The question styles to have ready — each linked to its evidence and to a question in the practice paper.
Built by a six-model AI panel and backtested against the hidden 2025 papers — how we did it.
Built from a six-model AI analysis of every HSC Ext 2 paper, marking guideline and marking-centre feedback report since 2020 — backtested against the 2025 paper before publishing. 2026 is the FINAL year of the current syllabus. NESA's "2026 sample format" is a verbatim reprint of the 2025 paper, so it tells you structure only: 100 marks, 10 multiple choice, then Questions 11–16 at roughly 15 marks each, ramping to Q16. Its one real signal is the consolidated Section II Writing Booklet — one booklet with fixed page ranges per question, not a booklet per question — so practise working within a page budget and labelling parts clearly. Final-year papers historically favour well-trodden formats — which makes style preparation unusually valuable this year.
The fixture pair of proof MC items (2023 Q4, 2024 Q2, 2025 Q2): state the contrapositive, converse or negation of a worded implication, and translate between words and formal quantifier...
Decompose $(ax^2+bx+c)/((x-p)(x^2+q))$ using a $Bx+C$ numerator over the quadratic, integrate to a logarithm-plus-arctan pair, with absolute-value signs on the log and (if definite)...
From $\ddot{x} = -n^2(x-c)$ or $v^2$ given as a quadratic in $x$, extract the centre, $n$ and amplitude via $v^2 = n^2(A^2-(x-c)^2)$, then find the period, maximum speed/acceleration,...
The fixture items (2023 Q4, 2024 Q2, 2025 Q2): state the contrapositive, converse or negation of a worded implication, and translate between words and quantifier notation. The distractor logic hasn't changed in three years: converse swapped for contrapositive, only one clause negated, the quantifier left as $\forall$ when negation demands $\exists$. Converse/contrapositive language was flagged by the marking centre in 2021 and 2023–2025.
write all four variants (converse, inverse, contrapositive, negation) of one implication until the distinctions are automatic.
Every Q11 from 2020 to 2025 opens the same way: conjugate products, realising $1/z$ or a quotient, then a surd complex number (usually involving $\sqrt{3}$) converted to modulus–argument or exponential form and raised to a power of 7–10 by De Moivre, back to exact Cartesian form. One model gives this its highest probability anywhere (95% chance).
$(\sqrt{3} - i)^7$-style chains until the quadrant bookkeeping is clean — and quote principal arguments in $(-\pi, \pi]$, the flagged weakness of 2022, 2023 and 2025.
Five models independently name the same denominator shape: $(x-p)(x^2+q)$, decomposed with a $Bx+C$ numerator over the quadratic, integrating to a logarithm plus an arctangent. The recurring mark-losers, flagged in 2022, 2024 and 2025: absolute values dropped from the log, and log laws fumbled when a definite integral must match a stated form.
the full chain — decompose, integrate, simplify to the given form — not just the decomposition.
Complete the square in $v^2 = n^2\!\left(A^2 - (x-c)^2\right)$ to read off the shifted centre, then find the period, amplitude, maximum speed or acceleration, or the first time at a stated position. The two stock traps are exactly the multiple-choice distractors: treating the origin as the centre, and reading the amplitude off the constant term. Graph interpretation of $v(x)$ and $a(x)$ is a flagged weakness (2025 Q8, 2024 Q5).
completing the square under time pressure, and sketching $v^2$ against $x$.
It has appeared in all six papers 2020–2025: define $I_n$ as a definite integral, "show that" $I_n$ relates to $I_{n-1}$ or $I_{n-2}$, then "hence" evaluate $I_2$ or $I_3$. Two models predict the derivation reverts to integration by parts after 2025's identity-based cot version. The mark the centre protects every single year (2020–2025): explicitly naming $u$, $dv$, $v$ and $du$, and substituting the limits.
one trig-power, one log-power and one $x^n e^x$ reduction, writing the parts table every time.
Angle between vectors via the dot product to the nearest degree; the vector equation of the line through two points; deciding with reasons whether a third point lies on it via a consistent parameter; unit vectors perpendicular to two given vectors. The MC distractors use the position vector as the direction vector, or $A - B$ instead of $B - A$. Vector notation and scalar–vector confusion has been flagged every year from 2020 to 2025 — underline your vectors; a dot product is a scalar.
