathematical reasoning (formulation, solution, interpretation) used in this process

Three key knowledge points and two key skills here are new in 2023: computational thinking as a named construct with its four elements (abstraction, decomposition, pattern and algorithm); "the purpose and effect of sequencing, decision-making and repetition statements"; "use computational thinking, algorithms, models and simulations to solve problems"; and "design and implement simulations and algorithms using appropriate functionalities of technology".

6.4 How the outcomes map to the papers

[SPEC], verbatim:

"Examination 1 will cover all areas of study in relation to Outcome 1. The examination is designed to assess students' knowledge of mathematical concepts, their skill in carrying out mathematical algorithms without the use of technology, and their ability to apply concepts and skills."

"Examination 2 will cover all areas of study in relation to all three outcomes, with an emphasis on Outcome 2. The examination is designed to assess students' ability to understand and communicate mathematical ideas, and to interpret, analyse and solve both routine and non-routine problems."

The practical reading:

That last row is the one to internalise. Newton's method is examinable technology-free. [SAMP] Exam 1 sample Question 6 does exactly that: verify f(−1) > 0 and f(−2) < 0 for f(x) = ⅓x³ + 2x + 4, then with x₀ = −1 find x₁ by hand. The corpus confirms it in live papers — "Newton" appears in the 2023 Exam 1, the 2024 NHT Exam 1, the 2025 Exam 1 and the 2026 NHT Exam 1.

Pseudocode, by contrast, appears only in Exam 2 material in the corpus (2024 NHT Exam 2 and the Exam 2 sample questions), consistent with the Outcome 1 / Outcome 2 boundary. That is a reasoned inference from [SPEC], not an explicit VCAA exclusion — [SPEC] never says "Examination 1 will not contain pseudocode". But the outcome mapping is unambiguous and four years of papers agree with it.

---

7. Examination structure

7.1 Overall conditions

[SPEC], verbatim, in full:

"There will be two end-of-year examinations for VCE Mathematical Methods — examination 1 and examination 2.

The examination will be sat at a time and date to be set annually by the Victorian Curriculum and Assessment Authority (VCAA). VCAA examination rules will apply.

Examination 1 will have 15 minutes of reading time and 1 hour of writing time. Students are not permitted to bring into the examination room any technology (calculators or software) or notes of any kind.

Examination 2 will have 15 minutes of reading time and 2 hours of writing time. Students are permitted to bring into the examination room an approved technology with numerical, graphical, symbolic and statistical functionality, as specified in the VCAA Notices to Schools and the VCE Exams Navigator. One bound reference (which may be annotated) may also be brought into the examination room. This may be a textbook, a securely bound lecture pad, an exercise book or a permanently bound student-constructed set of notes without foldouts. Specifications for the bound reference are published annually in the VCE Exams Navigator.

A Formula Sheet will be provided with both examinations.

The examination will be assessed by a panel appointed by the VCAA.

Examination 1 will contribute 20 per cent to the study score. Examination 2 will contribute 40 per cent to the study score."

The [SD] general section adds the single sentence that defines the architecture of VCE mathematics assessment:

"Examination 1 for Mathematical Methods and Examination 1 for Specialist Mathematics are technology-free examinations. All other VCE mathematics examinations assume student access to VCAA approved technology."

The mark-per-minute rate is identical on the two papers. The difficulty of Exam 1 is not that it is faster — it is that every mark has to come out of your head and your hand.

7.2 Examination 1 format

[SPEC], verbatim:

"The examination will be in the form of a Question and Answer Book.
The examination will consist of short-answer and extended-answer questions.
All questions will be compulsory. The total marks for the examination will be 40.
A Formula Sheet will be provided with the examination. The Formula Sheet will be the same for examinations 1 and 2.
Answers are to be recorded in the spaces provided in the Question and Answer Book."

Under the current design the paper has run to eight or nine questions each year: 9 in 2023, 8 in 2024, 9 in 2025, 9 in the 2026 NHT paper. Individual questions have run from 2 to 8 marks. The 2025 November paper is representative: Q1 3 marks, Q2 2, Q3 6, Q4 4, Q5 4, Q6 3, Q7 6, Q8 5, Q9 7 — total 40.

The printed instruction page (2025 Exam 1, verbatim):

"Answer all questions in the spaces provided.
Write your responses in English.
In all questions where a numerical answer is required, an exact value must be given unless otherwise specified.
In questions where more than one mark is available, appropriate working must be shown.
Unless otherwise indicated, the diagrams in this book are not drawn to scale."

Those five lines deserve more study than most students give them. The exact-value default and the show-working requirement are the two rules the examination reports invoke most often when explaining lost marks.

7.3 Examination 2 format

[SPEC], verbatim:

"The examination will be in the form of a Question and Answer Book.
The examination will consist of two sections.
Section A will consist of 20 multiple-choice questions worth 1 mark each and will be worth a total of 20 marks.
Section B will consist of short-answer and extended-answer questions, including multi-stage questions of increasing complexity, and will be worth a total of 60 marks.
All questions will be compulsory. The total marks for the examination will be 80.
A Formula Sheet will be provided with the examination. The Formula Sheet will be the same for examinations 1 and 2.
Answers to Section A are to be recorded on the Answer Sheet provided for multiple-choice questions.
Answers to Section B are to be recorded in the spaces provided in the Question and Answer Book."

The phrase "multi-stage questions of increasing complexity" is the specification's licence for the 11–19 mark Section B questions that walk from a 1-mark "state the range" opener to a 3-mark abstract parameter question at the end. Section B has carried four or five questions per paper under the current design:

(The 2024 row sums to 59 in [QJSON]; one mark is missing from the extraction, most likely from Question 3.)

The drift towards four longer questions is real but only two years old; the specification permits either.

Section A instructions (2025 paper, verbatim):

"Answer all questions in pencil on your Multiple-Choice Answer Sheet.
Choose the response that is correct for the question.
A correct answer scores 1; an incorrect answer scores 0.
Marks will not be deducted for incorrect answers.
No marks will be given if more than one answer is completed for any question.
Unless otherwise indicated, the diagrams in this book are not drawn to scale."

There is no penalty for a wrong multiple-choice answer. Leave nothing blank.

7.4 Permitted materials, the bound reference, and the CAS

[SPEC] lists approved materials:

"Examination 1 — Basic stationery requirements (pens, pencils, highlighters, erasers, sharpeners and rulers)

Examination 2 — Basic stationery requirements (pens, pencils, highlighters, erasers, sharpeners and rulers); Protractors, set squares and aids for curve sketching; An approved technology with numerical, graphical, symbolic and statistical functionality; One scientific calculator; One bound reference"

The VCAA Authorised materials and equipment for 2026 VCE external assessments page states the Examination 2 entry as:

"Mathematical Methods Examination 2
- one approved CAS calculator or CAS software and one scientific calculator
- one bound reference that may be annotated
- protractor, set square and aids for curve sketching"

Mathematical Methods Examination 1 has no entry at all in that page's specific-materials list — basic stationery only.

