5 · The backtest: we sat the test first
Before predicting 2026, we hid the 2025 papers from the panel, had it predict them from
2019–2024 evidence only, then scored every prediction against the real papers using the
official marking-guideline mapping. Two pilot subjects: Chemistry and Maths Extension 1.
Topic level saturated , as expected: every topic the panel rated ≥90%
appeared — 37 of 37 calls across both subjects. That validates the pipeline but can't
separate models. Question level is the honest test , graded strictly —
the form must match, not just the topic:
Fable 5
HIT (p 0.8): Projectile with r(t) supplied 'do not prove': extract condition then prove result, Q13/Q14 → Q13(c) (4m) angle condition from given r(t); Q14(b) (4m) prove V/U depends on k
PARTIAL (p 0.65): Routine Q11/Q12 component algebra: perpendicularity dot product zero gives quadratic or cubic → Q11(e) (1m) parallel condition; Q14(c) perpendicular clock hands
MISS (p 0.55): Geometric proof with vectors: parallelogram, rhombus, circle or midpoint via dot products
PARTIAL (p 0.6): Separable DE in modelling context (cooling/heating), solve for constant then time → Q12(d), Q13(a): pure separable ODEs with initial conditions
HIT (p 0.7): Volume of revolution stepped up: two curves or about y-axis needing x in terms of y → Q12(b) (2m) y=1/x region about the y-axis
HIT (p 0.6): Direction-field task, 1-2 marks, possibly MC matching field to equation → Q7 (1m) MC match DE to slope field
PARTIAL (p 0.85): Integration by given substitution, 3 marks, surd family, convert limits → Q3 (1m) MC transform integral under x=5sin(t)
PARTIAL (p 0.75): Standard inverse-trig calculus item, differentiate arcsin/arctan composite, 1-2 marks Q11 → Q14(d) (3m) differentiate arccos(sin x) with domain subtlety
HIT (p 0.55): Q13/Q14 fusion: sin^2/cos^2 identity definite integral, or inverse-function derivative at point → Q11(g) (3m) cos^2(3x) via double angle; Q10 MC g''(1)
PARTIAL (p 0.7): Normal approximation with printed z-table: standardise and read tail probability, 3 marks → Q13(d) (4m) normal approximation with z-table
HIT (p 0.4): Harder inverse problem: given probability bound, solve for n or a threshold → Q13(d) (4m) find k with P(X>=k)=0.0668
HIT (p 0.6): Short Bernoulli/binomial MC: expected value or variance from n and p → Q4 (1m) MC mean and variance of a Bernoulli variable
PARTIAL (p 0.7): 3-mark inequality with unknown in denominator or absolute value, interval solution → Q1 (1m) MC solve |2x+3| < 5
MISS (p 0.75): Graphical-relationship MC: identify 1/f(x), |f(x)|, f(|x|) from given graph
MISS (p 0.55): Parametric form returns: convert x=f(t), y=g(t) to Cartesian
HIT (p 0.65): Section II counting with restriction: committee, word, or circle with adjacency limits → Q13(b) (2m) round table, two guests refuse to sit together
MISS (p 0.55): Pigeonhole principle in worded context, ceiling argument, 2 marks or MC
HIT (p 0.45): Pascal's triangle nCr identity manipulation using the addition rule, 2 marks → Q13(e)(i)-(ii) (3m) rearrange Pascal relation, prove hockey-stick sum
HIT (p 0.55): 3-mark Q12 series induction where the inductive step needs factorisation not expansion → Q12(c) (3m) induction on sum k(k!) = (n+1)!-1
MISS (p 0.35): Alternative divisibility induction, a^n + b pattern, 3 marks Q12
HIT (p 0.6): Full auxiliary-angle solve: express as R-form AND solve over 0 to 2pi → Q12(e) (3m) express sqrt(3)sinx - cosx = 2sin(x-a), hence solve
