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 Mathematics Advanced 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 the paper's shell has not moved in six years: 100 marks, 10 multiple choice, then 21 short questions (Q11–31) worth 90 marks. Final-year papers historically favour well-trodden formats — which makes style preparation unusually valuable this year.
The panel's headline call: a two-part optimisation where (a) 'Show that' reduces a composite geometric constraint (wire/fence/container) to a one-variable objective with a fractional...
Find where a parabola meets a line or a second parabola, then integrate the difference for an exact area, with the intersections asked as a separate opening mark.
The 6–7 mark financial centrepiece: 'Show $A_2 = P(1+r)^2 - M(1+r) - M$', then the closed form $A_n$ by summing the geometric series, then a logarithmic solve for the month a balance...
Part (a) is a "show that": reduce a fenced enclosure, container or composite shape to a one-variable formula with a fractional term. Part (b) is where the marks die: differentiate, solve, verify the nature (second derivative or sign table), and answer the quantity actually asked. The traps the marking centre has flagged four times (2020 Q25b, 2023 Q24b, 2024 Q31b, 2025 Q26b): nature never verified, and the optimised cost/area confused with the variable. One model tips a twist for 2026: a cost objective (dollars, not just centimetres) after two years of pure geometry — and don't forget maxima can sit at domain endpoints (flagged 2022, 2024, 2025).
Two separate questions, most years. The big one (5–7 marks): "Show $A_2 = P(1+r)^2 - M(1+r) - M$", then the closed form by summing the geometric series, then a logarithm solve for when the balance first crosses a threshold. The traps with years attached: wrong number of terms in the series (2021 Q29, 2022 Q32, 2023 Q25, 2025 Q17) and log errors isolating $n$. The small one (2–4 marks): a supplied interest-factor table — convert the annual rate to the compounding period first, then decide whether to multiply (future value of deposits) or divide (required contribution). Students rebuilding the series instead of reading the table were flagged in 2021, 2023 and 2025. Practise an investment-with-withdrawals variant: 2025 already used a home loan.
Find $k$ by integrating the pdf to 1; find the mode; find the median from $F(x) = 0.5$. Two traps own this question: if the density is monotonic, the mode is an endpoint — do not differentiate (2025 Q21a caught exactly this) — and pdf/CDF confusion, flagged every year from 2021 to 2025. Expect an exact surd or log answer for the median, not a decimal.
Standardise, look up, convert to an expected count — then the reverse part: given a tail probability or "the top 10%", recover the cutoff (2024 Q23c) or the standard deviation. The marking centre's exact words, three years running: a z-score is not a probability, and the empirical rule cannot handle non-integer z-scores. Practise reading $P(Z \le z)$ tables both directions.
Area between curves (3–6 marks): find the intersections first — they're usually a separate mark — then top-minus-bottom with bracketed substitution (order-of-subtraction errors flagged 2022, 2023, 2024). The "hence" pair: differentiate a product like $x^2 \tan x$ (2024) or $\sin x - x\cos x$ (2025), then "hence find" the matching integral by recognition. Every single year's feedback flags students ignoring the word "hence" and attempting the integral from scratch. If part (a) hands you a derivative, part (b) wants you to use it.
Tides, Ferris wheels, sound: fit $k$, $a$ and $c$ in $y = c + k\cos(at)$ from a stated max/min, sketch over a restricted domain (draw only the stated domain — a full period drawn anyway was flagged in 2024 and 2025), then solve $f(t) \ge$ value for a duration. Adjust the domain before solving, work in radians, and find every quadrant solution (flagged 2021, 2022, 2023, 2024).
Differentiation from first principles (MA-C1) is the panel's only genuinely rested call: five of six models rate a standalone appearance under 55%. But the final-year logic cuts the other way too — a syllabus dot point never substantially examined is exactly what a last-chance paper sweeps up. Two models call the 2-mark comeback, and two more flag the other never-examined dot point: logarithmic scales (decibels, Richter, pH). Neither costs more than an evening to prepare; both are cheap insurance. The same caution applies in reverse: one model argues the loan recurrence itself could rest this year — streaks break, so master the method (building the series term by term), not the memorised template.