The bound reference

The binding rules are published annually in the VCE Exams Navigator. From the 2026 edition, verbatim:

"Specifications for bound references
- Bound references must be in book format of A4 size or smaller when closed.
- The number of pages is not specified.
- Pages must be permanently bound and securely attached to the spine.
- There must be a single horizontal or vertical spine.
- The bound reference may be:
- a textbook
- a securely bound lecture pad
- a permanently bound student-constructed set of notes without fold-outs
- an exercise book.
- The form of binding is not specified but it must be secure, and pages must not be readily detachable or designed to be removed. Binding can include cloth, glue, staple, spiral or comb binding."

"You are allowed to:
- consult your bound reference during reading and writing time
- annotate the material
- design your own written index
- fold pages
- cut page corners
- colour code pages
- insert dividers into your own sets of notes
- firmly attach additional material to pages in the bound reference (for example, by glue, adhesive tape or staples)."

"Your bound reference must not include:
- pages or parts of pages that can be detached from the bound reference during the examination
- fold-outs, maps or brochure-style components
- removable tabs, sticky notes or other pages or material designed to be detached
- forms of collation or binding that are designed to be non-permanent and the content modified by insertion, including
- ring-binder folders
- plastic A4 sleeves (permanent or removable) from which pages may be removed
- manila and similar folders with clip, clamp, slide and metal-prong binding of loose-leaf material."

"If any page or part of a page is detached from the rest of the bound reference, the page will be removed by the supervisor for the duration of the examination and the incident will be reported as a potential breach of rules."

"A suitably qualified member of the school teaching staff will check the appropriateness of the bound reference as you enter the examination room for Mathematics examinations where these items are permitted."

Practical consequences for a student building notes: there is no page limit; a written index is explicitly allowed; cut corners and colour-coded pages are explicitly allowed as navigation aids; sticky-note tabs are explicitly banned; printed pages glued or stapled in are fine provided they cannot come out; ring binders and plastic sleeves are prohibited outright.

For schools approved to use CAS software rather than a handheld:

"If your school receives written approval from the VCAA to use approved CAS software, you are permitted to have your bound references as stored files on a CD-ROM, DVD or USB."

Approved technology

VCAA Approved technology page, 2026, verbatim:

"Mathematical Methods and Specialist Mathematics
Either one approved CAS calculator or one approved CAS software may be used in Mathematical Methods Examination 2 and Specialist Mathematics Examination 2 only.
One scientific calculator may also be used in Mathematical Methods Examination 2 and Specialist Mathematics Examination 2.
No calculators of any kind are permitted in Mathematical Methods Examination 1 and Specialist Mathematics Examination 1."

"The full functions of approved CAS calculators may be used (that is, memories do not have to be cleared prior to entering the examination).
Casio — Algebra or ClassPad series.
Hewlett Packard — HP 40/48/49/50 or HP Prime series.
Texas Instruments — TI-89/92/Voyage or TI-Nspire CAS series."

Approved CAS software, for approved schools only: "Casio ClassPad Manager, HP Prime Emulator, Mathematica, Maple, MATLAB or TI-Nspire and files of that software type stored on a USB".

Memory does not need to be cleared. This is the rule that makes a well-prepared CAS a genuine asset: stored programs, saved functions and prepared documents may be used. It has been the rule throughout the archive — the 2006 Exam 2 cover already said "one approved CAS calculator (memory DOES NOT need to be cleared)".

The Exams Navigator adds the operating conditions:

"The calculator must be silent and of the handheld type containing its own power source. You are not permitted to take portable chargers into the examination room."
"You will be entirely responsible for ensuring adequate power supply to your calculator. You must supply your own spare batteries. Any technical fault or battery failure that limits the usefulness of a calculator during an examination will not be taken into consideration by the assessors."
"You may not borrow a calculator from another student after entering the examination room."
"A scientific calculator does not have graphic, symbolic or programming capabilities. It does not have extended memory capable of storing text and/or symbols."

A change is already announced for 2027. VCAA Notice to Schools 52 (28 May 2026) and the Approved technology page:

"Following broad consultation, the VCAA will require custom functionality – including User Defined Functions (UDFs) – on Computer Algebra System (CAS) calculators to be restricted during VCE Mathematics examinations from 2027."

"There are no changes made to arrangements for the 2026 VCE examinations."

From 2027 the approved list narrows to specific models (Casio fx-CP400 ClassPad II; HP Prime G2; TI-Nspire CX CAS and TI-Nspire CX II CAS), and calculators must be placed in a restricted mode that blocks "retrievable information, including user-defined functions, databanks, dictionaries, mathematical formulas and text". Maple and MATLAB drop off the approved-software list, and USB storage devices are barred. Students sitting in 2026 are unaffected; students sitting from 2027 should not build a preparation strategy around stored user-defined functions.

Reading time

VCE Exams Navigator 2026, verbatim:

"During reading time, you may study the instructions, the question book and a dictionary or bound reference (where these items are permitted)."

"You must not begin to write or mark your paper or response materials in any way, or use a calculator (where one is permitted), until the announcement that writing time has commenced."

"Do not use calculators during reading time."

Examination rules, rule 15:

"Students must not begin to write or mark their paper or response material in any way, or use a calculator, until advised by a supervisor that writing may commence."

So in Exam 2's fifteen minutes you may read the paper and consult your bound reference, but you may not annotate, you may not write, and you may not touch the calculator. In Exam 1 you have the paper and the formula sheet and nothing else.

Unresolved. VCAA does not state anywhere whether the Formula Sheet may be read during reading time. The Navigator's reading-time sentence names "the instructions, the question book and a dictionary or bound reference" and does not mention the formula sheet. Examination rules rule 13 permits removing formula sheets in general — "Students must not remove or tear out any part of a bound reference, answer book, question/task book or question and answer book except where permitted, for example, formula sheets" — and since 2016 the sheet has been a separate item rather than a centrefold, so there is nothing to detach. I could not find a ruling and am flagging this as genuinely unresolved rather than guessing.

7.5 The formula sheet — exactly what is on it

[SPEC]: "A Formula Sheet will be provided with the examination. The Formula Sheet will be the same for examinations 1 and 2." The two published sheets were text-extracted and diffed; they differ only in the words "Examination 1" / "Examination 2" in the header and footer. The current sheets are labelled "2024 Formula Sheet" (August 2024); no later edition has been published as of September 2026.

