NHT separators

Nht Methods

Companion document to corpus/mm/nht-methods.json. Covers every Northern Hemisphere Timetable examination in VCE Mathematical Methods, 2017–2026, both papers.

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0. The problem this document exists to solve

For every November examination, VCAA publishes an assessment report containing, for each question part, the percentage of the state that earned each possible mark. That table is the backbone of this entire project. A "separator", everywhere else in GM-seperators, is a question with a published full-mark rate at or below 50% — a question that actually split the cohort, verified against the state's own count.

For every Northern Hemisphere Timetable (NHT) examination, VCAA publishes a Question and Answer Book, a Formula Sheet, and an external assessment report. Since 2025 it has also published an Assessment Guide — the internal marking scheme, with the M/A credit structure written out part by part. What it has never published, for any NHT sitting, in any subject, in any year, is a mark distribution. The NHT reports say so on their own first page:

"This report provides sample answers or an indication of what answers may have included. Unless otherwise stated, these are not intended to be exemplary or complete responses."
— 2017 Mathematical Methods Examination 1 (NHT) report; identical wording in 2018 and 2019.

That sentence is the whole report's scope. There is no "this question was not answered well", no average, no percentage, no cohort size. The 2019 NHT Exam 2 report for Section A is literally a two-column table of question number and answer letter, with a one-line hint attached to about a third of the rows and nothing at all against the rest.

The consequence for this project is absolute. corpus/mm/questions.json holds 1,917 question-part rows. The 1,504 November rows carry pct, dist, answer and comment. The 413 NHT rows carry pct: null and nothing else numerical. No NHT question in Mathematical Methods can be called a separator by measurement. Applied to an NHT question, the word can only mean a question that would very likely have recorded a full-mark rate below 50% had VCAA published one.

That is a judgement, and nht-methods.json is a list of 301 judgements. Every entry therefore carries its reasoning in an evidence field, and 301 of 301 entries carry an analogue field naming a closely comparable November question with its real, published percentage. The list is auditable in the only way a list of this kind can be: a reader who disagrees can go to the cited November question, read it, and decide whether it really is analogous. Every analogue citation in the file has been machine-checked against questions.json, so the percentages quoted are the published ones, not remembered ones.

This document sets out the calibration used, the criteria applied, what the comparison of NHT with November actually shows, and — at the end, at length — what the exercise cannot do.

0.1 Sources

0.2 Corpus defects that bear directly on this exercise

• There is no 2020 NHT sitting. The Northern Hemisphere Timetable was suspended in 2020. The list therefore covers nine years — 2017, 2018, 2019, 2021, 2022, 2023, 2024, 2025, 2026 — and eighteen papers, not ten years and twenty papers.
• The 2025 NHT papers have no text layer. 2025-05_2025-NHT-mathsmethods1.txt and ...2.txt are 20 and 28 bytes — header only. The PDFs are image scans. The 2025 NHT entries were built by reading the rendered page images in corpus/mm/pages/2025-E1-NHT_p*.png and 2025-E2-NHT_p*.png, cross-checked against the 2025 NHT Assessment Guides, which do carry the full mark allocation for every part. This is the one paper pair in the list whose wording was read visually rather than extracted.
• The 2026 NHT sitting has no report at all. The 2026 NHT papers were sat in June 2026; the papers and the Assessment Guides exist, but the external assessment report does not, and [QJSON] has no 2026 NHT rows. Every 2026 entry therefore rests on the paper text and the Assessment Guide, with no VCAA commentary whatever.
• questions.json NHT metadata is thin. Of the 413 NHT rows, only 40 carry max_mark and only 64 carry a comment. The mark values in nht-methods.json were therefore taken from the printed mark labels in the papers themselves, and cross-checked three ways. First, the printed per-question totals were extracted from every paper with a text layer and confirmed to sum to 40 on each Exam 1 and 60 on each Exam 2 Section B. Second, the marks the list attributes to the parts of a given question were confirmed never to exceed that question's printed total — on all 301 entries, in every question, in every paper. Third, for the two papers where the mark scheme is published in full — 2025 NHT Exam 1 and 2026 NHT Exam 1 — every mark value in the list matches the Assessment Guide exactly, part for part, with no exceptions.
• papers.json under-detects first roman sub-parts. Its geometric label extractor frequently misses a part labelled i. immediately under its parent — it records Q4f, Q4fii, Q4fiii but not Q4fi. Thirty-three entries in the list carry labels that papers.json does not contain; each was verified against the paper text, and in every case the part exists and papers.json is the file at fault.
• Mathematical notation is lossy throughout. Every plain-text extraction in this corpus drops MathType and OMML content. The description fields are written in ASCII transliteration. Where a rule could not be read with confidence the description says what the question does rather than reproducing the expression.
• 2011 is unusable as calibration and is excluded from the November statistics below, for the reasons set out in 01-study-design.md §0.1.

