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 1 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, and NESA's sample paper confirms the familiar 70-mark format (10 multiple choice + four 15-ish-mark questions). Final-year papers historically favour well-trodden formats — which makes style preparation unusually valuable this year.
Separate, integrate, fix the constant from the given point, make y the subject — with a branch-choice or domain-restriction justification (opus), or embedded in a cooling/bounded-growth...
Express $a\sin x - b\cos x$ in auxiliary-angle form with exact $R$ and $\alpha$ (quadrant care with a negative coefficient — the 2022 11(e) trap), hence solve $= c$ over a stated radian...
Projectile in Q13–14 with $\mathbf{r}(t)$ supplied "Do NOT prove this", carrying a structural twist: two objects launched at different times, a moving target, or launch from a non-origin...
It has appeared in every paper since 2020: an integral with the substitution supplied ($u = x - a$ or $u = x^2 + k$). Transform the integrand AND $dx$, change the limits if definite, integrate fractional powers, revert to x. The harder version needs algebraic massaging before it lands on an arcsin/arctan form.
in 2025 this shrank to a transform-only multiple-choice — so also practise recognising the transformed integral among distractors.
"Do NOT prove this" means the derivation marks are gone; the marks are in the twist: two objects launched at different times, a moving target, or a launch from a height. The trap the 2025 marking centre named explicitly (Q14(b)): the two objects do NOT share a time variable. Set each vertical displacement to zero separately, equate horizontal positions at the meeting event.
Express $a\sin x \pm b\cos x$ as $R\sin(x \pm \alpha)$, then solve over $[0, 2\pi]$ listing every solution. The trap (2022 paper): a negative coefficient forcing quadrant care in $\alpha$. Two of our six models predicted the identical expression ($\sqrt{3}\sin x - \cos x$) — it's that canonical.
Six straight years. The alternation (series 2023/2025, divisibility 2022/2024) points to divisibility in 2026. The middle mark is always the same skill: rearrange the assumption and substitute it into the $k+1$ step — restating it scores nothing. If it's a series instead, the step will close by factorising, not expanding.
(a) A separable DE with an initial condition — often with a branch choice (justify the negative root or restricted domain when making y the subject). (b) A direction-field question: sketch the particular solution through a marked point respecting the horizontal asymptote — or explain why a solution can never cross it.
Our 2025 backtest is a caution: pigeonhole and the vector-geometry proof were each predicted by five of six models and neither appeared. Streaks break. Both remain solid preparation (pigeonhole where you must construct the holes yourself; perpendicularity proofs via $\mathbf{a} \cdot \mathbf{a} = |\mathbf{a}|^2$), but treat them as candidates, not certainties — and expect this year's paper to break a streak somewhere too.
Backtesting this method against the real 2025 paper: 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 near-certain 3-mark integral with the substitution supplied ($u = x-a$ or $u = x^2+k$): transform integrand and $dx$, change limits if definite, integrate fractional powers, revert to $x$. Grok gives this its single highest question probability (0.88). Harder variant (fable): the integrand needs algebraic massaging before landing on an arctan/arcsin form, per the 2024 13(d) lineage.
What each model said
Projectile in Q13–14 with $\mathbf{r}(t)$ supplied "Do NOT prove this", carrying a structural twist: two objects launched at different times, a moving target, or launch from a non-origin height; students equate horizontal components and set each vertical displacement to zero SEPARATELY. The named discriminator (opus, fable): the two objects do not share a time variable — the exact error the 2025 marking centre flagged on 14(b).
What each model said
In the practice paper: Q14(d)
Express $a\sin x - b\cos x$ in auxiliary-angle form with exact $R$ and $\alpha$ (quadrant care with a negative coefficient — the 2022 11(e) trap), hence solve $= c$ over a stated radian domain listing every solution. Both deepseek and grok independently name the SAME expression: $\sqrt{3}\sin x - \cos x$.
What each model said
In the practice paper: Q11(d)
The six-straight-years 3-mark induction in Q12. Panel consensus: a divisibility form (e.g. $a^n + b \cdot c^n$ divisible by $m$) rather than a series, following the series(2023/2025)/divisibility(2022/2024) alternation. The middle-criterion discriminator: the assumption must be REARRANGED and substituted into the $k+1$ step, not restated — a repeated marking-centre flag. Fallback (4 models): a factorial/$n \cdot 2^n$ series where the step closes by factorising.
What each model said
In the practice paper: Q12(a)
Separate, integrate, fix the constant from the given point, make y the subject — with a branch-choice or domain-restriction justification (opus), or embedded in a cooling/bounded-growth context solved for time or limiting value (fable, sol, gemini's logistic variant).
What each model said
In the practice paper: Q12(b)
Given a printed slope field, sketch the solution through a marked point respecting the horizontal asymptote — or justify why a solution cannot cross it (grok: explain why the curve through S cannot pass through T on the other side; gemini: why population cannot exceed carrying capacity). MC variant matches a field to its $dy/dx$ with sign-error distractors (2025 MC7 logic).