The sheet runs to four pages: a cover, two content pages, and a back page. The cover carries the line "You may keep this Formula Sheet."

Mensuration

Calculus — derivatives on the left, anti-derivatives on the right

plus:

• product rule d/dx (uv) = u dv/dx + v du/dx
• quotient rule d/dx (u/v) = (v du/dx − u dv/dx)/v²
• chain rule dy/dx = (dy/du)(du/dx)
• Newton's method xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ)
• trapezium rule approximation Area ≈ ((xₙ − x₀)/(2n)) [ f(x₀) + 2f(x₁) + 2f(x₂) + … + 2f(xₙ₋₂) + 2f(xₙ₋₁) + f(xₙ) ]

Probability

• Pr(A′) = 1 − Pr(A)
• Pr(A ∪ B) = Pr(A) + Pr(B) − Pr(A ∩ B)
• Pr(A|B) = Pr(A ∩ B)/Pr(B)
• mean μ = E(X); variance var(X) = σ² = E((X − μ)²) = E(X²) − μ²
• binomial coefficient ⁿCₓ = n!/(x!(n − x)!)

Sample proportions

• P̂ = X/n
• mean E(P̂) = p
• standard deviation sd(P̂) = √(p(1 − p)/n)
• approximate confidence interval ( p̂ − z√(p̂(1 − p̂)/n), p̂ + z√(p̂(1 − p̂)/n) )

What is deliberately not on the sheet

This list matters as much as the sheet itself. None of the following is provided, and all of it is examinable:

• Exact values of sin, cos and tan for the standard angles. The 2025 Exam 1 report is explicit: "Students are reminded that the exact values of […], […] and […] for values of […] between 0 and […] are expected key knowledge for the study, as specified in the study design." (The function names and interval bounds in that sentence are embedded images in VCAA's .docx and did not survive text extraction. The sentence structure is verbatim; the omitted symbols are almost certainly sin, cos, tan, θ and 2π, but verify against the source PDF before republishing the sentence with symbols filled in.)
• The Pythagorean identity sin²θ + cos²θ = 1, and tan θ = sin θ / cos θ.
• Symmetry and complementary relations for circular functions.
• Index and logarithm laws.
• The average value of a function, (1/(b − a))∫ₐᵇ f(x) dx.
• The average rate of change, (f(b) − f(a))/(b − a).
• The quadratic formula, and the discriminant.
• z ≈ 1.96 for a 95% confidence interval. The sheet gives the interval in terms of a general z; the quantile is key knowledge.
• Anything about inverse functions, composite domains, or transformations.
• d/dx aˣ — only e^{ax} is given.
• Second derivatives, in any form.

How the sheet has changed

The 2006 sheet was headed "MATHEMATICAL METHODS AND MATHEMATICAL METHODS (CAS)" — a single shared sheet for the two parallel studies of that era. The transition-matrix formula appears on the 2010 and 2015 MM(CAS) sheets and not on the 2006 shared sheet; see §9.2.

7.6 The multiple-choice answer sheet — and the four-option change

Answers to Section A go on a separate machine-read Multiple-Choice Answer Sheet. From [MCAS] (October 2025), verbatim:

"Use a pencil for all entries.
If you make a mistake, erase the incorrect answer — do not cross it out.
Marks will not be deducted for incorrect answers.
No mark will be given if more than one answer is completed for any question.
For each question, shade the box that indicates your answer."

That sample answer sheet has four boxes per question: A, B, C, D.

This is a genuine, recent and under-publicised change. From 2006 through the November 2023 examination, every Mathematical Methods multiple-choice question had five options, A–E. From the November 2024 examination onward there are four, A–D.

The evidence is unambiguous and threefold:

• The 2023 Exam 2 report's Section A table has columns "% A | % B | % C | % D | % E | % N/A". The 2024 Exam 2 report's table has "% A | % B | % C | % D | % N/A". The E column is gone.
• Across [QJSON], the distribution of correct-answer letters includes E every year from 2006 to 2023 and in the May 2024 NHT paper, but contains no E at all for November 2024 (A×5, B×6, C×5, D×4), May 2025 NHT, or November 2025.
• The 2025 and 2026 NHT paper texts contain zero lines beginning "E." in Section A; the 2023 and 2024 NHT papers contain 19 each.

The change therefore landed between the May 2024 NHT paper (five options) and the November 2024 paper (four options).

[SPEC] is silent on the number of options. Version 3 of the specifications says only "Section A will consist of 20 multiple-choice questions worth 1 mark each". Everything above is established from the papers, the reports and the sample answer sheet, not from the specifications document.

Two practical consequences:

1. A blind guess is now worth 0.25 marks, not 0.20. Over 20 questions, guessing everything has an expected value of 5 marks rather than 4. Elimination is correspondingly more powerful: removing one option from four leaves you at 1/3.
2. Pre-2024 multiple-choice questions remain excellent practice, but the published percentages are not directly comparable. A 2016 question answered correctly by 25% of the state was at chance level; a 2025 question answered correctly by 25% is below chance.

7.7 What VCAA publishes after each examination

Since 2024 VCAA publishes an Assessment Guide for each paper alongside the external assessment report. The Assessment Guide is the actual marking scheme used by assessors, with every question's marks itemised as A (answer) and M (method) allocations — for example, from the 2025 Exam 2 guide, Question 2a: "A – simultaneous equations[,] M – for […] or equivalent".

The guides also publish VCAA's marking policies. From [AG] (2025 Examination 1 Assessment Guide), verbatim:

"The Assessment Guide indicates the basis for awarding marks for each item. This may involve either counting correct answers/features of a response or marking holistically, whereby making a judgement about the overall quality/qualities of a response."

"The Assessment Guide will demonstrate how marks are to be awarded for a response, not where or how marks are to be deducted."

Three of those are directly actionable:

• Consequential ("follow-through") marks exist. An arithmetic slip in part (a) does not automatically destroy parts (b) and (c). This is why abandoning a multi-part question after an early error is the most expensive habit in the subject.
• Contradictory answers cost you everything. Write two different final answers without indicating which is intended and full marks cannot be awarded. The 2023 and 2024 Exam 1 reports both say so in the general comments: "If multiple, conflicting final answers are provided, full marks cannot be awarded."
• Two complete correct methods both score. Showing a second approach is not penalised, provided both are correct.

