NHT separators

Nht Specialist

Companion document to corpus/sm/nht-specialist.json. Covers every Northern Hemisphere Timetable examination in VCE Specialist Mathematics, 2017–2026, both papers.

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0. The problem this document exists to solve

VCAA publishes, for every Northern Hemisphere Timetable (NHT) examination, a Question and Answer Book, a Formula Sheet, and an external assessment report containing sample answers. Since 2025 it has also published an Assessment Guide — the internal marking scheme, with the M1/A1/H1 credit structure written out question by question.

What it does not publish, and has never published for any NHT sitting in any subject, is a mark distribution. There is no row of percentages, no average, no "this question was answered well". The November reports carry all of that; the NHT reports carry none of it.

The consequence for this project is absolute. corpus/sm/questions.json holds 1,469 graded question-parts. For the 1,427 November rows it carries pct — the percentage of the state that earned full marks — and for the 42 NHT rows it carries pct: null. No NHT question can be called a separator by measurement. The word "separator", everywhere else in this project, means a question with a published full-mark rate below 50%. Applied to an NHT question it 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 the whole of nht-specialist.json is a list of judgements. Every entry therefore carries its reasoning in an evidence field, and 309 of 309 entries carry an analogue field naming a closely comparable November question with its real percentage. The list is auditable in the only way a list like this can be: the reader can check whether the analogue really is analogous.

This document sets out the calibration, the criteria, 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 and twenty.
• The 2025 NHT papers have no text layer. 2025-05_2025-NHT-specialistmaths1.txt and ...maths2.txt are 24 and 36 bytes respectively; the PDFs are bilevel scans. The 2025 entries were built by reading the rendered page images in corpus/sm/pages/2025-E1-NHT_p*.png and 2025-E2-NHT_p*.png against the Assessment Guide and the report. This is the only paper pair in the list where the question wording was read visually rather than extracted.
• The 2023 NHT Exam 2 report is missing. For that paper the judgements rest on the paper text and on analogy alone, with no VCAA commentary of any kind.
• Mathematical notation is lossy throughout. Every plain-text extraction in this corpus drops MathType and OMML content. Descriptions in the JSON are written in ASCII transliteration and, where a rule could not be read with certainty, they say what the question does rather than reproducing the expression. Where a transliteration is uncertain the description hedges ("of the form", "-type").
• questions.json was rewritten during the compilation of this document and its topic field is currently null on all rows. The topic-level statistics quoted in §1.4 were computed from the earlier state of the file and should be re-derived before being relied on; the pct values, which do the real work here, are unaffected.

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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 need stating first. All figures below are from [QJSON], November rows only, using the percentage of the state earning full marks.

1.1 Mark value is the dominant signal

This is the single most useful fact in the whole calibration. A three-mark written part in Specialist Mathematics is already a separator on the balance of probability; a four-mark part is one at better than five-to-one odds; every five-mark part in twenty years of November papers has scored below 50%.

The reason, as [CRAFT] argues, is that mark value is a proxy for the number of separate instructions packed into one sentence. A four-mark question is rarely four times as hard as a one-mark question; it is four independent opportunities to be incomplete.

1.2 Position within a question is the second signal

And more sharply still, 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 four times out of five, with a median of 28%. This is by some distance the strongest structural predictor available, and it is the one that does most work in the judged list.

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 in which exact values are the default. Multiple choice is the softest part of the assessment and a multiple-choice item has to work hard to be a separator.

A note on the option count. November moved from five options to four at the 2024 sitting; NHT, which runs in May and therefore precedes the November sitting of the same year, was still on five options in 2024 NHT and moved to four at 2025 NHT [NHTP]. The naive expectation is that four options would raise scores by raising the guessing floor from 20% to 25%. The November data do not show that: the 376 five-option items have a median of 62% and the 40 four-option items a median of 58%. The sample is small and the difference is not significant, but there is certainly no evidence that four-option items are easier, and the judged list does not discount post-2024 multiple-choice items on that basis.