HIT (p 0.5): Trig equation by factorising or double-angle without dividing away solutions → Q11(b) (3m) solve sin2t - sint = 0
HIT (p 0.4): Late-paper fusion of trig equations with polynomials: tan/compound angle, reject invalid root → Q14(e) (3m) tan roots of a cubic via tan addition formula
PARTIAL (p 0.8): Inverse-trig MC on principal domain, arcsin(sin a), identities, or transformations → Q6 (1m) MC odd/even symmetry of inverse-trig integrands
HIT (p 0.45): Short written item: sketch inverse trig graph with correct endpoints → Q11(d) (2m) sketch y = (1/3)arccos(2x)
HIT (p 0.55): Roots-and-coefficients: evaluate symmetric expression such as sum of reciprocals → Q11(f) (2m) evaluate 1/ab + 1/ac + 1/bc via Vieta
MISS (p 0.5): Factor/remainder theorem: unknown coefficients or multiplicity MC
0.648
GPT-5.6 Sol
PARTIAL (p 0.78): Integral with supplied substitution: transform integrand, change limits, exact answer → Q3 (1m) MC transform under x=5sin(t)
PARTIAL (p 0.52): Inverse function through known point: reciprocal-derivative rule then tangent gradient → Q10 (1m) MC g''(1) for the inverse
HIT (p 0.48): Trig integral via power-reduction identity over exact radian limits → Q11(g) (3m) integral of cos^2(3x) via double angle
PARTIAL (p 0.75): Separable DE modelling growth/cooling/draining with equilibrium interpretation → Q12(d), Q13(a) pure separable ODEs
HIT (p 0.68): Volume of revolution, curve and coordinate lines, possibly rewrite x as function of y → Q12(b) (2m) y=1/x about the y-axis between y=1 and y=a
PARTIAL (p 0.56): Direction field stimulus: select or sketch solution, explain equilibrium → Q7 (1m) MC identify the DE from the field
MISS (p 0.67): Vector quadrilateral/circle configuration proof via dot product
HIT (p 0.62): Projectile position vector: impose collision or max-height condition, prove bound → Q14(b) (4m) land-together, show V/U depends on k; Q13(c) (4m) angle condition
HIT (p 0.84): Induction: divisibility with powers, or finite sum, formal base/hypothesis/conclusion → Q12(c) (3m) sum k(k!) = (n+1)!-1
MISS (p 0.24): Inspect a supplied flawed induction argument and repair it
MISS (p 0.57): MC: identify transformed relation 1/f, |f|, f(|x|) from supplied graph
PARTIAL (p 0.54): Rational or absolute-value inequality with variable in denominator → Q1 (1m) MC |2x+3| < 5
MISS (p 0.42): Parametric curve: eliminate parameter, restricted interval, correct branch
HIT (p 0.59): Rewrite a cosx + b sinx as shifted sine/cosine, solve on radian interval → Q12(e) (3m) express and hence solve
HIT (p 0.51): Polynomial-looking trig equation: factorise via double/triple angle, reject extraneous branches → Q11(b) (3m) sin2t - sint = 0; Q5 MC cos5x + sinx = 0
HIT (p 0.56): Sums and products of roots evaluate a reciprocal or symmetric expression → Q11(f) (2m) 1/ab + 1/ac + 1/bc
MISS (p 0.53): Factor and remainder information gives equations for unknown coefficients
PARTIAL (p 0.62): MC: constrained arrangement or selection with circular seating or separated groups → Q13(b) (2m) written circular seating with separation
HIT (p 0.43): Supplied Pascal identity extended to an nCr sum by double counting → Q13(e) (3m) Pascal relation then hockey-stick sum
PARTIAL (p 0.61): Exact binomial probability, mean or expected score in a practical Bernoulli setting → Q4 (1m) MC Bernoulli mean and variance
PARTIAL (p 0.5): Sample proportion: mean, sd, z-score, tail probability, justify approximation → Q13(d) (4m) normal approximation, find threshold k