All six models predict exactly one ~3-mark induction in Q12–14. Five favour an inequality with a non-unit base case — the $2^n > n^2$ / $n! > 2^n$ family — where the inductive step cites an auxiliary inequality and states exactly where the assumption turns equality into inequality (induction setting-out and inequality direction: flagged 2020, 2021, 2023, 2024, 2025). The live outsider (~0.35, two models): the first divisibility induction of this syllabus's life, gap-filling in its final year — the syllabus's own printed example is $3^{2n+4} - 2^{2n}$ divisible by 5. An evening on each form is cheap insurance.
Whatever appears: "show that" means derive the printed result — restating or assuming it scores nothing, and insufficient working in show-thats has been flagged every year from 2020 to 2025.
When we backtested this method against the real 2025 papers (the pilot covered chemistry and Maths Ext 1): every topic we rated ≥90% appeared (37/37 across both pilot subjects), roughly half of our specific question predictions recognisably appeared, and the misses clustered where the examiners twisted a format or moved a question into multiple choice. The lesson for revision: master the skill chains and setting-out habits above — they survive every format twist; a memorised question doesn't.
The fixture pair of proof MC items (2023 Q4, 2024 Q2, 2025 Q2): state the contrapositive, converse or negation of a worded implication, and translate between words and formal quantifier notation. The distractor logic is stable across years — swap converse with contrapositive, negate only one clause, keep the original quantifier instead of switching $\forall$ to $\exists$. Four models give this their highest question probability.
What each model said
Every Q11 from 2020–2025 opens with N1 arithmetic: conjugate products, realising a reciprocal or quotient, then converting a surd complex number (typically involving $\sqrt{3}$) to modulus–argument or exponential form and raising it to a power of 7–10 via De Moivre, back to exact Cartesian form. Fable's single highest question probability (0.95).
What each model said
Decompose $(ax^2+bx+c)/((x-p)(x^2+q))$ using a $Bx+C$ numerator over the quadratic, integrate to a logarithm-plus-arctan pair, with absolute-value signs on the log and (if definite) log-law simplification to a stated form. Five models name the same denominator shape independently. (DeepSeek's variant uses three distinct linear factors yet still claims an arctan term — internally inconsistent; the panel's centre of mass is the $(x-p)(x^2+q)$ form.)
What each model said
From $\ddot{x} = -n^2(x-c)$ or $v^2$ given as a quadratic in $x$, extract the centre, $n$ and amplitude via $v^2 = n^2(A^2-(x-c)^2)$, then find the period, maximum speed/acceleration, distance over a period, or the first time at a stated position. The stock distractor errors (grok's MC): treating the origin as the centre, or reading the amplitude off the constant term. Graph interpretation of $v(x)$ and $a(x)$ is a flagged weakness (2025 Q8, 2024 Q5).
What each model said
The annual recurrence (all six papers 2020–2025): define $I_n$ as a definite integral of a trig power, a log power, or $x^n$ times an exponential; 'show that' $I_n$ relates to $I_{n-1}$ or $I_{n-2}$ via integration by parts, then 'hence' evaluate $I_2$ or $I_3$. Fable and opus both predict the derivation REVERTS to integration by parts after 2025's identity-based cot version — marks for explicitly stating $u$, $dv$, $v$, $du$ (flagged every year 2020–2025).
What each model said
In the practice paper: Q13(a)
The Q11–12 (and MC) staples: angle between two component vectors via the dot product to the nearest degree; vector equation of the line through two points; decide with reasons whether a third point lies on it via a consistent parameter; unit vectors perpendicular to two given vectors from simultaneous dot-product equations. MC distractors use the position vector as the direction vector or $A-B$ instead of $B-A$.
What each model said
Appeared in every paper 2020–2025 (13(c), 15(a), 12(a)+16(c), 13(b), 13(d), 13(c)): part (i) proves AM–GM starting from $(\sqrt{a}-\sqrt{b})^2 \ge 0$, part (ii) applies it — possibly repeatedly, in 2–4 variables — to an unfamiliar chained inequality, preserving strict versus non-strict signs. Feedback repeatedly rewards starting from known truths, not working backwards from the target.