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 panel's headline call: a two-part optimisation where (a) 'Show that' reduces a composite geometric constraint (wire/fence/container) to a one-variable objective with a fractional term, and (b) differentiates, verifies the nature by second derivative or sign table, and answers the quantity actually asked — with endpoint/domain checking to justify the global answer (fable). Gemini's structural twist: the 2026 finale shifts to a COST/financial objective after 2024–2025 both used perimeter/area. DeepSeek names a concrete instance (box, square base, open top, $V = 500\,\text{cm}^3$, $A = x^2 + 2000/x$) — a single-model textbook-style surface, treat the constants as illustrative only.
What each model said
In the practice paper: Q31
The highest per-question probabilities in the whole panel (grok 0.84, fable and opus 0.85): a one-mark MC giving the domain of $1/(1-x)$, $\sqrt{a-x^2}$ or a composite like $\sqrt{\ln(x-1)}$, with distractors encoding the wrong inequality direction and open/closed bracket confusion. A domain MC has appeared in 2020, 2021, 2023, 2024 and 2025. Gemini's F1 votes went to the composite-range and odd/even variants instead.
What each model said
In the practice paper: Q1
Find where a parabola meets a line or a second parabola, then integrate the difference for an exact area, with the intersections asked as a separate opening mark. Variants: gemini has a trig-curve-vs-line form with exact values; gpt-5.6-sol has a parameter recovered from a stated area. DeepSeek's concrete pair reuses $y = 4x - x^2$, a curve that appears verbatim in a past paper in the evidence pack — grounded, not echoed. Marking-centre lineage: subtracting in the correct order and bracketed limit substitution (2022 Q16, 2023 Q32a, 2024 Q14).
What each model said
In the practice paper: Q22
The 6–7 mark financial centrepiece: 'Show $A_2 = P(1+r)^2 - M(1+r) - M$', then the closed form $A_n$ by summing the geometric series, then a logarithmic solve for the month a balance first crosses a threshold or the largest sustainable repayment/withdrawal. Gemini flips it to a superannuation/contribution goal; deepseek adds a mid-term interest-rate rise. Grok is the hedge: its bold call says the recurrence may rest entirely this year, leaving finance to a series plus the factor table — its 0.52 is the savings-GP form.
What each model said
In the practice paper: Q30
Weights/marks context with a cumulative z-table supplied: standardise, read the probability, convert to an expected count in a population — then a REVERSE part (fable, gpt-5.6-sol, gemini, deepseek): given a tail probability or percentile, recover the cutoff value or the standard deviation. Opus adds the one-mark comparison sentence across two differently-parameterised populations. Marking-centre lineage: z-scores are not probabilities; the empirical rule cannot handle non-integer z-scores (2021, 2023, 2024, 2025).
What each model said
In the practice paper: Q23
A pdf on a finite interval with an unknown constant fixed by integrating to 1, then the mode — including the monotone-density edge case where the mode sits at an ENDPOINT (2025 Q21a; fable, opus) — then a median or quartile from CDF = 0.5 or 0.25, answer as an exact surd/log value. DeepSeek's instance $f(x) = kx(2-x)$ on $[0,2]$ and gemini's quadratic-pdf median are single-model surfaces of the same chain. The repeated marking-centre flag: pdf confused with CDF, and the mode sought by differentiation when the density is monotone.
What each model said
In the practice paper: Q27
Two realisations the panel splits across: the MC identifying $y = f(2x-1)$, $y = -f(-x)$ or $4f(2x)$ from sketches with intercepts as the decision points (grok, fable, gpt-5.6-sol; gemini's variant uses $|f(x)|$ vs $f(|x|)$), and the written sketch of $y = kf(a(x+b))+c$ or $2f(1-x)+1$ from a labelled graph (opus, deepseek). The constant trap either way: the horizontal dilation acting on x-values, not the ordinate (2021 Q21, 2024 Q7, 2025 Q6 lineage).
