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HSC 2026 final syllabus year published Aug 2026

Mathematics Extension 1 question styles to look out for

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.

About the 2026 exam & how this page was built

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.

The near-certainties

Section II · 2–4 marks 6 of 6 models expect this

Differential equations two ways

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...

Try it → Q12(b) Why we expect this
Section II · 3–4 marks 6 of 6 models expect this

Auxiliary-angle (R-form) solve

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...

Try it → Q11(d) Why we expect this
Section II · 3–7 marks 6 of 6 models expect this

Projectile with the position vector supplied — plus a twist

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...

Try it → Q14(d) Why we expect this
On this page
  1. 1. The given-substitution integral (Q11/Q12, 3 marks)
  2. 2. Projectile with the position vector supplied — plus a twist
  3. 3. Auxiliary-angle (R-form) solve
  4. 4. The 3-mark Q12 induction
  5. 5. Differential equations two ways
  6. Where to spend study time
  7. Practice paper
  8. Check our working

The near-certainties (every model, every year)

1. The given-substitution integral (Q11/Q12, 3 marks)

5 of 6 models expect this — consensus probability 0.76

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.

Watch

in 2025 this shrank to a transform-only multiple-choice — so also practise recognising the transformed integral among distractors.

Try it → Q11(e) Try it → Q14(a) 5 of 6 models expect this — see the evidence

2. Projectile with the position vector supplied — plus a twist

6 of 6 models expect this — consensus probability 0.64

"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.

Try it → Q14(d) 6 of 6 models expect this — see the evidence

3. Auxiliary-angle (R-form) solve

6 of 6 models expect this — consensus probability 0.67

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.

Try it → Q11(d) 6 of 6 models expect this — see the evidence

4. The 3-mark Q12 induction

6 of 6 models expect this — consensus probability 0.61

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.

Try it → Q12(a) 6 of 6 models expect this — see the evidence

5. Differential equations two ways

6 of 6 models expect this — consensus probability 0.69

(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.

Try it → Q12(b) 6 of 6 models expect this — see the evidence

Strong candidates

  • Volume of revolution about the $y$-axis — rewrite $x^2$ in terms of $y$; expect an exact answer with $\pi$ and often a logarithm.
  • Normal approximation to the binomial, run backwards — given a tail probability, find the threshold or sample size from the z-table; round in the direction the context demands (overbooking rounds differently from quality control!).
  • Rational/absolute-value inequality — multiply by the squared denominator, find all critical values, and exclude the value that zeroes the denominator. (2025 moved this to multiple choice — practise both forms.)
  • Vector projection — the three distractor errors are always the same: dividing by $|\mathbf{u}|^2$ instead of $|\mathbf{v}|^2$, attaching the scalar to the wrong vector, and sign slips.
  • Factor + remainder theorems together — unknown-coefficient cubic, one factor and one remainder condition, solve the $2 \times 2$ system.
  • Derivative of an inverse function at a point — $(f^{-1})'(b) = 1/f'(a)$; the multiple-choice version with second derivatives was 2025's hardest MC.

Broken streaks — don't over-rely on the pattern

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.

The honest fine print

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.

Want to check our working? every call above, with each model's own prediction
5 of 6 models expect this — consensus probability 0.76 Integration by a GIVEN substitution (Q11/Q12 3-marker) 5 of 6 models expect this
ext1-q1-substitution-integral Section II 3–4 marks mid range consensus 0.76

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

  • Grok 4.6 0.88
  • Claude Fable 5 0.80
  • Claude Opus 5 0.75
  • GPT-5.6 Sol 0.74
  • DeepSeek V4 0.65

In the practice paper: Q11(e) Q14(a)

6 of 6 models expect this — consensus probability 0.64 Projectile with supplied position vector — two objects / elevated or delayed launch 6 of 6 models expect this
ext1-q2-projectile-twist Section II 3–7 marks discriminator consensus 0.64

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

  • Gemini 3.1 Pro 0.80
  • Claude Fable 5 0.65
  • Claude Opus 5 0.62
  • GPT-5.6 Sol 0.61
  • Grok 4.6 0.58
  • DeepSeek V4 0.55

In the practice paper: Q14(d)

6 of 6 models expect this — consensus probability 0.67 R-form: $a\sin x \pm b\cos x$ → $R\sin(x\pm\alpha)$, then solve on $[0, 2\pi]$ 6 of 6 models expect this
ext1-q3-auxiliary-angle Section II 3–4 marks mid range consensus 0.67

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

  • DeepSeek V4 0.70
  • Grok 4.6 0.70
  • Claude Opus 5 0.70
  • Gemini 3.1 Pro 0.70
  • GPT-5.6 Sol 0.67
  • Claude Fable 5 0.50

In the practice paper: Q11(d)