---

8. What each examination can and cannot ask

8.1 The specifications' own constraints

[SPEC], verbatim:

"The VCE Mathematics Study Design (From 2023) ('Units 3 and 4: Mathematical Methods') is the document for the development of the examination. All outcomes in 'Units 3 and 4: Mathematical Methods' will be examined."

"All of the content from the areas of study and the key knowledge and key skills that underpin the outcomes in Units 3 and 4 are examinable."

"From 2023, the VCE Mathematical Methods examinations will be prepared according to the examination specifications above. Each examination will conform to these specifications and will test a representative sample of the key knowledge and key skills from all outcomes in Units 3 and 4."

"Students should use command/task words, other instructional information within questions and corresponding mark allocations to guide their responses."

Read that carefully. "All … are examinable", but each paper samples "a representative sample". There is no published blueprint allocating marks to areas of study — unlike General Mathematics, whose specifications assign an exact mark count to each content area, Mathematical Methods publishes no mark weighting by topic at all. Nothing in [SPEC] guarantees that statistics will appear in a given year, or how many marks calculus will carry. In practice every paper covers all four areas, but the balance shifts year to year and cannot be predicted from the published documents.

[SPEC] also names the supporting documents:

"The following resources should be referred to in relation to the VCE Mathematical Methods examinations: VCE Mathematics Study Design (From 2023) ('Units 3 and 4: Mathematical Methods'); VCE Mathematical Methods — Support materials; VCE Exams Navigator (published annually); VCAA Bulletin; VCAA Notices to Schools."

and points to the sample questions:

"Separate documents containing sample questions have been published on the VCE Mathematical Methods 'Examination specifications, past examinations and examination reports' page on the VCAA website. The sample questions provide an indication of the types of questions teachers and students can expect until the current accreditation period is over. Answers to multiple-choice questions are provided on page 12 of the sample questions document for examination 2. Answers to other questions are not provided."

That phrase — "until the current accreditation period is over" — means the January/March 2023 sample questions remain live guidance through 2027. They are the only official statement of how the new 2023 content will be framed, and they are under-used because students assume 2023 material is superseded by later real papers.

8.2 What Examination 1 may assume without technology

[SPEC] defines the intent: "to assess students' knowledge of mathematical concepts, their skill in carrying out mathematical algorithms without the use of technology, and their ability to apply concepts and skills."

The operational boundaries come from the [SD] Outcome 1 key skills, the only place the study design uses the phrase "by hand". Collected:

Two asymmetries are easy to misread and worth isolating:

• Anti-differentiation is narrower than differentiation. The differentiation key skill lists xⁿ (n ∈ Q), sine, cosine, tangent, eˣ and logₑ(x). The anti-differentiation key skill lists xⁿ (n ∈ Q), eˣ, sine or cosine — no tangent and no logₑ. There is no anti-derivative of tan in the course, and no anti-derivative producing a logarithm other than the ∫(1/x)dx form on the formula sheet.
• n ∈ N for by-hand sketching, n ∈ Q for by-hand differentiation. Sketching by hand is guaranteed only for natural-number powers; differentiating by hand is guaranteed for rational powers.

Beyond the study design, the reports supply the implicit conventions:

• Exact values are the default. Printed on every paper: "In all questions where a numerical answer is required, an exact value must be given unless otherwise specified."
• Exact circular-function values are assumed knowledge (2025 Exam 1 report, quoted in §7.5).
• The arithmetic is non-trivial. The reports name arithmetic and algebraic slips as the leading cause of lost marks in Exam 1, every single year. The 2017 report: "While many students could make solid progress towards a solution, in some cases their efforts were hampered by incorrect arithmetic or algebraic manipulation. This was evident in Questions 4, 5a., 5c., 8a., and 9a. — all of which involved fractions. Students are advised to practise simplifying algebraic expressions that involve fractions, negatives, square roots and inequalities. Correct placement of brackets is crucial." The 2025 report repeats the point about fractions and factorising.
• CAS syntax is not acceptable as working, on either paper. VCAA's Mathematical Methods FAQs: "Students should use conventional mathematical notation in developing their responses. It should also be noted that the various calculators have different syntax and therefore CAS syntax is not considered to be standard."
• Units 1 and 2 content is fair game. The same FAQ: "Assumed knowledge and skills for VCE Mathematical Methods Units 3 and 4 are contained in Units 1 and 2 and may be drawn on as applicable. Similarly, content from the Victorian Curriculum F–10 Version 2.0 Mathematics may also be drawn on as applicable."

What Examination 1 will not ask. [SPEC] gives one hard constraint and one practical one:

1. Outcome 1 only. Outcome 2 key knowledge (algorithm design, pseudocode) and Outcome 3 key knowledge (computational thinking, selecting technology functionality) are therefore outside Exam 1's remit. No pseudocode question has appeared in any Exam 1 paper in the corpus, across 2023, 2024, 2024 NHT, 2025, 2025 NHT and 2026 NHT.
2. Nothing requiring numerical evaluation that cannot be done by hand. "Correct to three decimal places" does not appear on Exam 1. Newton's method is the interesting edge case: [SAMP] Exam 1 sample Question 6 asks for x₁ from x₀ = −1 for f(x) = ⅓x³ + 2x + 4 — a single iteration producing an exact fraction, not a decimal.

Note that the exclusion of pseudocode from Exam 1 is a reasoned inference from the outcome mapping in [SPEC], backed by four years of papers. [SPEC] never says "Examination 1 will not contain pseudocode". Treat it as very likely, not as a guarantee.

8.3 Where Examination 2 expects technology

[SPEC]: "Examination 2 will cover all areas of study in relation to all three outcomes, with an emphasis on Outcome 2. The examination is designed to assess students' ability to understand and communicate mathematical ideas, and to interpret, analyse and solve both routine and non-routine problems."

[SD]: "Student access to an approved technology with numerical, graphical, symbolic and statistical functionality will be assumed."

