How VCAA constructs a question in each of the four current General Mathematics topics, and what the separator questions have in common

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0. Scope, data and method

0.1 The frame

Everything counted in this document comes from the November sittings, restricted to the four current topics (Data analysis; Recursion and financial modelling; Matrices; Networks and decision mathematics), for the years in which those four topics exist: 2016–2025. That gives:

Measured in marks rather than items: of the 615 Exam 2 marks graded in this period, 312 (50.7%) sit inside separator parts. Half of the written paper's marks are contested.

A narrower cut — 2023–2025 only, the current General Mathematics study design with no module choice — behaves the same way but slightly harder on Exam 2: 284 items, 116 separators (40.8%); Exam 1 23.3%; Exam 2 53.7%.

0.2 Definitions and provenance

• Separator = a question (or question part) where ≤50% of the state earned full marks. This is the sep column in corpus/export/separators.csv and the separator flag in corpus/questions.json; the two agree exactly on all 964 items (384 flagged, 384 with pct ≤ 50).
• pct throughout = percentage of students awarded full marks for that item, as published in the VCAA examination report / assessment guide. For a 1-mark item this is the same as "got it right". For a 2-mark item it is not — partial credit is invisible in this number, which matters for the mark-value analysis in §2.2.
• Primary source used: corpus/questions.json (964 in-scope rows). corpus/export/nov_all.csv lists 958 of the same rows; the six extra are 2020 Exam 1 Q25–Q30 (Recursion), which are present in the JSON with valid percentages but absent from the CSV export. Using the CSV instead moves no headline number by more than 0.3 percentage points.
• Command-word and stem-feature analysis (§2.6, §2.8, §2.9) required the actual wording of each question, which is not in the CSVs. Question stems were parsed programmatically from the exam papers in corpus/text/, then joined to the graded data on (year, topic, question label). The join succeeded for 494 of the 554 Exam 2 parts (89%). The gap is almost entirely 2024, whose Exam 2 PDF has no extractable text layer, plus a handful of part-less questions. All stem-feature percentages therefore rest on n = 494 across nine years (2016–2023, 2025), not ten.
• Where a claim is interpretation rather than measurement it is labelled (interpretation).
• Topic-level structural material in Part 1 — scenario shells, staples, distractor design — builds on 02-data-analysis.md, 03-recursion-financial.md, 04-matrices.md, 05-networks.md and 07-exam-craft.md and is cited to them rather than re-derived. Every percentage in this document, including those attached to cited questions, was re-checked against questions.json.

0.3 One caveat about cross-year comparison

Exam 1 moved from five options (A–E) to four (A–D) at the November 2024 sitting (07-exam-craft.md §5.1), lifting the guessing floor from 20% to 25%. Exam 1 facility rose in 2024–25 partly for that reason. Exam 2 is unaffected.

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PART 1 — QUESTION ANATOMY, TOPIC BY TOPIC

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1. DATA ANALYSIS

Measured profile (2016–2025): 369 items. Exam 1: 164 items, 30 separators (18.3%), mean 65.0 — the easiest block in the subject. Exam 2: 205 parts, 85 separators (41.5%), mean 58.2. Exam 2 by mark value: 1-mark 34.5% separator rate; 2-mark 69.2% (mean 42.5).

1.1 The scenario shells

VCAA does not invent contexts; it dresses a small set of datasets in interchangeable real-world clothing — animal biology (moth egg clusters, mammal sleep/brain weight), meteorology (daily minimum/maximum temperature, humidity, rainfall), anthropometry and health (height, arm span, neck size, body density, BMI), sport (high jump, Tour de France, javelin, winning times), demographics and economics (house price vs distance from CBD, traffic congestion by city, ice-cream consumption vs temperature) (02-data-analysis.md §0, §1).

What matters structurally is not the context but the form in which the data arrives, because that is what determines the first two parts:

The annual staples — present in essentially every current-era paper — are: variable classification as the opener; boxplot construction and fence/outlier justification; an association question (either two-way table or parallel boxplots); scatterplot description; least-squares fitting with slope/intercept/r² interpretation; a residual or linearity question; and an interpolation/extrapolation justification. Rotated are: which transformation (log, reciprocal, squared) is used and whether the student chooses it; which smoothing order appears and whether seasonal indices are asked; the 68–95–99.7 "reverse" problem; comparing two fitted lines (02-data-analysis.md §1, §3.12).

1.2 How a question escalates

Data analysis is the one topic where a single question is a long scaffold on one dataset — 2023 Q1 alone is worth 9 marks. The ladder is consistent:

1. (a) Orientation, 1 mark. Read one number, or classify one variable. Facility is routinely 84–96%: 2024 Q1ai (read the 1996 value) 96%; 2025 Q1a (median) 84%; 2025 Q4a 94%.
2. Early-middle: one-step computation. A z-score, a percentage from a table, a fence, a five-number summary entry.
3. Late-middle: fit and interpret. Find the least-squares equation → state r or r² → interpret the slope → interpret the intercept. This is where the first reliable separators appear, and they are verbal: 2019 Q5a (interpret slope) 44%; 2020 Q5d (interpret slope) 44%; 2022 Q4c (interpret slope) 44%; 2023 Q3d (interpret intercept) 43%; 2016 Q3bii (interpret intercept) 28%.
4. Late: predict, then justify the prediction. 2025 Q4d (interpolation/extrapolation with a brief explanation) 27%.
5. Final part: a 2-mark synthesis, usually either an association justification quoting statistics, or a transformation/forecast step. 2018 Q3e (compare two fitted lines, quoting statistics) 2% — the hardest Data analysis item in the corpus.