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1. The calibration set: what November actually shows separates

Everything in the judged list is anchored to the November data, so the anchors have to be stated first. All figures in this section are computed from [QJSON], November rows only, using the percentage of the state earning full marks on that part. Of the 1,504 November rows, 779 — 51.8% — are at or below 50%. Anyone who assumes that "separator" means "unusual" has the base rate wrong: in Mathematical Methods, slightly more than half of all published question parts are separators. A judged list that flags 40–50% of a paper's marks is therefore not being alarmist; it is being consistent with what November measures.

1.1 Mark value is the dominant signal

This is the single most useful fact in the calibration. A two-mark written part in Mathematical Methods is already a separator on the balance of probability. A three-mark part is one at five-to-one odds. A four-mark part is one at nine-to-one.

The mechanism, as [CRAFT] argues, is that mark value is a proxy for the number of separate instructions compressed into one sentence. A three-mark question is rarely three times as hard as a one-mark question; it is three independent opportunities to be incomplete. In Methods specifically, the most common three-mark shape is "find X and state Y" or "find the value of a and the maximum area" — two answers, and the state reliably supplies one of them. The 2022 NHT Exam 1 report says this in its own words about Q6b.ii:

"This question required two answers: the value of x and the probability for this value of x. Many students did not give an answer for the probability of the value of x. Students are reminded to check they have answered all parts of a question."

That is one of only three comments in the entire NHT corpus that says anything about performance, and it is about the two-answer failure.

1.2 Position within a question is the second signal

By part letter, across all November written parts:

And more sharply, restricting to multi-part questions with three or more graded parts:

The final part of a multi-part Section B question is, in November, a separator in 93 cases out of 100, with a median of 17.5%. This is by a wide margin the strongest structural predictor available and it is the one that does the most work in the judged list. [CRAFT] §4.4 gives the same picture from a different angle — mean 63.5% at the first part falling to 20.0% at the last — and names the important qualification: the staircase is not monotone. Percentages jump back up mid-question wherever a "show that" or a fresh sub-scenario re-supplies the input. The judged list respects that: a part is not flagged merely for being late in a question if it is also the point at which the question restarts.

1.3 Written versus multiple choice, Exam 1 versus Exam 2

Exam 1 is harder per mark than Exam 2, which is what one would expect of a technology-free paper on which an exact value is the default and "in questions where more than one mark is available, appropriate working must be shown" is a standing instruction. Multiple choice is the softest part of the assessment: a multiple-choice item has to work hard to be a separator, and the judged list flags multiple choice sparingly and with a specific rationale each time.

Within Section A the ramp is real. [CRAFT] §5.2 gives the mean correct rate by question number across 2006–2025: 82% at Q1, falling through the fifties in Q9–Q13, a local easy patch at Q14–Q15, and then a genuine cliff — 41% at Q17, 45% at Q18, 44% at Q19, 34% at Q20. Fifty-six of the 68 Section A entries in the judged list sit at Q11 or above, and 33 of them at Q16 or above.

1.4 Topic is worth much less than students assume

Across all November written parts:

A six-point spread across the four areas, against a 42-point spread across mark values. Restricted to the 2023–2025 papers under the current study design, and including multiple choice, the ordering shuffles again — Data analysis median 53, Calculus 51, Functions 47, Algebra 42 — which is itself evidence that the topic effect is noise at this sample size.