What each model said
Tides/Ferris wheel/sound: read or fit $k$, $a$, $c$ in $y = c + k \sin/\cos(at)$ from stated max/min or a graph, sketch over a restricted domain, then a harder part solving $f(t) \ge$ value for a duration, or comparing two phase-shifted functions (both decreasing — 2020 Q31b, 2025 Q15c; heights equal — 2024 Q28c), worked in radians over an adjusted domain. Grok notes 2025's sound-wave story makes an exact repeat of that dressing less likely; deepseek's tide constants (5.2 m at 2 am / 1.4 m at 8 am) are single-model and illustrative.
What each model said
In the practice paper: Q29
The traditional Q11–13 arithmetic/geometric warm-up: identify $a$ and $d$ (or $r$), find $n$ from the last term, then $S_n$ — with the number 2026 planted as a term, sum or limit, as 2021 (sum 2021), 2024 (last term 2024) and 2025 (sequence ending 2025) all did (fable). DeepSeek's variant is a limiting sum feeding a perpetuity. Marking-centre lineage: $n$ shown as a positive integer; the correct reference-sheet formula.
What each model said
In the practice paper: Q11
Tree diagram with first-stage chances given as a RATIO converted to probabilities (2025 Q19 lineage), each branch carrying a different success rate; find total probability of the outcome, then reverse it — $P(\text{a nominated branch} \mid \text{the outcome})$ — the Bayes-flavoured structure where the conditioning event is the result, not the stage. DeepSeek's disease-test dressing (95% sensitivity / 90% specificity / 2% prevalence) is the canonical textbook screening problem — single-model, constants illustrative only. The perennial flag: 'given' treated as 'and'.
What each model said
In the practice paper: Q16
The linked pair: (a) product/quotient rule on a polynomial times trig, exponential or log factor ($x^2 \tan x$ in 2024, $\sin x - x\cos x$ in 2025), exact gradient at a $\pi$-based point; (b) 'hence find' the matching integral by reverse-recognition after a constant adjustment, possibly a definite integral. Fable gives this its single highest question probability (0.85). Gemini's adjacent vote (0.80) is the quotient-rule-and-factorise half without the hence link. Every year's feedback flags 'hence' ignored and the integral attempted from scratch.
What each model said
In the practice paper: Q15
A tower/ship figure combining an angle of elevation or two-leg journey with the cosine rule at a ground vertex, the sine rule for a second angle, then converting an internal angle to a three-figure bearing (2024 Q20, 2025 Q29 lineage) — with the non-right-angle trap flagged in the diagram. Gemini sharpens it to the AMBIGUOUS CASE of the sine rule (obtuse angle required), which grok and deepseek independently flag as bold-call revival material (last written 2021). Grok expects a shorter item after two long 3D questions in a row.
What each model said
In the practice paper: Q25
A supplied table of annuity interest factors: convert an annual rate and term to the compounding period, select the factor, then decide whether to multiply (future value of deposits) or divide (required contribution) — possibly two-stage (annuity phase then pure compounding, 2021 style) or comparing a lump sum with regular deposits. The perennial flags: wrong cell, and rebuilding the geometric series instead of using the table. Corpus-echo check: fable, grok and deepseek all quote a 6% p.a. rate — verified PRESENT in the evidence pack (6% p.a. annuity contexts and a factor-table column at $r = 0.005/0.06$), so this is pack-grounded convergence, not a training-data echo; no contamination note required.
What each model said
In the practice paper: Q17
Scatterplot with the least-squares line given (or built from the $(\bar{x}, \bar{y})$ property): interpret gradient and intercept in context WITH values, interpolate a prediction, then explain why a distant extrapolation is unsafe because it yields an impossible value (negative usage, a score over 100). Gemini's variant adds a residual plot and an outlier's effect on $r$; the shared marking-centre flag is 'gradient is not correlation' (2021, 2023, 2025).