0.571
Grok 4.6
HIT (p 0.64): Volume about y-axis of reciprocal-curve region, rewrite x in terms of y → Q12(b) (2m) y=1/x about the y-axis
PARTIAL (p 0.56): Related rates in a cone via similar triangles, dV/dt to dh/dt → Q12(a) (3m) related rates on a constant-area sector
HIT (p 0.72): Separable DE with initial condition, plus possible early direction-field item → Q12(d), Q13(a) separable ODEs; Q7 MC direction field
PARTIAL (p 0.82): Integral with given substitution u=g(x), change limits, fractional power → Q3 (1m) MC transform under x=5sin(t)
PARTIAL (p 0.52): Derivative of an inverse: evaluate (f^-1)'(b) via reciprocal rule → Q10 (1m) MC g''(1)
PARTIAL (p 0.5): Rewrite integrand with double-angle then integrate to inverse-trig primitive → Q11(g) (3m) cos^2(3x) via double angle
PARTIAL (p 0.78): Q11 routine: components and dot product, perpendicular condition gives polynomial → Q11(e) (1m) parallel condition
MISS (p 0.5): Geometric proof: parallelogram, rhombus or midpoint result via dot products
HIT (p 0.38): Projectiles return: given r(t) 'do not prove', show-that on flight or perpendicular-velocity → Q13(c) (4m) velocity-acceleration angle condition; Q14(b) (4m) projectile proof
HIT (p 0.7): Q12 3-mark sum-identity induction for n>=1 with full scaffold → Q12(c) (3m) sum k(k!) = (n+1)!-1
MISS (p 0.32): Divisibility induction repeating the 2022/2024 type
PARTIAL (p 0.74): Binomial/sample-proportion: compute mu and sigma, standardise, read N(0,1) table → Q13(d) (4m) normal approximation
HIT (p 0.58): MC on E(X)=np, Var=np(1-p) or complementary binomial probability → Q4 (1m) MC Bernoulli mean and variance
MISS (p 0.28): Validity sentence on when normal approximation to p-hat fails
PARTIAL (p 0.7): Rational or absolute-value inequality with critical points and sign chart → Q1 (1m) MC |2x+3| < 5
MISS (p 0.42): Given sketch of f, draw 1/f or sqrt(f) with asymptotes
HIT (p 0.4): Find f^-1 by swapping variables, choose branch, state domain → Q11(a) (2m) inverse of f(x) = 1 - 1/(x-2)
PARTIAL (p 0.72): MC counting: repeated letters, committee product, or circular seating with restriction → Q13(b) (2m) written circular seating item
MISS (p 0.48): Section II pigeonhole naming pigeons and holes
HIT (p 0.3): Use Pascal's rule or symmetry to collapse a binomial-coefficient sum into one pCq → Q13(e)(ii) (2m) hockey-stick sum collapses to 2051C2001
HIT (p 0.58): R-form rewrite then solve equal to c on [0,2pi], all solutions → Q12(e) (3m) express and hence solve
HIT (p 0.4): Trig equation via double-angle, factorisation or t-formulae, check domain → Q11(b) (3m) sin2t - sint = 0; Q5 MC
HIT (p 0.54): Sum and product of roots evaluate sum of reciprocals or sum of squares → Q11(f) (2m) 1/ab + 1/ac + 1/bc
MISS (p 0.42): Factor and remainder theorems, 2x2 system for unknown coefficients
MISS (p 0.55): MC: evaluate sin^-1(sin a) outside principal range
PARTIAL (p 0.4): MC on domain/range of a dilated inverse-trig function → Q11(d) (2m) sketch y = (1/3)arccos(2x)
0.558
Gemini 3.1 Pro
HIT (p 0.85): Projectile from elevated position: time of flight from vertical displacement, horizontal range → Q14(b) (4m) horizontal launches from heights, land together, show V/U depends on k
PARTIAL (p 0.75): Vector projection then perpendicular distance from point to line → Q2 (1m) MC projection of u onto v
PARTIAL (p 0.8): Volume of revolution of region between two intersecting curves about x-axis → Q12(b) (2m) single curve about the y-axis