6 of 6 models expect this — consensus probability 0.61 3-mark Q12 divisibility induction (divisibility due on the alternation) 6 of 6 models expect this
ext1-q4-divisibility-induction Section II 3 marks mid range consensus 0.61

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

  • Gemini 3.1 Pro 0.75
  • Grok 4.6 0.72
  • DeepSeek V4 0.60
  • GPT-5.6 Sol 0.58
  • Claude Fable 5 0.50
  • Claude Opus 5 0.50

In the practice paper: Q12(a)

6 of 6 models expect this — consensus probability 0.69 Separable differential equation with initial condition (context model) 6 of 6 models expect this
ext1-q5-separable-de Section II 2–4 marks mid range consensus 0.69

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

  • Grok 4.6 0.82
  • Gemini 3.1 Pro 0.80
  • Claude Opus 5 0.70
  • GPT-5.6 Sol 0.70
  • DeepSeek V4 0.60
  • Claude Fable 5 0.50

In the practice paper: Q12(b)

6 of 6 models expect this — consensus probability 0.61 Direction/slope field: sketch the particular solution vs an asymptote 6 of 6 models expect this
ext1-q6-direction-field Section II 1–3 marks mid range consensus 0.61

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

  • Gemini 3.1 Pro 0.80
  • Claude Fable 5 0.65
  • Grok 4.6 0.62
  • GPT-5.6 Sol 0.58
  • DeepSeek V4 0.50
  • Claude Opus 5 0.50

In the practice paper: Q12(c)

4 of 6 models expect this — consensus probability 0.62 Volume of revolution about the y-axis (re-express x in terms of y) 4 of 6 models expect this
ext1-q7-volume-y-axis Section II 2–5 marks mid range consensus 0.62

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

  • DeepSeek V4 0.70
  • GPT-5.6 Sol 0.62
  • Claude Fable 5 0.60
  • Claude Opus 5 0.55

In the practice paper: Q12(d)

5 of 6 models expect this — consensus probability 0.64 Binomial normal approximation with the supplied z-table — often run BACKWARDS 5 of 6 models expect this
ext1-q8-normal-approximation Section II 3–4 marks discriminator consensus 0.64

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

  • Grok 4.6 0.72
  • DeepSeek V4 0.70
  • Claude Opus 5 0.65
  • GPT-5.6 Sol 0.58
  • Claude Fable 5 0.55

In the practice paper: Q13(c)

6 of 6 models expect this — consensus probability 0.58 Rational/absolute-value inequality (multiply by squared denominator) 6 of 6 models expect this
ext1-q9-rational-inequality Section II 2–4 marks discriminator consensus 0.58

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

  • Gemini 3.1 Pro 0.75
  • Claude Fable 5 0.60
  • Claude Opus 5 0.60
  • DeepSeek V4 0.55
  • GPT-5.6 Sol 0.54
  • Grok 4.6 0.44

In the practice paper: Q11(c)

5 of 6 models expect this — consensus probability 0.66 Vector projection item with the three classic distractor errors 5 of 6 models expect this
ext1-q10-projection Section I 1–2 marks routine consensus 0.66

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

  • GPT-5.6 Sol 0.76
  • Gemini 3.1 Pro 0.75
  • DeepSeek V4 0.70
  • Claude Fable 5 0.55
  • Claude Opus 5 0.55

In the practice paper: Q2

6 of 6 models expect this — consensus probability 0.57 Factor + remainder theorems in tandem (unknown-coefficient cubic) 6 of 6 models expect this · one echo discounted
ext1-q11-factor-remainder Section II 2–4 marks mid range consensus 0.57

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

  • Gemini 3.1 Pro 0.70
  • Grok 4.6 0.56
  • DeepSeek V4 0.55
  • GPT-5.6 Sol 0.55
  • Claude Opus 5 0.50
  • Claude Fable 5 0.45

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)

4 of 6 models expect this — consensus probability 0.52 Derivative of an inverse function at a point 4 of 6 models expect this
ext1-q12-inverse-derivative Section mixed 1–3 marks mid range consensus 0.52

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

  • GPT-5.6 Sol 0.57
  • DeepSeek V4 0.50
  • Claude Fable 5 0.50
  • Claude Opus 5 0.50

In the practice paper: Q9

Watch list — worth having ready (9)

  • $\sin^2(kx)/\cos^2(kx)$ 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

Where to spend your study time

How likely each topic is to appear this year.

