Anatomy of a separator

How VCAA builds a question, where the cohort falls off, and what the 779 measured separators have in common.

Compiled 15 September 2026. This is the cross-cutting document. Areas of study 1–4 are catalogued in 02-functions-graphs.md, 03-algebra-number.md, 04-calculus.md and 05-probability-statistics.md; the study design and examination specifications are in 01-study-design.md; VCAA's wording conventions are in 07-exam-craft.md. Nothing here repeats those catalogues. Everything here is a claim that can only be made by looking across all four areas and both papers at once.

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Table of contents

0. Method, definitions, and what the data can and cannot support
1. How a Methods question is constructed
2. The measured anatomy of difficulty
3. The failure mechanisms, ranked
4. The five shapes that separate reliably
5. What does not separate
6. A diagnostic

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0. Method, definitions, and what the data can and cannot support

0.1 What a separator is, precisely

A separator is a graded question part for which pct ≤ 50 — that is, half the state or more failed to earn full marks on it. pct is VCAA's published percentage of the cohort awarded the maximum mark for that part. It is not a mean score and it is not a "percentage correct" in the loose sense: a 3-mark part on which most students scored 2 has a low pct and is still a separator.

The threshold is a convention, not a natural boundary. Its usefulness is that it is symmetric and mark-independent, which lets a 1-mark multiple-choice item and a 4-mark extended-response part be counted in the same table. Its cost is that it understates the difficulty of high-mark parts — §2.2 shows exactly how much.

0.2 The corpus

Every statistic below is computed from corpus/mm/questions.json with Python, restricted to November rows only. The Northern Hemisphere Timetable papers carry no state statistics (pct is null for all 413 NHT rows), so they contribute nothing to any count here.

Weighted by marks rather than by parts, the picture is worse: of 2 379 November marks in the corpus, 1 427 sit inside separators — 60.0%. Mean pct across all November parts is 48.2; the median is 49.

That is the single number to hold on to. Three-fifths of every mark VCAA has set in twenty years sits in a part that most of the state could not complete. A Methods paper is not a body of routine work with a hard tail attached. The hard part is the paper; the routine work is the first part of each question.

0.3 Data-quality caveats that bind this document

These are inherited from 01-study-design.md §0.1 and are restated because they constrain specific tables below.

• 2011 is OCR-damaged. Question labels are duplicated and some distributions are unreliable. 2011 rows are included in the aggregate tables (they are 72 of 1 504 parts and move no headline figure by more than 0.3 points) but no individual 2011 part is named as evidence anywhere in §1, §4 or §5, and the one 2011 item that does appear in an extremes list is flagged.
• 2008 and 2009 Section A are partially extracted — 8 of 22 and 17 of 22 items respectively. Section A rates for those two years rest on small samples.
• The 2024 November paper texts are empty files. 2024 statistics are complete (they come from the assessment reports), but 2024 question wording is only available through the report commentary. Where a 2024 part is dissected below, that is stated.
• Multiple-choice option distributions stop after 2019. VCAA published the A/B/C/D/E breakdown from 2006 to 2019 (281 of 401 items) and has published only the correct-response percentage since 2020. Every claim about which distractor won is therefore a 2006–2019 claim.
• Report commentary exists for 1 099 of the 1 504 November parts (73.1%) — 650 separators and 449 non-separators. §3's ranking is computed over those 1 099 only.

0.4 The question-text extraction used in §4 and §5

Statements about wording (as opposed to statistics) require the question text, which lives in the paper files, not in questions.json. Question blocks were located by walking the Question N headers in each paper, parts were split on the a. / i. markers, and each part's own text was truncated at its first N mark(s) token. A part was accepted only if that token matched its recorded max_mark or no token was present.

That yields 831 validated November written parts — 55.4% of them separators, mean pct 45.8, against 55.4%/45.8 for the subset as a whole. The subset is representative but it is a subset: it excludes the 2024 November paper entirely, excludes multiple choice, and skews slightly towards Section B. Every marker rate in §4 and §5 is quoted against that subset's own base rate, never against the whole-corpus base rate. Where a marker's count falls below about fifteen, it is labelled as indicative only.

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1. How a Methods question is constructed

1.1 The four components, named

Read across twenty years of papers and the same skeleton appears in every extended-response question, in all four areas of study, on both papers. It has four parts.

The stem. The context and the object. On Exam 1 it is usually one line — a function definition, sometimes with a restricted domain. On Exam 2 Section B it is a paragraph plus a graph, and it carries the modelling frame (a zip-line, a Ferris wheel, a delivery company, a box folded from card). The stem's job is to fix notation and supply everything the early parts need. It almost never contains the difficulty.

The given. One or more objects handed to you outright: a rule, a printed graph, a table of probabilities, a number to be verified, or — most importantly — a "show that" result. The given is VCAA's error-containment device. It is what makes a nine-part question survivable: if part (a) asks you to show that Vbox(x) = 2x(25 − 2x)(25 − x), then every later part can use that rule whether or not you derived it. 07-exam-craft.md §2 covers the "show that" contract in full; the structural point here is that a "show that" is a reset switch, and VCAA places them deliberately.

The scaffold. The ordered parts. This is the staircase: 1-mark retrieval, then 1–2-mark computation, then 2–3-mark synthesis. 07-exam-craft.md §4.4 measures the staircase by mean pct; §2.3 below measures it by separator rate, which is a sharper instrument, and §2.4 crosses it with mark value, which is sharper still.

The sting. The final part — sometimes the final two. It takes the object the whole question has been building and does one of five things to it (§4). It is worth 1–4 marks, it averages 2.15 marks against 1.57 for the opening part, and 94.5% of the time it is a separator.

Two further structures recur often enough to name:

The re-stem. New information introduced mid-question, usually with a fresh diagram: "The cable for the zip-line is connected to a pole at the origin at a height of 10 m…" (2019 Exam 2 Section B Q2, between parts b and c). A re-stem resets the context without resetting the difficulty.

The reset. A part whose pct jumps up by 20 points or more from the part before it. Across the 593 consecutive part-pairs inside Section B's 91 multi-part questions, 80 (13.5%) are resets and 178 (30.0%) are falls of 20 points or more. The staircase is emphatically not monotone. A collapse in part (d) does not condemn part (e), and §6 turns this into a rule.

1.2 Area of Study 1 — Functions, relations and graphs

1.2.1 The minimal anatomy: 2019 Exam 1 Question 8 (4 marks)

Three parts, 4 marks, and it is the cleanest illustration in the archive that the sting does not need a long question to work.

"The function f : R → R, f(x) is a polynomial function of degree 4. Part of the graph of f is shown below. The graph of f touches the x-axis at the origin." — with the graph marked at (−1, 0) and (1, 0), and with two labelled turning points at height 1.

There is no scaffold here at all. The stem is two sentences; the given is a graph; and all three parts are stings. Part (a) looks like a 1-mark gift and is not: the report [RPT] records "This question was well attempted but not done well, with many students overlooking the dilation factor." The graph fixes the roots but the turning-point height fixes the leading coefficient, and 86% of the state did not use it.

Part (b) then compounds two maximal-domain conditions — g(x) > 0 read off the graph, and x³ + x² > 0 solved algebraically — and part (c) requires you to simplify the logarithmic difference before you can see the range at all. The report on (c) is three words long in substance: "Some students sketched various graphs with limited success… Not many students attempted this question. Only a few students used logarithm laws."

