Anatomy of a separator

What this document is. The six area-of-study documents (02–06, 08) catalogue what VCAA asks in each area. 07-exam-craft.md catalogues how VCAA words it. 09-nht-specialist.md uses the November data to judge the unmeasured NHT papers. This document does the thing none of them can do alone: it dissects the construction of a Specialist Mathematics question, area by area, and then measures — across 1,428 graded November question-parts from 2006 to 2025 — exactly which structural features make a question separate.

A separator is a question-part on which 50% or less of the state earned full marks (pct ≤ 50). Every percentage in this document is VCAA's own published figure: the proportion of the cohort awarded the maximum mark for that part.

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0. Scope, method, and what the numbers are

0.1 The population

All statistics are computed from corpus/sm/questions.json, November rows only — NHT rows carry no pct and are excluded throughout.

By marks rather than by parts: the twenty November sittings carry 1,975 written marks, of which 1,174 (59%) sit inside separator parts, plus 416 multiple-choice marks of which 122 (29%) do. Across the whole corpus, 54% of all marks ever set are inside a question that at least half the state could not fully answer.

0.2 How question text was recovered

questions.json carries answer and comment (the report's commentary) but not the question stem. Stems were extracted from the plain-text paper files in corpus/sm/text/, split first into questions by the Question N heading sequence, then into parts by the a. / b. / i. / ii. marker sequence. This recovers an individual stem for 843 of the 1,012 written parts (83%). Two gaps:

• The 2024 November text files are empty (24 and 32 bytes; a known corpus defect noted in 01-study-design.md §5.7). Eighty 2024 rows therefore have no stem text. Their answer and comment fields are intact and are used instead.
• The 2011 text extracts with a shifted font encoding and is unsearchable. Sixty-two 2011 rows are invisible to any keyword classifier used below.

Two further corpus gaps affect mark totals: 2022 Exam 1 sums to 38 marks rather than 40, and 2022 Exam 2 Section B to 57 rather than 60. Every other sitting reconciles exactly.

0.3 A note on what "separator" measures

pct is the full-mark rate, not the mean mark. A 3-mark part on which the state averages 2 out of 3 can still be a separator, because "full marks" is an all-or-nothing test and 3-mark parts have three ways to fall short. This is not a defect of the measure — it is the point. The examination separates candidates by the completeness of an answer far more than by whether the candidate had any idea at all. §2.7 quantifies this directly.

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1. How a Specialist question is constructed

1.0 The four organs

Every extended-response question in the archive is built from the same four components. The names are this document's; the construction is VCAA's, and it is visible in every Section B question from 2006 to 2025.

1. The stem — the context paragraph. It establishes the object (a function, a complex number, a position vector, a random variable) and, in Exam 2, the modelling situation. Stems range from 13 characters to over 2,000. Stem length is itself a difficulty signal (§2.9).
2. The given — the piece of information the candidate is handed, usually inside a "show that" or a stated result, so that a failure early in the question does not propagate. This is VCAA's own stated purpose: the 2006 Exam 2 report says the "show that" instruction is intended to "help keep them on track and enable access to subsequent marks for later parts of the same question, even if the student could not 'show' a given result."
3. The scaffold — the middle parts. These are the routine applications: differentiate it, integrate it, find the asymptotes, compute the p-value. They are where the bulk of the marks are and where the state performs at or near its baseline.
4. The sting — the final part. It changes one thing: a parameter becomes general, a modelling assumption is altered, an answer becomes a set rather than a number, or the object is replaced by a family of objects. It is typically worth 1–3 marks and it is a separator four times in five (§2.2).

The rest of §1 dissects real questions, area by area, with each part's pct alongside.

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1.1 Discrete mathematics — logic and proof

This area entered the course in 2023 and holds only 10 graded November parts to date, so the sample is small; but the construction is already fixed, and it is unlike every other area in one respect: the question has no scaffold at all.

2023 Exam 1 Question 8 (4 marks, one part, 21%)

"A function f has the rule f(x) = x·e^(2x). Use mathematical induction to prove that f⁽ⁿ⁾(x) = (2ⁿx + n·2^(n−1))e^(2x) for n ∈ Z⁺, where f⁽ⁿ⁾(x) represents the nth derivative of f(x)."

The organs are all present but compressed into one undivided instruction. The stem is the function. The given is the closed form. The scaffold is the induction skeleton — which the candidate must supply from memory, because VCAA does not print it. The sting is the inductive step.

The distribution is the most informative object here. The modal score is 2 out of 4, taken by 39% of the state, and only 16% score zero. Almost everyone knows the ritual: state the base case, assume P(k), conclude. That is worth two marks. The report says exactly where the other two went:

"Many students were able to begin the proof by showing the base step and making an assumption for the n = k case. Students were then required to differentiate f⁽ᵏ⁾(x) with respect to x to show that the n = k+1 case followed. A number of students either did not differentiate the function or differentiated incorrectly. Many students appeared to be thinking of index laws and assumed that f⁽ᵏ⁺¹⁾ was equal to 2 × f⁽ᵏ⁾."

The construction is deliberate: the proposition is about derivatives, so the inductive step is a differentiation, not a multiplication. The question separates on whether the candidate understands what the inductive step of this proposition actually is, rather than on whether they can recite the skeleton.

2025 Exam 1 Question 7 (4 marks, one part, 29%)

"Use mathematical induction to prove that Σ(i=1 to n)(i+1)² = n(2n² + 9n + 13)/6 for n ∈ N."

Same shape, gentler content (a series identity rather than an nth derivative), and the distribution shifts one mark to the right: the mode is now 3, and 63% of the state score 3 or 4. The report's list of what cost the fourth mark is a pure rigour list, not a mathematics list:

"This question was not answered well. Some common errors included: Not properly verifying the base case. Misstating the assumption. For example, 'Suppose the proposition is true for n = k. Then …' Assuming equality at the beginning of the inductive step."

2024 Exam 1 Question 2 (3 marks, one part, 65%) — the contrast

A direct proof by integer parametrisation: show that a stated expression is even when n is odd. Distribution {0: 8%, 1: 4%, 2: 23%, 3: 65%}. The report: "This question was answered well by students. Substituting 2k+1 for n in the expression and obtaining a multiple of 2 … was a reasonable approach. Occasional arithmetic or algebraic errors were seen."

What these three questions establish about proof construction. VCAA does not scaffold proof and does not intend to. There is one instruction, one object, and three or four marks that are awarded for separate acts of rigour — base case, correctly stated assumption, a valid step of the right kind, and a conclusion. Direct proof scores 65%; induction scores 21–29%. Compare the two multiple-choice proof items, which are the softest things in the archive: 2024 Exam 2 Section A Q1 (contrapositive, 72%) and 2025 Exam 2 Section A Q1 (contrapositive, 93%). Recognising a proof technique is trivial; executing an induction is a 21–29% event.

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1.2 Functions, relations and graphs

The anatomy here is the most stable in the entire archive and has not changed since 2006: manipulate → describe → draw → generalise.

2021 Exam 2 Section B Question 1 (10 marks, 5 parts)

Stem: f(x) = (2x+3)(x−5) / ((x−1)(x+2)).