Two things follow for the judged list. First, topic is never used as evidence on its own. No entry says "this is hard because it is Calculus". Second, the one genuine topic-level effect worth naming is not an area of study at all but a technique: transformation descriptions. Of the 18 November parts whose report commentary mentions transformations, 17 are below 50% and the median is 20%. The worst is 2024 Exam 1 Q5b at 2% — two marks for describing a sequence of transformations, earned by one student in fifty. That is the most extreme single data point in the Methods corpus and it is the anchor behind a large share of the transformation entries in the judged list.

1.5 The shape families, with their November anchors

These are the recurring question shapes the November data show to be strongly associated with separators. They are the vocabulary in which almost every evidence field in the JSON is written. Percentages are full-mark rates from [QJSON]; sample sizes are the number of November parts whose report commentary names the shape.

The bottom five rows of [CRAFT] §6 give the same picture from the reports' side: rounding errors (88 questions), approximate-for-exact (78), domain (65), brackets (58), coordinates where an x-value was given (56). Those are not shapes but failure modes, and they are why several one-mark entries appear in the judged list that would otherwise look too small to matter.

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2. How the NHT papers compare with November

2.1 They are the same examination in every structural respect

The papers are written by the same panel against the same [SPEC]. The 2026 NHT Exam 1 question and answer book is typeset from the same template as the 2025 November paper, with the same "Do not write in this area" gutters and the same front matter. There is no structural reason to treat an NHT question as a different kind of object from a November question.

One real difference: the multiple-choice option count changed at different sittings. November moved from five options to four at the 2024 sitting. NHT, which runs in May or June and therefore precedes the November sitting of the same year, was still on five options at 2024 NHT and moved to four at 2025 NHT — the 2024 NHT answer key contains two E answers, the 2025 NHT key contains none, and the 2026 NHT Assessment Guide's key runs A–D only. The naive expectation is that four options raise scores by lifting the guessing floor from 20% to 25%. The November data give no support to that: the 2023 five-option paper has a Section A median of 49% and the 2024 four-option paper 53%, well inside year-to-year noise, and the 2025 four-option paper sits at 56% against a twenty-year mean of 58%. The judged list therefore applies no discount to post-2024 NHT multiple-choice items on option-count grounds.

2.2 The wording is the same dialect, with a measurable accent

Counting instruction tokens per paper across the sixteen NHT papers with a usable text layer and the sixteen November papers from 2017 onwards:

Four differences are large enough to act on.

NHT uses "Show that" about 50% more often — 2.1 per paper against 1.4. The "show that" contract is unforgiving: the answer is printed, so every mark is for the working, and [CRAFT] §2.4 lists the three things that void it. The 2026 NHT Exam 1 Assessment Guide makes the contract explicit on Q7a — "Show that. M — must see set up, explicitly see [the intermediate expression] and then expressed as [the target], either line 2 or line 3" — a one-mark part on which a correct final answer with no visible intermediate line scores zero.

NHT uses "Determine" nearly twice as often and "State" and "Write down" markedly less. [CRAFT] §1.4 establishes that "Determine" is a synonym for "Find" rather than an escalation, so this is stylistic rather than substantive; but the corresponding scarcity of "State" and "Write down" is substantive. Those are the two retrieval verbs — the cheapest marks on a Methods paper — and the NHT papers hand out fewer of them.

NHT uses "Use …" almost twice as often. [CRAFT] §1.19 is blunt about this verb: the named method is compulsory. "Use calculus to show that the tangent at the origin has equation y = −px" (2024 NHT Exam 2 Section B Q1d.i) cannot be answered by substitution, however correct the substitution is.

NHT uses "Hence" and "hence, or otherwise" about half as often. This cuts the other way. "Hence" is a gift as well as a constraint: it tells the student which earlier result to reach for. NHT parts are more often left to stand on their own, which removes a signpost.

2.3 Where NHT is more demanding in style

Four recurring features of the NHT papers, none of which is unknown in November but all of which are more concentrated in NHT.

1. Longer chains built on a single object. The 2017 NHT Exam 2 Section B contains only four questions for 60 marks — two of them worth 18 marks each. Question 4 takes one function, f(x) = 4√x − x on [0, 16], and builds ten graded parts on it: find the maximum; sketch it; find the area under it; maximise a triangle with a vertex on it; prove an algebraic relation between two points at equal height; find the area of an inscribed rectangle in terms of one of them; maximise that; express the maximum as an exact surd; maximise an inscribed trapezium; and finally take the ratio of that maximum to the area under the curve. By the last part, six earlier results are in play. The 2018 NHT Exam 2 Question 4 is a 20-mark chain of the same kind built on f(x) = x − x·logₑ(x), reaching a part that asks the student to show that p^q = q^p. Nothing in a November Section B since 2016 runs that long on one object.