The anatomical lesson. When VCAA declines to build a scaffold, it is because the question is short enough that the cohort will still attempt every part. The 4-mark Exam 1 question with no scaffold is more dangerous per mark than the 12-mark Section B question with nine steps.

1.2.2 The one-step-then-cliff: 2016 Exam 1 Question 5 (11 marks)

95 → 15. A drop of 80 points between two consecutive parts of the same question, on the same function.

Part (a)(i) is transcription: substitute one rule into another. Part (a)(ii) asks what that object actually is. The report:

"A small proportion of students gained full marks for this question. While poor notation was a contributing factor, students appeared to experience difficulty in determining the range of the composite function, h. A quick sketch over the given domain would have been helpful. Students are reminded that the domain and range of a function are key aspects of a function."

and on (b)(ii):

"Most students utilised the fact that Range of k⁻¹ = Domain of k, but found stating the domain of the inverse function more difficult. Again, poor notation was evident."

The anatomical lesson. VCAA's cheapest sting in this area is to ask for the set attached to an object you have just written down. Writing the rule of a composite is 95%-level work. Stating its range is 15%-level work. The mathematics has not increased; the type of the answer has changed from an expression to a set. §4, Shape 2.

1.2.3 The full Section B build: 2017 Exam 2 Section B Question 2 (12 marks)

The Ferris wheel. This is the archetype of a modelling question with two re-stems and a terminal geometric synthesis.

Stem. "Sammy visits a giant Ferris wheel… The height of P above the ground, h, is modelled by h(t) = 65 − 55cos(πt/15), where t is the time in minutes after Sammy enters the capsule and h is measured in metres. Sammy exits the capsule after one complete rotation."

Three features to read off this.

First, the reset at part (e) is real and large: 36 → 91. VCAA re-expresses the path as an explicit function precisely so that a student who failed parts (c) and (d) can still bank a mark. Part (e) is a one-line chain-rule derivative on a supplied rule.

Second, part (f) is where the question turns, and the mechanism is the parameter. The report:

"Many students were able to find the gradient of the line segment in terms of u, using their answer from Question 2e. Others used h(t) or y = √(3025 − x²) instead of y = √(3025 − x²) + 65. Many students were unable to find the second gradient expression where they were required to use rise over run for the line segment P₂B."

Two gradient expressions for the same line — one by calculus, one by coordinate geometry — set equal to each other and solved for u. Neither is hard. Holding both at once, in terms of an unknown, at minute 90 of a two-hour paper, is 8%-level work.

Third, part (h) is a 2% part whose report is entirely about presentation:

"This question was not answered well. Some students wrote 7 minutes without showing any working. As indicated in the instructions on the examination, for questions worth more than one mark, appropriate working must be shown."

The answer is 7 minutes. Students who reached it and wrote only the number scored zero. That is the sting doing double duty: it is conceptually the hardest part and the part where the show-your-working rule is enforced most brutally, because a bare number could have been guessed.

1.2.4 The transformation sting: 2024 Exam 1 Question 5

The 2024 November paper text is not in the corpus; the structure is reconstructed from the report and assessment guide.

95 → 2 in one step. The expected answer, per the assessment guide, is a dilation and a translation, each stated with both the factor and the correct axis language; several equivalent phrasings and mapping-notation forms are accepted. The report:

"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."

Note what this part is not: it is not a computation. Nothing needs solving. The 98% who failed it knew which transformations were involved. They lost the marks on vocabulary. §4, Shape 3.

1.3 Area of Study 2 — Algebra, number and structure

This is the hardest area in the subject by separator rate — 61.5% of its 192 November parts, against 46.1% for functions and graphs — and the reason is visible in its anatomy: algebra questions have almost no stem and almost no scaffold.

1.3.1 The one-shot question: 2024 Exam 1 Question 2 (3 marks, single part)

A single-part Exam 1 question asking for the values of a parameter for which a 2×2 linear system has no solution. pct = 37, 22% of the state scoring zero, meaning most of those who failed still wrote something creditable.

The report is unusual and worth quoting at length because it is VCAA describing method-selection as the difficulty:

"There were multiple ways to approach this question; however, generally students approached this by one of the following: equating gradients and y-intercepts separately; using a matrix/determinant method; forming ratios; or attempting to solve simultaneously. These methods were met with varying degrees of success. Those who knew that the two lines needed to have identical gradients were generally successful."

The anatomical lesson. Across the corpus, the 52 single-part November questions separate at 73.1% with a mean pct of 40.9 and a mean of 2.73 marks each. A question with no scaffold is a question with no partial-credit pathway designed in. VCAA uses this form when the content is a single named technique — and the mean mark value tells you it does so deliberately, reserving it for 3-mark work.

1.3.2 The parameterised equation: 2025 Exam 1 Question 9 (7 marks)

The most recent Exam 1 sting in the archive, and a textbook Shape 1.

"Consider the functions f : R{1} → R, f(x) = w²/(x − 1)² and g : R → R, g(x) = (x − w)², where w ∈ R."

Part (a) substitutes a number for the parameter — and is still a 19% question, because the efficient route (take square roots to get two quadratics) is not the route most students chose. The report:

"Many students expanded the expression and formed a quartic equation but did not proceed further. Students who took the more efficient approach of taking square roots to form two quadratic equations generally reached the correct solutions. Many students did not consider x ≠ 1 in their solution process and thus simplified the solution process inappropriately."

Part (b)(i) restores the parameter and hands you a scaffold — a minimum point, in terms of w, of a quadratic that is not the equation you are solving but is a factor of it. Part (b)(ii) is the sting: the "exactly three solutions" condition. 94% of the state scored zero.

The anatomical lesson. VCAA builds these in the order specific case → general object → counting condition. The scaffold at (b)(i) is genuine — the assessment guide's own solutions use it — but only 22% of the cohort could produce it, so the "hence" in (b)(ii) had nothing to attach to. A scaffold only functions for the students who cleared the previous step. This is why the reset (§1.1) matters so much: a "show that" scaffold works for everyone; a "find, then hence" scaffold works only for the survivors.

1.3.3 The twenty-one-mark build: 2016 Exam 2 Section B Question 4

The longest Section B question in the corpus, and the most complete anatomy available. It is nominally an algebra question and it visits four areas of study.

Four structural observations.

1. The reset at (b)(iii). Part (b)(ii) requires an integral; part (b)(iii) requires only the observation that the region between f and f⁻¹ is twice the region between f and y = x, by symmetry. Both scored 62%. The report: "Some students realised that the answer to this question was double that of the previous result." VCAA placed a one-line symmetry argument immediately after a computation so that both are worth 1 mark.

2. The parameter is introduced at (d), not before. Parts (a)–(c) run on a concrete function. g(x) = (kx+1)/(x+k), k > 1, is defined in a one-line re-stem between (c) and (d), and from that moment pct never exceeds 38.

3. Both 2-mark "show that" parts are catastrophic — 6% and 2%. These are not the "show that this rule follows from this geometry" kind; they are general claims quantified over an interval and over a parameter. The report on (d): "Many students did not attempt this question. Some just substituted in specific values, which was not acceptable." On (f)(ii): "Many students did not attempt this question."