Dependency chains are explicit and punished. 2017 Q4b: "Some students did not recognise that the rounded slope value from part a. was a required value in part b." (37%). 2021 Q5a (apply a reciprocal transformation, 16%) → Q5b (predict using that equation, 14%), where VCAA records the most common wrong answer as "0.2 gained by using the correct coefficients but using difference rather than the reciprocal of difference". 2021 Q3e.i (show that the predicted 2032 time is 49.252 s) → Q3e.ii (state the assumption behind that forecast, 18%).

1.3 Mark-allocation grammar

VCAA's marking shorthand is M1 (method), A1 (answer), H1 (consequential/holistic). Since 2017, no Exam 2 part in the whole corpus is worth more than 2 marks, with exactly one exception — 2016 Q3b.i, 3 marks, 28% (07-exam-craft.md §5.2). The 2023 and 2024 papers carry 52 one-mark and 4 two-mark parts each; 2025 carries 44 and 8.

1-mark tasks are single discrete acts: read a value; classify a variable; name the explanatory variable; state shape; compute a fence; state "linearity"; predict from a given equation; interpret the slope (one sentence, fixed template); draw the line on a grid.

2-mark tasks are always two tasks bolted together, and the second one is the one the cohort loses:

• Association justification = [a verdict / change statement] + [the actual conditional percentages or statistic values, for every group]. 2022 Q2b, 41%: "Many students gave the correct values for each median but did not specifically mention a change or difference." 2023 Q2bii, 50%: students had to say explicitly that farm A's percentage was higher than farm B's.
• Least-squares equation = [correct unrounded computation] + [correct rounding of both coefficients]. 2023 Q1d, 37%: "Many students appeared to have difficulty in giving the coefficients rounded to four significant figures." 2025 Q5a, 28%.
• Residual = [predicted value] + [signed subtraction in the right order].
• Outlier "show that" = [fence calculation] + [comparison and conclusion] — the 2024 guide requires both fences for a "no outliers" show-that.

1.4 Exam 1 vs Exam 2

Data analysis is Questions 1–16 of Exam 1 (16 of 40 marks) and 24 of the 60 marks of Exam 2 — 40% of each paper (07-exam-craft.md §5.1–5.2). In the current design the Exam 2 block is Q1–Q4 (2023, 2024) or Q1–Q6 (2025).

Exam 2 owns everything that must be constructed: drawing a boxplot or a least-squares line with a ruler, plotting a residual point, marking smoothing crosses, completing a stem plot, and every free-text justification. Exam 1 owns everything that needs a lattice of near-miss options: "which display is appropriate", "which transformation linearises this", and the association-vs-causation grids.

1.5 How the multiple-choice distractors are built

The named most-chosen wrong options in Data analysis fall into a small number of manufacturing rules (02-data-analysis.md §1.3, §2.4, §3; 07-exam-craft.md §5.1.5):

1. Wrong percentage base — the grand total instead of the row/column conditional (2018 Q1d/e: 17% offered instead of 25%).
2. Sign flip on r — the positive square root of r². Named in 2018 E1 Q9 and 2019 E1 Q10 with word-for-word identical report prose; in 2019 the distractor (46%) outscored the key (41%). In Exam 2 the same trap gives 2020 Q5f 25%, 2021 Q3b 19%, 2025 Q4b 21%.
3. Sibling-statistic swap — r reported where r² was wanted, mean where median was wanted, or the complement of a normal-curve percentage (2021 Q1d: "the most common incorrect answer was 16%"; 2018 Q2e: "92% was a very common incorrect answer" for r² where r = 0.92).
4. Surface-form variable-type trap — a categorical variable with numeric-looking labels (postcode, day number), or an ordinal one dressed as nominal. VCAA's own generalisation: "the use of numbers in a variable definition does not automatically make the variable numerical" (2017 E1 Q7).
5. Log-axis literalism — reading a log₁₀ scale as raw values. 02-data-analysis.md calls this family "consistently the hardest DA MC item".
6. Causal rewording — a correct association statement re-voiced with "causes" / "is due to".
7. Explanatory/response reversal inside an interpretation option.
8. Off-by-one counting — variable counts, smoothed-point counts, boundary values (2022 Q3ai: "6 was a common error" where the answer was 5).

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2. RECURSION AND FINANCIAL MODELLING

Measured profile (2016–2025): 191 items — the smallest block and the hardest. Exam 1: 79 items, 28 separators (35.4%), mean 57.0. Exam 2: 112 parts, 64 separators (57.1%), mean 49.8 — the only topic where the median Exam 2 part is a separator. 2-mark Exam 2 parts: 11 items, 10 separators (90.9%), mean 27.4. In 2023–2025 the Exam 2 rate is 61.8%.

2.1 The scenario shells

A closed set of six financial objects, each with a signature recurrence (03-recursion-financial.md §1):

The given form is the real variable: a bare recurrence relation; a rule Vₙ = a·bⁿ with boxes to fill; a table of the first few terms; a graph of balance vs time; an amortisation table with blanks; or nothing but words. The last of these is the highest-value Exam 2 task — constructing the relation from prose.

VCAA never hands students a Finance Solver screenshot. The solver input block (N=…, I%=…, PV=…, PMT=…, FV=…, P/Y=C/Y=…) appears only in the reports, as the examiners' model working — which is itself the hint that showing it is acceptable evidence for a method mark (07-exam-craft.md §4.1).

2.2 How a question escalates

1. (a) Read a value off the model, 1 mark. "How much did she initially deposit / borrow?" — 87–96% every year.
2. Middle: convert the model. Extract the interest rate from R (Vₙ₊₁ = 1.04Vₙ → 4% p.a.), or write the recurrence relation from the scenario — which appears in virtually every Exam 2 paper and is far harder than it looks: 2016 Q6b 33%, 2019 Q9c 24% (2 marks), 2020 Q8b 30%, 2022 Q7c 35%, 2023 Q6c 41%, 2017 Q6b 39% (2 marks).
3. Middle: one Finance Solver run = 1 mark. Find a payment, a balance, a rate.
4. Last part: the discriminator. Total interest paid; the number of payments; the final irregular repayment; a lump sum paid mid-schedule; or a condition that changes part-way through. This is the single most reliable hard-item family in the subject:

Dependency is structural here, not incidental. The two-stage chain — solve stage 1, feed its unrounded future value into stage 2 as the present value — is the standard construction for the hardest item. VCAA is explicit that the consequential mark for reusing a wrong earlier answer requires visible working: on 2019 Q9b, "Some students followed through with the incorrect response they obtained for Question 9a. but did not show the working required for the consequential mark."