2. Probability density functions treated as full objects. November examines a given density function and asks for one or two things. The NHT papers repeatedly take a density and work through the whole apparatus: mean, standard deviation, median, a probability, a conditional probability, and then an inversion. 2017 NHT Exam 2 Q3 does mean → standard deviation → tail probability → labelling error → conditional probability → binomial → exact sample-proportion probability → confidence interval, nine parts on one context. 2018 NHT Exam 2 Q2, 2019 NHT Exam 2 Q3, 2021 NHT Exam 2 Q4 and 2022 NHT Exam 2 Q4 have the same shape. Standard deviation of a general continuous random variable — a two-integral calculation, since it needs E(X²) before it needs anything else — is asked outright in three of the nine NHT Exam 2 papers (2017 Q3c, 2022 Q4a.ii, 2024 Q3d.iii), which is a higher rate than November manages.

3. Sample proportions asked exactly, with the approximation explicitly forbidden. 2017 NHT Exam 2 Q3h reads: "Find Pr(P̂_A > 0.04 | P̂_A < 0.08). Give your answer correct to four decimal places. Do not use a normal approximation." Three marks, and the instruction removes the only method most students have practised. 2021 NHT Exam 2 Q4h is the same idea without the warning — Pr(P̂ > 0.15) for samples of 25, which means more than 3.75 defective items, which means at least four, which is a binomial tail — and Q4i then inverts it, asking for the least n with Pr(P̂ₙ < 1/n) < 0.15. The November corpus contains nothing quite this explicit about the discreteness of the sampling distribution.

4. Transformations specified as mappings rather than described in words. November's hardest transformation questions ask the student to describe a sequence in VCAA's vocabulary (2024 Exam 1 Q5b, 2%). NHT more often specifies a mapping T: R² → R² and asks what it does, or asks for the parameters that make the image coincide with a named function. 2018 NHT Exam 2 Q1d gives T as a horizontal translation by d and asks for the d that maps one constructed point onto another; 2021 NHT Exam 1 Q4b gives T with both a horizontal and a vertical component and asks for c and d such that the image of g is f⁻¹; 2024 NHT Exam 2 Q4 builds an entire tiling pattern from transformations of a cubic and ends by asking the student to complete a table defining three further families of functions in terms of f or g and an integer parameter k. That last part is the most demanding single item in the 2024 NHT paper and has no November counterpart of comparable openness.

2.4 Where NHT is less demanding

Two honest counterweights, and one candidate counterweight that the data refused to support.

Contexts are simpler. November Section B stems in recent years run to half a page of modelling narrative before the first part. NHT stems are typically three or four sentences. Less reading is less opportunity to misread.

Interpret-in-context marks are no more common, and that is itself worth knowing. The "explain why" and "justify your answer" verbs appear at statistically identical rates in both series — 0.2 and 0.1 occurrences per paper — and a direct count of the Exam 2 papers with a usable text layer confirms it: five such parts across seven NHT papers, six across eight November papers. The widespread belief that the NHT papers are lighter on written reasoning is not supported. What is true is that NHT's instances tend to be short mathematical justifications attached to a calculation ("justify your answer" after a yes/no), whereas November's are more often attached to a statistical inference — "explain why this confidence interval suggests …" — where the marked answer is a full sentence about a population.

The multiple choice is, until about 2023, more conventional. The abstract, parameter-driven Section A items that [SD] §2.1's "theoretical investigations" clause licensed after 2023 arrive in NHT slightly later than in November. The 2017–2022 NHT Section A papers are dominated by the classical stem forms of [CRAFT] §5.3 — "The period of … is", "… is equal to" — and the judged list flags five or six items per paper across those years (5, 6, 5, 5, 5), against seven in 2023, nine in 2024, eleven in 2025 and fifteen in 2026.