What each model said
In the practice paper: Q12(c)
Region bounded by a curve, an axis and a horizontal line rotated about the $y$-AXIS: rewrite $x^2$ in terms of $y$, watch the limits, exact answer with $\pi$ (and often a logarithm). DeepSeek names a concrete instance ($y = 1/(x+2)$, $y$ from 1 to 4). Grok and gemini hold the x-axis variant.
What each model said
In the practice paper: Q12(d)
Quality-control/polling/overbooking context: $\mu = np$, $\sigma = \sqrt{np(1-p)}$, z-table lookup. Three models specifically predict the REVERSE form — given a tail probability (e.g. 0.0668), solve for the threshold $k$ or sample size $n$, rounding in the direction the context demands (2021 14(d), 2022 14(d), 2025 13(d) lineage).
What each model said
In the practice paper: Q13(c)
Solve an inequality with the unknown in a denominator (possibly inside absolute value): multiply by the squared denominator or split cases, find the three critical values, EXCLUDE the value zeroing the denominator, answer as a union of intervals (2024 12(e) pattern).
What each model said
In the practice paper: Q11(c)
Projection of $\mathbf{u}$ onto $\mathbf{v}$, most likely MC: distractors encode dividing by $|\mathbf{u}|^2$ instead of $|\mathbf{v}|^2$, attaching the scalar to the wrong vector, and sign slips (2025 Q2 distractor logic). Opus adds a 4-mark inverse variant: recover an unknown vector from its projections onto two non-parallel vectors.
What each model said
In the practice paper: Q2
Unknown-coefficient cubic with one factor and one remainder condition: form $P(a)=0$ and $P(b)=r$, solve the $2 \times 2$ system — the question TYPE is well-grounded in the pack (2023 11(c) lineage).
What each model said
Why we discounted part of this agreement
DeepSeek and Grok emitted the SAME surface constants ($x^3 + ax^2 + bx - 12$, factor $(x+1)$, $P(2) = -18$) — 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 the surface form; the type-level consensus above is unaffected.
Per our corpus-echo rule, identical invented details count as one vote, not independent confirmation.
In the practice paper: Q11(b)
Given monotonic $f$ with $f(a) = b$, evaluate $(f^{-1})'(b)$ as the reciprocal of $f'(a)$ — as a Section II 2–3 marker or the Section I discriminator (second-derivative version, 2025 MC10 lineage).
What each model said
In the practice paper: Q9
$\sin^2(kx)/\cos^2(kx)$ definite integral via the reference-sheet double-angle identity (5 models, ~0.56)
Vector geometry proof by dot product — perpendicularity in a quadrilateral/circle (4 models, ~0.52)
Double-angle trig equation where dividing (not factorising) loses a solution family (4 models, ~0.55)
Sum/product of roots: symmetric expression via reciprocals of pairwise products (4 models, ~0.55)
Pigeonhole where students must CONSTRUCT the holes (opus discriminator variant, 0.55; MC guarantee form grok 0.58)
Word arrangements with repeated letters, 2-mark Q11 fluency item (4 models, ~0.54)
Inverse-trig graph sketch $y = a\cos^{-1}(bx)$ with endpoints marked (4 models, ~0.54)
Binomial-expansion coefficient question, unexamined since 2022 — fable coverage-gap call (50% chance)
ME-S1_binomial and ME-T1_inverse_trig carry the panel's only rested votes (one each) and the highest stddev — the closest thing to contested calls in this subject
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 short answer ×1 stimulus based ×1
What each model expects
Chance of a big question (4+ marks) here: 91%
Question types predicted here extended response ×12 multiple choice ×5
What each model expects
Chance of a big question (4+ marks) here: 76%
Question types predicted here extended response ×9 multiple choice ×4 short answer ×2
What each model expects
Chance of a big question (4+ marks) here: 49%
Question types predicted here extended response ×12
What each model expects
Chance of a big question (4+ marks) here: 83%
Question types predicted here extended response ×10 short answer ×4 multiple choice ×3
What each model expects
Chance of a big question (4+ marks) here: 60%
Question types predicted here extended response ×8 short answer ×5 multiple choice ×3
What each model expects
Chance of a big question (4+ marks) here: 50%
Question types predicted here extended response ×6 short answer ×4 multiple choice ×4
What each model expects
Chance of a big question (4+ marks) here: 43%
Question types predicted here extended response ×7 multiple choice ×6 short answer ×2
What each model expects
Chance of a big question (4+ marks) here: 73%
Question types predicted here multiple choice ×6 extended response ×5 stimulus based ×1 short answer ×1
What each model expects
Chance of a big question (4+ marks) here: 46%
Question types predicted here extended response ×7 multiple choice ×5
What each model expects
How likely each topic is to appear. Open a topic for the question types to practise there.
70 marks · 14 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.