2.3 Mark-allocation grammar

• 1 mark: one recursion step; one solver run; one rate conversion; or a complete recurrence relation. The last is the trap — the relation is graded as one unit requiring two correct components (initial value and rule). The 2025 guide: "BOTH parts must be correct." 2016 Q6b (33%) failed on exactly this: "failure to include the initial value, C₀; writing the initial value as Cₙ; using different symbols for different parts of the recurrence."
• 2 marks = either a derived input plus a solver run (2020 Q11 carried a method mark for finding the \$2400 repayment), or two chained solver calls, or two recursion steps shown in full (2021 Q9a, 21%: "Many students correctly calculated the factor of 1.00425 but either added the \$900 or did not show the recursive calculations in full.").

2.4 Exam 1 vs Exam 2

Exam 1 Q17–24 (8 marks); Exam 2 12 marks across 3–4 questions (Q5–Q7 in 2023, Q5–Q8 in 2024, Q7–Q10 in 2025). Exam 1 is structurally the hardest block of that paper in every current-design year. Exam 1 owns classification MCQs ("which recurrence could model this"), reverse-solve items, graph identification, and nominal-vs-effective comparisons. Exam 2 owns recurrence construction, amortisation-table completion, "use recursion to show that", total-interest calculations, and every changed-condition problem.

2.5 How the multiple-choice distractors are built

(03-recursion-financial.md §6; 07-exam-craft.md §5.1.5)

1. Rate per period vs rate per annum — the most repeated distractor in the corpus, and symmetrical: 2020 Q9b, "Many gave the annual interest rate percentage"; 2020 Q10b in the same paper, "0.24% per month was sometimes given"; 2022 Q8b, "0.2% was a common incorrect answer"; 2016 Q5c, "Common incorrect answers were 1.04 or 0.04%."
2. R vs the rate — offering 0.85 where 15% was wanted (2018 Q5a), or 1.05 where 5% was wanted.
3. Sign convention — PV/PMT/FV entered positive. 2019 Q9a (27%): "\$7954.54 was a common incorrect answer obtained by entering the FV as a positive rather than as −262 332.33." 2025 Q10 (11%): the payment answered as positive \$22 216.27.
4. Add vs subtract d — savings plans add, loans and annuities subtract. 2019 Q9c: "added rather than subtracted the 3517.28." 2023 Q5c (25%): "Some students added the \$0.14 future value instead of subtracting."
5. The value one step before the answer — 2021 Q8c (15%): "A common incorrect response was \$1197.39. This was the balance before the last payment but does not include the interest to be added." 2017 Q6c (26%): the total charged rather than the interest.
6. Simple vs compound, and flat rate vs reducing balance vs unit cost, offered as sibling options (2022 Q6d: "Many students answered 'flat rate', while others gave 'unit cost'.").
7. Ignoring the compounding period in a nominal-rate comparison (2018 E1 Q19: students "simply select[ed] the lowest interest rate").
8. Perpetuity mistaken for annuity — 2022 Q7d: "The annuity payment of \$5214.28 was the most common mistake." 2023 E1 Q24 (perpetuity R-value) scored 27%.

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3. MATRICES

Measured profile (2016–2025): 203 items. Exam 1: 85 items, 26 separators (30.6%), mean 62.3. Exam 2: 118 parts, 61 separators (51.7%), mean 51.8. Exam 2 2-mark parts: 5 items, 5 separators (100%), mean 24.8. In 2023–2025 the Exam 2 rate is 60.0%.

3.1 The scenario shells

(04-matrices.md §1)

• Transition / Markov flow between named categories — the dominant shell. Given as a transition diagram (arrows with percentages, plus self-loops) to be converted to a matrix, or as a matrix to be drawn back as a diagram.
• Leslie matrices (2023+ only) — births in row 1, survival on the sub-diagonal, with a life-cycle diagram.
• Communication / binary matrices — a 0/1 sender-receiver matrix with two worked "In this matrix:" bullets.
• Dominance matrices — round-robin results ranked by D + D²; almost exclusively Exam 1.
• Permutation matrices — a roster or timetable rotation; tests Pⁿ cycling and Pⁿ = I.
• Cost / order matrices — a price matrix against a quantity matrix, often with a summing matrix [1 1 1 …].
• Diagonal "different % per row" matrices, and inverse / simultaneous-equation templates with blank elements to complete.

The reliable opener is a labelled data matrix; the reliable hard middle is a transition diagram that must be read in the right direction.

3.2 How a question escalates

1. (a) State the order, or read one element. 91–96% across years; 2025 Q11a 96%, 2023 Q9d 100%.
2. Middle: compute a product and interpret it. The split is sharp and repeatable — computing the product is a high-facility task, interpreting what it means is not.
3. Middle: complete a transition diagram or matrix, or write a matrix calculation "to show that" a target value.
4. The signature hard part: the backward percentage. "Of those who chose X in year 2, what percentage had chosen Y in year 1?" Students who read the answer straight off the transition matrix get the seductive wrong number. Measured, year after year:

5. Last part: long-run / absorbing state / Sₙ₊₁ = T·Sₙ + B iteration. 2025 Q13bi 9%; 2025 Q14c (what P⁴ = I means for the roster) 11%; 2025 Q12b 13%; 2024 Q12b (absorbing state) 24%; 2024 Q11ai (complete the transition diagram — arrows required) 24%; 2021 Q3e 15%; 2019 Q3bii 12%.