1.4 Topic is worth much less than students assume

Across all November rows, the median full-mark rate by area of study runs from 51% (Calculus) to 58% (Data analysis, probability and statistics) — a spread of seven points, against the 46-point spread across mark values. Restricted to the 2023–2025 papers under the current study design, the ordering is:

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 effect worth naming is that graph sketching of rational and quotient functions is the reliable weak point, and it is weak in a specific way: not the shape but the labelling.

1.5 The shape families, with their November anchors

These are the recurring question shapes that the November data show are strongly associated with separators. They are the vocabulary in which almost every evidence field in the JSON is written.

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2. How the NHT papers compare with November

2.1 They are the same examination in every structural respect

The one structural departure across nine years is 2018 NHT Exam 2, which has seven Section B questions rather than six, with a five-mark and a four-mark question at the end [NHTP]. Every other NHT Exam 2 in the corpus has exactly six. Since short final questions are systematically easier than long ones — the first part of a question has a November median of 71% — 2018 NHT Exam 2 is, structurally, the mildest Section B in the set.

Note also that Section B is 60 marks in six questions in every NHT paper from 2017 on, whereas November only moved from five Section B questions (2006–2015, 22 multiple-choice) to six in 2016 and briefly back to five in 2020. The NHT series has been more consistent than November over the same period.

2.2 The instruction verbs are statistically indistinguishable

Because [CRAFT] establishes that the instruction verbs are where the marks are lost, the most direct comparison available is to count them. The table below is per-paper averages over the 2016–2026 papers whose text extraction is usable (2025 NHT excluded: no text layer; 2024 November excluded: empty files).

The counts are approximate — the extraction loses symbols, and "label" catches both the instruction and the answer-space furniture — but the picture is unambiguous. NHT and November are written to the same specification, by the same process, with the same verb budget. There is no measurable sense in which the NHT paper is a softer or a harder paper in aggregate.

Two small differences are worth recording because they bear on individual judgements:

1. "In the form" is used more in NHT Exam 2 (2.9 per paper against 1.8) and less in NHT Exam 1 (1.4 against 2.6). Prescribed answer forms are the third-ranked recurring loss area in the reports, with 44 explicit mentions in the November commentary [CRAFT]. The NHT Exam 2 papers lean on the device noticeably: 2026 NHT Exam 2 Question 5a asks for a triangle area "in the form a√b/c where a, b, c ∈ Z⁺ and c = a + 1" — a constraint inside a constraint, which has no parallel anywhere in the November archive.
2. "Sketch" and "label" are slightly lower in NHT Exam 2 (2.1 and 3.6 against 2.8 and 5.0). NHT Section B leans marginally less on graph work than November does. Since graph sketching is the most reliable separator family in the archive, this is the one systematic respect in which the NHT Section B papers are a shade gentler.

2.3 Where NHT is measurably more demanding in style

Aggregate parity does not mean question-by-question parity, and there are four respects in which the NHT papers are noticeably sharper.

(a) NHT is where VCAA trials the unusual object. The NHT sitting is a small cohort and the papers read as a place where new or peripheral content gets its first outing. The clearest cases:

• A parabolic asymptote. 2026 NHT Exam 1 Question 9 asks for "the equation of the parabolic asymptote" of a cubic-over-linear rational function, then asks for a sketch of the whole thing. Non-linear asymptotes appear nowhere in the graded November archive. Students who have drilled oblique asymptotes have no routine for this.
• Continuity. 2026 NHT Exam 2 Section A Question 2 asks for the value of a parameter that makes a piecewise arctan/rational function continuous. "Continuous" is not a term of art anywhere in the study design.
• A reduction formula. 2024 NHT Exam 2 Section A Question 11 asks for Iₙ in terms of Iₙ₋₁ for a general positive integer index. Symbolic reduction formulae are not VCE content and have no formula-sheet support.
• A removable discontinuity in a sketch. 2025 NHT Exam 2 Question 1c requires a graph with a "hole"; the Assessment Guide [NHTAG] awards one of the three marks specifically for "Shape 'hole' at … and passes through (0, 3)".
• The De Moivre inductive step as an extended-response question. 2024 NHT Exam 2 Question 2a. The study design names "De Moivre's theorem, proof for integral powers" [SD], but November has never examined the inductive step in Section B.
• An Apollonius circle. 2022 NHT Exam 1 Question 5 gives √3|z − i| = |z| and asks for the centre and radius. The standard complex loci — perpendicular bisector, circle about a point, ray — are all drilled; a modulus ratio is not.
• A triangle-area form constraint tied to itself (2026 NHT Exam 2 Q5a, above).