"Assumed" is the operative word. Exam 2 questions are written on the premise that you have CAS, which means:

• Numerical answers to a stated accuracy are routine — "correct to three decimal places", "correct to the nearest whole number", "correct to four decimal places". But the exact-value default still applies wherever no accuracy is stated, and this is where marks bleed. 2023 Exam 2 report: "Students need to make sure they give their answers to the required accuracy. In most of Question 1, Questions 3b. and 3h., and Question 4i., exact values were required. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. A number of students gave approximate answers as their final response to these questions."
• Trial and error is legitimate. 2023 Exam 2 report: "A number of questions could be answered using trial and error in this year's paper, especially in relation to probability, Questions 4f. and 4g. Drawing a diagram can often be helpful to show the output for some of the trials. Students are allowed to use their technology…"
• Reading the CAS output correctly is itself assessed. The same report: "There were a number of transcription errors, and incorrect use of brackets and vinculums, in Questions 1b., 1ci., 1d. and 3ci. Students needed to take more care when reading the output from their technology." And: "Some students, however, need more practice at interpreting the output from their technology, especially when the technology uses numerical methods to find solutions."
• Rounding-mode error is a named failure. "Students must make sure they have their technology set to the correct float or take more care when reading and transcribing the output."
• Sliders and graphical exploration are expected tools. "In general, students appeared to have made good use of their technology, for example in finding the equations of tangent lines, finding bounded areas and using graph sliders to get approximate answers to complicated questions."
• Algorithms and pseudocode live here. [SAMP] Exam 2 includes three consecutive pseudocode multiple-choice items: a While-loop implementation of the trapezium rule (Q5), a bisection method built from If … Then … Else If … Else (Q6), and an incomplete Newton's-method implementation where the two missing lines must be identified (Q7). In live papers, 2025 Exam 2 multiple-choice Question 7 is a compact while n > k trace; the 2023 Exam 2 and 2024 NHT Exam 2 both contain algorithm items.
• "Show that" still requires by-hand reasoning even with CAS on the desk. 2024 Exam 2 report: "Students should ensure they practise 'show that' questions. Most students substituted the correct values into the equation in Question 2f.i but Questions 4c.i and 5b.ii were not done well."

8.4 Command words

[SPEC] instructs students to "use command/task words, other instructional information within questions and corresponding mark allocations to guide their responses" but does not define them. The 2025 Exam 1 report refers to "command terms as outlined in the examination specifications and study design", which overstates what those documents contain — neither publishes a command-term glossary for Mathematical Methods. The operative definitions come from the reports themselves:

The mark allocation is itself an instruction. A 1-mark part wants an answer; a 3-mark part wants three identifiable steps. [SPEC] says so directly.

One further notation point runs through every recent report: use the function names the question gives you. 2023 Exam 1 report: "students should use the names of functions as given in the stem of the question. If the question required f (x), it was not acceptable to write 'y'; nor, when asked to determine the maximum area, was it appropriate to name the derivative function A′(x) when the variable being used was k." 2025 Exam 1 report: "An integral or integration statement must be accompanied by a 'dx'", and "Correctly using brackets eliminates the potential for ambiguity or errors in calculations… In particular, students need to consider the use of brackets when enacting the product and quotient rules for differentiation."

---

9. How the assessment has changed, 2006–2026

This section exists because the archive this site draws on spans four different regimes. A student working through twenty years of papers needs to know which questions are still fair practice, which are practice for skills that have been removed, and which years have no examples of the newest content at all.

9.1 Timeline at a glance

Assessment weighting also changed with each new study design:

I was unable to obtain the 2006–2015 study design document and therefore cannot quote its weightings; treat that row as unknown.

9.2 The 2006–2015 "Mathematical Methods (CAS)" era

Two parallel studies. From the pilot years through 2009, Victoria ran two separate mathematics studies at this level: Mathematical Methods (no CAS permitted) and Mathematical Methods (CAS). The 2006 Exam 1 assessment report [RPT] covers both at once and gives the split:

"The number of students who sat for the 2006 examination was 16 604, comprising 16 065 Mathematical Methods students and 539 Mathematical Methods (CAS) students. Almost 16% scored 90% or more of the available marks and 3% received full marks. The mean and median scores were 22 out of a possible 40 marks. There was no significant difference between the responses of Mathematical Methods students and Mathematical Methods (CAS) students. The use of matrices by a relatively small number of CAS students was seen in Question 10."

The migration from one study to the other took four years:

Sources for each figure: the 2006 and 2007 combined Exam 1 reports (16,604 and 15,770 total); the 2008 and 2009 MM(CAS) Exam 1 reports (4,108 and 7,223); the 2010 Exam 2 report, which states "There were 15 610 students who sat the Mathematical Methods (CAS) examination in 2010 (8517 students sat the Mathematical Methods examination in 2009)"; and the 2011 Exam 2 report (15,983). The 2008 non-CAS figure is not stated in any report in the corpus and I have not estimated it.

Exam 1 was shared, then diverged. The 2006 and 2007 Exam 1 reports are titled "Mathematical Methods & Mathematical Methods (CAS) GA 2: Exam 1" and cover a single cohort. From 2008 VCAA published separate Exam 1 reports for the two studies. But content-wise, Exam 1 remained restricted to material common to both studies until 2010. The 2010 Exam 1 report [RPT] says so plainly:

"This was the first year that material specific to this study as well as material in common with the former Mathematical Methods study was included in examination 1, for example Question 6. Students who chose the matrix approach to this question were more successful than those who attempted it by starting with a descriptive approach to transformations."

Exam 2 had 22 multiple-choice questions, not 20. Every Exam 2 paper from 2006 to 2015 carries the same structure table: Section 1 = 22 questions / 22 marks, Section 2 = 4 or 5 questions / 58 marks, total 80. The sections were numbered "1" and "2"; they became "A" and "B" in 2016.

Exam 1 was longer in question count. 11 questions in 2006, 12 in 2007, then 10 or 11 through 2015 — versus 8 or 9 from 2016. The marks stayed at 40 throughout; the questions simply got bigger and more multi-part.

The formula sheet carried two formulas that no longer exist. The 2010–2015 MM(CAS) sheets include "transition matrices: Sₙ = Tⁿ × S₀" — the Markov-chain formula — and "approximation: f(x + h) ≈ f(x) + h f′(x)", the linear (tangent-line) approximation. Neither is on any sheet from 2016 onward. The linear-approximation formula was also on the shared 2006–2009 sheet; the transition-matrix formula was not, appearing first in 2010 alongside the CAS-specific Exam 1 content.

A caveat on transition matrices. Searching every paper text in the corpus for "transition" or "Markov" returns hits only in the formula-sheet region of the 2010–2015 papers. I found no examination question in the archive that uses a transition matrix. The formula was provided but, on the evidence available, never examined. Do not spend time on Markov chains on the strength of that formula sheet.

No statistical inference at all. Sample proportions and confidence intervals do not appear anywhere in the 2006–2015 papers, reports or formula sheets. Every statistics question in that era is discrete or continuous random variables and normal distributions.

9.3 The 2016–2022 design

The new study design renamed the areas of study and reshaped Exam 2.