3.3 Mark-allocation grammar

1 mark: order; one element; one scalar multiplier; one long-run value; "explain why the product is not defined". 2 marks: compute + interpret, or method + extraction. 2016 Q3eii (46%) is the canonical shape — "Many students found the correct matrix R₂₀₁₈ but did not extract the [required number]"; a method mark was available for a correct and labelled R₂₀₁₈ even with a wrong final answer.

3.4 Exam 1 vs Exam 2

Exam 1 Q25–32 (8 marks); Exam 2 12 marks across 3–4 questions (Q8–Q11 in 2023, Q9–Q12 in 2024, Q11–Q14 in 2025). Exam 1 owns: order-of-a-defined-product items, build-from-rule aᵢⱼ = f(i, j), named-matrix-type vocabulary (2023+), and essentially all dominance-matrix ranking. Exam 2 owns: written "explain why not defined", the boxes "show that", the full backward-percentage calculation, and the recurrence Sₙ₊₁ = T·Sₙ + B.

3.5 How the multiple-choice distractors are built

(04-matrices.md §6)

1. The raw transition-matrix element offered where a computed backward percentage is required (the family above).
2. Off-by-one in the power of T — T³ where T² was needed; renaming S₁ as S₀. VCAA's own rule: "the power by which the transition matrix must be raised is one less than the number of the required state matrix" (2014 report).
3. Wrong multiplication order (AB vs BA), with the report enumerating what each wrong product actually computes.
4. Row/column transposition — reading q₃₂ for q₂₃; giving a 3×1 where a 1×3 was asked (2017 Q1cii, 28%).
5. Applying +B before T, or squaring T instead of iterating.
6. Confusing "maximum", "first time", "long run" and "total" — 2022 Q3c (19%): "Many students incorrectly assumed that the long run number was required." 2017 Q3d: "239 was the most common incorrect response from the steady state matrix" when the maximum was asked.
7. Percentage vs proportion vs multiplier — 0.05 offered where 1.05 was wanted (2021 Q1b).
8. Sign/meaning of a negative element in B (2016 Q3ei, 14%: the −80 meant removal from the study, not "80 chose not to travel").

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4. NETWORKS AND DECISION MATHEMATICS

Measured profile (2016–2025): 201 items. Exam 1: 82 items, 34 separators (41.5%) — the hardest Exam 1 block, mean 57.8. Exam 2: 119 parts, 56 separators (47.1%), mean 52.8. The topic's distinguishing feature is not its average but its tail: it supplies the lowest-scoring item on the paper almost every year.

4.1 The scenario shells

(05-networks.md §1)

• Road/track network with distances — weighted undirected graph; shortest path, Eulerian trails, Chinese-postman repeats.
• Flow network with capacities — directed graph, source and sink labelled; cuts and maximum flow. Dressed as water pipes, stormwater, traffic, visitors, deliveries.
• Project/activity network with durations — an activity table (Activity | Duration | Immediate predecessors, sometimes with EST/LST columns part-filled) plus a directed network to complete. Always the last question of the paper.
• Allocation / cost table — a 4×4 or 5×5 matrix of times or costs, solved by inspection or the Hungarian algorithm.
• A literal map to be converted into a graph or an adjacency matrix.

The systematic difference between the two papers: Exam 1 gives a complete labelled diagram and asks a closed question about it; Exam 2 gives an incomplete structure and makes the student build it up across the parts. That incompleteness is the escalation engine (interpretation).

4.2 How a question escalates

1. (a) Read the diagram, 1 mark. Degree of a vertex, number of edges, identify odd vertices, name the route type. 2025 Q15a 88%, Q15b 91%; 2023 Q12bi 90%.
2. Early-middle: shortest distance; draw a minimum spanning tree and state its length.
3. Late-middle: an "explain why" odd-vertex justification; a cut capacity then a maximum flow; or an allocation minimum.
4. Final block — the project network. EST → LST → float → crash to a target at minimum cost. The final part is a three-fold compound: identify every path tied for critical, choose a globally cost-minimal combination of reductions, and verify no other path becomes critical part-way through.

The final part of the Networks block is a separator in all ten years measured, with a mean facility of 11.9%:

Other very low items cluster in the same territory: 2021 Q3bii (minimum capacity increase) 6%; 2024 Q15c (draw and label a dummy) 10%; 2023 Q13c 12%; 2020 Q3c (name the repeated edges) 25%; 2020 Q5a (dummy box-fill) 26%.

4.3 Mark-allocation grammar

1 mark buys a bare integer, one vertex or activity label, one named term, or one filled table cell — and VCAA states repeatedly that no sentence is wanted. 2 marks are built by pairing identify with quantify: "state the pipe that should be changed and its new capacity" (2022 Q3d, 2%: "Some students listed the vertices correctly, but not the new capacity"); "write down the capacity of Cut B and Cut C"; "determine the new minimum completion time and the minimum associated cost". Where such an item has three blanks, the guide sometimes builds a partial ladder — 2025 Q16 (20%) awards A1 for any two of x, y, z and A1 for all three.

4.4 Exam 1 vs Exam 2

Exam 1 Q33–40 (8 marks); Exam 2 12 marks across 3–4 questions (Q12–Q14 in 2023, Q13–Q15 in 2024, Q15–Q18 in 2025). Exam 1 names algorithms only as distractor labels — Dijkstra, Prim, Hungarian are never executed by name. Exam 2 owns drawing on the supplied diagram (a spanning tree, a cut, a dummy), every "explain why" justification, and the crash-cost table.