The fall from 79% to 6% inside ten marks is the whole anatomy in one question. Three things did it:

• Part c is not a drawing question, it is a checklist question. The report: "A significant number of responses did not include the middle branch. Setting the calculator screen to match the grid provided would help avoid this error. Many responses lacked at least one of the required details such as coordinates of the point of inflection or coordinates of one of the axial intercepts. Students need to read the question carefully and fully address the requirements of the question."
• Part d i changes the answer type from a number to a set. The report: "Very few students gave all three values. Many responses included only one value."
• Part d ii compounds it with a condition on stationary points: "A common error was to include other incorrect values of k. Many students left this question blank."

Part c's distribution is {0: 24%, 1: 32%, 2: 23%, 3: 22%} — an almost uniform spread across the four possible scores, which is the signature of a conjunctive mark scheme applied to a task most candidates can partly do.

2025 Exam 1 Question 9 (6 marks, 3 parts) — the same skeleton, technology-free

Stem: f: R\{−1,1} → R, f(x) = (x³ − x² − 2x)/(1 − x²).

The report on part c enumerates the marking scheme in prose:

"Students were required to label the asymptotes with their equations. An open circle to indicate the point of discontinuity needed to be shown. A number of students included an incorrect vertical asymptote or had curves that did not pass through the axis intercepts. The point of discontinuity was often missing or was placed incorrectly. Students who were most successful used a ruler to draw the asymptotes and had graphs that did not curve away from the asymptotes."

2024 Exam 1 Question 3 (6 marks, 3 parts)

Distribution on part c: 0 marks 51%, 1 mark 13%, 2 marks 25%, 3 marks 10%. Half the state scored nothing on a sketch whose algebra they had already completed two parts earlier at 63% and 65%. The report: "Some students only drew the right-hand branch of the graph. … Additional or incorrect asymptotes were submitted, and some students who did have reasonable-looking graphs did not label asymptotes or axis intercepts appropriately."

What these three establish. In this area the separator is almost never the calculus and almost never the algebra: it is the sketch, and inside the sketch it is the labels and the branches, not the shape. Across all November written parts whose own stem contains the word sketch, the separator rate is 64% against a written baseline of 48%, and the median full-mark rate is 43%.

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1.3 Algebra, number and structure — complex numbers

The complex-number question has a signature construction: solve → plot → describe the locus → generalise the locus. The first three stages are routine; the fourth is one of the hardest things in the archive.

2019 Exam 2 Section B Question 2 (10 marks, 7 parts)

2019 Exam 2 Section B Q2d is the joint-hardest written part in the corpus at 1%. Its distribution is {0: 72%, 1: 27%, 2: 1%}: a quarter of the state got one of the two constants and almost nobody got both. The report:

"Many students did not attempt this question. Of those who attempted it, most made errors relating to signs; giving the negative of the correct p value or not accounting for the sign of a."

On part c, at 7%: "Many students did not attempt this question. Of those who did, most abandoned a potentially correct approach before they reached a conclusion. Those who reached a conclusion generally got there via the quadratic formula but unfortunately most of these students found only one end point of the interval."

Note the symmetry with §1.2: in both areas, the sting works by changing the type of the answer — from a number to a set (part c) or to an expression in free parameters (part d).

2023 Exam 2 Section B Question 2 (10 marks, 8 parts) — the current-design version

Stem: w = cis(2π/7).

Two constructions worth naming.

The mid-question sting. Part d ii (18%) is not the last part. VCAA drops a hard item in the middle and then re-supplies a fresh given at part e (54%), so the question recovers. This is the "show that at the point of maximum dependency" pattern that 07-exam-craft.md §4.4 identifies, used here defensively.

A "show that" whose answer is printed, and which still scores 7%. Part f ii is the clearest demonstration in the archive that the given does not make a part easy when the derivation is the mark. The report:

"This question was not well done. Many students were able to express the given equation in terms of powers of w but most students did not 'show that' the required result arose through a series of logical steps."

That sentence is the sharpest statement of the Specialist marking contract anywhere in the corpus: the printed answer is not evidence, the chain is.

2024 Exam 1 Question 1 (4 marks, 3 parts) — the same construction in miniature

The report on part b names two distinct failures: "some students neglected to show that they were solving an equation and moved directly from the factorised form of the polynomial to writing down the solutions"; and "With the known root, a small number of students tried inappropriately to apply the conjugate root theorem." On part c: "Some students did not recognise that the radii of the circles on the Argand diagram were positive integer multiples … Some students, with the correct solutions, incorrectly plotted them along the real axis, rather than the imaginary axis."

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1.4 Calculus

The calculus question is built as a model, not a technique drill. The construction is: set the model up → operate on it analytically → operate on it numerically → change the model.

2020 Exam 2 Section B Question 3 (10 marks, 6 parts)

Stem: f(x) = x²e^(−x).

This is the widest internal fall in the archive: 91% → 2% across ten marks, with 89% and 91% immediately preceding the 2%. Nothing about the technique changed — part d was answered by 91% of the state and part e ii uses nothing else. What changed is that the answer became a classification of an integer parameter into cases. The report:

"Some students gave intervals of real numbers for n. The majority of responses indicated n = 0 gave zero points of inflection and n = 1 gave one point. However, very few students were able to distinguish between even and odd values of n when considering multiple points of inflection."

Note also part c at 45%: "This question was done quite well, with the turning point almost universally correctly labelled … However, students lost marks either for sketching a poor shape in the second quadrant or for incorrectly labelling points of inflection, including having the x-value of the left-most point of inflection rounded to 0.58 instead of 0.59." A rounding error in a label cost a third of a sketch.

2024 Exam 2 Section B Question 3 (10 marks, 6 parts) — the modelling staircase

Report, part d: "Many students skipped this question without making an attempt to answer it. As the depth of the pond is constant, the surface area can be found by dividing the volume by the depth." Report, part e: "Many students skipped this question without attempting to answer it. The most common error was not taking the 5-day delay into account." Report, part b (37%): "Students who recognised this as a related rates question managed this well. Some students did not convert the depth measurement to metres."

The sting here is not mathematical at all. Part d requires the observation that a constant-depth pond has surface area equal to volume divided by depth — a single sentence of modelling. Part e requires re-running an existing model with a time shift. Both are 2-mark items and both were abandoned rather than failed.

2023 Exam 2 Section B Question 3 (10 marks, 6 parts) — the compound-quantity sting

The definition in part c ("the total surface area consists of the curved surface area plus the areas of the two circular discs at each end") is printed in the stem, and the report's complaint is that it was not read: "Many students found the curved surface area only and did not include one or both ends. Of those who included two ends, errors with an incorrect radius were frequent." Part d repeats the trap at 24%: "Omission of the ends of the solid, and ends with incorrect radii, were the most frequent errors."

Part b ii at 55% is the rounding tax in isolation: "Incorrect rounding was a frequent final response. Students are reminded to set their calculators to display sufficient decimal places."

What the calculus dissections establish. The technique — differentiate, integrate, separate variables, apply Euler's method — is scaffolded and the state does it. The separator is (i) an unfamiliar composite quantity defined in the stem, (ii) a changed modelling assumption, or (iii) an answer that classifies a parameter rather than evaluating one.

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1.5 Space and measurement

Vectors and vector calculus produce the longest questions in the archive (up to 10 graded parts) and the anatomy is describe the object → differentiate it → impose a geometric condition → optimise.