4. (e)(iii) at 3% is a set-valued answer, and the report records the single most common near-miss: "Some students had 1 ≤ k ≤ 4" — the inequality direction and the endpoints, not the algebra.

1.4 Area of Study 3 — Calculus

1.4.1 The owner switch: 2019 Exam 2 Section B Question 2 (11 marks)

The zip-line. The most-studied single step in the archive: 93 → 3 between parts (a) and (b), the largest consecutive fall in twenty years.

Stem. "An amusement park is planning to build a zip-line above a hill on its property. The hill is modelled by y = 3x(x − 30)²/2000, x ∈ [0, 30]…"

The report on (b):

"This question was not done well. Most students interpreted the question as asking where the function modelling the hill was strictly decreasing, rather than the gradient of the hill and so the most common incorrect response was [10, 30] or a combination of round and square brackets with those two values."

The answer is (0, 20]. The question does not ask where the hill decreases; it asks where the gradient decreases, which is a statement about y″. The noun that owns the property moved one derivative to the right, and 97% of the state did not notice.

Note also that part (b) is worth 1 mark and is harder than part (d), worth 3. The mark allocation is not a difficulty scale. §2.4 quantifies this.

Part (c) is a reset — it simply asks you to write y + 3 — and recovers to 62%.

1.4.2 Numbers, then a parameter, in six parts: 2021 Exam 2 Section B Question 2 (10 marks)

The purest Shape 1 in the corpus, because the mathematics is held fixed across the whole question and only the parameter changes.

Parts (a), (c) and (e) are 80–96% work. Part (d) transplants the identical rectangle technique onto an unfamiliar printed graph and drops to 16%. Part (f) takes the identical area computation from part (e), puts a parameter in the curve and in the terminal, and drops to 2%.

The report on (f):

"Many students were able to find [one boundary] or [the other] but not both. Others found [the intersection] but did not set up the definite integral properly."

The zero rate on (f) is 48% — unusually low for a 2% part. Half the cohort earned something. That is the signature of a 4-mark separator: the marks are spread across the setup, and a student who wrote the correct integral without evaluating it correctly banked two of them. §2.7.

1.4.3 The new-study-design build: 2023 Exam 2 Section B Question 3 (12 marks)

The first paper under the 2023 design, and the question in which VCAA introduced points of inflection and Newton's method to a live cohort. Built on h(x) = 2ˣ − x².

Three things stand out.

The genuinely new content was not the difficulty. Newton's method, brand new to the course, scored 54%. The point of inflection, brand new to the course, scored 58%. The 2023 report says so directly:

"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 old content in a new dress was the difficulty. Part (e) — strictly decreasing, a topic examined every year since 2006 — scored 35%, and the report is entirely about brackets:

"Round brackets were often seen; these were incorrect as the largest interval of x values was required, which included the interval endpoints. In some cases, it was impossible to determine whether the student meant round or square brackets."

Part (g) is the "explain why" sting. At 21%, it asks for a reason rather than a number. The report: "Some students only mentioned the two solutions" — that is, they stated the fact without connecting it to the failure of the method.

1.5 Area of Study 4 — Data analysis, probability and statistics

1.5.1 Three parts, and the third is the trap: 2012 Exam 1 Question 4 (6 marks)

"On any given day, the number X of telephone calls that Daniel receives is a random variable with probability distribution given by:" x = 0, 1, 2, 3 with Pr = 0.2, 0.2, 0.5, 0.1.

Part (c) contains no new distribution, no new technique, and one extra sentence. That sentence — "Daniel receives telephone calls on both Monday and Tuesday" — is a condition, and it changes the sample space from all 16 (Monday, Tuesday) pairs to the 9 pairs in which both days are non-zero. The report:

"Most students were not aware that the condition of 'receives telephone calls on both Monday and Tuesday' would affect the result. A significant number of students incorrectly thought that two calls on Monday and two calls on Tuesday was different from two calls on Tuesday and two calls on Monday. Students who used a key or tree diagram were less likely to make this error."

Two distinct failures in one part: not recognising the conditioning, and double-counting the unordered outcomes. Only 3% of the state avoided both. Note again the zero rate: 41%, meaning 56% of the state earned 1 or 2 of the 3 marks. A separator is rarely a wipeout. §2.7.

The anatomical lesson. In probability, the sting is usually a sentence, not a symbol. There is no Pr(A | B) notation anywhere in that question. The conditioning is prose.

1.5.2 The full statistics staircase: 2020 Exam 2 Section B Question 3 (12 marks)

Normal distribution → conditional probability → parameter → binomial → n → algebra.

Every one of the four constructions in §4 appears in this one question.

Part (b) is a conditioned probability written in prose — "of a delivery being no later than three minutes after its scheduled delivery time, given that it arrives after its scheduled delivery time" — and the report catches the classic inversion:

"Many students were able to recognise that this was a conditional probability question. Some were unable to write [the conditional statement] correctly. Others had 0.77 as the numerator and 0.5 as the denominator, creating an answer greater than 1. Some rounded too early…"

Part (c) asks for values, plural, of a parameter — a set-valued answer — and the report is one sentence: "Many students did not find [the second value]." The distribution is symmetric; there are two k. 94% of the state gave one.

Part (e)(i) demands the answer "in terms of n" and (e)(ii) inverts it over the integers, with the classic rounding trap: "Some students left their answer as 18.43 or rounded down to 18."

Part (f) at 3% asks for the minimum and maximum of a quantity constrained by a law-of-total-probability identity — a set-valued answer over a parameter range. The report: "Students who used a tree diagram were generally successful. Some gave approximate answers when exact answers were required."

1.5.3 What the four areas share

The construction does not vary by area of study. VCAA writes the same question in four vocabularies. The stem changes; the anatomy does not.

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2. The measured anatomy of difficulty

2.1 The base rates

2.2 Separator rate by mark value

The relationship is monotone and steep: the second mark adds 28 percentage points to the probability that the part is a separator, the third adds 19, and the fourth adds 7. It saturates around three marks.

The same pattern holds independently on both papers, which rules out a paper effect:

What this means. The pct ≤ 50 threshold is a much weaker test for a 3-mark part than for a 1-mark part, because full marks on a 3-mark part requires three independent things to be right. A 3-mark part at pct = 30 may be easier, step for step, than a 1-mark part at pct = 30. This is the single most important correction to make when reading any separator list, including the ones in 02–05.

The practical consequence runs the other way from what students expect. A 3-mark part is not three times as risky as a 1-mark part; it is about twice as likely to be a separator but far more likely to yield partial credit (§2.7). The parts to fear are 1-mark parts with low pct, because on those there is no partial credit at all.

At the extremes: the only 5-mark written part in the corpus is 2006 Exam 1 Q11 at 46% — itself a separator. Of the 21 four-mark parts, exactly two were not separators — 2010 Exam 2 Section B Q4a (54%) and 2008 Exam 1 Q2 (57%, a sketch) — and the worst are 2021 Exam 2 Section B Q2f (2%), 2024 Exam 1 Q6 (9%), 2017 Exam 1 Q9d (9%) and 2020 Exam 1 Q6c (10%).