2.5 The recurring NHT question types

Counting across the 301 entries by what the description field actually asks for:

Two of those rows are the NHT signature. Optimisation of a constructed geometric figure — a rectangle, triangle or trapezium inscribed under a curve, with the objective function assembled from the geometry before any differentiation happens — appears in 2017 NHT Exam 2 Q4 (triangle, rectangle and trapezium on one curve), 2018 NHT Exam 1 Q9 (a trapezium with a cubic removed from it), 2018 NHT Exam 2 Q3 (a glass panel between two parameterised sine curves), 2025 NHT Exam 2 Q5 (a garden of maximum area for a fixed perimeter) and 2026 NHT Exam 1 Q7 (a rectangle inscribed under y = 12 − x with a vertex at the origin). Tangent-construction chains — form the general tangent at a parameterised point, then equate two of them, or intersect one with the curve again — appear in 2018 NHT Exam 2 Q4, 2019 NHT Exam 2 Q5, 2021 NHT Exam 2 Q1 and Q5, 2022 NHT Exam 2 Q1, 2024 NHT Exam 2 Q1 and 2026 NHT Exam 2 Q2. A student who has run out of November papers and wants more of exactly these two shapes will find them at higher density in NHT than in November.

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3. The criteria applied

3.1 The three qualifying tests

A question was entered in the list when at least one of the following held. In practice the great majority of entries satisfy two or three.

(a) A closely analogous November question is itself a separator. This is the primary test and it produced the analogue field. "Closely analogous" means same task, same shape, comparable mark value, and — where the analogue is from a different study-design era — a task that survived the 2023 rewrite. The mean analogue percentage behind a SEPARATOR verdict is 14.6% and the median 12%; not one of the 272 SEPARATOR entries cites an analogue above 42%. The 29 BORDERLINE entries cite analogues with a mean of 36.9% and a median of 38%, spanning 23% to 54%.

(b) The NHT report or Assessment Guide flags the difficulty or prescribes a demanding mark scheme. Only three NHT report comments in the whole corpus say anything about performance, so in practice this test is carried by the four Assessment Guides. They are genuinely informative. The 2026 NHT Exam 1 guide awards Q8b's method mark for "2 of 4" key indicators and the accuracy mark only for all four — meaning three correct features out of four on a two-mark sketch scores one mark. The same guide's Q9b.ii spells out three acceptable methods for justifying the nature of a stationary point and, for each, requires that "the correct conclusion must come from correct working with x and gradient values above" — a correct conclusion reached by inspection earns nothing. Mark schemes of that shape are the strongest direct evidence available about an NHT paper.

(c) The question has a structural feature the November data show is strongly associated with separators. In descending order of strength, as established in §1: it is the final part of a multi-part question (93% of November instances below 50%); it carries three or four marks (83% and 90%); it is a multi-mark "show that"; it requires a transformation to be described (94%); it requires an area between curves (100%); it requires an interpret-in-context response; it requires two answers in one part; it requires an exact form on a technology-active paper; or it asks for a domain or a range as a set.

Questions that satisfied none of these were left out, and most of each paper was left out. The list flags 38% to 72% of the marks in a given paper, with a median of 49% — very close to the 51.8% of November parts that are measured separators.

3.2 SEPARATOR or BORDERLINE

SEPARATOR means very likely below 50% full marks had it been measured — read as somewhere around 80% confidence or better. BORDERLINE means around the line, and it could fall either way. The practical test used was the analogue: if the closest November comparison sits below about 30%, the entry is a separator; if it sits between roughly 30% and 50%, and there is no second structural reason to push it down, the entry is borderline.

Twenty-nine of 301 entries are BORDERLINE. That is a low proportion, and it reflects a deliberate decision: where a question looked borderline and the reasoning for it was thin, it was omitted rather than recorded. A borderline verdict is only useful when the uncertainty is about the question, not about the evidence.

3.3 Confidence

high (242 entries) means the analogue is tight and at least one structural feature agrees with it, or the Assessment Guide settles the matter directly. medium (59 entries) means the analogue is looser, or the November instances of the shape are few, or the question has an offsetting feature — early position, small mark value, a scaffolded previous part — that argues the other way.

No entry in the list carries low confidence. The schema permits it; nothing used it. A judgement that could only be stated with low confidence is a judgement that adds no information to a list whose whole purpose is to point a student at the right practice, and those calls were dropped instead of recorded. Readers should treat the absence of low as a statement about the editorial threshold, not as a claim that every call is secure.