Structural changes: - "(CAS)" dropped from the study name — the papers from 2016 read simply "MATHEMATICAL METHODS". - Exam 2 Section 1 (22 MC, 22 marks) became Section A (20 MC, 20 marks); Section 2 (58 marks) became Section B (60 marks). Total stayed at 80. - The formula sheet became a separate, keepable document rather than a detachable centrefold. The 2016 paper cover adds the line "You may keep the formula sheet" and lists "Formula sheet" under Materials supplied rather than describing a centrefold. - Exam 1 dropped from 10–11 questions to 8–9.

Content added in 2016: - Statistical inference for sample proportions, in full: the concept of P̂ = X/n as a random variable, its approximate normality, its mean and standard deviation, simulation of random sampling, and approximate confidence intervals for a population proportion. This was the single biggest content addition in twenty years. The formula sheet gained a "Sample proportions" block at the same time. - Formula-sheet additions d/dx (ax + b)ⁿ = an(ax + b)ⁿ⁻¹ and ∫(ax + b)ⁿ dx.

Content removed or restricted in 2016: - Transition matrices and the linear-approximation formula left the formula sheet. - Points of inflection and the second derivative were excluded. [OLDSD] Area of Study 3, verbatim: "identification of the maximum rate of increase or decrease in a given application context (consideration of the second derivative is not required)". The corpus confirms the effect: the phrase "point of inflection" appears in the 2009, 2010 and 2014 papers, then in none of the 2016–2022 papers, then returns in 2023. - "approximation to the area under a curve using rectangles" is the 2016–2022 method. The trapezium rule was not in this design.

Content retained from the earlier era that has since gone: - Matrix representation of transformations. [OLDSD] Outcome 1 key knowledge: "the matrix representation of points and transformations of the plane"; key skill: "apply matrices to transformations of functions and their graphs". This was examined regularly. The 2021 Exam 1 Question 9b defines T : R² → R², T([x, y]) = [[1, 0], [0, q]] [x, y] and asks for the values of q for which the transformed line meets the unit circle. The 2022 Exam 2 Section B Question 2 defines a transformation Q : R² → R² combining a 2×2 dilation matrix with a translation column and asks for an average value under it. - Simple functional relations. [OLDSD] Area of Study 2, verbatim: "use of simple functional relations such as f(x + k) = f(x), f(xⁿ) = n f(x), f(x) + f(−x) = 0, f(xy) = f(x) f(y), to characterise properties of functions including periodicity and symmetry, and to specify algebraic equivalence, including the exponent and logarithm laws". 2015 Exam 2 Question 18 is the type specimen.

Outcome 3 in 2016–2022 was about selecting and using technology, not about computational thinking. Its opening line, verbatim: "should be able to select and appropriately use numerical, graphical symbolic and statistical functionalities of technology…". There is no mention of algorithms, pseudocode, abstraction or decomposition anywhere in the 2016–2022 outcomes.

9.4 The 2023–2027 design

Area-of-study names changed to align with the Victorian Curriculum strands:

Content added:

Content removed:

9.5 The four-option multiple-choice change, November 2024

Covered in detail in §7.6. In summary: five options (A–E) from 2006 to the May 2024 NHT paper; four options (A–D) from the November 2024 paper onward. Established from the papers, the report tables and the October 2025 sample answer sheet; not stated in [SPEC].

9.6 Which archive questions are still worth doing

This is the table the site should encode.

One further structural point about pre-2016 Exam 2 practice. Those papers have 22 multiple-choice questions and 58 Section 2 marks, in two hours. A modern paper has 20 and 60. If you are timing yourself on a 2006–2015 paper, the pacing is close enough to be useful, but the mark arithmetic is not identical.

---

10. Mark distribution and grading

10.1 How a raw mark becomes a study score

The study score is a rank transform, not a mark. VCAA, Score aggregation, verbatim:

"The normalised scores are then converted to a scale with a mean of 30 and standard deviation of 7, truncated at zero and 50. This produces a possible study score ranging from zero to 50, with most study scores between 23 and 37. Further adjustments are made for studies that have small numbers of students."

The mechanics: each graded assessment score is standardised as (final score − state mean) / state standard deviation; each standardised score is multiplied by its percentage contribution; the weighted totals are summed, ranked, and the ranks are mapped onto the N(30, 7) scale. Ties take the group's highest rank.

The weightings VCAA actually aggregates with are not the four in the study design. [SD] states four components (SAC Unit 3 20%, SAC Unit 4 20%, Exam 1 20%, Exam 2 40%), but the VCAA VCE and VET assessment summary lists Mathematical Methods (study code MA11) as having three graded assessments:

So the aggregation is 0.40 · z(SAC) + 0.20 · z(Exam 1) + 0.40 · z(Exam 2). The two SACs are combined into a single graded assessment before standardisation. The published grade-distribution tables confirm this — GA1 is labelled "COURSEWORK UNIT 3/4" and is marked out of 100.

Two consequences worth internalising:

1. Because each component is standardised separately, a mark is worth more on a paper the state found hard. In 2023, when the Exam 2 mean was 36.8/80, a raw 60 sat far further above the mean in standard deviations than a raw 60 did in 2025 when the mean was 44.1/80. There is no fixed "you need X out of 80".
2. Statistical moderation does not change your rank within your school. VCAA, verbatim: "Statistical moderation does not change the rank order of students as determined by the school's school-based scores. A student given the top score for school-based assessments by his or her school will have the top score after statistical moderation, no matter how they perform on the exam(s)." And: "Any adjustment to a student's score is determined by the external scores for the whole group, not by the student's own external score." What moderation does is align your school group's SAC distribution to that group's exam distribution — the highest, upper-quartile, median and lower-quartile moderated scores are aligned to the corresponding external scores.

The GAT does not contribute to a study score. Since 2023 it has three roles: a possible (minor) input to statistical moderation "only if [GAT scores] provide a better match with school-based assessments throughout the state" — VCAA notes "The external assessment scores will always have the major influence"; a check on anomalous external-assessment grading, where "Scores may go up or stay the same; however, they will not go down because of this final check"; and as one input to a Derived Examination Score. VCAA does not publish which studies use GAT in moderation, so whether Mathematical Methods is one of them is unverified.

On percentiles, VCAA publishes exactly one figure: "A study score of 40 or above in any study represents exceptional performance (among the top eight per cent in the state)." There is no published figure for 45+ or 50, and no published per-study distribution of study scores. Applying the N(30, 7) model with a continuity correction gives ≥40 → 8.7% (which reproduces VCAA's "top eight per cent", a useful sanity check), ≥45 → about 1.9%, and exactly 50 → about 0.27%. Those last two are derived, not published. Truncation at 50 and small-cohort adjustments distort the tails, so treat them as indicative only.