2023 Exam 1 Question 10 (6 marks, 4 parts) — the technology-free version

Stem: r(t) = (5 − 6sin²t)i + (1 + 6 sin t cos t)j, t ≥ 0.

Part d's distribution is {0: 44%, 1: 49%, 2: 7%}. Half the state earned exactly one of the two marks. The report explains the split precisely: "While many students realised that they needed to solve r·ṙ = 0, many were not able to get to the final result." One mark for the condition, one for the complete solution set. This is the archetype of the Specialist separator: the method is worth half and the completeness is worth the other half, and the state consistently buys the first half only.

Part c is worth noting for a different reason — it is a 1-mark arc-length item that 64% of the state failed, and the report's own solution is geometric, not integral: "Some students were able to apply a geometric argument or use circle mensuration to obtain the answer. A number of students correctly evaluated an integral for the arc length."

2024 Exam 2 Section B Question 4 (11 marks, 9 parts) — the two-object optimisation

Part c i at 23% is instructive: the mathematics is one line, and the report's diagnosis is entirely about reading. "Many students did not answer in terms of t. Several students did not find the square of the speed, but left the answer as a velocity or speed." The question asked for |v|² and the state answered |v|.

Part b at 41%: "Students often did not draw this graph well, and it was often not symmetrical. Negative signs were often left off the coordinates of the end points. The direction of the path of the yacht was often left out or in the wrong direction." Part c iii at 48%: "The common error was that some students forgot to take the square root of the square of the speed." Part e, the sting: "This question part was often not attempted. Students who found the correct expression for the distance were generally able to progress."

2017 Exam 2 Section B Question 2 (10 marks, 6 parts) — the model that changes partway

The construction is a two-regime model: constant acceleration for two seconds, then resisted motion. Parts a and b establish the handover values (88% and 93%). Parts d and e require the candidate to notice that the integral starts at v = 19.6, not at v = 0, and that the two seconds already elapsed must be added back. The report:

"This question was often misinterpreted by students, either by assuming that the model applied from the start of the skydiver's fall (integrating from 0 to 30) or by giving an answer that only gave the time after 2 seconds. Many students did not attempt this question."

And on part e: "the errors apparent in Question 2d i., as a result of not taking the first 2 seconds of motion into account, also appeared in responses to this question." One misreading, compounded across 5 of the question's 10 marks.

2025 Exam 2 Section B Question 5 (10 marks, 6 parts) — the new 3-D geometry construction

The sting is again a set-valued answer, and the report's diagnosis uses the same words as 2019, 2023 and 2024: "Many responses did not demonstrate that the modulus needed to be used and consequently only one of the solutions was found." Note also part b ii at 51.2%, a pure-form failure: "some responses gave the Cartesian equation of the line rather than the parametric equations and were not awarded the mark." And part c at 65%: "Several responses included only the answer so they only gained the answer mark. It is essential that students show the mathematics behind their solution to be awarded the full marks."

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1.6 Data analysis, probability and statistics

The statistics question is the most formulaic in the paper and the easiest — median pct 58, separator rate 37%, the lowest of any area. Its construction is a fixed conveyor: describe the sampling distribution → compute a probability → build an interval → state hypotheses → compute a p-value → state a conclusion → invert the test.

2025 Exam 2 Section B Question 6 (10 marks, 10 parts) — the conveyor at full length

Every part is worth one mark; none is a separator. But the three inversion parts (d, g, h) sit 20–35 points below the conveyor parts around them, and the ordering is exactly the ordering of how many steps must be run backwards. The report on part d: "Some responses rounded down to quote 96, but this would have resulted in more than 1 mL." On part g: "Some responses used the wrong tail of the distribution." On part h: "Most students were able to find this Type II error if they were successful in part g" — part h's difficulty is inherited, not intrinsic. And on f ii (68%): "Responses needed to comment on the company's claim and also quote the significance level."

2021 Exam 2 Section B Question 6 (10 marks, 7 parts) — what happens when the conveyor is not used

This is the only Section B question in the archive whose first part is a separator at 14%. Parts a and b are not sampling-distribution questions at all: they are sums of n independent random variables, which candidates reflexively treat as sample means. The report on part a: "Successful students used a trial-and-error approach or used a standardised value to solve for n. A common error was to approach this as a sampling problem with σ/√n." On part b: "There was evidence of confusion between the correct sum of four random variables and incorrectly scaling a random variable by a factor of four."

Then the conveyor runs normally (75%, 70%, 55%), and the two inversion parts collapse again: part d at 16% — "Some students calculated 63,108.7 but did not proceed to answer the question correctly as a range of values" — and part e at 9%, with 89% of the state scoring zero.

2024 Exam 2 Section B Question 6 (9 marks, 8 parts) — the same shape, softer

What the statistics dissections establish. The area is easy where it is procedural and hard in exactly two places: when a sum of random variables is disguised as a sample mean, and when the test is run backwards (find n, find the critical value, find β). Across all November parts whose text mentions a confidence interval, the separator rate is 22%; across parts that mention hypotheses or a p-value, 29–32%; but the individually worst statistics parts in the corpus are all inversions: 2021 Exam 2 Q6e (9%), 2021 Exam 2 Q6a (14%), 2021 Exam 2 Q6d (16%), 2018 Exam 2 Q6f (11%).

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1.7 What the six dissections share

Across all six areas, the sting works by one of exactly four moves:

None of the four is a mathematics move. All four are reading moves.

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2. The measured anatomy of difficulty

2.1 Separator rate by mark value

Written November parts only.

Split by paper, the pattern is identical and the technology-free paper is slightly steeper:

Interpretation. A mark in Specialist Mathematics is a unit of required completeness, not a unit of difficulty. A 3-mark part is not three times harder than a 1-mark part; it is three separate opportunities to be incomplete, and the full-mark test is conjunctive. That is why the separator rate more than doubles from 1 mark to 3 marks while the mean score per mark barely moves: on separators the state earns 0.43 of the available mark on average; on non-separators, 0.73.

Named extremes. Every 5-mark written part in twenty November papers is a separator, led by 2018 Exam 1 Q10 (2%), 2019 Exam 2 Section B Q5d (9%), 2016 Exam 1 Q10 (14%) and 2008 Exam 1 Q1 (19%). Among 4-mark parts, 2008 Exam 1 Q10c (3%) and 2018 Exam 1 Q5 (15%) are the worst.

2.2 Separator rate by position within a question

Multi-part written questions (≥2 graded parts), position by order of appearance:

Restricted to questions with three or more graded parts, the effect sharpens:

Restricted further to Exam 2 Section B alone (109 questions with ≥3 parts): first part 23.9% separator rate with a median of 69; final part 82.6% with a median of 28.

By part letter the monotone fall is visible without any grouping:

Roman-numbered sub-parts are easier than plain lettered parts (250 parts, 41.6% separator rate, median 55, against 762 parts at 53.5% and median 48) — because a part split into i/ii/iii is a part VCAA has chosen to scaffold.