(b) NHT Exam 1 carries the harder integrals. Comparing the two Exam 1 papers of the same year, the NHT paper is repeatedly the one with the nastier antiderivative: 2019 NHT Exam 1 Question 6 is a volume of revolution requiring a four-term partial-fraction decomposition with repeated factors (5 marks), and Question 8 is an arc length that only works if 1 + (dy/dx)² is spotted as a perfect square (4 marks). 2023 NHT Exam 1 Question 10 is a nested-logarithm integral needing two successive substitutions. 2021 NHT Exam 1 Question 9c is an arc length whose integrand is |sec x| over an interval straddling zero.

(c) NHT Exam 1 runs to more questions with more parts. 2025 NHT Exam 1 has nine questions but thirty labelled parts, four of which are one-mark "show that" items inside Question 7 alone (b.i, b.ii, b.iii). The Assessment Guide marks three of those "A1* ans. given", meaning the supplied answer is worth nothing and the entire mark hangs on the displayed reasoning. That density of unrewarded-answer show-thats in a single Exam 1 question is without November precedent.

(d) The Assessment Guides confirm a strict mark scheme. From 2025 the Guides are public, and they are more revealing than the reports ever were. Two of their standing notes bear directly on difficulty:

"Where a question explicitly requires the student to show working out, partial marks should be awarded for correct completion of key steps required to produce the correct answer." — [NHTAG] 2025 Exam 1, marking policies

"If contradictory responses are given (i.e.: the response conflicts with earlier comments or working out) full marks cannot be awarded." — ibid.

And, question by question, notes such as "Need proper working for 'show that'", "Must provide convincing argument for 'Show that'", "correct deduction of given result", "Convincing show that", "null vector — insist on tilde or equivalent vector notation", "Need to conclude correctly for their p". Each of those is a named way to lose the mark with correct mathematics, and each is used in the evidence field of the corresponding entry.

2.4 Where NHT is less demanding

Three respects, all minor.

1. Slightly less graph work in Section B, as noted in §2.2.
2. The statistics question is usually the last question and is usually a staircase of one-markers. 2025 NHT Exam 2 Question 6 has nine parts for ten marks; 2023 NHT Exam 2 Question 6 has nine parts for nine marks. The November statistics questions are similarly shaped, and statistics is the highest-scoring area in November at a 65% median under the current design, so this is common ground rather than an NHT softening — but it means that in most NHT papers only the last two parts of the last question are judged separators, not the whole question.
3. 2018 NHT Exam 2's seven-question Section B shortens the average question and so reduces the number of deep final parts.

2.5 The recurring NHT question types

Across nine years, the following appear in almost every NHT paper and should be treated as the standing shape of the series:

• Exam 1: one complex-number question requiring polar form and/or a root set in Cartesian form; one implicit-differentiation question; one volume or surface area or arc length; one differential equation with a "show that" closed form; one statistics question of two or three parts (confidence interval inversion or linear combination of random variables); one vectors/lines/planes question; from 2024, one proof by induction.
• Exam 2 Section A: one direction-field matching item; one substitution-identification item; one Euler's-method item; two to four vector items (resolute, angle, linear dependence, cross product, planes); one kinematics item; two statistics items, usually a linear combination and a sampling-distribution probability; from 2024, one proof-technique or algorithm item.
• Exam 2 Section B: a rational-function question built as express in partial fractions → asymptotes → derivative → sketch → parameter family; a complex-plane question built as show the Cartesian form → sketch the locus → find an intersection → find an area; a differential-equation modelling question, from 2024 usually logistic; a vector-kinematics question with two moving objects and a minimum-distance or meeting final part; a lines-and-planes question ending in a shortest distance; a statistics question ending in a Type II error.