What each model said
In the practice paper: Q26
Exponential growth/decay context model — find $k$ by logs, rate = derivative, threshold time (6 models, ~0.63; narrowly outside the cluster cut — gemini's bold call is a Newton's-Law-of-Cooling variant with the ambient asymptote found first)
Trapezoidal rule from a table, then over/underestimate justified by concavity (6 models, ~0.60; grok expects no repeat of the 2022/2025 e-inequality chain)
Full calculus curve sketch of a quartic or polynomial-times-exponential with concavity-change justification (5 models, ~0.62)
Discrete random variable table: missing probability, $E(X)$, $\sigma$ via $\text{Var} = E(X^2) - \mu^2$ (5 models, ~0.55)
Arc/sector/segment in radians inside a composite shape (5 models, ~0.51)
Composite-function range via the inner function's range, 2025 Q18 lineage (4 models, ~0.60)
Parallel box plots / data-display comparison needing distinct contextual statements (4 models, ~0.53)
Parabola translated by the SAME constant both ways, quadratic in $k$ with a rejected root — 2025 Q30 lineage (4 models, ~0.48)
Trig equation reducing to a quadratic in sin/cos, factorise not divide (gemini 0.75, deepseek 0.50, opus adjacent)
Logarithmic-scale application (decibels/Richter/pH) — the E1 dot point never examined 2020–2025; fable (35% chance) and gpt-5.6-sol (38% chance) both make it their coverage-gap bold call
Differentiation from first principles returns — MA-C1 is the panel's only rested topic (5 of 6 models), yet deepseek (50% chance) and opus (bold, 0.30) call the 2-mark coverage-gap comeback
Parameter-count trig finale (for what $p$ does $\cos px = c$ have exactly two solutions) — 2025 Q31 lineage (3 models, ~0.49; grok argues a straight repeat is less likely)
Section I hardest item: derived-function reasoning from a graph of $f'$ (fable structural 0.75; gpt-5.6-sol's estimate-$f$-from-$f'$ variant 0.36)
How likely each topic is to appear this year.
Chance of a big question (4+ marks) here: 91%
Question types predicted here extended response ×9 short answer ×8
What each model expects
Chance of a big question (4+ marks) here: 94%
Question types predicted here extended response ×13 short answer ×4
What each model expects
Chance of a big question (4+ marks) here: 85%
Question types predicted here short answer ×10 extended response ×7
What each model expects
Chance of a big question (4+ marks) here: 82%
Question types predicted here extended response ×10 multiple choice ×4 short answer ×2
What each model expects
Chance of a big question (4+ marks) here: 71%
Question types predicted here short answer ×7 extended response ×6 multiple choice ×3
What each model expects
Chance of a big question (4+ marks) here: 51%
Question types predicted here short answer ×9 multiple choice ×6 extended response ×1
What each model expects
Chance of a big question (4+ marks) here: 54%
Question types predicted here short answer ×8 multiple choice ×4 extended response ×2
What each model expects
Chance of a big question (4+ marks) here: 39%
Question types predicted here short answer ×8 multiple choice ×5 extended response ×2
What each model expects
Chance of a big question (4+ marks) here: 63%
Question types predicted here extended response ×8 short answer ×7 multiple choice ×1
What each model expects
Chance of a big question (4+ marks) here: 55%
Question types predicted here short answer ×8 extended response ×4 multiple choice ×3
What each model expects
Chance of a big question (4+ marks) here: 59%
Question types predicted here extended response ×5 short answer ×5 multiple choice ×4 stimulus based ×1
What each model expects
Chance of a big question (4+ marks) here: 58%
Question types predicted here short answer ×8 extended response ×4 multiple choice ×2
What each model expects
Chance of a big question (4+ marks) here: 40%
Question types predicted here short answer ×2
What each model expects
How likely each topic is to appear. Open a topic for the question types to practise there.
100 marks · 31 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.