2.3 The cross-tabulation: position beats mark value

This is the single most useful table in the document. Written multi-part questions, November, cross-tabulating position against mark value:

Read down the first column: a 1-mark part is a separator 12% of the time when it opens a question and 70% of the time when it closes one — a factor of six, with the mark value held constant. Read across the top row: a first part goes from 12% to 82% as it grows from one mark to three. Both factors are real and comparable in size, but position is free to observe and is the one candidates systematically ignore.

Single-part written questions — the whole of Exam 1's short questions — behave like final parts: 96 parts, 75% separator rate, median 37.5. There is no scaffold to fall back on. Of those, the 93 worth 3+ marks separate at 75% with a median of 37.

2.4 Separator rate by exam and by section

Exam 1 is the harder paper per mark, and the reason is structural rather than mathematical: its questions average 1.8 graded parts against Section B's 6.1, and its parts average 2.31 marks against Section B's 1.77. Exam 1 is a paper made mostly of final parts and undivided questions; Section B is a paper made mostly of scaffold.

Within Exam 1, difficulty rises to the end of the paper:

Within Exam 2 Section B, difficulty rises to Q5 and then falls at Q6, because Q6 is the statistics question:

Within Section A, position has almost no effect: Q1–Q5 27% separator rate, Q6–Q10 27%, Q11–Q15 32%, Q16–Q20 30%. The multiple-choice paper is not ordered by difficulty; it is ordered by area of study.

2.5 Separator rate by area of study

All November rows with a pct, multiple choice included:

Written parts only, the ordering is much the same: Discrete 66.7% (n=6), Calculus 56.0%, Functions 51.6%, Space 51.3%, Algebra 45.2%, Statistics 38.3%.

The full spread across areas is 11.7 percentage points of separator rate. The spread across mark values (§2.1) is 69.6 points; across positions (§2.2), 51.9 points. Topic is by far the weakest of the three structural signals, and this is the most commonly misjudged fact about the examination. Restricted to the current design (2023–2025) the ordering barely changes: Functions 48.5%, Space 45.7%, Discrete 42.9%, Calculus 36.5%, Algebra 25.7%, Statistics 25.6%.

2.6 Separator rate by year

Year-to-year variation is real but bounded: the separator rate has ranged from 29.3% (2025) to 60.3% (2008), with no trend until the 2023 redesign, after which it drops (§7). The hardest and easiest sittings in the archive are 2008 and 2025; on the written papers specifically, 2008 put 82% of the available marks inside separator parts and 2015 only 41%.

2.7 The shape of a separator's mark distribution

This is the part of the anatomy that pct alone does not show. Using the dist field, which gives the percentage of the state at each score:

Three readings.

(i) On the typical separator, the most common outcome in the state is zero. Not "a partial mark", not "most of it" — nothing. This is true of 62% of separators and of no non-separator at all. 43% of separators had at least half the state score zero, and 33 separators (6%) had at least 80% of the state score zero. The extreme is 2017 Exam 2 Section B Q4f, where 99% of the state scored zero on a 1-mark item.

(ii) The modal-zero property is almost entirely a property of small parts.

A 3-mark separator and a 1-mark separator have almost the same full-mark rate (30.7% vs 33.4%) but completely different shapes. The 1-mark separator is bimodal by construction — two-thirds of the state at zero, one-third at full. The 3-mark separator has only a third at zero and spreads the rest across 1 and 2. The 3-mark separator is where partial credit lives; the 1-mark separator is where it does not. The practical consequence: a 1-mark final part is the highest-variance object on the paper, and the only defence against it is completeness, since there is no partial credit to fall back on.

Distribution of separators by zero-share band:

(iii) Separators worth 3 marks and above are U-shaped. Of the 204 separators worth 3+ marks, 171 (83.8%) have both the zero bar and the full-marks bar above the minimum interior bar: the state divides into candidates who did it completely and candidates who did not start, with a thin middle. 2023 Exam 1 Q8 (induction, 4 marks, mode 2) is the exception that proves the point — the induction ritual is worth half the marks whether or not the mathematics is right.

Position drives the shape as much as it drives the rate:

2.8 The extremes, named

The twenty hardest written parts in the November archive:

Sixteen of the twenty are 1-, 2- or 3-mark parts, and fifteen are the final or penultimate part of their question. Severity is not carried by big questions.

At the other extreme, the highest written pct values are all 1-mark opening parts: 2023 Exam 2 Section B Q6h (100%), 2010 Exam 2 Section B Q1ai (96%), 2025 Exam 1 Q5a (94%), 2010 Exam 2 Section B Q1aii (94%), 2025 Exam 2 Section B Q4a (93.4%).

Multiple choice. The hardest items are 2017 Exam 2 Section A Q10 (6% correct; 45% chose the distractor that included the extra root where f″ = 0 without a sign change), 2022 Exam 2 Section A Q16 (17%), 2023 Exam 2 Section A Q15 (18%), 2022 Exam 2 Section A Q10 (21%), 2015 Exam 2 Section A Q16 (23%, where 53% chose a scalar component equation over the vector equilibrium condition). Of the 298 November items whose full option distribution is recorded, a distractor outpolled the key on 10 (3%); among the 78 multiple-choice separators with a distribution, that rises to 13%. The concentration of wrong answers is not itself a difficulty signal: on both separators and non-separators, the single most popular distractor carries a mean 46% of the wrong-answer mass.

2.9 Stem length

Written parts with a recovered individual stem (n = 843), split into quartiles by the character length of the part's own stem:

The effect is real but confounded — long stems are also where the modelling twists and the labelling checklists live. The usable version of it: a part whose instruction runs over three lines is carrying more than one requirement, and the full-mark test is conjunctive over all of them.

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3. The failure mechanisms, ranked

3.1 Method

Of the 634 November separators, 474 (75%) carry report commentary. Each mechanism below is a regular expression over that commentary. The right-hand columns repeat the measurement over the 429 commented non-separators, which is what makes the table diagnostic rather than merely descriptive: a mechanism that appears equally often in easy and hard questions does not explain separation.

3.2 The table

3.3 The mechanisms that cost a mark, and the mechanisms that cost the question

The concentration ratio splits the table cleanly in two, and that split is the practical output of this section.

Mechanisms that cost a mark (ratio near or below 1) — they are just as common on questions three-quarters of the state answered perfectly:

• Algebra and arithmetic (1.18). The commonest single complaint in the corpus and the least diagnostic. The 2012 Exam 1 report's formulation is the useful one: "many students made algebraic slips at the end of an answer, which meant the final mark could not be awarded. This was especially unfortunate when they had a correct answer and there was no need for further simplification."
• Required form and rounding (0.84). Costs the last mark, never the question. 44 explicit mentions in the corpus, and 2020 Exam 2 Q3c shows the mechanism in its purest form: a point of inflection "rounded to 0.58 instead of 0.59" inside an otherwise correct sketch.
• Technology and transcription (0.86). Slightly more common on easy questions, because easy questions are where technology gets used unthinkingly — degree mode, insufficient displayed digits, a calculator window that does not match the printed grid.
• Notation (1.34) and insufficient working in "show that" (1.08). Both are real and both are named constantly, but neither discriminates: a candidate who writes an unconvincing "show that" on a 77%-rate 1-mark item loses that mark and keeps the question.