The last item is worth emphasising. Seven of the nine NHT Exam 2 papers end the statistics question with a Type II error calculation or its unnamed equivalent (2017 Q6e, 2018 Q6c in disguised form, 2019 Q6f, 2022 Q5g, 2023 Q6b.ii, 2024 Q6f, 2025 Q6i, 2026 Q6e). The November archive's two instances of this shape scored 44% and 9%. It is the most consistently placed deep separator in the entire NHT series.

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3. The criteria applied

A question was admitted to the list only if at least one of the following held. In practice most entries satisfy two or three, and the evidence field says which.

Criterion A — a closely analogous November question is itself a separator. The analogue must be the same shape, not merely the same topic: same technique, comparable mark value, comparable position in the question. Where the analogue is weaker than that, the analogue field says so ("… family") and the confidence drops to medium.

Criterion B — the NHT report or Assessment Guide flags the difficulty or prescribes a demanding mark scheme. This is the only direct evidence available and it is used wherever it exists. Instances include:

"Each part of Question 9a. was a 'show that' question. Success in 'show that' questions requires students to set out solutions explicitly." — [NHTR] 2018 Exam 1 NHT

"A 'show that' question such as this requires an explicit solution showing how the Cartesian equation of L was obtained from the given relation." — [NHTR] 2018 Exam 2 NHT, Q2a

"Appropriate working leading to the given result was required." — [NHTR] 2019 Exam 2 NHT, on Q3b, Q4d and Q5b

"Students were required to show convincing working that led to this result." — [NHTR] 2021 Exam 2 NHT, on Q2c, Q3aii and Q4a

"Convincing working leading to the result was required." — [NHTR] 2022 Exam 2 NHT, on Q3b and Q4c

"M1 invert / M1 partial fractions / M1 must have logs / A1* ans. given" — [NHTAG] 2025 Exam 1, Q5a

"Shape 'hole' at … and passes through (0, 3) 1A, asymptotes & labelled 1A, x-intercepts labelled 1A" — [NHTAG] 2025 Exam 2, Q1c

"null vector — insist on tilde or equivalent vector notation" — [NHTAG] 2026 Exam 2, Q4c.ii

Note the asterisk convention: in the 2017 and 2025/2026 materials VCAA marks certain lines "Answer given" or "A1 ans. given". Those are questions where the printed result earns nothing and the mark is entirely for the chain of reasoning. Every such flagged part is in the list.

Criterion C — a structural feature the November data show is strongly associated with separators. The four used are:

• a multi-mark "show that" or "prove" (the November show-that band runs 7%–35%);
• a final part that depends on every earlier part (November median 28%, below 50% in 82% of cases);
• a sketch with labelling requirements (November band 10%–27%);
• a conclusion or interpretation that must be written in context (November band 17%–45%).

To these the mark-value rule from §1.1 was applied as a floor: a three-mark written part needs only a weak second signal to qualify, a four-mark part needs almost none, and a five-mark part was admitted on mark value alone where no counter-indication existed.

3.1 The SEPARATOR / BORDERLINE line

SEPARATOR means: on the calibration, I would expect the published full-mark rate to be comfortably under 50% — as a rough internal threshold, under about 40%. BORDERLINE means: I would expect it to land within roughly ten points either side of 50%.

Questions judged routine were simply left out. Routine here means: one or two marks, first or second part, single technique, no prescribed form, no labelling, no interpretation. Roughly half of every NHT paper falls into that category, which is as it should be — a paper in which every question separates is a paper that discriminates nowhere.

3.2 Confidence

high was used where an analogue matches on shape, mark value and position, or where a report or Assessment Guide note directly supports the call. medium covers everything else. low was not used at all. That is a deliberate choice: a judgement I would rate low-confidence is one I should not be making, and those questions were left off the list rather than added with a disclaimer. The reader should treat the absence of low as meaning the list is a filtered set, not a complete ranking.