HIT (p 0.7): Solve DE by separation of variables, find value from initial conditions → Q12(d) (3m) and Q13(a) (3m) separable ODEs with initial conditions
MISS (p 0.85): Induction of an inequality or divisibility property with exponential expression
MISS (p 0.2): MC: identify the error in a flawed induction proof
PARTIAL (p 0.75): Integrate with provided u-substitution, change limits, fractional powers → Q3 (1m) MC transform under x=5sin(t)
HIT (p 0.65): Integrate sin^2 or cos^2 by first applying the double angle formula → Q11(g) (3m) definite integral of cos^2(3x)
MISS (p 0.8): Pigeonhole: minimum picks to guarantee a shared characteristic
PARTIAL (p 0.7): Arrangements of a word with repeated letters kept apart → Q13(b) (2m) circular seating with two kept apart
MISS (p 0.75): MC: exact value of inverse trig composed with trig function
PARTIAL (p 0.7): Derivative of compound inverse trig function, then tangent equation → Q14(d) (3m) differentiate arccos(sin x)
MISS (p 0.85): Cubic with unknown coefficients via Factor and Remainder theorems
HIT (p 0.6): Sum of squares of roots of a cubic via root-coefficient relations → Q11(f) (2m) 1/ab + 1/ac + 1/bc via Vieta
HIT (p 0.85): Solve a cosx + b sinx = c via R cos(x-alpha) auxiliary angle → Q12(e) (3m) express as 2sin(x-a), hence solve
PARTIAL (p 0.5): Trig equation requiring the t-substitution → Q11(b) (3m) sin2t - sint = 0
PARTIAL (p 0.7): Normal approximation to binomial: probability sample proportion exceeds a value → Q13(d) (4m) count-based, find threshold k
HIT (p 0.6): MC: expected value and variance of a binomial in a game context → Q4 (1m) MC Bernoulli mean and variance
0.528
Opus 5
HIT (p 0.6): Volume about y-axis: write x in terms of y, integral plus cylinder, exact answer → Q12(b) (2m) y=1/x region about the y-axis
PARTIAL (p 0.7): Printed direction field: sketch particular solution and explain equilibrium behaviour → Q7 (1m) MC identify DE from slope field
PARTIAL (p 0.6): Separable DE modelling cooling or population, two data points, time to nearest minute → Q12(d), Q13(a) pure separable ODEs
HIT (p 0.75): Projectile with supplied position vector: show bounded result, collision or range condition → Q14(b) (4m) land-together condition, show V/U depends on k; Q13(c) (4m)
PARTIAL (p 0.55): Two component vectors with parameter a, dot product zero, solve quadratic or cubic → Q11(e) (1m) parallel condition for (1,m) and (2,6)
MISS (p 0.5): Vector geometry proof on quadrilateral or chord/radius via dot product expansion
PARTIAL (p 0.85): Integration by stated substitution with algebraic rearrangement and limit changes → Q3 (1m) MC transform under x=5sin(t)
MISS (p 0.55): 2-mark integral rewritten to a Reference Sheet inverse-trig primitive
PARTIAL (p 0.5): Derivative of inverse function at a point via reciprocal rule → Q10 (1m) MC g''(1) for g = f^-1
HIT (p 0.5): Induction on summation whose step is completed by factorising the assumed sum → Q12(c) (3m) sum k(k!) = (n+1)!-1
MISS (p 0.4): Divisibility induction a^(bn)+c, rearrange assumption and substitute
MISS (p 0.2): Induction with base case n=0 catching reflexive n=1 starts
PARTIAL (p 0.7): Normal approximation to sample proportion: standardise, read table, give probability → Q13(d) (4m) normal approximation on the count
HIT (p 0.45): Inverse design: smallest n or largest count meeting a tail probability → Q13(d) (4m) find k with P(X>=k)=0.0668