3.4 How topic was assigned

topic follows the skill being tested, mapped onto the [SD] dot points, not the surface vocabulary of the question. The rules applied:

• Functions, relations and graphs — key features of a graph; maximal, implied or natural domain; range; transformations of y = A f(n(x + b)) + c; graphs of sums, products and composites; modelling with a named function family.
• Algebra, number and structure — solving equations, including general solutions and solutions over a stated interval; literal equations and parameter conditions on the number of solutions; simultaneous linear systems; inverse function rules and the conditions for their existence; composition as an operation.
• Calculus — differentiation and anti-differentiation; tangents and normals; stationary points, inflection points and strict monotonicity; optimisation including endpoint cases; definite integrals, areas and average value.
• Data analysis, probability and statistics — discrete and continuous random variables, the binomial and normal distributions, densities, sample proportions and confidence intervals.

Where a question straddles two areas the topic follows the step that does the work. An optimisation set inside a probability context is Calculus if the difficulty is the differentiation; a conditional probability whose difficulty is an improper integral is still Data analysis, because the conditional-probability structure is the thing being tested. questions.json's own NHT topic field, which was assigned by keyword scoring over the paper text, disagrees with this list on about a third of the rows it covers; in the cases inspected the keyword scorer was wrong more often than not — it assigned "Functions, relations and graphs" to an area-under-a-curve question because the stem contained the phrase "the graph of", and "Data analysis" to a calculus question because the expression E(x) matched its probability pattern.

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4. What the list contains

301 entries, across nine years and eighteen papers.

Coverage by paper:

Every entry carries an analogue. The 301 entries draw on 131 distinct November questions; the most heavily reused are 2016 Exam 2 Section B Q4d (6%, eleven times), 2018 Exam 1 Q9d (4%) and 2016 Exam 1 Q8bii (7%) at eight times each, and 2021 Exam 1 Q3c (17%), 2016 Exam 2 Section A Q20 (17%) and 2018 Exam 2 Section B Q4dii (11%) at seven each. Reuse on that scale is intended: a small number of November questions are the canonical instances of the shapes that separate, and pointing repeatedly at them is more useful than manufacturing weaker comparisons for variety.

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5. A few individual calls, and why they went the way they did

2017 NHT Exam 1 Q4a — SEPARATOR, high, 4 marks. Sketch f(x) = tan(2x) + 1 on (−π/2, π/2) with asymptotes labelled by equation and endpoints and intercepts labelled by coordinate. Four-mark written parts in November average 20.8% full marks with 90% below 50%, and trigonometric sketching is the worst-performing sketching family. Two structural reasons and a tight analogue; this is as confident as a judged call gets.

2019 NHT Exam 2 Section B Q3e — SEPARATOR, high, 2 marks. The expected value of a density function 8/(x + 2)³ on [0, ∞). Only two marks and it sits in the middle of the question, so the structural signals are weak; the call rests entirely on the improper upper terminal. A student who types a finite terminal gets a number that looks right, and the November reports record exactly that failure on density means. This is an entry where the evidence is a mechanism rather than a statistic, and it is flagged as such in the evidence field.

2021 NHT Exam 2 Section B Q4b — BORDERLINE, not SEPARATOR. An inverse normal stated in the upper tail: Pr(X > a) = 0.9, find a. The tail-direction trap is real and the November analogue scored 31%. But it is an early part, two marks, and the calculation itself is one command. Thirty-one per cent is inside the band where a question can go either way, so it is borderline.

2023 NHT Exam 2 Section B Q2d — SEPARATOR, high, one mark. "When t ≥ 4, is C₂ strictly increasing, strictly decreasing or neither?" One mark, three words of answer, and it is flagged with high confidence because the word "strictly" applied to a hybrid function is among the most reliably fatal constructions in the corpus. The closest November comparison, 2019 Exam 2 Section B Q2b, scored 3%. Small mark value is not a defence when the failure mode is conceptual.