Annual staples: degree/edge terminology; planarity and Euler's formula; adjacency matrices; path/trail/circuit/cycle naming (present in 16 of the last 17 sittings); minimum spanning trees; shortest path; flow/cut; the project network; crashing. Rotated: isomorphism (Exam 1 only), Chinese postman, full Hungarian mechanics, multi-source flow. Retired: dominance matrices moved out of Networks into Matrices from 2016 and never returned.

4.5 How the multiple-choice distractors are built

(05-networks.md §6)

1. Eulerian vs Hamiltonian — the trip that covers every edge vs every vertex (2018 Q4b, 14%).
2. A bare noun for a compound term — "path", "cycle", "circuit" offered where "Hamiltonian path" or "Eulerian trail" is required. The bare noun never scores.
3. A cut capacity that counts a reverse-direction edge, or a cut that does not separate source from sink — restated near-verbatim by VCAA at least four times across the corpus.
4. A near-minimal spanning tree, generated by the plausible-but-wrong heuristic of always extending from the most recently added vertex.
5. EST vs EFT vs LST swaps, and taking the shortest rather than the longest path into a node (2018 Q3a: "the longest path to I was required").
6. Crashing without re-scanning for a newly critical path — the master error. 2020 Q5d (12%): 19 offered instead of 17 because path B–F–H–I ties the original critical path.
7. The total of the reduced allocation table rather than the original cost table.
8. Non-planar drawing not redrawn before counting faces (2008 E1 Q7, 11% correct).
9. Minimise where the question says maximise (2022 E1 Q3, 39%).
10. Off-by-one route counts (2020 Q4a: "9 was a common incorrect response"; correct 10).

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PART 2 — WHAT THE SEPARATORS HAVE IN COMMON

Everything in this Part is computed from corpus/questions.json (964 in-scope items) unless labelled (interpretation).

2.1 The shape of the distribution

Separators are not a small tail. They are 39.8% of all items and 48.0% of Exam 2 parts. But the hardest band is genuinely small:

Half of all separators sit between 30% and 50% — they are nearly accessible. Only 50 items in ten years (5.2%) sit below 20%. (Interpretation: the revision payoff is concentrated in the 30–50% band, which is large, learnable and structurally predictable; the sub-20% band is small and dominated by the single worst part of the Networks block.)

2.2 Separator rate by mark value

Yes — a 2-mark part is far more likely to separate. Exam 2, 2016–2025:

A 2-mark part is 1.67× more likely to be a separator than a 1-mark part, and the cohort's mean full-mark rate drops by 18 percentage points.

By topic, the effect is strongest exactly where 2-mark parts are rarest:

In 2023–2025 alone: 1-mark 50.0%, 2-mark 87.5% (14 of 16), mean 33.7.

Why. A 2-mark part is not "a harder 1-mark part" — it is two 1-mark tasks fused, graded on the conjunction. pct records full marks only, so a student who does one half perfectly is invisible in this statistic. The mark-allocation grammar in Part 1 is the same finding read from the other side: association justification = verdict and statistics; recurrence relation = initial value and rule; cut question = the edge and its new capacity; regression = the coefficients and the rounding.

Corroborating measurement: of the 365 Exam 2 parts with a published answer, those whose published answer contains two or more elements separate at 62.8% (mean 45.6) against 43.7% (mean 56.8) for single-element answers.

2.3 Separator rate by part position

The drop-off within a question is steep, monotonic and large.

First vs middle vs last (Exam 2 questions with ≥2 parts):

The last part of a question is 2.3× more likely to separate than the first, and the cohort loses 26 percentage points of facility between them.

By ordinal position, restricted to questions with at least four parts so the comparison is like-for-like:

Roman sub-parts behave the same way in miniature: a part labelled i. separates at 32.8% (mean 63.5); its sibling ii. separates at 56.2% (mean 50.8). Splitting a part into i./ii. is VCAA signalling that the second half is the real question (interpretation).

Exam 1 ramps too, even though every question is worth 1 mark and they are formally independent. Within each topic's block of consecutive MCQs:

The final MCQ of a topic block is 7.3× more likely to be a separator than the first, and the last two together separate at 61.3%.

First half vs second half of each Exam 1 block:

2.4 Separator rate by question position within the topic block

The ramp operates a level up as well: not just across the parts of a question, but across the questions of a topic block.

And the two effects compound. The last part of the last question of a topic block is a separator in 38 of 40 cases (95%), with a mean facility of 20.6%. The two exceptions scored 53% and 58%.

Per topic, first-part-of-first-question versus last-part-of-last-question, ten years each:

VCAA states this as design intent (2013 report, quoted in 07-exam-craft.md §5.2): "Examination 2 is designed to present students with straightforward questions at the commencement of each module … Questions then become more challenging towards the end." The data is that statement, measured.

2.5 Dependency chains

Across the 399 consecutive part-pairs in modern Exam 2, the mean change in facility from part n to part n+1 is −9.6 percentage points (median −10). Facility falls at 66.9% of steps.

Being downstream of trouble is itself a strong predictor:

Independently, parts whose stem explicitly reuses an earlier result (referring to "your answer to part …", "this equation", "the least squares line", "from part a.") separate at 70.4% (mean 39.7) against 44.2% (mean 56.5) for parts that do not — measured on the 494 parsed stems.

This is the most recoverable separator mechanism, because the marking scheme explicitly allows for it. A consequential (H) mark requires: the prior wrong answer must not trivialise the question; a calculation applying it must be visible; the result must match that calculation and be rounded as required; and it must be reasonable in context (07-exam-craft.md §4.2). Students routinely forfeit it: 2019 Q9b (19%) — "Some students followed through with the incorrect response they obtained for Question 9a. but did not show the working required for the consequential mark." Conversely 2018 Q6bii awarded full marks to an answer of \$20 488.88 built on an unrounded value from the preceding part.