10.2 Reconstructing the paper means — method and validation

VCAA stopped publishing paper means after 2011, but from 2012 onwards the per-question tables in each report give the full mark distribution as percentages. Summing Σ (mark × proportion at that mark) across every question part reconstructs the paper mean. For multiple-choice questions, the "percentage correct" is the mean mark for that question directly.

Because this reconstruction underpins every number in §10.3, it is worth stating how accurate it is. Four checks against means VCAA published in the 2006–2011 reports:

and eight further checks against the mean scores in VCAA's published grade distribution tables for 2022–2025. Those tables report exam scores on a doubled scale (Exam 1 out of 80, Exam 2 out of 160); halved, they read:

(* the two starred papers have one mark missing from the corpus extraction, which accounts for most of the gap.)

The reconstruction is accurate to within about 0.35 of a mark wherever the extraction is complete. Every mean in the table below can be trusted to that tolerance.

Note that the doubled scale in VCAA's grade-distribution tables is an inference — VCAA does not state it — but it is confirmed both by cross-study consistency (every maths study's published maxima are exactly twice the paper marks) and by the agreement above.

10.3 Where the state's marks actually fall

Reconstructed means, November papers, 2006–2025. Exam 2 percentages for 2008 and 2009 are computed over the marks recoverable from those reports (66 and 75 respectively), not 80. 2011 is omitted entirely — the corpus data for that year is corrupt.

Observations that matter for a student aiming at 45+:

• The state averages roughly half marks on both papers, every year. Exam 1 has run between 44.9% and 58.3%; Exam 2 between 45.8% and 57.0%. There is no year in which the state did well.
• The multiple-choice mean has fallen. In the 22-question era it sat at 12–14 out of 22 (55–65%). In the 20-question era it has sat at 9.4–12.5 out of 20 (47–63%), and in 2023 it hit 9.4/20 — the lowest multiple-choice mean in the entire twenty-year archive. Section A is no longer the easy half of Exam 2.
• 2020, 2021 and 2024 were the hardest recent Exam 1 papers; 2007 and 2021 the hardest overall. 2023 was the hardest recent Exam 2.
• The easiest recent papers were 2022 and 2025. Both had Exam 2 means above 55%.

10.4 The difficulty profile of a paper

Classifying every question part by the fraction of its marks the state actually earned (state mean mark ÷ max mark):

Across the current design, roughly 30–40% of every paper consists of marks the state earns less than 40% of. That is where a 45+ student separates, and it is a stable, structural feature of the assessment, not an accident of a particular year.

10.5 The shape of difficulty within a question

[QJSON] makes one pattern unmistakable. Taking all 47 Section B extended-response questions from the November papers 2016–2025 and grouping their parts by position:

The same pattern holds on Exam 1, across 74 multi-part questions 2016–2025: the first part averages 60.7% full marks, the last part 30.4%.

And difficulty rises monotonically through the Exam 1 paper. Mean percentage of the state earning full marks, by question number, 2016–2025:

The implication for exam strategy is concrete: the final two questions of Exam 1 and the final part of every Section B question in Exam 2 are where the top 10% is decided. They are also the parts most often left blank. VCAA's own marking policy makes clear that a genuine attempt scoring zero and a blank response are recorded differently ("Not Attempted" versus "0"), but both score nothing — and consequential-error marking means a partially wrong attempt at a final part frequently scores something.

10.6 The hardest questions in the archive

Question parts by the percentage of the state awarded full marks, all November papers 2006–2025 excluding 2011.

Written (Section B and Exam 1) — the twenty hardest:

Note how many of those are 1- and 2-mark parts. The hardest questions in Methods are rarely the long ones; they are short, late parts that require one non-obvious idea.

Two worked examples of what "1% of the state" looks like:

• 2019 Exam 1 Question 8c. Question 8 shows part of the graph of a degree-4 polynomial f that touches the x-axis at the origin and has x-intercepts at (−1, 0) and (1, 0), with two turning points labelled on the diagram. Part (a) asks for the rule of f (1 mark). Part (b) defines h : D → R, h(x) = logₑ(g(x)) − logₑ(x³ + x²), where g has the same rule as f, and asks for the maximal domain D (1 mark). Part (c) asks for the range of h (2 marks). The whole question collapsed: 14% full marks on (a), 9% on (b), 1% on (c) — the lowest of any written part in the archive. Part (c) requires simplifying the difference of logarithms, recognising what the restricted domain does to the simplified expression, and then reasoning about its range. The report's entire comment on part (c) is: "Some students sketched various graphs with limited success."
• 2021 Exam 1 Question 9c i. An 8-mark question built on the unit circle x² + y² = 1 and its tangent at a point P, with A(2, 0) fixed. Part (a) is a "show that" for the line through A and P. Part (b) applies a matrix transformation T : R² → R², T([x, y]ᵀ) = [[1, 0], [0, q]][x, y]ᵀ and asks for the values of q giving intersections with the unit circle. Part (c) asks for a function definition and its domain. The full sequence of state full-mark rates is 13% → 6% → 4% → 1% → 4% across parts a, b i, b ii, c i, c ii. The report on part c i: "Students are reminded of the need to consider domains when defining functions. Many were able to write [the rule], but very few stated the domain of the function." This question also illustrates §9.6 neatly: part (b) is a matrix transformation and is therefore out of scope for a 2026 student, while parts (a) and (c) are perfectly current.

Multiple choice — the hardest ten:

2025 Exam 2 Question 19 is the equal-hardest multiple-choice question in the archive — and it is the only one of the two that had just four options. 14% correct against a 25% chance baseline means the distractors actively misled: a student who knew nothing and guessed would, on average, have done better than the state did. Verbatim: "Let A be a point on the line y = x + c and B be a point on the curve y = logₑ(x + 1). If A and B are placed such that the line segment AB has the minimum possible length, and this length is √2, the value of c must be…" It requires recognising that the minimum distance occurs where the curve's tangent is parallel to the line, which forces f′(x) = 1, and then working backwards through the perpendicular distance.

Note the positional pattern: seven of the ten hardest multiple-choice questions in the archive are Q16 or later. Section A is ordered by difficulty in practice, whether or not VCAA says so.

10.7 Grades, raw thresholds and enrolments

VCAA publishes a Grade distributions for VCE graded assessments table for each study each year, reporting the mean, standard deviation, grade percentages and the score band for each grade. Exam scores are reported on a doubled scale (Exam 1 out of 80, Exam 2 out of 160); the raw equivalents below are halved.

Mathematical Methods, 2025 (16,339 assessed on GA1; 16,040 on Exam 1; 16,044 on Exam 2):

A+ raw thresholds move every year, because the bands are set from that year's cohort:

The 2023 Exam 2 A+ cut of 61/80 and the 2024 Exam 1 A+ cut of 33/40 are the two lowest in the period, and both fall in the years with the lowest means. Grade cut-offs are not fixed percentages — they track the paper.