Mechanisms that cost the question (ratio ≥ 2):

• Non-attempt (5.43). The strongest single discriminator in the corpus. Thirty separators have commentary that opens with a variant of "Many students did not attempt this question", against five non-separators. Nearly all are final or near-final parts: 2024 Exam 2 Q3d (17%) and Q3e (4%), 2024 Exam 2 Q4e (24%), 2019 Exam 2 Q2c (7%) and Q2d (1%), 2017 Exam 2 Q2di (17%) and Q3d (26%), 2016 Exam 2 Q3e (23%), 2018 Exam 2 Q4e (28%), 2015 Exam 2 Q2bii (23%), 2014 Exam 2 Q4c (32%), 2019 Exam 2 Q6f (36%). A substantial share of the state's separation is not error at all; it is time and abandonment. 2019 Exam 2 Q6f (36%) is the sharpest case: "This question was often not attempted. Most students who did attempt it answered correctly."
• Wrong or inefficient method (2.85). A distinctively Specialist failure. 2013 Exam 1 Q2 (47%): "Few students who used an unnecessarily complicated approach were successful." 2022 Exam 1 Q4 (36%): "Such approaches were inefficient and often resulted in students doing significantly more work than would otherwise be required." 2015 Exam 1 Q8a (47%): "There were many instances of poor choices of substitution … These attempts led to a more complicated solution and were rarely successful."
• Only one of two solutions (2.41). 2024 Exam 1 Q10 (14%): "Some students considered only [one case] and so did not find both values." 2025 Exam 2 Q5dii (33.8%): "Many responses did not demonstrate that the modulus needed to be used and consequently only one of the solutions was found." 2016 Exam 1 Q10 (14%): "A large number of students, when confronted with a square equals a constant, gave only the positive root. Many gave both roots but did not realise that only the negative root satisfied the initial conditions." 2019 Exam 2 Q2c (7%): "most of these students found only one end point of the interval." 2013 Exam 2 Q1b (41%): "a number of students gave only one answer for t, and others gave extra solutions outside the specified domain."
• Domain, range and endpoint inclusion (2.02). 2021 Exam 2 Q1di (6%): "Very few students gave all three values." 2014 Exam 1 Q7a (4%) — a 1-mark "write down the range" opener on which 96% of the state scored zero: "Few realised that x and the arctan function are both positive for the same values, negative for the same values and zero for the same values. … Many students seemed to use the product of the ranges of each of the 'parts', some ignored one part and others found the product of the range of one part and the variable x." 2012 Exam 1 Q10a ii (33%): "Many made unfortunate slips with inclusion/exclusion of values at the boundaries."

Notice that three of the four question-costing mechanisms are the same defect wearing different clothes: the answer is a set, and the candidate produced an element of it.

3.4 Setting out, and why the Specialist reports are blunt about it

07-exam-craft.md §6 quotes the standing 2011–2017 Exam 1 general comment in full — the paragraph that ends "If there are inconsistencies in the student's working, full marks will not be awarded. For example, if an equals sign is placed between quantities that are not equal, full marks will not be awarded." What the question-level commentary adds is the specific form the complaint takes, and there are three.

(a) An equals sign between things that are not equal. 2012 Exam 1 Q7 (41%): "Equals signs must not be placed between quantities that are not equal… nor are statements that equate an indefinite integral with a definite integral."

(b) Assertion in place of a step. 2015 Exam 2 Q4c (52%): "Some students simply asserted that r(t)·r′(t) = 0, without setting out the scalar product to show it." 2020 Exam 2 Q4d (51%): "It was not sufficient to simply assert that the pair of equations had no solution." 2025 Exam 2 Q5c (65%): "Several responses included only the answer so they only gained the answer mark. It is essential that students show the mathematics behind their solution to be awarded the full marks." 2024 Exam 2 Q2a (63%): "Some students did not provide sufficient working to gain both marks."

(c) A "show that" answered by verification. 2019 Exam 2 Q2ai (68%): "In a 'show that' question such as this, students are expected to explicitly show that the given information leads to the required conclusion rather than 'verify' that the given values of z are solutions of the equation." 2014 Exam 1 Q8b (40%): "Several students simply substituted a few values in for θ and then asserted that the result was therefore true for all values. Others attempted to demonstrate the result with a graph. Neither approach was sufficient." 2014 Exam 1 Q6a (86%): "many students did not know how a verification or proof should be set out. Some arguments were not convincing, and some eventually showed that a = a or similar" — the circular-proof failure named explicitly.

VCAA's own statement of the standard, from 2024 Exam 2 Q4a (78%): "A 'show that' question requires logical steps set out to indicate how the solution could be found."

A related, purely mechanical complaint recurs in the Exam 2 reports and is worth separating out because it costs marks without any mathematical error: "untidy working, lack of logical development and lack of clarity about what a student intends to be their final answer"; "work being done in very light pencil"; "graphs being done in pen rather than pencil" (2012 Exam 2 Q1b, 42%: "A number of students drew their graphs in pen rather than pencil, which made it very messy when corrections had to be made").

3.5 Proof rigour, 2023 onward

The proof area is new and the reports have already converged on a fixed list of four rigour faults, all of which cost marks independently of the mathematics:

1. The base case not actually verified. 2025 Exam 1 Q7: "Not properly verifying the base case."
2. The assumption misstated. Same report: "Misstating the assumption. For example, 'Suppose the proposition is true for n = k. Then …'" — the fault being an unquantified or un-instantiated k.
3. Assuming what is to be proved. Same report: "Assuming equality at the beginning of the inductive step."
4. The inductive step performed by the wrong operation. 2023 Exam 1 Q8: "Many students appeared to be thinking of index laws and assumed that f⁽ᵏ⁺¹⁾(x) was equal to 2 f⁽ᵏ⁾(x)."

And the general-case version, from 2023 Exam 2 Q2fii (7%): "most students did not 'show that' the required result arose through a series of logical steps."

The measured consequence is that the two induction items in the November archive are both separators, with pct 21 and 29 and a combined median of 25 — the lowest of any content family that appears in the current design.

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4. The five shapes that separate reliably

These are the constructions that produce separators across the whole twenty-year archive, ranked by how badly the state does on them. Each is defined structurally, not by topic, and each is measurable.

Shape 1 — The set-valued answer

Construction. The answer is a set, an interval, a family, or a list of cases, and the question does not say how many elements there are.

Measured. Written parts whose own stem contains "all values of", "for what values of" or "values of k for which": 13 parts, 11 separators (85%), median pct 26, 54% of them below 30%. This is the highest separator rate of any measurable stem feature in the corpus. Broken down by mark value: at 1 mark, 60% separator rate; at 2 marks, 100% separator rate with a median of 7. A broader net — stems mentioning a set, interval or range of values — gives 32 parts at 44% and median 52.8, which is the point at which the wording stops being explicit and the effect washes out: it is the word "all" that predicts, not the mathematical content.

Archive evidence. 2021 Exam 2 Q1di (6%, three values of k), 2019 Exam 2 Q2c (7%, the interval −1 ≤ d ≤ 5), 2023 Exam 1 Q10d (7%, all t with r ⊥ ṙ), 2020 Exam 2 Q3eii (2%, classify n by parity), 2021 Exam 2 Q1dii (13%), 2024 Exam 1 Q10 (14%, two values from a ±), 2024 Exam 2 Q1di (27%), 2012 Exam 2 Q4e (29%, two roots of a trigonometric equation), 2025 Exam 2 Q5dii (33.8%, two values of m from a modulus).