PARTIAL (p 0.5): Binomial parameters in context: expression for P(X=r) or compute E(X), Var(X) → Q4 (1m) MC Bernoulli mean and variance
PARTIAL (p 0.55): Inequality with denominator and absolute value, graph supplied, case split → Q1 (1m) MC |2x+3| < 5
HIT (p 0.4): Inverse functions: find f inverse, state domain, sketch by reflection → Q11(a) (2m) find inverse of f(x) = 1 - 1/(x-2)
MISS (p 0.35): From graph of f, sketch reciprocal, modulus, or y^2 = f(x)
MISS (p 0.6): Pigeonhole justification in worded setting with ceiling argument
HIT (p 0.55): Binomial coefficients: extract coefficient or combine via Pascal's rule and symmetry → Q13(e) (3m) Pascal rearrangement and hockey-stick proof
HIT (p 0.5): Arrangements with restrictions: repeats, or line/circle where groups cannot sit together → Q13(b) (2m) circular seating, two guests apart
HIT (p 0.6): Auxiliary angle: express as R sin(x+alpha) then solve over stated radian domain → Q12(e) (3m) 2sin(x-a) form then solve on [0,2pi]
PARTIAL (p 0.5): Prove identity part (i) then 'hence' solve or integrate in part (ii) → Q12(e)(i)-(ii) express-then-hence-solve
HIT (p 0.45): Trig equation by factorising quadratic/cubic in sinx or cosx, keep all solutions → Q11(b) (3m) sin2t - sint = 0
MISS (p 0.6): MC on remainder/factor theorem or polynomial graph shape with multiplicity
HIT (p 0.5): Sum and product of roots applied to a symmetric expression over common denominator → Q11(f) (2m) 1/ab + 1/ac + 1/bc
MISS (p 0.4): Factor and remainder theorems giving simultaneous equations in unknown coefficients
PARTIAL (p 0.65): MC on inverse-trig domain/range or arcsin(sin a) outside principal range → Q6 (1m) MC odd/even inverse-trig integrand symmetry
PARTIAL (p 0.35): MC identifying dilation factors in transformed arcsin/arctan graphs → Q11(d) (2m) sketch y = (1/3)arccos(2x)
MISS (p 0.25): arctan(ax) + arctan(bx) = theta solved by taking tangents, monotonicity argument
0.517
DeepSeek V4
PARTIAL (p 0.7): Substitution u = sqrt(x-1) for integral of x sqrt(x-1), change limits → Q3 (1m) MC transform under x=5sin(t)
PARTIAL (p 0.55): (f^-1)'(3) via reciprocal rule for f = x^3+2x, then tangent → Q10 (1m) MC g''(1)
MISS (p 0.5): MC: recognise which integral equals dx/(4+9x^2), inverse-tan pattern
HIT (p 0.65): Volume about y-axis: y = ln x region, rewrite x = e^y, integrate in y → Q12(b) (2m) y=1/x about the y-axis
HIT (p 0.6): Solve dy/dx = y cos x with y(0)=1 by separation, evaluate solution → Q12(d) (3m) and Q13(a) (3m) separable ODEs with initial conditions
HIT (p 0.5): Direction field MC: identify the correct field for a given DE → Q7 (1m) MC match DE to slope field
PARTIAL (p 0.6): Projectile kicked at angle: show it clears a wall, inequality with time of flight → Q14(b) (4m) horizontal launches land together
MISS (p 0.5): Quadrilateral with perpendicular diagonals: prove sums of squared sides equal
HIT (p 0.45): MC: projection of 3a onto 2b, scalar effect on projection → Q2 (1m) MC projection of u onto v
PARTIAL (p 0.65): Normal approximation to p-hat: n=200, p=0.4, tail probability from z-table → Q13(d) (4m) count-based, find threshold k
MISS (p 0.5): MC: which condition justifies the normal approximation to binomial
MISS (p 0.45): Binomial probability: at least 8 of 10 correct by guessing
MISS (p 0.55): Induction: 7^n + 2(4^n) divisible by 3
HIT (p 0.45): Induction on sum of (2k-1)^2 with expansion and factorisation step → Q12(c) (3m) sum k(k!) = (n+1)!-1
MISS (p 0.3): MC: identify the flaw in a false induction proof