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4. What the list contains

309 entries across eighteen papers and nine years.

Coverage is deliberately even: eleven to fifteen entries per Exam 1 and eighteen to twenty-seven per Exam 2, in every year.

Two features of the topic split need explanation.

Discrete mathematics has only four entries because the area of study is new in 2023 and, in the NHT series, it is examined almost entirely as a single induction proof per Exam 1 (2024 Q8, 2025 Q3, 2026 Q2) plus the occasional Section A item on proof technique (2024 Exam 2 Q1). All three induction proofs are in the list as high-confidence separators; there is simply not much more of the area to judge. The De Moivre inductive step at 2024 NHT Exam 2 Q2a is tagged Algebra, number and structure rather than Discrete mathematics, because the study design places the proof of De Moivre in the complex-numbers content, with Area of Study 1 supplying the technique. That is a defensible call in either direction and a reader who prefers the other tagging should mentally move it.

Space and measurement is large (87) partly because the 2017–2023 NHT papers were set under the 2016–2022 study design, in which Mechanics was a full area of study. Following the convention used elsewhere in this project, mechanics questions — pulleys, inclined planes, friction, momentum, equilibrium of forces — are tagged Space and measurement, which is the area that absorbed vectors and mechanics when the six-area naming was applied retrospectively. Rectilinear kinematics without forces (velocity–time graphs, a = v dv/dx, constant acceleration) is tagged Calculus, following §1.7.3 of research/sm/01-study-design.md. This means a large minority of the Space and measurement entries — every mechanics entry from 2017 to 2023 — is out of scope under the current study design. They are in the list because the brief was to cover every NHT paper, and they remain valid judgements about those papers; they are not valid practice for a 2027 candidate. §6.3 returns to this.

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

2025 NHT Exam 1 Q7 (six marks, four parts, three of them "show that"). The Assessment Guide marks b.i, b.ii and b.iii each "A1* ans. given" [NHTAG]. Three consecutive one-mark parts where the printed answer is worth nothing is an unusual construction; the whole of the reasoning has to be visible in one or two lines each. All three are SEPARATOR, and part c — which needs the answers from all three and then a quadratic root selection — is SEPARATOR at high confidence. Part a, the velocity–time sketch, is also in the list despite being worth one mark, because everything downstream reads values off it.

2026 NHT Exam 1 Q3 (three marks, points of inflection of x⁵ + x⁴ − x). This looks like a two-line differentiation. It is not: f″ = 0 has two roots and only one of them is a point of inflection. The Assessment Guide spends an M1 on "viable method" for the concavity argument and lists three acceptable ways to make it [NHTAG]. The November question that asked for verification of inflection points scored 8%. SEPARATOR, high.

2018 NHT Exam 2 Q1d (one mark: "What is the minimum distance the bee will need to travel?"). No formula is named, arc length is never mentioned, and the answer 31.4 is the length of the outside profile of the vase. A one-mark final part that is an unsignalled arc length, in a family whose November instances run 2%–30%. SEPARATOR, high — and one of the entries I would most like to see a real percentage for.

2024 NHT Exam 1 Q1b ("write down the average speed of the car in terms of V for the first 6 seconds"). One mark, no computation, and the answer is V/4. It is in the list as BORDERLINE rather than SEPARATOR because one-mark parts have a November median of 62% and the insight, once seen, is instant. But the report's own phrasing — "since the car starts from rest and accelerates uniformly, the average speed over 12 seconds is …" — reads like commentary on a question that did not go well.

2017 NHT Exam 2 Section A Q10. The analogue cited is 2017 November Exam 2 Section A Q10 at 6% — the lowest multiple-choice score in the November archive. These are different questions; the analogy is by shape (a calculus multiple-choice item requiring two identity manipulations before the answer form becomes visible), not by content. The evidence field says so. A reader who thinks that analogy is too loose should downgrade the entry; it is the loosest analogue in the list and it is flagged here for that reason.