2.6 Separator rate by command word

Measured on the 494 Exam 2 parts whose stems were parsed (2016–2023, 2025). The verb is the first sentence-initial instruction in the part; where a part's instruction sits in a shared lead-in ("Determine: i. … ii. …") the lead-in's verb is inherited.

Grouped into families:

Four things to say honestly about this table:

1. "Interpret" is the single most dangerous verb in the subject. All six interpretation parts in the parsed set are separators, with a mean facility of 36.7%. The failure is never arithmetic; it is the missing clause. 2019 Q5a (44%): "Many gave a response that was almost correct but failed to reference the one-unit increase." 2020 Q5d (44%): "failed to reference the 1 cm increase in waist measurement." 2022 Q4c (44%): "did not include the 1 degree increase in temperature." 2023 Q3d (43%): "providing a response that interpreted the slope rather than the intercept."
2. "Describe" is the opposite, and the low n (7) should be read with care — but the mechanism is documented: describe questions name their attributes ("in terms of strength and direction"), so a student who answers exactly those scores. The risk is over-answering, not under-answering: 2020 Q6b (51%) — "Some students gave additional information that negated an otherwise correct answer"; 2022 Q4b (28%) — "Others gave additional answers rather than simply commenting on strength and direction."
3. "Use … to …" is the safest verb (28.6%). (Interpretation: naming the method removes the hardest decision — which tool to reach for — and these parts are typically mid-question, not terminal.)
4. "Show that" is not, by itself, a separator flag. Measured across all parts whose stem contains "show that" (n = 19), the rate is 42.1% — below the Exam 2 baseline of 48.0%. This cuts against the intuition the reports create, and the reason is structural: a show-that question hands the student the answer, which means the mark is available for the working alone and the next part is protected (07-exam-craft.md §2.3: "With this number, students can attempt the following question, even if they cannot complete the show-that"). Show-that items fail on form, not content — working backwards from the given value, a bare restatement, CAS solve() notation, or ignoring a named compulsory method — and those failures are real (2025 Q4fi, 41%) but they do not make the class as a whole a separator class. (Interpretation: the show-that rules matter enormously for the individual student's mark, but the cohort handles them better than it handles interpretation.)

2.7 Separator rate by exam and by topic

Three readings:

• Exam 2 separates 1.7× more often than Exam 1 (48.0% vs 28.8%). Some of that is format — a four- or five-option MCQ has a guessing floor and no presentation requirements — and some is genuine: Exam 2 demands construction, justification and visible working.
• Data analysis is the friendly topic by volume and the ordinary topic by difficulty. It is 40% of both papers and the easiest Exam 1 block by a wide margin (18.3%), but its Exam 2 rate (41.5%) is only a little below average and its 2-mark parts are brutal (69.2%).
• The two hardest blocks sit in different papers. Recursion is hardest on Exam 2 (57.1%); Networks is hardest on Exam 1 (41.5%) and owns the paper's worst item on Exam 2. (Interpretation: a student who only ever practises Exam-2-style questions will under-prepare for Networks Exam 1, where the terminology and theory items live.)

By year (all four topics, both papers), the separator rate is remarkably stable — 33.7% to 51.6%, with no trend:

2.8 The mechanisms of failure, ranked

Ranked by how many of the 237 tagged Exam 2 separators each feature explains, with the prevalence of the same feature among non-separators for contrast, and the cumulative union.

90% of Exam 2 separators carry at least one of these six features. 10% (23 items) carry none — those are the genuinely conceptually hard 1-mark openers, e.g. 2021 Networks Q3a (maximum flow) 24%; 2023 Matrices Q9a (complete the matrix equation) 25%; 2020 Networks Q5a (dummy-activity box-fill) 26%; 2023 Data analysis Q4a (identify a seasonal feature) 26%; 2022 Matrices Q4a 32%; 2023 Data analysis Q3a (draw the least-squares line) 40%.

And the features stack:

(The 3-flag bucket dips below the 2-flag bucket; with n = 35 that is within noise. The trend across 0 → 4+ is the signal.)

Mechanism 1 — Escalation: the answer is late in the question

Explains 189 of 237 tagged separators (80%). 41% of all Exam 2 separators are literally the last part of their question; only 20% are the first.

This is the same finding as §2.3 and §2.4 stated as a cause. VCAA builds each question as a ladder — read → compute → interpret → chain → extend — and prices the rungs equally at 1 mark each. Real cases where the ladder is visible inside a single question:

• 2025 Matrices Q14 (permutation matrix, timetable rotation): (a) identify the fixed activities 65% → (b) determine the day-3 order 27% → (c) explain what P⁴ = I means 11%. Facility roughly halves at each rung.
• 2025 Matrices Q12: (a) reverse the recurrence to find the 2023 state 53% → (b) total enrolment excluding the absorbing category 13%.
• 2019 Networks Q3: (a) count critical activities → (b) LST of E → (c) longest float → (d) crash by 2 weeks → (e) the reduction table, 3%.
• 2023 Recursion Q7: (a) 32% → (bi) 47% → (bii) 40% → (c) 32% → (d) 11%.

Mechanism 2 — The answer must contain two distinct elements

Explains 108 of 237 (46%); present in only 24% of non-separators. 2-mark parts alone: 74.6% separator rate. Two-element published answers: 62.8%.

VCAA builds a 2-mark part by fusing two tasks and grading the conjunction. Students supply one half and score zero for the part.

• 2022 Data analysis Q2b (41%) — "Many students gave the correct values for each median but did not specifically mention a change or difference." The verdict was missing.
• 2022 Networks Q3d (2%) — "Some students listed the vertices correctly, but not the new capacity." The quantity was missing.
• 2016 Matrices Q3eii (46%) — "Many students found the correct matrix R₂₀₁₈ but did not extract the [required number]." The extraction was missing.
• 2016 Recursion Q6b (33%) — a recurrence relation missing its initial value, or with the initial value written as Cₙ. One of the two mandatory components was missing.
• 2018 Data analysis Q2a (41%) — "Some students gave the correct median percentage for the morning peak period but not for the evening peak period." One of two required values was missing.
• 2025 Networks Q16 (20%) — three values x, y, z required; "The value for y was often given as 3."