Applications: related rates, DEs, volumes of revolution 99% likely

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

  • DeepSeek V4: A 4-mark volume of revolution about the y-axis with a rational function, and a 3-mark separable DE with initial condition, mirroring 2024 Q12b and Q11d.
  • Claude Fable 5: A separable differential equation in a physical context worth 3-4 marks in Q12 or Q13, plus a direction-field item, with the DE-related total again at 8 or more marks.
  • Gemini 3.1 Pro: A 5-mark related rates or logistic growth discriminator placed in the final section.
  • GPT-5.6 Sol: At least one four-mark application combines a differential equation or volume model with interpretation rather than presenting calculus in isolation.
  • Grok 4.6: Q13 or Q12 will carry a 3–5 mark DE or volume application, with a 2-mark direction-field sketch still more likely than 2025’s identify-the-DE multiple choice.
  • Claude Opus 5: A three- to four-mark separable differential equation in Question 11 or 12 plus a direction-field or volumes part later, giving ME-C3 nine to fifteen marks across both sections.
Introduction to vectors incl. projectiles 98% likely

Chance of a big question (4+ marks) here: 91%

Question types predicted here extended response ×12 multiple choice ×5

What each model expects

  • DeepSeek V4: A 5-mark projectile collision problem with two particles and a 3-mark vector proof involving midpoints or perpendicular diagonals, plus an MC on projection.
  • Claude Fable 5: A 4-mark adapted projectile question in Q13 or Q14 with the position vector supplied and 'Do NOT prove this', for the sixth consecutive year.
  • Gemini 3.1 Pro: Projectiles will form a major 7-mark question in Q13, using pure vector notation.
  • GPT-5.6 Sol: Vectors receive both a one-mark component or projection item and a three-to-four-mark geometric or projectile argument in Questions 13–14.
  • Grok 4.6: Q11 will open with two one-mark vector calculations, and a 3–4 mark given-r(t) projectile will sit in Q13 or Q14 rather than another two-height horizontal pair.
  • Claude Opus 5: Vectors again carries the paper's heaviest Section II load, thirteen to sixteen marks, including a four-mark projectile in Question 13 or 14 and at least two Section I items.
Trigonometric equations 95% likely

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

  • DeepSeek V4: A 4-mark auxiliary angle question with subsequent equation, and a 3-mark trig equation using double-angle, plus an MC on number of solutions.
  • Claude Fable 5: Q11 or Q12 carries a 3-mark factorise-and-solve trig equation, and trig equations resurface inside the Q14 discriminator as a hybrid with polynomials or vectors.
  • Gemini 3.1 Pro: A t-formula substitution will be the primary mechanism for a 3-mark equation in Q12.
  • GPT-5.6 Sol: The principal trigonometric equation is a three-mark Section II problem with an explicit domain and at least one easily lost solution.
  • Grok 4.6: Section II will ask an auxiliary-angle conversion then a solve on [0,2π], most likely in Q11 or Q12, rather than another 2025-style standalone double-angle factorisation.
  • Claude Opus 5: The auxiliary-angle conversion returns as a split (i)/(ii) part in Question 11 or 12, worth three or four marks combined, with the domain given in radians.
Proof by mathematical induction 95% likely

Chance of a big question (4+ marks) here: 49%

Question types predicted here extended response ×12

What each model expects

  • DeepSeek V4: A 3-mark induction proof on divisibility, likely with a base case n=1 and an expression like a^n + b×c^n.
  • Claude Fable 5: One induction proof, exactly 3 marks, placed in Q12, and a divisibility form after series forms in 2023 and 2025.
  • Gemini 3.1 Pro: Divisibility induction will return in Q13 with a specific mark allocated to logical justification.
  • GPT-5.6 Sol: A self-contained three-mark induction proof appears in Question 12, most likely a divisibility result after the factorial-sum proof in 2025.
  • Grok 4.6: Q12 will contain a standalone 3-mark divisibility induction, not a sum, continuing the 2022-sum / 2023-sum / 2024-divisibility / 2025-sum alternation.
  • Claude Opus 5: Induction is worth exactly three marks and sits in Question 12, as it has in every paper from 2020 to 2025.
Further calculus skills 94% likely

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

  • DeepSeek V4: A 3-mark substitution integral with u = x² + a, a 2-mark inverse function derivative, and an MC on trigonometric integral identity.
  • Claude Fable 5: A 3-mark given-substitution integral appears in Q11 or Q12 for the seventh consecutive year, with limits changed to u.
  • Gemini 3.1 Pro: Volume of revolution will require squaring a trig function and applying a double-angle formula.
  • GPT-5.6 Sol: Question 11 or 12 contains a three-mark supplied-substitution integral, with a second calculus-skills item elsewhere on the paper.
  • Grok 4.6: A 3-mark given-substitution integral will appear in Q11, almost certainly with fractional powers of u.
  • Claude Opus 5: A three-mark given-substitution integral returns to Section II after appearing only as multiple choice in 2025, plus one inverse-trigonometric or inverse-function derivative item.
Further functions, graphs, inequalities (Y11) 94% likely