What each model said
In the practice paper: Q13(c)
Sketch the region for a perpendicular-bisector inequality $|z-z_1| > |z-z_2|$ or a modulus-ratio locus, intersected with a disc or an argument range. Marks sit in the conventions: dashed strict boundaries, excluded endpoints, correct shading, principal-argument range $(-\pi, \pi]$ — the flagged weakness of 2022/2023/2025. Grok and opus file it under N1, fable/deepseek/gpt under N2; same question either way.
What each model said
In the practice paper: Q13(b)
Particle projected upwards against gravity plus resistance $kv$ or $kv^2$: derive height with $v\,dv/dx$ and time with $dv/dt$ — the question is SEQUENCED to force both acceleration forms (the marking-centre theme flagged in 2020, 2021, 2023, 2024, 2025) — then relate landing speed to launch speed or state the terminal velocity $\sqrt{g/k}$. Grok extends to the full up-and-down journey with reversed resistance. Opus holds the horizontal variant instead (see watch list).
What each model said
In the practice paper: Q15(a)
Assume $\sqrt{p} = a/b$ in lowest terms, or $\log_a b = p/q$, and reach an integer contradiction by parity or a prime-divides argument. Marks are explicitly allocated to the logical frame — stating the assumption, exhibiting the contradiction, writing the conclusion — as the 2025 11(e) and 16(a) criteria did. Models name different constants (deepseek $\log_2 5$, grok $\log_n(n+1)$, fable $\log_a b$): type consensus, no shared surface.
What each model said
In the practice paper: Q11(e)
A tetrahedron, parallelogram or cevian-intersection diagram: express one point two different ways as linear combinations of non-parallel vectors $\underset{\sim}{a}$ and $\underset{\sim}{b}$, equate coefficients (justified by non-parallelism) to find a ratio such as BL:LC, prove a midpoint/centroid property, or establish collinearity — the 2022 14(a) / 2024 14(e) template, absent in 2025 and due back. Marking penalises undefined vectors and scalar-vector confusion (flagged 2020–2025).
What each model said
In the practice paper: Q14(a)
A definite integral transformed by a substitution given in the question: $t = \tan(x/2)$ on an integrand rational in $\sin x$ and $\cos x$ (fable's $1 + \sin x + \cos x$ denominator), a trig substitution $x = a\sin\theta$ (deepseek), or the symmetry substitution $u = a - x$ that reproduces the integral so it can be collected and halved (opus, gpt). Marks for converting $dx$ AND both limits; gpt predicts a two-decision chain (substitution then symmetry) rather than one formula.
What each model said
Two convergent sub-variants of the same Q14–16 chain: (i) expand $(\cos\theta + i\sin\theta)^n$ by De Moivre and the binomial theorem, equate real parts for a $\cos n\theta$ polynomial, then solve $\cos n\theta = 0$ to extract an exact surd cosine, justifying the root choice by quadrant/monotonicity (fable, grok); (ii) use the vanishing sum of the nth roots of unity and $z + 1/z = 2\cos\theta$ pairings to derive a quadratic for a specific cosine (deepseek's $\cos 2\pi/5$, opus). Grok's named identity $\cos 5\theta = 16\cos^5\theta - 20\cos^3\theta + 5\cos\theta$ appears verbatim in the evidence pack (past-paper worked solution) — grounded lineage, not an echo; a 2026 repeat would need fresh surface. Fable and grok both note 2025's double roots-of-unity serving argues for the trig-polynomial pivot.
What each model said
In the practice paper: Q14(b)
All six models predict a single induction in Q12–14. The favoured form (fable, gpt, grok, opus, gemini) is an inequality with a non-unit base case — the $2^n > n^2$ / $n! > 2^n$ family, both of which sit in the evidence pack (syllabus dot-point example, and the $n \ge 9$ factorial past question) — with the inductive step citing an auxiliary inequality and stating exactly where the assumption turns equality into inequality. The live outsider (fable and opus bold calls, ~0.35): the first divisibility induction of this syllabus's life, gap-filling in its final year; the syllabus's own printed example is $3^{2n+4} - 2^{2n}$ divisible by 5 (verified present in the pack, so fable and opus naming it is grounded, not an echo).