Why it discriminates. Every other question type has a self-evident stopping condition: you stop when you have the number. A set-valued question has no stopping condition except a correct argument about exhaustiveness, and the mark scheme is conjunctive over the elements. The failure mode is uniform across twenty years and six areas: the candidate finds an element, recognises it as an answer, and stops. 2025 Exam 1 Q5c (25%) shows the other edge of the same blade — the report notes that students who gave extra values "were not awarded the mark for this question". The set must be exactly right in both directions, and the archive contains no partial credit for getting the count wrong in a 1-mark part.

Shape 2 — The terminal generalisation

Construction. The final part replaces a constant from the earlier parts with a parameter and asks for the answer in terms of it, or asks which parameter values produce a stated qualitative feature.

Measured. Final parts of multi-part written questions: 206 parts, 164 separators (79.6%), median pct 32; restricted to questions with three or more parts, 82.2% and median 28; restricted to Section B alone, 82.6% and median 28. Final parts are modal-zero 62% of the time, with a mean of 48% of the state scoring nothing. Separately, parts whose stem says "in terms of": 60 parts, 42% separator rate, median 55 — so the wording is weak and the position is strong. It is the combination that is lethal: a final part that says "in terms of" is a near-certainty.

Archive evidence. 2019 Exam 2 Q2d (1%, p and q in terms of a, b, c), 2020 Exam 2 Q3eii (2%, g(x) = xⁿe^(−x) for general n), 2008 Exam 1 Q10c (3%), 2021 Exam 2 Q1dii (13%), 2023 Exam 2 Q3d (24%, the same efficiency ratio for a second solid), 2024 Exam 2 Q1di (27%), 2025 Exam 2 Q1dii (45.9%).

Why it discriminates. The generalisation is usually easier mathematics than the specific case that preceded it — 2020 Exam 2 Q3d (write down g″(x) for general n) scored 91% immediately before Q3eii scored 2%. What fails is not the algebra but the shift from computing to classifying: the candidate must reason about which of several qualitatively distinct behaviours the parameter produces, and enumerate them. It is Shape 1 in disguise, which is why the two share their worst cases.

Shape 3 — The multi-regime model

Construction. The question establishes a model, runs it for a while, then changes one assumption — a delay, a tap turned off, a force removed, air resistance switched on, a second stage of motion — and asks for a quantity spanning both regimes.

Measured. There is no single keyword, but the family is identifiable from the report commentary, and it is where the non-attempt mechanism concentrates (§3.3). Every instance below is a final or penultimate part with commentary that names either abandonment or a handover error.

Archive evidence. 2024 Exam 2 Q3e (4%, "the most common error was not taking the 5-day delay into account"), 2019 Exam 2 Q5d (9%, two-stage motion), 2021 Exam 2 Q4c (6%, the smooth join between two track sections), 2017 Exam 2 Q2di (17%) and Q2e (16%, the skydiver's two regimes), 2025 Exam 2 Q3g (18%, the tap turned off), 2023 Exam 2 Q3d (24%), 2018 Exam 2 Q4e (28%). 2016 Exam 2 Q5 carries the canonical diagnosis: "The most common misconception arising in this question was not realising that acceleration was now constant, and some students proceeded to use their equation for the displacement obtained in Question 5c."

Why it discriminates. The candidate must identify the correct initial condition for the second regime — which is an output of the first regime, not a number printed in the stem. Every error the reports name is a handover error: integrating from 0 instead of from the handover value, forgetting to add back the first regime's elapsed time, or carrying the first regime's equation into the second. The mathematics in each regime is routine and was already done, at high pct, earlier in the same question. It is also the shape with the worst compounding: 2017 Exam 2 Q2 lost 5 of its 10 marks to a single misreading.

Shape 4 — The itemised sketch

Construction. A 2–3 mark sketch whose instruction enumerates what must be labelled: asymptotes with their equations, turning points and inflections with coordinates to a stated accuracy, intercepts, endpoints, open circles, direction of travel.

Measured. Written parts whose stem contains "sketch": 59 parts, 38 separators (64%), median pct 43, 24% below 30%. By mark value: 1 mark 45% separator rate, 2 marks 63%, 3+ marks 76%. Across the corpus, "sketch", "graph" and "asymptote" account for 198 mentions in the question-level commentary — the largest single cluster of any topic word.

Archive evidence. 2024 Exam 1 Q3c (10%), 2025 Exam 1 Q9c (16%), 2024 Exam 2 Q1a (17%), 2008 Exam 1 Q1 (19%, 5 marks), 2013 Exam 1 Q7b (22%), 2021 Exam 2 Q1c (22%), 2023 Exam 1 Q1b (39%), 2025 Exam 2 Q1a (40.9%), 2024 Exam 2 Q4b (41%), 2012 Exam 2 Q1b (42%), 2023 Exam 2 Q4f (43%).

Why it discriminates. The mark scheme is a conjunction of four to six independently checkable items, and candidates treat it as one drawing. The reports are unanimous that the shape is usually right and the items are missing:

• 2024 Exam 2 Q1a (17%): "Students generally succeeded in drawing and labelling the asymptotes and demonstrated asymptotic behaviour effectively" — but "the graph must be flatter near the x-intercept, with turning points and end points precisely positioned."
• 2025 Exam 2 Q1a (40.9%): "Many responses did not label the horizontal asymptote y = 0. … Several responses, incorrectly, sketched the point of inflection as a stationary one."
• 2021 Exam 2 Q1c (22%): "A significant number of responses did not include the middle branch."
• 2023 Exam 2 Q4f (43%): "Many students incorrectly labelled the asymptote … and some students did not follow the instruction to label the Q-intercept with its coordinate. Most students sketched the shape of the logistic curve well."
• 2008 Exam 1 Q1 (19%): "A large number of students did not give coordinates for the x-intercept or the turning point, and just gave the x-coordinate."

A second, mechanical failure sits underneath: transcription from CAS. "Students can sketch the function on their CAS calculator and set the domain, range and scale to match those provided in the question" appears in both the 2024 and 2025 Exam 2 reports; and the 2010 Exam 2 report warns that "graphs obtained using technology will usually show shape but will not distinguish between open and closed endpoints."

Shape 5 — The inverted or composite instrument

Construction. Two related constructions, joined by the same defect. (a) Inversion: the standard procedure is run backwards — given the confidence interval, find n; given the significance level, find the critical value of x̄; given the required precision, find the sample size; given the resolute, find the vector. (b) Composition: a quantity is defined in the stem as a combination of two things the candidate can compute separately, and must be assembled.

Measured. Inversion in statistics: 2021 Exam 2 Q6e (9%), Q6a (14%), Q6d (16%); 2018 Exam 2 Q6f (11%); 2023 Exam 2 Q6c (28%), Q6g (39%); 2024 Exam 2 Q6c (44%), Q6g (46%), Q6f (51%); 2025 Exam 2 Q6d (53.1%), Q6h (53.7%). In every one of the four statistics questions dissected in §1.6, the inversion parts sit 20–35 points below the conveyor parts beside them. Inverse resolutes: 2020 Exam 1 Q5b (28%). Composite quantities: 2019 Exam 2 Q4e (2%, pyramid volume via a scalar resolute), 2024 Exam 2 Q3d (17%), 2024 Exam 2 Q4ci (23%, speed squared), 2023 Exam 2 Q3c (38%).