Multiple-choice items generally. Only 43 of 309 entries are Section A items, from a pool of 180 NHT multiple-choice questions. That ratio is deliberate: with a 62% November median and only 28% of items below 50%, a multiple-choice question has to be doing something unusual to qualify. The ones that made it are almost all of three kinds — abstract vector geometry with no numbers, a separation or substitution requiring two prior identity steps, or a parameter condition where every option is structurally plausible.

The 2023 NHT papers. These were set under the old (2016–2022) study design, as the brief notes. That shows: 2023 NHT Exam 1 Q4 and Exam 2 Q5 are pure statics-and-dynamics questions, Exam 2 Q3 is a lift with reaction forces, and there is no proof, no cross product and no plane anywhere in either paper. They are judged on the same criteria as the rest, and their analogues are drawn from the 2006–2022 November papers where the corresponding content was live.

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6. The limits of this exercise

This section is the most important one in the document, and it is written to be read before the JSON is used for anything.

6.1 None of this is measurement

Every verdict in nht-specialist.json is an inference from a different examination sat by a different cohort. The chain is: this NHT question resembles that November question; that November question scored X%; therefore this NHT question would probably have scored something like X%. Each link is contestable.

The resemblance link is the weakest. "Same shape" is a judgement I made by reading both questions, and reasonable people would draw the boundary differently in perhaps a fifth of cases. Where the boundary is drawn loosely the analogue field says "family" rather than naming a single question, but that is a signal of looseness, not a measurement of it.

6.2 The NHT cohort is not the November cohort

This is a bigger problem than the question-matching, and it cuts in an unknown direction.

The NHT cohort is small — a few hundred students in schools running the Northern Hemisphere school year, concentrated in international schools and a handful of Victorian schools with accelerated programs. Its composition is not the composition of the 3,500-odd students who sit Specialist Mathematics in November. If the NHT cohort is on average stronger, then a question I have judged a separator on November calibration might have recorded 60% full marks in the actual NHT sitting. If it is weaker, the reverse.

VCAA publishes nothing that would let this be estimated — no NHT cohort size, no NHT grade distribution, no statistical-moderation figures broken out by sitting. So the list is best read as "this question has the properties that make November questions separate", not as "this question separated". Those are different claims and only the first is supported.

For the intended use of this list — building a practice set for a student targeting a high study score — the first claim is the one that matters. A student wants to know which questions are constructed to be discriminating, and that is a property of the question, not of the cohort.

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

Of the eighteen papers, seven (2017, 2018, 2019, 2021, 2022 and 2023 — twelve papers in total across both exams) were set under the 2016–2022 study design. Under that design, Mechanics was a full area of study: connected particles, pulleys, inclined planes with friction, resolution of forces, momentum, and Newton's second law as a modelling step. All of that was removed at the 2023 transition [SD].

Concretely: 2017 NHT Exam 2 Question 5 (ten marks, three connected masses over a pulley), 2018 NHT Exam 2 Question 3 (ten marks, crate on an incline), 2019 NHT Exam 2 Question 5 (twelve marks, pallet and cable with a variable mass), 2021 NHT Exam 2 Question 5 (nine marks, berry on a plank), 2022 NHT Exam 2 Question 4 (eleven marks, two sliders with friction) and 2023 NHT Exam 2 Question 5 (ten marks, mass on an incline with a horizontal string) are all unexaminable content under the 2023–2027 design. That is roughly sixty marks of Section B across the series, and about 30 of the 309 entries.

Equally, the pre-2023 papers contain no proof by induction, no cross product, no planes, no integration by parts, no surface area of revolution and no logistic equation, because none of it existed as content. A student practising only the 2017–2022 NHT papers would miss six of the most heavily examined new topics.

The JSON does not flag which entries are out of scope. A downstream consumer that wants only current-design material should filter to year >= 2024, or to year >= 2024 plus the non-mechanics entries from 2023 — noting that the 2023 NHT papers themselves were set under the old design even though the 2023 November papers were not.