2.3 Separator rate by position within a Section B question

There are 91 Section B questions with three or more parts in the twenty November Exam 2 papers. Every Section B question in the corpus has at least three parts.

Eighty-six of the ninety-one final parts of a Section B question, across twenty years, are separators. The five that are not are:

No final part of a Section B question has ever exceeded 58%. By contrast, 31 of the 91 final parts scored 10% or less.

By ordinal position, the ramp is smooth and long:

Normalised by question length, in quintiles of the way through:

The 50% crossover happens between 40% and 60% of the way through a Section B question. Before that point most parts are gettable; after it most are not.

The staircase is not monotone

Of the 593 consecutive part-pairs inside those 91 questions:

• 178 (30.0%) fall by 20 percentage points or more.
• 80 (13.5%) rise by 20 percentage points or more.

The largest single-step falls:

One consecutive pair in seven is a reset. That is the number that should govern exam behaviour: after a part you could not do, the prior probability that the next part is easier than the one you just failed is about 1 in 7, and the probability that it is within 20 points is much higher again. Skipping forward is nearly free.

2.4 Mark value crossed with position

Neither variable explains the other. Both matter, and they compound.

Separator rate:

Mean pct:

Read the corners. A 1-mark opening part is a separator 10% of the time and averages 74%. A 2-mark closing part is a separator 97% of the time and averages 21%. Those are two different subjects.

Note also the anomaly in the first column: a 3-mark opening part separates at 80%, barely below a 3-mark closing part at 97%. When VCAA opens a question with three marks, it is not warming you up — it is asking you to construct the object the rest of the question will use, usually as a "show that" or a model-fitting step. (This clarifies rather than contradicts 02-functions-graphs.md §5.6: most separators are 1- and 2-mark parts, because most parts are 1- and 2-mark parts. The rate runs the other way.)

2.5 Separator rate by exam and by section

Exam 1 is by a wide margin the harder paper per part, and it is not close. It is also the paper with fewer marks and half the study-score weight. That asymmetry is the strongest strategic fact in the subject: 20% of the study score sits in the part of the assessment where the state performs worst.

Within Exam 1, by question number:

Normalised for the varying number of questions per paper (8 to 12 across the eras):

And the strongest single result in the whole document:

Across all twenty November Exam 1 papers, the final part of the final question is a separator. Twenty out of twenty. Mean pct 12.3, mean mark value 2.40. The best any cohort has ever done on it is 46% (2006 Exam 1 Q11); the worst is 3% (2020 Exam 1 Q8dii). Eleven of the twenty scored 9% or less, and only four reached 20% or more.

The whole final question of Exam 1 separates at 84.3% across its 70 parts (mean pct 28.0), against 17.1% for the whole first question (41 parts, mean 63.5).

Within Section A, by question number:

Aggregated: the last four multiple-choice items of each paper separate at 72.5% (mean pct 43.0); the first four separate at 10.0% (mean pct 72.1). A seven-fold difference inside a section where every item is worth exactly one mark and takes roughly the same time to read. (07-exam-craft.md §5.2 gives the same ramp in mean-pct form, including the Q14–Q15 local easy patch, which is visible here too: 26% and 32% against 42% at Q13.)

2.6 Separator rate by area of study and by year

Algebra is the hardest area and the smallest — 192 parts, 12.8% of the corpus, against 505 for functions and graphs. It is also, per 01-study-design.md §3.2, the area rewritten most aggressively in 2023, and the area whose content most often appears as the last step of someone else's question.

Crossed with section, the picture sharpens considerably:

Two findings here are not visible in any single-area document.

First: statistics is easy in Section A and hard in Exam 1. 32.3% versus 67.9% — the largest gap of any area. With technology, a normal or binomial probability is a two-keystroke operation. Without it, the same content requires standardising by hand, expanding (1−p)ⁿ, or manipulating a conditional statement algebraically. The area whose reputation is "calculator work" is the area that punishes the technology-free paper hardest.

Second: algebra is the only area that is hard everywhere. It is above 50% in all three sections and it is the only area whose Section A rate exceeds 50%. The multiple-choice items that are genuinely about algebra — simultaneous systems with a parameter, solution counting, logarithm identities — sit in the Q16–Q20 band by design.

By year:

The year-to-year spread is 43.0% (2022) to 63.4% (2007), and there is no trend. Grouped by era:

The examination has not become harder or easier in twenty years. VCAA is targeting a constant difficulty and hitting it to within about two percentage points per era. What has moved is the distribution: functions and graphs is harder under the 2023 design (46% → 54%) and statistics is easier (57% → 45%). The functions shift is consistent with the study design's new licence for "theoretical investigations" (01-study-design.md §2.1); the statistics shift is consistent with the binomial formulas moving onto the formula sheet in 2023 (01-study-design.md §5.3). Three years is a short base; treat both as provisional.

The 2023-onwards Section A rate (55%, 40%, 40%) sits well above the long-run average of 35.7%, which is worth noting for anyone budgeting Section A time from pre-2020 papers.

2.7 The shape of a separator's mark distribution

This is the part of the anatomy that is invisible in a pct table. Computed over the 1 103 November written parts that carry a full distribution — 636 separators, 467 non-separators.

For a 1-mark part the modal-zero result is definitional (pct ≤ 50 forces zero ≥ 50). The informative rows are the multi-mark ones:

So: on a typical 2-mark separator, more of the state scores nothing than scores anything. On a typical 3-mark separator, zero is still the single most common outcome, achieved by three students in eight.

The average distributions, which are the clearest single picture of what a separator does to a cohort:

Three consequences.

The distribution is U-shaped, and separators are more U-shaped than the rest. On 2-mark parts, the 1-mark bar is the smallest of the three in 64.9% of separators against 57.9% of non-separators, and averages 19.7% against 16.4%. Methods marking is largely binary at the part level: you either had the idea or you did not.

But separators award more partial credit, not less. Across all multi-mark parts, the share of the cohort scoring strictly between zero and full is 23.8% on separators against 17.6% on non-separators (medians 21% and 18%). The all-or-nothing share (zero plus full) is 80.4% on 2-mark separators against 83.7% on non-separators, and 67.8% against 74.8% at three marks. The harder the part, the wider the middle band.

This is the practically important finding in the whole section. On a separator, writing the first correct line is worth more than it is on an easy part, because the mark scheme on a hard part has more places to give you something and the cohort you are being compared against is mostly on zero. 2021 Exam 2 Section B Q2f is the extreme case: pct = 2%, but the zero rate is only 48%, meaning half the state earned 1–3 of the 4 marks on a part almost nobody finished.

The very worst parts are genuine wipeouts. The 127 parts where three-quarters or more of the state scored zero are a different animal. The top of that list:

Note that nine of those eleven are worth one mark, and all but one are final or near-final parts. A 1-mark part late in a question with no partial credit available is the most efficient marking instrument VCAA has, and it uses it.

2.8 The extremes

The lowest-pct written parts in the corpus (November only; 2011 items flagged):

And the lowest-pct multiple-choice items:

Look at the 2018 Q18 and 2016 Q19 splits: 17/22/24/21/14 and 16/25/22/20/15. Those are indistinguishable from uniform. When a Section A item reaches that state the cohort is not making a particular mistake — it is guessing, and the correct answer is drawing fewer selections than chance. 2015 Q3, where the sign-error distractor drew 61% against the key's 20%, is the opposite pathology and is covered in 07-exam-craft.md §5.4.