Enrolments, Units 3 & 4 (from the same source; 2024 and 2025 include NHT students):

Roughly 3–4% of enrolled students are not assessed on the examinations in any given year.

10.8 What raw performance corresponds to 45+

Neither VCAA nor VTAC publishes this. There is no published mapping from raw marks or graded-assessment scores to study scores, and no per-study distribution of study scores. Anybody quoting "you need X/40 and Y/80 for a 45 in Methods" is offering a reconstruction, not a published figure.

What is published, and is the closest legitimate anchor:

• A study score of 40+ is "among the top eight per cent in the state" (VCAA).
• The 2025 grade percentages give exact cumulative percentiles. On Exam 2: A+ = top 9.2%; A+ and A together = top 21.9%; down through B+ = top 36.2%. On Exam 1: A+ = top 9.0%; A+ and A = top 22.0%; through B+ = top 35.8%. On Coursework: A+ = top 7.7%; A+ and A = top 16.9%.

The honest inference, clearly labelled as inference: since 40+ is roughly the top 8% and an A+ on either paper is roughly the top 9%, a study score around 40 broadly corresponds to A+-boundary performance across all three graded assessments in the same year. A 45 sits at roughly the top 2%, which is well inside the A+ band on every component — and the published grade data cannot resolve any further, because VCAA does not publish sub-A+ percentiles. I will not put a raw-mark number on 45.

What the data can tell you, and it is more useful than a threshold: at the A+ boundary you are already conceding 4–7 marks on Exam 1 and 10–19 on Exam 2. Going further means converting the marks in the "separator" band of §10.4 — the 30–40% of each paper on which the state earns under 40% — and that band lives almost entirely in the final parts of questions (§10.5).

10.9 Scaling

For the ATAR, VTAC scales each study score. From the VTAC 2025 Scaling Report (published 11 December 2025):

The 2024 report gives essentially identical figures for Mathematical Methods (scaled mean 34.5, SD 8.4; 30 → 35, 40 → 46, 45 → 49).

Two features of the mathematics scaling are worth knowing. From VTAC's ATAR and Scaling Guide 2026: "all four mathematics studies are scaled against each other as well as being scaled against all other studies. The higher of the two resulting scales is used." And scaled study scores run on a 0.00–55.00 scale — so Methods at a raw 50 scales above 50, to 51.

Note also that a raw 45 scales to 49 and a raw 40 to 46: the scaling increment shrinks as you go up. The marginal ATAR value of moving from 40 to 45 in Methods is three scaled points, not five.

---

11. Open questions and things this document could not establish

Listed explicitly, because a reference document that hides its gaps is worse than useless.

1. The 2006–2015 study design could not be obtained. VCAA no longer publishes it and I could not find an archived copy. Everything said about that era in §9.2 is inferred from the examination papers, the formula sheets and the assessment reports — all primary sources, but none of them a statement of what was in scope. The 2006–2015 column of the table in §9.6 should be treated as evidence-based rather than authoritative.
2. Whether the second derivative is examinable technology-free. The 2023 design names points of inflection but never the second derivative, and the formula sheet carries no second-derivative notation. Every inflection question in the 2023–2026 archive is in Exam 2 and answerable numerically. Unresolved.
3. Whether the formula sheet may be read during reading time. VCAA's reading-time rule names "the instructions, the question book and a dictionary or bound reference" and does not mention it. Unresolved.
4. Why the multiple-choice option count changed, and where it was announced. [SPEC] Version 3 (March 2025) is silent on the number of options despite postdating the change. Established from evidence, not from a published statement.
5. Whether Mathematical Methods is one of the "few studies" whose statistical moderation uses GAT scores. VCAA says "in some studies" and does not name them.
6. The accreditation end year. VCAA's current study design page says "Accreditation period from 2023" with no end date. "2023–2027" appears on the original cover and is universally cited, but I could not confirm against a live VCAA page that it has not been extended. Treat 2027 as probable, not certain.
7. The doubled scale in the grade-distribution tables (Exam 1 out of 80, Exam 2 out of 160) is an inference. It is confirmed by cross-study consistency and by agreement with reconstructed means to within 0.35 of a mark, but VCAA does not state it. Where possible, quote thresholds as a percentage of the paper, which is scale-independent.
8. No mark weighting by area of study is published for Mathematical Methods. Unlike General Mathematics, there is no blueprint. Any topic-weighting claim on this site must be presented as an observed pattern from past papers, never as a specification.
9. 2011 data is unusable and 2008/2009 Exam 2 data is partial, as set out in §0.1.
10. NHT papers carry no state statistics. They are content evidence only.
11. The 2025 Exam 1 report's sentence about exact circular-function values has its symbols embedded as images. The sentence structure is verbatim; the symbols are read from context and should be verified against the source before being republished with the symbols filled in.

---

12. One-page summary for a student

• Four areas of study, all compulsory, all examinable on both papers: Functions relations and graphs; Algebra number and structure; Calculus; Data analysis probability and statistics.
• Three outcomes. Exam 1 is Outcome 1 only. Exam 2 is all three, with an emphasis on Outcome 2.
• Exam 1: 1 hour, 15 minutes reading, 40 marks, 8–9 questions, no technology, no notes, formula sheet provided. 20% of the study score.
• Exam 2: 2 hours, 15 minutes reading, 80 marks. Section A = 20 multiple-choice, four options each since November 2024, 1 mark each, no penalty for a wrong answer. Section B = 4–5 extended questions, 60 marks. One CAS plus one scientific calculator, memory not cleared. One bound reference, no page limit, no sticky tabs, no ring binders. 40% of the study score.
• The formula sheet is the same for both papers, and you keep it. It does not give you: exact trig values, the Pythagorean identity, index or log laws, the average value formula, the average rate of change, the quadratic formula, or z ≈ 1.96.
• Exact values are the default on both papers wherever no accuracy is stated.
• Show working whenever more than one mark is available. Consequential errors are followed through; contradictory final answers void the marks.
• The state averages about half marks on both papers. Around a third of every paper consists of marks fewer than 40% of the state earns.
• The last part of every question is where you separate. Across ten years, the first part of a Section B question is answered fully by 72% of the state; the last part by 18%.
• When practising the archive: skip matrix transformations and functional relations (removed in 2023); expect no Newton's method, trapezium rule or pseudocode before 2023; expect no confidence intervals before 2016; expect no points of inflection between 2016 and 2022.