6.4 The extraction is lossy and some descriptions are approximations

The description fields are one-sentence summaries written from plain-text extractions that have lost their mathematical notation, or in the 2025 case from rendered page images. Several descriptions therefore say "of the form" or "-type" where the exact expression could not be recovered with confidence. Specifically:

• 2017 NHT Exam 1 Q2 and Q3, where the integrand and the relation are partly garbled in the extraction;
• 2022 NHT Exam 1 Q10a, where the function rule contains several lost surds;
• 2023 NHT Exam 1 Q3 and Q6, where the rules extract incompletely;
• 2024 NHT Exam 2 Q1, where the function rule reads as 1/(x² + 4) but the leading constant is uncertain;
• 2026 NHT Exam 2 Q1, where the numerator coefficients are partly lost.

In each case the shape of the question — the technique required, the mark value, the position, the instruction verb — is certain, and the shape is what the judgement rests on. But a reader reproducing these questions should go to the PDF.

6.5 The 2023 NHT Exam 2 has no report at all

For that one paper there is no VCAA commentary, no sample answers and no assessment guide in the corpus. Its twenty-one entries rest entirely on the paper text and on November analogy. They are not marked differently in the JSON but they are the thinnest-evidenced group in it.

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

Roughly a third of the entries lean substantially on §1.1 — "this is a four-mark written part, and 84% of November four-mark parts fall under 50%". That is a legitimate prior, but it is a prior about a population, and applying it to an individual question is exactly the inference that goes wrong when the individual question happens to be mechanically straightforward. Four-mark questions that are one long routine computation exist, and some of them score above 50%. Where the only evidence was mark value, the verdict was set to BORDERLINE rather than SEPARATOR, or the confidence was set to medium.

6.7 What would falsify the list

If VCAA ever released NHT mark distributions, the check is direct: for each entry, compare the published full-mark rate with the verdict. A calibrated list would put most SEPARATOR entries below 45% and most BORDERLINE entries between 40% and 60%. My own expectation is that the list would be found to be over-inclusive — that is, that some SEPARATOR calls would come back in the 50s — for two reasons: the NHT cohort is plausibly more selective than the November cohort, and the criteria deliberately admit anything satisfying a single strong structural signal. Anyone using this list should read a SEPARATOR verdict as "worth drilling" rather than "was demonstrably hard".

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7. How to use the list

For a candidate targeting 45+, the practical ordering is:

1. Work the three induction proofs first (2024 NHT Exam 1 Q8, 2025 Q3, 2026 Q2). They are the highest-value-per-minute items in the set: the technique is closed, the marking scheme is published in full for 2025 and 2026, and the November evidence (21% and 29%) says the state cannot do them.
2. Then the eight final parts of the statistics questions. Seven of nine NHT Exam 2 papers end on a Type II error or a critical-value inversion, and the November anchors are 9% and 16%. This is the most predictable deep separator in the series.
3. Then every "show that" the Assessment Guides mark with an asterisk. These are the questions where a correct answer is worth zero and the reasoning is worth everything — precisely the failure mode the November reports name 28 times.
4. Then the graph-sketching parts, in year order, checking each against the labelling requirements in the Assessment Guide rather than against the shape alone.
5. Then the arc length, surface area and volume-of-revolution parts, which between them account for the four lowest November percentages in the calibration table.

Skip, or triage last, the entries tagged Space and measurement from 2017–2023 that involve forces, tension, friction or momentum. They are good mathematics and they are no longer examinable.

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8. Summary

• 309 judged entries, covering all eighteen NHT Specialist Mathematics papers from 2017 to 2026 (there is no 2020 NHT sitting).
• 235 SEPARATOR, 74 BORDERLINE; 148 high confidence, 161 medium, none low.
• Every entry carries a named November analogue with a real published percentage.
• The NHT and November papers are, by instruction-verb count and by structure, the same examination; NHT is marginally lighter on graph work and noticeably heavier on prescribed answer forms and on trialling unusual objects.
• Nothing in the list is a measurement. VCAA has published no NHT mark distribution in nine years, and until it does, every verdict here is an inference from a different cohort sitting a different paper.