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3. The failure mechanisms, ranked

3.1 Method

07-exam-craft.md §6 ranks the report complaints by raw frequency across all 1 105 commented questions. That ranking answers "what does VCAA complain about?" It does not answer "what makes a question a separator?" — because the most frequent complaints attach disproportionately to questions the state got right.

The analysis below re-runs the categorisation on the 1 099 November parts with report commentary and splits them: 650 separators against 449 non-separators. The column that matters is the last one, the lift — the prevalence of that complaint among separators divided by its prevalence among non-separators. A lift above 1 means the complaint is characteristic of hard questions. A lift below 1 means it is characteristic of easy ones.

Categories overlap; a commentary can raise several.

3.2 The ranked table

Two caveats on the table. Rows with fewer than ten separator matches — "answered a different question", "gave one solution", "units", "coordinates", "failure to simplify", "sign error" — are indicative only; their lifts rest on single-figure counts. Every row above 1.5× except those two clears that bar.

And one category had to be split. A naive search for the word "units" returns a 2.6× lift, which is an artefact: nineteen of the twenty-four matches are the phrase "translate k units" inside a transformation commentary, not a complaint about measurement. Scoring only the genuine measurement complaints ("incorrect units, such as mm for milligrams" — 2014 Exam 2 Q3a, 75%) gives 3 separators and 3 non-separators, lift 1.0. The contamination is itself informative: transformation language is so over-represented among separators that it leaks into any keyword that touches it.

The split is stark and clean. Everything above the line is about deciding what to do. Everything below it is about executing or presenting what you decided.

3.3 The mechanisms that cost you the question

1. Not attempting it at all (lift 24.9×, mean pct 18.3). Thirty-seven parts in the corpus have a report that says the cohort did not attempt them; 36 of the 37 are separators and the mean pct is 18.3. This is the highest-lift signal in the data by a factor of two.

"Many students did not attempt this question." — 2013 Exam 2 Section B Q4diii (2%), 2016 Exam 2 Section B Q4fii (2%), 2016 Exam 2 Section B Q4d (6%), and nine more, verbatim and identical.

"This question was attempted by only a small number of students. When the correct answer was given, it was sometimes accompanied with incorrect values of m and n… The key word in this part is restrictions." — 2020 Exam 2 Section B Q5h (2%).

"Many students did not attempt Questions 5e. and 5f., which were more demanding questions." — 2007 Exam 2, general comments.

"Time management appeared to be an issue for some students this year and Question 10 was either rushed or not attempted. Students are reminded that they do not need to answer questions sequentially. They should think about completing as much as they can of the straightforward questions before they embark on the longer, more involved questions." — 2011 Exam 1, general comments.

Non-attempt is partly time and partly recognition. Both are addressable and §6 addresses them.

2. Choosing the wrong method, or not recognising the concept (lift 3.1×, mean pct 32.2). The largest category by count among separators: 85 of 650.

"Most students were not aware that the condition of 'receives telephone calls on both Monday and Tuesday' would affect the result." — 2012 Exam 1 Q4c (3%).

"Many students were unable to set up the correct equations. The terminals were often incorrect." — 2021 Exam 2 Section B Q4h (2%).

"Many students had difficulty with this question. Students who recognised that the graph for this question was simply a combination of translations and reflections of an earlier simpler graph were able to use symmetry to determine [the answer]." — 2018 Exam 1 Q9d (4%).

"This question was answered poorly. A complete solution to this question required setting up an equation for the area in one variable and then testing turning points…" — 2014 Exam 1 Q10bii (9%).

3. Transformation vocabulary (lift 5.1×, mean pct 31.8). Measured across the whole corpus by commentary keyword, parts whose report mentions a dilation, translation, reflection or transformation separate at 91.7% (n=48) with a mean pct of 29.4 — the worst of any content marker in the subject. See §4, Shape 3.

4. Conditional probability (lift 2.8×). Parts whose report names conditional probability separate at 84% (n=25) with mean pct 35.4. See §4, Shape 5.

5. Domain, endpoints and restrictions (lift 1.7×, 59 separators).

"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." — 2021 Exam 1 Q9ci (1%).

"Some students did not consider the domain and chose the incorrect value for x. Others gave two sets of coordinates." — 2016 Exam 2 Section B Q4ei (24%).

"Round brackets were often seen; these were incorrect as the largest interval of x values was required, which included the interval endpoints." — 2023 Exam 2 Section B Q3e (35%).

6. The owner switch (lift 1.9×). Parts whose report mentions confusion between a function and its derivative, or between average value and average rate of change, separate at 73.5% with mean pct 36.4 (n=34). The canonical instance is 2019 Exam 2 Section B Q2b at 3% (§1.4.1). VCAA has flagged the average-value/average-rate pair in consecutive years:

"Some students had difficulty understanding some of the concepts, such as the difference between average value of a function and average rate of change." — 2023 Exam 2 report.

"Some students found the average value when the average rate of change was required." — 2024 Exam 2 report.

3.4 The mechanisms that cost you a mark

Every category below lift 1.0 is a presentation failure, and they cluster on questions the state largely got right.

Rounding (lift 0.63, mean pct of matches 49.4). The single most frequent complaint in the whole corpus and it is negatively associated with separators. Its natural home is a question where 60–70% of the state produced the right number:

"Students should always work to suitable accuracy in intermediate calculations to support rounding the answer to the required accuracy." — 2014 Exam 2 Q3ci (72%).

"Some students rounded their answer to 0.47." — 2021 Exam 2 Section B Q2b (60%).

Differentiation rule slips (lift 0.26, mean pct 58.0). The lowest lift in the table. If the report is complaining about a chain-rule error, you are almost certainly looking at a question most of the state answered.

"This question was well attempted and required students to use the chain rule to find the derivative then evaluate the derivative… A correct answer must emerge from correct working." — 2024 Exam 1 Q1b (54%) and 2025 Exam 1 Q1b (61%), near-identical wording.

Coordinates (lift 0.30, mean pct 61.3) and simplification (lift 0.35, mean pct 55.4). Both attach almost exclusively to non-separators.

"Some students, however, only gave the x-values. Both coordinates were required." — 2025 Exam 2 Q1a (91%).

Insufficient working (lift 0.88). Near-neutral in aggregate — but this conceals the most dangerous single case. The six parts whose reports invoke the working rule explicitly split into four high-pct parts and two catastrophic ones:

"This question was not answered well. Some students wrote 7 minutes without showing any working. As indicated in the instructions on the examination, for questions worth more than one mark, appropriate working must be shown." — 2017 Exam 2 Section B Q2h (2%).

"It should be understood that answers are only accepted if they are a result of correct working. When a correct answer is presented without working, the maximum score that can be awarded is the one mark for the answer. The marks awarded are an indication of working involved. Students attempting Question 2b. and Question 9 could end up with the seemingly correct answer from incorrect working and so have a zero score for these questions." — 2011 Exam 1, general comments.

Notation (lift 1.08). Exactly neutral, and it is the only presentation category that is. Notation costs marks uniformly across the difficulty range, which is why it never leaves the reports.

3.5 What the asymmetry means

Two students lose ten marks on a paper in two different ways.