Why it discriminates. Forward procedures are muscle memory; inverse ones require knowing which quantity in the formula is unknown and which tail the probability sits in. The reports name the two errors every time: "Some responses used the wrong tail of the distribution" (2025 Exam 2 Q6g); "students sometimes did not find the critical value for x̄ when H₀ is true; students used the wrong tail" (2024 Exam 2 Q6c); "Some students calculated 63,108.7 but did not proceed to answer the question correctly as a range of values" (2021 Exam 2 Q6d). Composite quantities fail for a related reason: the candidate computes the part they recognise and stops — "Many students found the curved surface area only and did not include one or both ends" (2023 Exam 2 Q3c); "Several students did not find the square of the speed" (2024 Exam 2 Q4ci).

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5. What does not separate

These are the shapes that look forbidding and are not. Every figure is against a written baseline of 48% separator rate and median pct 52 on the 843 parts with a recovered stem.

Seven readings.

(i) "Show that" is protective, and this is by design. A 1-mark "show that" is answered by 77% of the state at the median against a 62% baseline for 1-mark parts, and separates only 14% of the time against a 30% baseline. VCAA says why: the instruction exists to "enable access to subsequent marks for later parts of the same question". The exception is the 3+-mark "show that", where 83% are separators — at that size the instruction is no longer a handrail, it is the whole task (2023 Exam 1 Q8, 2023 Exam 2 Q2fii).

(ii) The new 2023 content is not the problem. Cross product, planes and lines in space, surface area of revolution and integration by parts all sit at or below baseline. VCAA's own 2023 Exam 1 report anticipated this: "While some students had difficulty with proof by induction, a majority of students were able to demonstrate that they understood what was required in the questions on the new topics." The 2024 report repeats it: "It was pleasing to see that many students were able to partially or fully answer these questions." The one new topic that is hard is proof by induction, and it is hard for rigour reasons, not novelty reasons.

(iii) Statistics does not separate. It has the lowest separator rate of any area (36.9%), the highest median (58), and Section B Q6 — where it lives — is the easiest question on the paper (29% separator rate against 50–58% for Q3–Q5). The only hard statistics is the inverted kind (Shape 5) and the disguised-sum kind (2021 Exam 2 Q6a, Q6b).

(iv) Multiple choice is the softest assessment. 29% separator rate; a distractor outpolls the key in only 3% of items. An MCQ has to work hard to separate, and when it does, the report almost always names a specific conceptual confusion rather than a computation: f″ = 0 without a sign change, a scalar equation offered where a vector equation is required, a cancelling factor removing a vertical asymptote, a release height forgotten in a total-distance calculation.

(v) The Argand diagram is not intrinsically hard. Plotting roots and sketching rays run at 42–83%. What is hard is the region and the area of a region in the complex plane — 2017 Exam 2 Q4f (1%), 2008 Exam 2 Q5f (6%), 2016 Exam 2 Q2f (7%) — which is Shape 5, a composite quantity, not complex-number work.

(vi) Setting up an integral without evaluating it is not hard. The 20 parts asking the candidate to "write down a definite integral" run at baseline with a median of 56. Separation in integral questions comes from the limits, from the form, and from what the integral is of — not from the modelling step. The exception proves it: 2017 Exam 2 Q2di (17%) asks exactly this, and fails because the limits span two regimes.

(vii) Being scaffolded into sub-parts is protective. A part numbered i/ii/iii separates at 42% against 53.5% for a plain lettered part. Where VCAA divides a task, it has decided the task needs dividing — and the division supplies the decomposition the candidate would otherwise have to find.

One counterexample worth holding onto. "State" and "write down" are the safest verbs on average, but they are not safe when the object asked for is a set. 2014 Exam 1 Q7a is a 1-mark, first-part, "write down the range of f" item — every structural signal says easy — and 96% of the state scored zero on it, because the range of 3x·arctan(2x) is [0, ∞) and requires an argument about signs rather than a lookup. Shape 1 overrides every other signal in the diagnostic.

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6. A diagnostic

6.1 Predicting a separator before you attempt it

Four observable features, in descending order of measured value:

6.2 The rule

Evaluated against all 1,012 November written parts:

The working rule: a part is a separator if it is worth three or more marks, or if nothing follows it. That one sentence flags 394 of the 1,012 written parts in the archive and is right about 78% of them, with 60% recall. The broader rule catches four separators in five at the cost of flagging 60% of the paper — useful for allocating revision, useless for allocating time in the room.

6.3 A finer score

Adding the verb and answer-type signals produces a monotone scale. Score a part as: marks (1 → 0, 2 → 1, 3 → 2, 4+ → 3) plus position (first 0, middle 1, single-part 2, final 3) plus 1 if Exam 1, plus 2 if the stem says "all values"/"for what values", plus 1 if it says "exact", plus 1 if it says "sketch", minus 2 if it says "show that", minus 1 if it is a 1-mark "state"/"write down".

At a threshold of 3 the scale gives 75% precision at 63% recall; at 5, 80% precision at 33% recall. It is not better than the two-clause rule at classification, but the ordering is informative: scores of 0 and 1 are indistinguishable (27% and 25%), which is to say that once a part is small and early, no other feature makes it dangerous. The scale's top band (≥ 7, thirteen parts) is a perfect classifier — every one of them is a separator, with a median of 27.

6.4 What to do differently on a flagged part

The measured failure mechanisms (§3.3) prescribe the behaviour directly. On a flagged part:

1. Attempt it. Non-attempt is the most concentrated failure mechanism in the corpus (5.4×), and the rubric deducts nothing for a wrong answer. On 2024 Exam 2 Q3d the report's entire diagnosis was that the answer is volume ÷ depth; on 2019 Exam 2 Q6f, "most students who did attempt it answered correctly".
2. Count the requirements in the instruction before starting. A 3-mark part has three, and the full-mark test is conjunctive. On a sketch, write the label list out before drawing: asymptotes with equations, turning points with coordinates, intercepts, endpoints, open circles, direction.
3. Decide whether the answer is a number or a set. If the question says all, values, for what, or in terms of, or if the working contains a square, a modulus, a trigonometric equation or a quadratic, the answer is a set. Finish by asking what else satisfies the condition — and check that nothing extra has crept in, which is penalised equally (2025 Exam 1 Q5c, 2013 Exam 2 Q1b).
4. If the model changed, find the handover values. The initial condition for the second regime is an output of the first, not a number in the stem. Write it down explicitly before integrating.
5. On a "show that", write the chain. The printed result is not evidence. Substituting values is not a proof (2014 Exam 1 Q8b). An equals sign must join equal things (2012 Exam 1 Q7). Ending at a = a is a circular argument and scores nothing (2014 Exam 1 Q6a).
6. Do not choose the elaborate method. 2.85× concentration. If a standard antiderivative is on the formula sheet, use it rather than a substitution; if a quadratic factorises, factorise it.
7. On a final part, budget the time before you need it. Eighty per cent of final parts are separators, and a measurable share of that is abandonment rather than error. The 1-mark final part is the worst risk-reward object on the paper: 70% separator rate, no partial credit, and one mark at stake.