The mirror image of this mechanism is over-supply: adding a second, wrong element to a correct answer destroys it. VCAA calls it "further engagement" and writes it into the assessor guide as a rejection instruction — 2019 Networks Q3c, where the correct answer was an activity letter and adding an incorrect float time voided the mark; 2022 Data analysis Q4b (28%), "Others gave additional answers rather than simply commenting on strength and direction"; 2020 Q6b (51%), "Some students gave additional information that negated an otherwise correct answer."

Mechanism 3 — Rounding and the form of the number

Explains 64 of 237 (27%); present in only 10% of non-separators.

A stem that tells you how to round is 1.7× more likely to separate the cohort than one that does not, and "to the nearest cent" is close to a guarantee: 19 of 22 such parts are separators, mean facility 32.1%.

Part of this is confounding — nearest-cent questions are Recursion questions, and Recursion is the hardest Exam 2 block. But the report evidence is that rounding is doing independent work:

• 2016 Data analysis Q3bi (28%, the only 3-mark part in the corpus) — "There was much evidence of confusion between decimal point rounding and significant figure rounding."
• 2023 Data analysis Q1d (37%) — "Many students appeared to have difficulty in giving the coefficients rounded to four significant figures."
• 2023 Recursion Q6b (40%) — "Incorrect rounding of values in the calculation sequence was frequently observed."
• 2025 Matrices Q13bi (9%) — premature rounding of an intermediate value.
• 2025 Recursion Q7c (40%) — "Students were instructed to use the values in the table. Using a finance solver resulted in a different balance to the nearest cent which was not appropriate."
• 2017 Data analysis Q3biv (47%) — "Some students rounded to 0.7 first and then converted to 70%."

And the governing rule changed under the current design: since 2023 the front of every paper reads "you should only round your answer when instructed to do so" — so rounding an answer that carries no instruction is now an absolute error scoring zero (07-exam-craft.md §3.1–3.2). The practical consequence is that rounding is a two-sided trap: round when told, exactly as told, once, at the end; and never otherwise.

Mechanism 4 — A later part that depends on an earlier answer

Explains 50 of 237 (21%); present in only 8% of non-separators. Separator rate 70.4% vs 44.2%.

• 2016 Recursion Q7b (8%) — the lump sum L requires: find the actual three-year balance, find the present value needed for the remaining term, subtract. Three chained results before the answer mark is reachable.
• 2021 Recursion Q9b (8%) — the extra amount is the difference of two separately computed balances (153 112.94 − 146 073.74).
• 2018 Recursion Q6bii (11%) — "Many found the future value after two years of \$467 131 but could not proceed further."
• 2021 Data analysis Q5b (14%) — uses the transformed equation from part (a); the common wrong answer used difference rather than its reciprocal.
• 2025 Data analysis Q6b (12%) and 2025 Matrices Q13bii (17%) — both require a value computed in the preceding part.
• 2017 Data analysis Q4b (37%) — "Some students did not recognise that the rounded slope value from part a. was a required value in part b."

Mechanism 5 — Interpretation in context

Explains 34 of 237 (14%); present in only 8% of non-separators.

These are the parts where the mathematics is trivial and the sentence is the assessment.

• 2018 Data analysis Q3e (2%) — "Explain why, quoting the values of appropriate statistics."
• 2025 Matrices Q14c (11%) — "Only a small proportion of students showed an understanding of the effect of the identity matrix."
• 2016 Matrices Q3ei (14%) — "Many students were unable to explain the −80 in matrix B. The answer needed to refer to the removal from the study of 80 people selected from the no-travel group."
• 2021 Data analysis Q3eii (18%) — "Students found it hard to convey the idea of the trend continuing. It was common to see reference to extrapolation or linearity but without linking it to the given context."
• 2025 Data analysis Q4d (27%) — the justification had to reference the explanatory variable's range, not the response variable's.
• 2016 Networks Q1bii (30%) — "Explain what the loop at D represents in terms of a driver departing from Dovenest."
• 2020 Matrices Q2a (37%) — "Many students did not recognise that a non-zero determinant is required."

The distinguishing feature is that a nearly correct sentence scores zero. The slope-interpretation family (2019 Q5a, 2020 Q5d, 2022 Q4c, all at 44%) fails on one missing clause: the "for each one-unit increase".

Mechanism 6 — "Show that" requiring visible working

Explains 8 of 237 (3%). Measured separator rate for show-that stems: 42.1%, slightly below the Exam 2 baseline.

Rare and, at cohort level, less lethal than the reports imply (§2.6, point 4). But the failure modes are absolute when they occur: starting from the given answer instead of working towards it; a bare restated value; CAS syntax; or ignoring the compulsory named method ("use recursion" forbids the closed-form shortcut). 07-exam-craft.md §2 records the rule VCAA restates most often: "if a student starts with the answer they have been asked to show, they will not be eligible for the mark." The compensating gift is that the given number is then available for every subsequent part, whether or not the show-that was earned.

A seventh mechanism, measured but weaker than expected: reading off a display

Parts whose stem references a table, graph, plot, diagram, network or matrix separate at 44.7% — slightly below the 49.5% rate for parts that do not. Reading a display is not, in itself, a separator flag. The hard display items are hard for other reasons: 2024 Q2b (3%) asked for the smallest possible number of values below Q1 — a boundary-reasoning question wearing a boxplot; 2020 Data analysis Q3c (78% scored zero) required counting across three boxplots; 2018 Q2d (42%) failed because "Many students did not find the actual value of 50 from the graph and used 47 instead". (Interpretation: the mechanism is not "a display is present" but "a value must be read precisely off a display and then used" — which is the dependency mechanism, not a display mechanism.)