Student A loses them to rounding, brackets, bare x-values and unsimplified answers, spread evenly across the paper. Those marks come off questions the state mostly answered, which means they come off the bottom of a study score that would otherwise have been high. They are recoverable by a checking routine — 07-exam-craft.md §8 is that routine.

Student B loses them to non-attempt and wrong-method on the last part of every Section B question. Those marks are 60% of the paper by weight. They are not recoverable by checking, because there was nothing to check.

The reports name the first kind far more often than the second, because the first kind is correctable by advice and the second is not. Do not read complaint frequency as a difficulty ranking. That is what the lift column is for.

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4. The five shapes that separate reliably

These are constructions, not topics. Each appears in all four areas of study. Each is measured against the 831 validated-text November written parts, whose own base rate is 55.4% separators, mean pct 45.8 — the comparison figure for every number below. Where a construction is better measured by report-commentary keyword across the full 1 504 parts, that is stated.

Shape 1 — The terminal generalisation

The construction. The question is worked through with numbers. In the final part — occasionally the final two — a number is replaced by a pronumeral, and you are asked either for the answer in terms of that pronumeral, or for the values of the pronumeral for which some property holds.

The evidence.

The archive. 2016 Exam 2 Section B Q4e(iii) — "Find the values of k such that s(k) ≥ 1" — 3%. 2016 Exam 2 Section B Q4f(ii) — "Show that 0 < A(k) < 2 for all k > 1" — 2%. 2021 Exam 2 Section B Q2f — the same area computation as part (e) at 88%, with a in the curve and the terminal — 2%. 2025 Exam 1 Q9b(ii) — "find the positive values of w for which f(x) = g(x) has exactly three solutions" — 4%. 2015 Exam 2 Section B Q4d(i)/(ii) — the same area "in terms of m and n", split by the parity of n — 12% and 9%. 2013 Exam 2 Section B Q4c — "Find the gradient of the tangent in terms of k" — 6%. 2017 Exam 2 Section B Q2f — "in terms of u" — 8%. 2020 Exam 2 Section B Q5g/Q5h — 3% and 2%.

Why it discriminates. Three reasons, and they compound.

First, a parameter destroys the verification loop. With a number, you can substitute back and check. With k, there is nothing to substitute into.

Second, technology stops helping. A CAS will solve f(x) = 3 instantly and will return something unusable for f(x) = k unless you have already decided what form you want. VCAA knows this; it is the Outcome 3 boundary made examinable.

Third — and this is the part students most often miss — a parameterised question usually has a hidden case split. "Exactly three solutions" means one factor contributes one root and the other contributes two, which is two cases. The 2025 assessment guide for Q9b(ii) lists five distinct valid methods, of which three proceed by cases. The 2016 Q4e(iii) near-miss, 1 ≤ k ≤ 4 instead of the correct set, is a case-split error, not an algebra error.

Shape 2 — The answer that is a set, not a number

The construction. The task is one you can do; the answer is an interval, a union of intervals, a solution set, a domain, a range, or a pair of bounds. Marks are awarded on the endpoints, the bracket types, and completeness.

The evidence.

Every part in the corpus whose report complains that students gave one answer where two or more were required is a separator, and their mean pct is 23.2 — worse than the mean for the final part of a Section B question. Incompleteness is not a partial success; it is the dominant failure mode of this shape.

The archive. 2019 Exam 2 Section B Q2b — "State the set of values for which the gradient of the hill is strictly decreasing" — 3%, wrong answer [10, 30]. 2023 Exam 2 Section B Q3e — largest interval on which h is strictly decreasing — 35%, lost on round-versus-square brackets. 2019 Exam 1 Q8b — a maximal domain compounding two conditions — 9%. 2021 Exam 1 Q9bii — "Find the values of q for which the coordinates of the points of intersection have only positive values" — 4%; the report: "There were students who correctly identified the endpoints, but then wrote an incorrect interval." 2020 Exam 2 Section B Q3c — two values of k from a symmetric normal distribution — 6%, "Many students did not find [the second value]." 2020 Exam 2 Section B Q3f — "find the minimum and maximum values of y" — 3%. 2016 Exam 1 Q5aii — "State the domain and range of h" — 15%. 2025 Exam 2 Section B Q4fii — "Determine the minimum and maximum possible values for the y-intercept" — 23%, and the report records exactly the expected failure: "Some students gave their answers in coordinate form without stating the minimum and maximum values of the y-intercept."

Why it discriminates. A number is one object and one mark event. A set is three or four independent mark events — the correct endpoints, the correct bracket at each end, the correct connective (union, not intersection), and completeness (both branches, both solutions). Each has an independent failure probability, and they multiply. A student with a 90% chance of getting each of four components right has a 66% chance of the part.

It is also the construction where notation stops being presentation and becomes content. (0, 20] and [0, 20] are different answers to 2019 Q2b, and only one earns the mark. 02-functions-graphs.md §5.3 catalogues the notation conventions; the point here is the measured cost.

Shape 3 — The transformation described in words

The construction. You are given two graphs, or two rules, related by a transformation, and asked to describe or state the sequence of transformations that maps one onto the other. Nothing is computed. The answer is English (or mapping notation), and it must use VCAA's vocabulary in VCAA's order.

The evidence. The strongest measurement comes from report commentary across the full corpus, because the wording marker is rare in the validated-text subset:

91.7% is the highest separator rate attached to any content marker in the subject. Its lift in the §3 failure table is 5.1×.

The archive. 2024 Exam 1 Q5b — 2%, following a part at 95%. 2017 Exam 2 Section B Q4gi/gii — "Describe the transformation that maps the graph of g₁ onto the graph of g_k" and the same question for the inverses — 31% and 30%. 2013 Exam 1 Q9ci/cii — apply a given sequence, then state the image's domain — 16% and 39%; the report on the latter, quoted in 02-functions-graphs.md, records the underlying belief: "The frequency of [−2, 2] as a preferred solution raises the concern that students believe that the domain does not change under transformations." 2010 Exam 1 Q6 — 23%; "Students who attempted to define the transformations… often misinterpreted both the dilations and the [translations]."

The contrast case matters as much as the failures. 2018 Exam 2 Section B Q3b — "Describe the transformation that maps the graph of y = h₂(x) to y = h₃(x)" — scored 78%. One transformation, vertical, unambiguous. The difficulty is not description; it is compound description with a horizontal component.

Why it discriminates. Four independent things must be right for each transformation named: the type (dilation/reflection/translation), the factor or amount, the axis, and the direction preposition ("from the x-axis" versus "parallel to the y-axis" — VCAA accepts both conventions but not a mixture that means something else). Then the transformations must be in an order that actually produces the image, and when a horizontal dilation and a horizontal translation are both present the translation amount differs between the two valid orders. And finally the map must go the right way: several reports record students describing the inverse map.

VCAA has made its expectations unusually explicit here:

"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." — 2024 Exam 1, general comments.

Shape 4 — The dependent region

The construction. An area, whose boundaries you must first derive. The integrand, the terminals, or both, are the answer to an earlier step; often the region crosses an axis, or is bounded by two curves whose intersection you must compute, or depends on a parameter.

The evidence.