2024 NHT Exam 2 Section B Q1c.ii — BORDERLINE, not SEPARATOR. "Find the values of p for which f(x) = x³ − px would have no stationary points." This is the classic parameter-condition frame, which November data place firmly in separator territory. But part c.i has just asked for the boundary case, so the student arrives at c.ii with the answer half-built. That is the "reset" effect from [CRAFT] §4.4 — a scaffolded previous part lifts the next one — and it is enough to pull the verdict back.

2026 NHT Exam 1 Q8b — SEPARATOR, high, 2 marks. The only entry in the list whose primary evidence is the published mark scheme rather than an analogue. The Assessment Guide lists four key indicators, awards the method mark for two of the four and the accuracy mark only for all four. A student who draws the right shape, locates the intercepts and finds the intersection but forgets to label the y-intercept scores one of two. Mark schemes written that way are separator-generating machines, and nothing else about the question would have revealed it.

Multiple choice generally. Sixty-eight of 301 entries are Section A items. That is 23% of the list drawn from 17% of the marks in the eighteen papers, which looks like over-representation until the ramp is taken into account: multiple choice as a whole is the softest part of the assessment (November median 59%, against 43% for Exam 1 written), but its last quarter is not, with a November mean of 34% correct at Q20. The items flagged are concentrated at the top of the ramp: 33 of the 68 are Q16 or later, and only twelve are Q10 or earlier. Where an early Section A item is flagged, the evidence field always names a specific reason — a distractor that is the answer to the most natural wrong method, an "is closest to" rider that punishes premature rounding, or a "must be true" stem of the kind [CRAFT] §5.3 describes.

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6. The limits of this exercise

6.1 None of this is measurement

The verdict field looks like the separator field elsewhere in this corpus and it is not the same kind of thing. A November separator is a fact: VCAA counted the scripts. An NHT separator is an inference from analogy and structure. The confidence field is a self-report, not a calibrated probability, and it has never been validated against an outcome, because there is no outcome to validate against and there never will be. Nothing in this list should be quoted as a statistic. If a sentence beginning "X% of students got this wrong" is ever written on the basis of this file, the file has been misused.

6.2 The NHT cohort is not the November cohort

Even if VCAA did publish NHT mark distributions, they would not be comparable. The NHT cohort is small — small enough that VCAA has judged per-question percentages not worth publishing — and it is not a random sample of Victorian Methods students. It is drawn from northern-hemisphere schools following the Victorian curriculum on a January-to-November academic year, with different teaching sequences, different SAC timing, and in many cases different first languages. A question that separated at 20% in Victoria might separate at 35% or at 8% in that cohort, and the direction is not predictable. Every judgement in this list is therefore best read as "this question has the properties that made comparable November questions separators for the Victorian cohort" — which is the useful claim for a student preparing for a Victorian examination, and is not a claim about the NHT cohort at all.

6.3 A large minority of the list is out of scope for a current candidate

The 2023 study design removed content that the 2017–2022 NHT papers examine. [SD] §3.2 sets out the deletions: functional relations such as f(x + y) = f(x)f(y), and the "equating coefficients" dot point. It also added content the older NHT papers cannot contain — Newton's method, the strengthened treatment of simultaneous linear systems with a parameter, points of inflection restored to the calculus dot points, and the explicit licensing of "theoretical investigations" that produced the abstract Section A items of 2023 onwards. Of the eighteen papers in this list, ten predate the current study design. Their questions remain excellent practice for the shapes that survived — every optimisation, every area, every conditional probability, every transformation — but a student should not treat a 2017 NHT paper as a model of the current examination's content mix.

6.4 The stringency is not constant across the nine years

The flag rate rises from 42% of Exam 1 marks in 2017 to 72% in 2025, and from five Section A items per paper in 2017–2022 to fifteen in 2026. Some of that is real: the Section A items written since 2023 are more abstract and the Section B questions carry more parameters. But the November data do not show a matching rise in difficulty — November Section A medians run 49% (2023), 53% (2024), 56% (2025), with no trend, and November written medians run 43%, 44%, 55% over the same years. The honest reading is that the later papers were judged with more evidence available — the 2025 and 2026 sittings are the only ones with published Assessment Guides — and that more evidence produced more confident, and therefore more numerous, calls. Readers comparing paper to paper should treat the 2017–2022 entries as a floor rather than a complete census.