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

  • DeepSeek V4: A 3-mark absolute value rational inequality, a 2-mark quadratic inequality, and an MC on graph transformation.
  • Claude Fable 5: A 3-mark denominator or absolute-value inequality appears in Q11 or Q12, continuing the 2022/2024 even-year pattern into the final paper.
  • Gemini 3.1 Pro: An early Section II question will require rigorous algebraic solution of an inequality.
  • GPT-5.6 Sol: Parametric representation returns after no dedicated parametric item in 2024–2025, most likely as a two-to-three-mark early Section II question.
  • Grok 4.6: Q11 will include a 2-mark inverse-function or parametric-to-Cartesian conversion, closing the 2024–2025 parametric gap.
  • Claude Opus 5: A three-mark inequality with a variable denominator or absolute value appears in Question 11 or 12, keyed to a supplied graph rather than solved blind.
Polynomials (Y11) 88% likely

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

  • DeepSeek V4: A 3-mark factor/remainder theorem problem, a 2-mark roots question, and an MC on polynomial division.
  • Claude Fable 5: A 2-mark roots-coefficients evaluation early in Q11, with polynomial machinery reappearing inside a hybrid later question rather than as a standalone 4-marker.
  • Gemini 3.1 Pro: Roots of a cubic will form a solid 3-mark algebra test in Q11 or Q12.
  • GPT-5.6 Sol: A roots-and-coefficients or factor/remainder calculation appears early, with a lower-probability double-root discriminator later in the paper.
  • Grok 4.6: A 3-mark factor-plus-remainder pair for two unknown coefficients will return in Q11, last seen in 2023, rather than another 2025-style 1/αβ sum.
  • Claude Opus 5: Roots-and-coefficients returns as a two-mark Question 11 part, with polynomials otherwise carried inside a vector or trigonometry question rather than standing alone.
Combinatorics and pigeonhole (Y11) 88% likely

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

  • DeepSeek V4: A 2-mark pigeonhole proof, and two MCs on permutations and combinations.
  • Claude Fable 5: Combinatorics contributes about 4-5 marks including a binomial-expansion coefficient question returning after its absence since 2022; the 2025-style Q14 combinatorial proof is rested.
  • Gemini 3.1 Pro: Circular arrangements will be tested as a tricky multiple choice distractor.
  • GPT-5.6 Sol: Combinatorics is reduced from its heavy 2025 presence to one restricted-counting item plus, at most, a short Pascal-identity part.
  • Grok 4.6: Combinatorics will be a 1-mark pigeonhole MC plus a 2-mark linear arrangement, not another circular-seating or Pascal-chaining item.
  • Claude Opus 5: Pigeonhole reappears as a two- or three-mark justify item; total combinatorics load falls back towards three to five marks after 2025's seven.
Binomial distribution and sample proportions 84% likely may rest

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

  • DeepSeek V4: A 3-mark normal approximation with z-table, and two MCs on binomial parameters and sample proportion.
  • Claude Fable 5: A 3-4 mark normal-approximation question in Q13 or Q14 with the z-table printed at the back, asked in reverse (find k or n) rather than forwards.
  • GPT-5.6 Sol: A three-to-four-mark normal-approximation problem requires working backwards from a tail probability to an integer threshold or sample size.
  • Grok 4.6: A 3-mark normal approximation using the printed z-table will appear in Q12, with n large enough that the 2022/2023 ‘sample too small’ critique does not apply.
  • Claude Opus 5: One nominated Section II part will be answered using a z-table printed on the paper's last page, and it will require reading the table in reverse from a probability to a z-score.
Inverse trig and further trig (Y11) 80% likely may rest

Chance of a big question (4+ marks) here: 46%

Question types predicted here extended response ×7 multiple choice ×5

What each model expects

  • DeepSeek V4: An MC on domain/range of inverse trig combination, a 3-mark inverse trig equation, and possibly an MC on graph.
  • Claude Fable 5: Inverse trig contributes one Section I item on domain/range or transformations plus a 2-mark written part, with a products-to-sums identity resurfacing inside an integral.
  • Gemini 3.1 Pro: Will appear primarily as a standard 1-mark multiple choice on recognizing the derivative.
  • Grok 4.6: Inverse trig will be a 2-mark sketch or a matching arcsin integral in Q11, not another 2025-style derivative of arccos(sin x).
  • Claude Opus 5: Inverse trigonometry stays light, three to five marks, delivered as one or two Section I items plus a two-mark identity or sketch in Section II.

How likely each topic is to appear. Open a topic for the question types to practise there.

Practise with the paper

Maths Extension 1 practice paper

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.

Read it on the web Download PDF Solutions (PDF)

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Practice paper (PDF)

Every style card and paper question has its own link — hover any card and use its copy-link icon to share exactly the thing you mean. Printing this page gives a clean copy too.

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.