The archive. 2021 Exam 2 Section B Q2f — 2%. 2015 Exam 2 Section B Q4di/dii — the enclosed area "in terms of m and n", split by parity — 12% and 9%. 2016 Exam 2 Section B Q4fi — "Give the rule for A(k)" — 18%; the report: "Most students were able to set up the integral… which was independent of k, was sometimes given. Some broke the area up into different sections and were successful, but this would have been time consuming." 2020 Exam 2 Section B Q4eiii — 11%. 2017 Exam 2 Section B Q1dii — "Find the area of the shaded region in terms of k" — 42%.

The contrast cases are again instructive. 2021 Exam 2 Section B Q2c ("Find the area between the graph of y = x², the x-axis and the line x = 1") scored 80%, and Q2e ("Find the area of the shaded region", between y = x² and y = √x, both printed) scored 88%. When the region is drawn for you and the boundaries are given, area is an 80–88% question. When you must find the boundaries, it is a 2–18% question.

Why it discriminates. There are four independent decisions, and the report commentary shows failures at each: which function is upper; where they meet; whether the region crosses the axis (and therefore whether the integral must be split and signed); and what the terminals are. 04-calculus.md §5.3 is the definitive treatment of the sign question. The measurement to add here is that the dependency is the difficulty, not the integration: the integration itself is a single CAS call.

The related marker — reports that name the constant of integration or anti-differentiation — separates at 87.5% with a mean pct of 42.0, notably higher than the area marker's 35.2. Anti-differentiation with a boundary condition is hard but not catastrophic; anti-differentiation whose terminals you must derive is catastrophic.

Shape 5 — The conditioned object

The construction. A probability, a solution set, or a value, restricted by a condition stated in prose rather than in symbols. The condition shrinks the sample space, the domain, or the solution set, and the restriction is never notated for you.

The evidence.

Note the last two rows. Probability as a topic is at the baseline. Probability with a condition is 25 points above it.

The archive. 2012 Exam 1 Q4c — conditioning stated as a fact, not as Pr(A|B) — 3% (§1.5.1). 2020 Exam 2 Section B Q3b — "of a delivery being no later than three minutes after its scheduled delivery time, given that it arrives after its scheduled delivery time" — 41%, with the report recording an answer greater than 1 from an inverted ratio. 2021 Exam 2 Section B Q4h — 2%, "Many students were unable to set up the correct equations. The terminals were often incorrect." 2020 Exam 2 Section B Q3f — a two-branch model conditioned on time of day — 3%.

Outside probability the same construction appears as a domain restriction: 2025 Exam 1 Q9a — 19%, where the report says "Many students did not consider x ≠ 1 in their solution process and thus simplified the solution process inappropriately." 2016 Exam 2 Section B Q4ei — 24%, "Some students did not consider the domain and chose the incorrect value for x. Others gave two sets of coordinates."

Why it discriminates. Three failures, all documented.

Not noticing the condition. The prose form gives no trigger. 2012 Q4c's condition is a standalone sentence with no probabilistic vocabulary in it at all.

Inverting the ratio. Pr(A∩B)/Pr(B) versus Pr(A∩B)/Pr(A). VCAA's own check, from the 2019 Exam 2 report, is that a probability cannot exceed 1 — and the 2020 Q3b report shows students submitting answers that did.

Computing the numerator wrongly. The intersection, not the event. The 2012 Q4c report records the specific arithmetic error — treating (1 call Monday, 3 Tuesday) and (3 Monday, 1 Tuesday) as one outcome or as four.

VCAA's prescription is consistent and is repeated in the reports: draw the tree or the table. 2012 Q4c: "Students who used a key or tree diagram were less likely to make this error." 2020 Q3f: "Students who used a tree diagram were generally successful."

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5. What does not separate

Preparation time is finite. These shapes look forbidding and are not. Each rate below is against the validated-text base of 55.4% separators, mean pct 45.8, or the corpus base of 51.8% / 48.2 where stated.

5.1 "Show that"

Below the baseline, on parts averaging 1.56 marks. Broken down by mark value, the pattern is clear: 1-mark "show that" parts separate at 24% with a mean pct of 62 — better than almost anything else in the paper. 2018 Exam 1 Q8a 87%. 2006 Exam 2 Section B Q4ai 86%. 2020 Exam 1 Q7a 85%. 2012 Exam 2 Section B Q4b 85%. 2020 Exam 2 Section B Q1a 83%. 2021 Exam 2 Section B Q1a 71%.

A "show that" hands you the answer and asks for the derivation. The mark scheme rewards writing down what you would have written anyway. It is the single best value-for-effort construction on the paper, and — critically — it insulates every later part, because the result is available whether or not you derived it.

The exception is narrow and should be named precisely. "Show that" separates when what must be shown is a general claim quantified over an interval or a parameter, rather than a specific value: 2016 Exam 2 Section B Q4d ("Show that x₁ < x₂ implies g(x₁) < g(x₂)") 6%; 2016 Exam 2 Section B Q4fii ("Show that 0 < A(k) < 2 for all k > 1") 2%; 2012 Exam 2 Section B Q2c (a tangent at a general point (p, q)) 10%; 2025 Exam 2 Section B Q2fi ("Show that it is not possible for…") 39%. That is Shape 1 wearing a "show that" costume, and it is the only version to fear.

5.2 Sketching

Sketching is below baseline at every mark value, despite carrying the highest mean mark value of any marker measured. A 3-mark sketch separates at 62% against 82% for 3-mark parts generally — a twenty-point discount.

Real examples: 2023 Exam 1 Q3a 66%, 2018 Exam 1 Q3b 66%, 2016 Exam 1 Q3a 57%, 2021 Exam 1 Q4a 56%, 2015 Exam 1 Q4b 54%, 2020 Exam 1 Q6b 69%, 2025 Exam 2 Section B Q1b 62%.

Sketching is the largest reliable block of marks on Exam 1. The marks are itemised — shape, domain, intercepts, asymptotes, endpoints — and awarded independently, which is exactly the property that makes set-valued answers hard and makes sketches easy. Label everything and collect them.

The exceptions are sketches of derived objects: 2008 Exam 1 Q10b (y = f(f⁻¹(x)) on its maximal domain) 19%, 2006 Exam 1 Q4b 14%, 2017 Exam 2 Section B Q3a 29%.

5.3 Differentiation by rule

The lowest lift of any complaint and one of the lowest separator rates of any marker. Exam 1 Question 1 — a derivative warm-up in every paper from 2016 to 2025, per 07-exam-craft.md §4.4 — separates at 17.1% with a mean pct of 63.5.

This is the most over-practised content in the subject relative to its yield. The reports on these parts are about brackets and sign tidiness, not about the calculus:

"This question was well attempted and required students to use the product rule to find the derivative. Many students did not tidy up the negative signs in their answer… Some students did not use brackets around terms and this had the potential to be misinterpreted." — 2024 Exam 1 Q1a (82%) and 2025 Exam 1 Q1a (88%), near-identical.

5.4 "State" and "Write down"

The verb is a reliable signal. 07-exam-craft.md §1.5–1.6 establishes that these verbs demand retrieval and transcription only; the measurement here is that VCAA honours that contract. A "State" part at one mark is an 18%-separator, 69%-mean question — the safest construction in the subject.