6.5 The 2025 papers were read from images and the 2026 papers have no report

For 2025 NHT the question wording came from page scans rather than from a text layer. Transliteration errors in the description fields are more likely there than anywhere else in the file, and a misread exponent or domain would change what the question is without changing how it looks. For 2026 NHT there is no external assessment report at all: the only VCAA commentary available is the Assessment Guide, which describes how marks are awarded but says nothing about how students actually went. Those four papers — 2025 Exam 1, 2025 Exam 2, 2026 Exam 1, 2026 Exam 2 — carry 84 of the 301 entries, 28% of the list, on the thinnest evidence base in it.

6.6 The mark-value rule is a base rate, not a mechanism

"Three-mark parts are separators 83% of the time" is a true statement about November and a weak statement about any particular question. A three-mark part that is three routine one-mark steps in sequence is not hard; a one-mark part that requires a general solution is. The list uses mark value as a prior and then looks for a mechanism, and where no mechanism could be named the entry was dropped even when the mark value argued for it. That is why several three-mark NHT parts do not appear.

6.7 The analogue can be wrong

The whole audit trail rests on the claim that the cited November question is genuinely analogous. That claim is a judgement too. The percentages attached to the analogues are verified and exact — every one of the 301 was machine-checked against questions.json — but a verified percentage attached to a badly chosen analogue is precision without accuracy. The single most useful thing a reader can do with this file is to disagree with an analogue and say why.

6.8 What would falsify the list

If VCAA published NHT mark distributions tomorrow, the test would be simple: what fraction of the 272 SEPARATOR entries came in at or below 50%, and what fraction of the 29 BORDERLINE entries landed between roughly 35% and 65%? A SEPARATOR hit rate below about 70% would mean the criteria are too loose. A hit rate near 100% would mean they are too tight and the list is missing separators it should have caught — which, given that the list flags a median of 49% of each paper's marks against a November base rate of 51.8%, is the more likely failure.

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7. How to use the list

As a practice set, not as a prediction. The right use is: work a November paper, find that you lose marks on areas between curves and on transformation descriptions, then filter this list to those shapes and work the NHT instances. The list is a supply of targeted practice at the shapes that separate, sorted by the judgement that they separate.

Read the evidence field before the verdict. The verdict is one word and it compresses everything. The evidence names the mechanism — the improper terminal, the strict inequality, the second answer nobody gives, the domain that has to be a set — and the mechanism is the transferable part.

Follow the analogue. Every entry points at a real November question with a real percentage. If an NHT question defeats you, the analogue is the November question that defeated the state, and the November report for it explains exactly how.

Do not count the flags as a difficulty score for a paper. The 2025 NHT Exam 2 shows 47 flagged marks and the 2019 NHT Exam 2 shows 30. That is mostly a statement about how much evidence was available for each, as §6.4 explains, not about which paper was harder.

Treat pre-2023 papers as shape practice only. Ten of the eighteen papers predate the current study design. Use them for optimisation, areas, tangents, conditional probability and transformations. Do not use them to calibrate what a current paper covers or how it is balanced.

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8. Summary

VCAA publishes enough about the NHT Mathematical Methods examinations to know exactly what was asked and exactly how it was marked, and nothing at all about how anyone went. This document and the file beside it convert twenty years of measured November difficulty into an estimate of where the NHT papers would have separated the cohort if anyone had counted.

The estimate rests on three things the November data establish firmly: that mark value predicts difficulty better than topic does, by a factor of seven; that the final part of a multi-part question is a separator 93 times in 100; and that a small number of recurring shapes — the described transformation, the labelled sketch, the area between curves, the conditional probability, the endpoint optimisation, the multi-mark "show that" — account for a wildly disproportionate share of the lowest-scoring questions in the subject. The NHT papers are written by the same panel to the same specification, with a measurable accent: more "show that", more "use this method", fewer retrieval verbs, fewer "hence" signposts, longer chains built on a single function, and a notably harder treatment of probability density functions and sample proportions.

Three hundred and one question parts across nine years are judged here: two hundred and seventy-two as separators and twenty-nine as borderline, two hundred and forty-two of the calls made with high confidence and none with low. Not one of those verdicts was measured. All of them carry the evidence that produced them, and every one of them names a real November question, with a real published percentage, against which the judgement can be checked.