MISS (p 0.55): MC: identify graph of 1/f(x) from graph of f
PARTIAL (p 0.5): Solve |2x-3| >= 5 in two cases, interval notation → Q1 (1m) MC solve |2x+3| < 5
HIT (p 0.45): f(x) = sqrt(x-2): find f^-1 with domain and range → Q11(a) (2m) inverse of f(x) = 1 - 1/(x-2)
HIT (p 0.6): Solve 2sinx + 3cosx = 1 via R sin(x+alpha), all solutions on [0,2pi] → Q12(e) (3m) express sqrt(3)sinx - cosx then hence solve
HIT (p 0.5): Solve cos2x + sinx = 0 via double angle to quadratic in sinx → Q11(b) (3m) sin2t - sint = 0; Q5 (1m) MC cos5x + sinx = 0
MISS (p 0.4): MC: which value solves tanx + cotx = 4
MISS (p 0.55): Cubic with factor (x+2) and given remainder: find a and b
MISS (p 0.4): MC: double root implies P'(2)=0, multiplicity concept
HIT (p 0.35): Cubic roots: alpha^2 + beta^2 + gamma^2 via sum and product of roots → Q11(f) (2m) 1/ab + 1/ac + 1/bc via Vieta
MISS (p 0.55): MC: cos^-1(cos(7pi/4)) principal-range evaluation
PARTIAL (p 0.4): Sketch sin^-1 x + cos^-1 x as the constant pi/2 → Q11(d) (2m) sketch y = (1/3)arccos(2x)
PARTIAL (p 0.3): Prove sin^-1(-x) = -sin^-1(x) from odd property of sine → Q6 (1m) MC odd/even symmetry of inverse-trig integrands
MISS (p 0.55): Pigeonhole: 21 balls, 5 colours, at least 5 share a colour
MISS (p 0.5): Coefficient of x^5 in (2 - x/3)^8 by binomial theorem
MISS (p 0.45): MC: arrangements of PARRAMATTA with repeated letters
PARTIAL (p 0.5): Product-to-sum on sin5x cos3x then integrate → Q11(c) (2m) integral of sin^3(x)cos(x)
MISS (p 0.4): Given tan = 3/4, t-formulae for sin 2theta and cos 2theta
MISS (p 0.35): Prove (sinA+sinB)/(cosA+cosB) = tan((A+B)/2)
PARTIAL (p 0.55): Related rates: deflating spherical balloon, dV/dt to dr/dt at r=10 → Q12(a) (3m) constant-area sector, dtheta/dt to dr/dt
MISS (p 0.45): Exponential decay dM/dt = -kM with half-life, find mass later
MISS (p 0.4): MC: ambient temperature in Newton's cooling model
0.375
Maths Extension 1 (2025):
one dot per question-level prediction —
hit ,
partial , grey miss; the figure at right is
the weighted hit rate (hits + ½·partials) / predictions. Hover any dot for the
prediction and what actually appeared.
GPT-5.6 Sol
PARTIAL (p 0.72): Unknown oxygenated compound from MS/IR/NMR: draw, name, justify each feature → Q36: 7m predict spectra FROM propanoic acid's structure
HIT (p 0.76): MC select isomer from spectrum; distractors miscount unique environments/symmetry → Q17: MC carbon environments equal proton environments; Q8 MS MC
PARTIAL (p 0.62): Ka or Kb from pH and concentration via ICE, no shortcut → Q34(a): 3m Ka from titration curve; Q31(b) pH from Kb
MISS (p 0.58): Strong acid with polyprotic/carbonate/hydroxide mixed, excess pH via pOH
HIT (p 0.65): Ksp: molar solubility, common ion, or precipitation threshold, 4-5 marks → Q32: 5m which precipitates form, justified by Q vs Ksp
MISS (p 0.57): Equilibrium disturbed by added species, find unknown amount via table
HIT (p 0.48): Standardisation, dilution and back titration chain, outlier, 6-7 marks → Q33: 7m back titration, %CaCO3 in chalk
PARTIAL (p 0.59): Supplied titration/conductivity curve: identify pair, equivalence, indicator, ions → Q34: curve supplied, but tasks were Ka (3m) and pH-limit explanation (2m)
PARTIAL (p 0.58): Pathway alkene/haloalkane to alcohol then oxidation, draw products, state conditions → Q15: 1m MC sequence; Q27(b): 3m single-step hydration equation
HIT (p 0.68): MC oxidation products of alcohol classes or reaction-type identification → Q2: MC classify butan-2-ol to butanone reaction; Q15 sequence MC