What each model said
Why we discounted part of this agreement
DeepSeek and Grok emitted the SAME divisibility instance (\$7^n - 2^n$ divisible by 5, base case and factorised step matching) — verified absent from the evidence pack, so this is a shared-training-data echo (a canonical textbook exercise), not independent confirmation. Per the corpus-echo rule their two votes count as one for that surface form. The type-level consensus above is unaffected; note the CONTRAST with fable/opus's $3^{2n+4} - 2^{2n}$ instance, which IS the pack's syllabus example and therefore legitimate independent grounding.
Per our corpus-echo rule, identical invented details count as one vote, not independent confirmation.
In the practice paper: Q12(d)
Shortest distance from a point to a 3D line via foot of perpendicular (deepseek 0.65, opus 0.65, gpt 0.58, gemini's skew-lines variant — ~0.63) — BUT fable and grok explicitly rest it after 2024 13(a) and 2025 16(c): the panel's sharpest split
Solve $z^n = c$ for negative or non-real $c$; roots equally spaced on an Argand diagram, booklet plot (deepseek 0.55, grok 0.70, opus 0.55, ~0.60); the pack's 2025 $z^5+1=0$ makes a straight repeat unlikely — expect fresh surface
Horizontal resisted motion 'show that': constant-plus-v(²) resistance, distance to rest as a supplied log form (opus 0.70, fable 0.55, ~0.63, 2 models)
Mechanics MC on $v$–$x$/$a$–$x$ graphs or $a = v\,dv/dx$ with the omitted-$v$ distractor (grok 0.72, gpt 0.48, deepseek trend, ~0.60)
Conjugate-root polynomial: real coefficients, one given complex zero, remaining zeros by sum/product (fable 0.55, gpt 0.54, grok 0.52, ~0.54; last set in Section II 2023 12(e))
Complex-coefficient quadratic via Cartesian square root of the discriminant (deepseek 0.50, fable 0.50, opus 0.45, ~0.48) — fable's bold call at 0.45: only MC exposure since 2021, a five-year Section II coverage gap in the syllabus's final year
Resisted projectile with Cartesian-path derivation (deepseek 0.50, opus 0.55, gemini bold call) — fable and grok rest it after the 5-mark 2025 16(b); if it returns it is the Q16 capstone
Q16 abstract bound proof: triangle inequality + contradiction on complex moduli or vector magnitudes (fable specific + structural prediction 0.65; 2021 16(a), 2022 15(d), 2025 16(a) lineage)
Argand transformation plot: locate $\bar{z}$, $i\bar{z}$, $z^2/|z|$ relative to a marked $z$ without computation (fable 0.55, gpt 0.46; 2025 11(a) / 2020 Q4 lineage)
Volumes of revolution revival, unused since 2021 (grok alone, 0.48) — grok's only structural outlier call
MEX-P2 carries the panel's lowest P(substantial) (0.494) and MEX-N1 the only rested vote — Q11 openers aside, both strands are one-question strands in 2026 on the panel's numbers
How likely each topic is to appear this year.
Chance of a big question (4+ marks) here: 94%
Question types predicted here extended response ×13 multiple choice ×2
What each model expects
Chance of a big question (4+ marks) here: 90%
Question types predicted here extended response ×11 short answer ×4
What each model expects
Chance of a big question (4+ marks) here: 78%
Question types predicted here extended response ×11 short answer ×3 multiple choice ×1
What each model expects
Chance of a big question (4+ marks) here: 59%
Question types predicted here short answer ×12 multiple choice ×2 extended response ×1
What each model expects
Chance of a big question (4+ marks) here: 81%
Question types predicted here extended response ×10 short answer ×3 multiple choice ×2
What each model expects
Chance of a big question (4+ marks) here: 75%
Question types predicted here extended response ×8 multiple choice ×4 short answer ×3
What each model expects
Chance of a big question (4+ marks) here: 49%
Question types predicted here extended response ×13
What each model expects
How likely each topic is to appear. Open a topic for the question types to practise there.
100 marks · 16 questions
Every question is traceable to the consensus prediction behind it — open the web version and each question carries a “why this question” link into the evidence. All questions are original Intuition compositions in NESA style.
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Published Aug 2026, before the exams. In November 2026 we score these predictions publicly against the real paper — per-model calibration and question-level hit rates, the same harness as the 2025 backtest. How we did it.