2.9 What a routine question looks like, by contrast

Comparing the 99 parsed Exam 2 parts at ≥80% full marks with the 237 at ≤50%:

A routine question is, almost literally, short. Its median stem is 86 characters — about one line. It is the opening part, worth one mark, with one instruction, no rounding rider, no reference backwards, and an answer that is a single number, word or label. It sounds like:

Write down the value of B₄, the balance of the savings account after four months. (2020, 64%)
State whether the variable type is numerical, nominal or ordinal. (2025, 77%)
Determine the degree of vertex A.
What is the order of matrix R? (91–96% every year)

A separator sounds like:

Of the senior students expected to choose investigation (I) in Term 3, what percentage chose service (S) in Term 2? (2017, 2 marks, 12%)
Explain why, quoting the values of appropriate statistics. (2018, 2 marks, 2%)
Determine this final repayment amount. (2021, 15%)
Interpret the slope of this least squares line in terms of a man's body density and waist measurement. (2020, 44%)
— and, in paraphrase, the shape every Networks paper closes on: given this table of which activities can be shortened and at what cost per day, find the minimum additional cost of finishing the project N days earlier (2025 Q18d, 21%; 2024 Q15e, 7%; 2022 Q3d, 2%)

The tell is not the mathematics named in the sentence. It is the number of things the sentence asks for, where it sits, and whether it points backwards.

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PART 3 — THE SEPARATOR CHECKLIST

For a student deciding where to spend revision time. Each item is a feature you can see on an unseen question before attempting it, with the measured separator rate attached.

Structural position — read this first (it explains 80% of separators)

In Exam 1 the same rule holds without parts: the final MCQ of each topic block separates at 72.5% (mean facility 40.8) and the last two together at 61.3%, against 10.0% for the first MCQ of the block. Under the current design that means Q16, Q24, Q32 and Q40 are the four most dangerous questions on Exam 1 — and Networks Q33–40 and Recursion Q17–24 are the blocks where the marks are lost.

The demand written into the sentence

Flags stack. Zero flags → 24% separator rate. One → 45%. Two → 66%. Four or more → 74%.

Topic-specific high-yield targets

• Recursion and financial modelling — the highest-yield topic in the subject to drill: Exam 2 separator rate 57%, and its 2-mark parts separate at 91%. Target: writing a complete recurrence relation (initial value and rule, correct subscripts, no trailing n); rate-per-period vs rate-per-annum; Finance Solver sign conventions; and every "changed condition mid-schedule" question — lump sums, final irregular repayments, interest earned in year 2 rather than year 1, total interest.
• Matrices — one question type, the backward percentage, has scored 12–18% in every year it has appeared. Learn it once and it is worth a mark most years. After that: absorbing states (a 1 on the leading diagonal), the "maximum vs long-run vs first time" distinction, and interpreting a negative element in B.
• Networks — the crashing / minimum-cost-reduction final part is a separator in all ten years measured, mean facility 11.9%. It is also the single hardest mark on the paper, so it is low-yield to chase last and high-yield to at least attempt systematically. Cheaper wins in the same block: exact terminology (never a bare "path" or "cycle"), cut direction, and re-checking for a newly critical path after any reduction.
• Data analysis — 40% of both papers and the safest place to protect marks (Exam 1 separator rate 18%). Protect them by fixing the two families that fail on wording rather than mathematics: the sign of r, and slope/intercept/r² interpretation sentences that must name both variables and the one-unit change.

Four habits that convert flagged questions into marks

1. Count the deliverables before you answer. If the part is worth 2 marks, or its sentence contains "and", or it asks you to identify and quantify — write both. Then check you have written both.
2. Show the calculation on anything worth more than one mark, and on anything that reuses an earlier answer. The consequential mark is only payable against visible working; 21% of separators are downstream parts where that mark was available.
3. Round only when told, once, at the end — and write the unrounded value first. An unrounded value shown before a wrongly rounded one converts an uncapped error into a capped one. "Nearest cent" means exactly two decimal places, trailing zero included.
4. Answer the named attributes and stop. On "describe … in terms of strength and direction", give strength and direction. Adding a third attribute — or a float time, or an explanation of what a percentage means — can void an otherwise correct answer.

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Appendix — reproducibility notes

• All counts were computed with the Python standard library (json, csv, re, statistics, collections) over corpus/questions.json, filtered to series == "Nov", topic ∈ {the four current topics}, pct is not None, year ≥ 2016 → n = 964.
• Part ordering within a question was derived by parsing qshort (e.g. Q3bii → question 3, part b, sub-part ii) and sorting on (part letter, roman numeral). Questions were ordered within a topic block by question number, which is unambiguous because module-era (2016–2022) numbering restarts per module and the module is identified by topic.
• Question stems were parsed from corpus/text/*furmath2-w.txt, *genmath2-w.txt and 2025-11_2025-GeneralMaths2.txt, segmented on Question N headers and a. / i. part markers, with page furniture and side-column text stripped. Join rate to graded items: 494 / 554 (89%). 2024 Exam 2 is absent from every stem-feature statistic because its PDF contains no text layer; the 2024 examination-report commentary and assessment guide were used qualitatively instead.
• Command-word classification assigns each part the first sentence-initial instruction verb in its stem, after stripping leading adverbs ("Briefly", "Hence") and subordinate lead-ins ("Using the graph above, …"); roman sub-parts inherit their parent part's verb where their own text is a bare noun phrase. 47 of 494 parts resisted classification and are reported separately rather than forced into a bucket.
• Pre-2016 years and the legacy modules (Graphs and relations, Geometry and measurement/trigonometry, Business-related mathematics, Number patterns) are excluded throughout; see 06-legacy-modules.md. NHT sittings are excluded; see 09a-nht-further.md.