6.5 Where the rule fails

The rule's 22% false-positive rate is concentrated in three places, worth knowing so as not to over-prepare for them: 3-mark "show that" parts inside a strong scaffold (2023 Exam 2 Q3bi, 62%); final parts of statistics questions, which are usually one more turn of the conveyor (2023 Exam 2 Q6h, 100%; 2025 Exam 2 Q6h, 53.7%); and final parts that merely evaluate something already derived (2025 Exam 2 Q3f, 60.7%). The false negatives are mostly 1-mark middle parts carrying a hidden set-valued answer or an inversion — 2023 Exam 2 Q2dii (18%) and 2021 Exam 2 Q6d (16%) are the type specimens.

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7. The 2023 discontinuity

7.1 The question

The 2023 study design deleted all of mechanics beyond single-particle rectilinear kinematics; the 2016 design had already deleted conic sections as objects. Both deletions touch large parts of the archive. How much of the measured separator stock is content that can no longer be examined, and what does the remaining archive look like?

7.2 Method, and its validation

Question stems were keyword-classified. A question was tagged mechanics if its stem contains any of: newton(s), tension, friction, pulley, momentum, impulse, normal reaction, in equilibrium, resultant force, light inextensible, coefficient of friction, force diagram, net force, acted on by two/three/four forces, force(s) of magnitude, forces. It was tagged conic-as-object if the stem names an ellipse, hyperbola, focus, directrix or eccentricity without also presenting the curve as a path traced by a vector function of time.

The classifier validates itself at the boundaries, which is the reason to trust it:

• Mechanics: 181 tagged parts, spread across 2006–2022, and exactly zero in 2023, 2024 or 2025.
• Conic-as-object: 18 tagged parts, spread across 2006–2015, and exactly zero from 2016 onward.

A keyword net cast over twenty years of paper text landing precisely on the two known deletion dates is strong evidence that it is catching the right thing.

Two blind spots must be stated. The 2011 paper text is encoding-corrupted, so its 62 rows cannot be classified; extrapolating from the 16.2% mechanics share of classifiable 2006–2022 rows, roughly 10 parts and 4–5 separators are missed. The 2024 November text files are empty (80 rows), but 2024 is post-redesign and contains no mechanics, so nothing is lost there.

7.3 How much of the archive is dead

Correcting for the 2011 blind spot, the true dead share is approximately 14–15% of parts and of separators.

7.4 The finding that matters: the deletion did not change the difficulty

The separator rate of the live archive (44.5%) is indistinguishable from the separator rate of the whole archive (44.4%). Mechanics questions separated at 44.2% — that is, at exactly the archive average. They were neither the hard part of the course nor the easy part. Removing them removed roughly one part in seven and left the difficulty profile untouched.

Within Space and measurement, the area that absorbed the deletion:

The live remainder is very slightly harder than what was removed. 06-space-measurement.md reaches the same conclusion from its own manual grouping and states the consequence bluntly: losing the mechanics "removed the part of it the state was relatively best at."

7.5 What the live archive looks like

Removing dead content makes the legacy papers look marginally harder, not easier, in both earlier eras — because the mechanics questions were slightly above-average for the cohort. The genuine discontinuity is elsewhere: the current design's written papers are 14–17 points less separating than either predecessor.

Within the current era the mark-value gradient is preserved but shifted upward:

Compare §2.1: 1-mark parts have gone from 30.4% to 22.4% separating, 2-mark parts are unchanged, 3-mark parts have eased from 77.7% to 71.4%, and 4-mark parts remain certainties. The current design has made the small parts easier and left the large ones exactly where they were. Multiple choice has not moved at all: 60 items, 35% separator rate, median 59 — statistically the same as the archive's 29%/62 given the sample size.

The area-of-study profile has changed more than the aggregate suggests. Under the current design, statistics and complex numbers have become markedly easier (25.6% and 25.7% separator rates, medians 67 and 61) while Functions, relations and graphs has not moved at all (48.5%, median 51.2). Rational-function sketching is now, measurably, the single weakest content area in the current course, which is exactly where 09-nht-specialist.md §1.4 places it.

7.6 The practical size of the usable archive

Counting only November papers with published percentages:

• 1,229 graded parts of live content, carrying 2,072 marks, of which 547 parts and 1,130 marks are separators.
• Of those, 247 parts (93 separators, 360 marks) come from the three current-design sittings — the only sittings that can contain proof, the cross product, planes, lines in space, integration by parts, surface area of revolution, the logistic equation, pseudocode, or the n-variable statistics content.
• The rest — 982 parts, 454 separators — are legacy papers whose content survives the redesign. They remain the best available drill for everything the archive does cover, which is the large majority of the course.

The asymmetry is worth stating plainly: for most of the course there are twenty years of measured separators; for the content added in 2023 there are three sittings and roughly forty graded parts. The measurement of the new content is therefore thin, and every conclusion about it in §5 carries that caveat.

7.7 Three corrections to the naive reading

(i) year >= 2023 is the wrong filter. The 2023 NHT papers were set against the old design with the old formula sheet and still contain mechanics; the 2024 NHT papers are current-design. The correct split is November 2023 onward, plus NHT 2024 onward (01-study-design.md §5.7).

(ii) The 2020 papers are the least representative in the archive, because the entire statistics area of study was deleted for that cohort — not merely absent from that year's paper, but struck from the study design and from the formula sheet. Statistics is now roughly a fifth of the assessment.

(iii) Pre-2024 multiple choice has a fifth option. November moved to four options at the 2024 sitting. The 376 five-option November items have a median of 62% and the 40 four-option items 58%, so there is no evidence that the change made items easier — but percentages across the boundary are not strictly comparable.

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8. Summary — the anatomy in nine sentences

1. A Specialist question has four organs: a stem, a given (usually a "show that"), a scaffold of routine parts, and a sting.
2. The sting is the final part, it is a separator 80% of the time, and its median full-mark rate is 32%.
3. It works by one of four moves, none of them mathematical: the answer becomes a set, a constant becomes a parameter, a modelling assumption changes, or a composite quantity must be assembled from the stem's own definition.
4. Mark value and position are the two strong structural signals — a 1-mark part separates 12% of the time when it opens a question and 70% of the time when it closes one — and topic is a weak third, worth 12 points of spread against 70 and 52.
5. On the typical separator the most common score in the state is zero: 62% of separators are modal-zero, 43% have at least half the state scoring nothing, and 84% of separators worth three or more marks are U-shaped.
6. The failure mechanisms that merely cost a mark — algebra slips, rounding, required form, notation, technology — are as common on questions the state answered perfectly as on separators.
7. The mechanisms that cost the whole question are concentrated 2–5× in separators, and three of the four are the same defect: the answer was a set and the candidate produced one element of it.
8. "Show that" at one or two marks, multiple choice, confidence intervals, hypothesis-test mechanics, roman-numbered sub-parts, and every topic added in 2023 except induction do not separate.
9. Fourteen per cent of the measured separator stock is mechanics and conics that can no longer be examined — and because that content separated at exactly the archive average, deleting it changed the difficulty of the course by nothing at all.

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