The exception is "State" applied to a set (2019 Exam 2 Q2b, 2019 Exam 1 Q8b/c) — which is Shape 2, and at two marks "State" separates at 60%. The verb protects you only when the object is simple.

5.5 Long contextual stems

The relationship is not monotone. The hardest band is 240–400 characters; the longest parts are back near baseline. A wall of modelling prose is generally VCAA setting up a scenario, and scenario-setting parts are early parts. Length of context is not a difficulty signal; length of the instruction sentence is. A 300-character part is usually a part carrying two or three chained demands in one sentence.

5.6 The first half of Section A

The first four multiple-choice items of each paper separate at 10.0% with a mean pct of 72.1. Items 1–10 sit between 5% and 32%, averaging 16.8%. On a 20-item section worth 20 of 80 marks, the first half separates at about one item in six and the last four at nearly three in four.

The scheduling implication is direct and is VCAA's own advice:

"There was evidence to suggest that some students spent too much time on the multiple-choice questions in Section 1 and were therefore not able to make a reasonable attempt at Section 2. Students should be encouraged to balance the amount of time they spend on each section of the paper with respect to the total marks available for that section." — 2006 Exam 2, general comments.

5.7 Inverse functions — partially

Below baseline at every mark value. Finding the rule of an inverse is mechanical and the cohort does it: 2016 Exam 2 Section B Q4bi 56%, 2016 Exam 1 Q5bi 16% only because the range determination was bundled in.

The inverse marks are lost at the domain, which is Shape 2, not at the inversion. The inverse function is not a separator; the inverse function's domain is. 02-functions-graphs.md §4.4 catalogues the sixteen inverse separators and the same split appears there.

5.8 New content, in its first years

The 2023 additions are the clearest natural experiment in the corpus, and they contradict the standard assumption that new content is dangerous.

Newton's method and points of inflection, in their first live year, outperformed the paper average. VCAA said so:

"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." — 2023 Exam 2 report.

New content is examined conservatively in its first appearances. The trapezium rule is drifting downward (45 → 30 → 24) as VCAA embeds it in longer constructions, which is the pattern to watch — but the content itself was never the difficulty.

5.9 Summary of what to stop drilling

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6. A diagnostic

6.1 Five flags

Read the part before you attempt it and count how many of these are true.

6.2 The scorecard

Computed over the 831 validated-text November parts:

Treating "two or more flags" as a prediction that the part is a separator: precision 73.0%, recall 58.3%. Tightening to three or more: precision 84.1%, recall 30.0%.

The two-flag rule is the useful one under exam conditions. It is right about three times in four, it catches most of what matters, and it can be applied in the time it takes to read a sentence.

A shortcut that requires no counting at all: is this the last part of the question? That single test is right 94.5% of the time in Section B and 100% of the time on the final question of Exam 1.

6.3 What to do differently when the score is high

Score 0–1 (73% of parts are gettable). Answer it in order, answer it fast, check the rider. The loss mode here is presentation — rounding, brackets, coordinates, dx, simplification — and the 07-exam-craft.md §8 five-minute drill is the correct defence. These are the marks that decide a 40 from a 45.

Score 2–3 (64–78% separator). Slow down at the sentence level. Specifically:

1. Underline the noun that owns the property. "The gradient of the hill is strictly decreasing" is a claim about y″, not y′. That single habit was worth a mark to 97% of the state on 2019 Exam 2 Q2b.
2. Name the answer's type before you start. Number, coordinate pair, equation, interval, set, sentence. If it is a set, write the skeleton [ , ] ∪ [ , ] first and fill it in; the endpoints and brackets are separate mark events (§4, Shape 2).
3. Count the demands against the marks. Two marks and one named object means you have missed something — a domain, a second solution, a justification. 2020 Exam 2 Q3c and 2017 Exam 2 Q4h both lost most of the state to a second value that the symmetry of the situation required.
4. If a condition appears in prose, notate it. Write Pr(A|B) or x ≠ 1 on the page before doing anything else.

Score 4–5 (93–100% separator). Change strategy entirely.

1. Do not attempt it in sequence. Non-attempt has a 24.9× lift precisely because students reach these parts with no time. Take them last, from the whole paper, in one pass.
2. Write the first line anyway. This is the single most under-used fact in the data. On multi-mark separators, 23.8% of the cohort scores partial credit against 17.6% on non-separators, and the middle band is wider the harder the part. 2021 Exam 2 Section B Q2f has a pct of 2% and a zero rate of only 48%: half the state banked marks on a part almost nobody finished. Setting up the correct definite integral, naming the distribution and its parameters, writing Pr(A∩B)/Pr(B), stating the equation you would solve — all of these are marked.
3. Never write a bare answer. On a part where 90% of the state scores zero, an unsupported number reads as a guess and is marked as one. 2017 Exam 2 Q2h is the warning: the answer was 7 minutes, students wrote 7 minutes, and they scored nothing.
4. Assume there is a case split. If a parameter is present and the question counts solutions, asks for "all values", or asks for a maximum and a minimum, there is more than one answer. The most common near-miss in this class is not a wrong answer; it is half of a right one.
5. Look for the reset. One consecutive pair in seven rises by 20 points or more. After a part you cannot do, read the next one before abandoning the question. 2017 Exam 2 Q2e (91%) sits between Q2d (36%) and Q2f (8%); 2016 Exam 2 Q4biii (62%) is one symmetry observation.

6.4 The triage pass

Apply during the 15 minutes of reading time, which VCAA has recommended be used exactly this way since 2011.

1. Mark every final part of every Section B question, and the final question of Exam 1. Those are your separators; there are four or five of them per Exam 2 paper and one cluster on Exam 1. Do not start there.
2. Mark Section A items 16–20. Those five carry a ~70% separator rate; budget them a quarter of your Section A time and no more, because there is no partial credit and no penalty for a wrong answer.
3. Mark every "show that" and every "State". These are the resets and the retrievals. They are available regardless of what happened before them, and they are where a paper is stabilised.
4. Work the paper out of order, banking flags 0–1 first across all questions. VCAA's own advice: "Students are reminded that they do not need to answer questions sequentially. They should think about completing as much as they can of the straightforward questions before they embark on the longer, more involved questions." (2011 Exam 1.)
5. Return to the flagged parts with the time that remains, writing setup lines even where you cannot finish.

6.5 The one-paragraph version

Sixty per cent of the marks in a Mathematical Methods examination sit in parts that most of the state does not complete. Those parts are identifiable before you attempt them: they are worth two or more marks, they sit at the end of their question, they contain a pronumeral where a number used to be, their answer is a set rather than a number, and their object is an area, an optimum, or a conditioned probability. Four of those five properties together predict a separator with 93% accuracy. The mechanisms that cost you those parts are not rounding, brackets or chain-rule slips — those complaints attach to questions the state got right. They are non-attempt, wrong method, transformation vocabulary, conditional misreading, and domain neglect. And the parts themselves are not all-or-nothing: the harder the part, the more of the cohort scores something, so the setup line is always worth writing.

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Appendix — provenance of every number

Excluded from every statistic: all 413 NHT rows (no published pct); all 2026 material (no published report at time of compilation). Flagged where used: 2011 (OCR-damaged), 2008–2009 Section A (partial extraction), 2024 November (paper text unavailable; statistics intact), post-2019 multiple-choice option splits (not published).