HIT (p 0.59): Disturbance graph: identify change, explain via forward/reverse collision rates → Q35: 5m collision-theory explanation of cooling; Q5 MC graph
HIT (p 0.72): MC exothermic gaseous equilibrium: temperature/pressure effect on yield and Keq → Q14: MC Keq and temperature across two HI experiments
PARTIAL (p 0.53): Water sample two ions: design or evaluate sequential test scheme → Q4: 1m MC distinguish Pb2+ from Na+
PARTIAL (p 0.55): Calibration graph: interpolate, reverse dilution, convert mol/L and mg/L → Q20: 1m MC AAS calibration + dilution
HIT (p 0.7): MC preferred IUPAC name with parent-chain and numbering distractors → Q3: MC structure of 1,2-dibromopentane
MISS (p 0.47): Draw and name all isomers of a formula, classify a pair
PARTIAL (p 0.42): Classify acid/salt under Arrhenius and Bronsted-Lowry with proton-transfer equations → Q11: MC Bronsted-Lowry classification only
MISS (p 0.55): MC familiar acid with metal/carbonate/base, identify products
HIT (p 0.42): Polymer segment: identify type, draw section or recover monomer → Q28(a): 1m draw Kevlar's missing monomer; Q16: MC polyester
PARTIAL (p 0.4): Acid/amine/amide/ester series boiling point or solubility trends via IMF → Q28(b): 3m IMF comparison; Q10: MC forces in butanoic acid
0.600
Grok 4.6
PARTIAL (p 0.62): Pathway A-B-C with spectra of each: identify, draw, justify, 7-9 marks → Q36: 7m spectra prediction (reversed); Q37: 4m pathway deduction without spectra
PARTIAL (p 0.48): Standalone unknown oxygenated liquid from MS/IR/NMR, draw and name → Q36: 7m predict spectra FROM structure
HIT (p 0.85): MC matching 1H NMR pattern or 13C peak count to correct isomer → Q17: MC environments counting across candidate compounds
MISS (p 0.42): Closed-vessel ICE: find amount of gas added at constant temperature
PARTIAL (p 0.58): Mixed solutions, precipitate mass given, equilibrium cation concentration from Ksp → Q32: 5m precipitation decision via Q vs Ksp
PARTIAL (p 0.8): MC Q-vs-Ksp precipitate decision or MX2 molar solubility → Q20: MC Ksp computed (reverse); decision appeared as Section II Q32
PARTIAL (p 0.6): Four-box flow chart from alkene/haloalkane: draw A-D with conditions → Q15: 1m MC X,Y,Z sequence
MISS (p 0.48): Odd-year fermentation: gas volume to mass of ethanol
MISS (p 0.7): MC/2m distinguish alkene or alcohol classes with bromine water/permanganate
PARTIAL (p 0.55): Standardise NaOH, outlier, diluted analyte, forward titration 6-7 marks → Q33: 7m BACK titration of chalk
PARTIAL (p 0.5): Acetate buffer with indicator: explain constancy via equilibrium equation → Q19: 1m MC buffer pH after dilution
PARTIAL (p 0.75): MC indicator matching a titration curve or identifying the acid-base pair → Q18: MC endpoint colour in argentometric titration
HIT (p 0.52): pH of salt of weak acid via Ka-Kw conversion, ICE, pOH, 4 marks → Q31(b): 4m pH of N2H5+ using Ka.Kb=Kw and Kb of hydrazine
MISS (p 0.28): Two weak acids same pH: show incomplete dissociation
PARTIAL (p 0.7): MC [OH-] from pH or pH after mixing unequal strong acid/base → Q6: MC pH of 0.25 mol/L HCl
HIT (p 0.55): Concentration-time sketch of remaining species plus collision-rate explanation, 5 marks → Q27(c): 3m sketch after addition; Q35: 5m collision-theory explanation
HIT (p 0.4): Energy-profile diagram: collision-theory explanation of temperature effect on Keq → Q35: 5m collision theory + Le Chatelier + energy profile on cooling
MISS (p 0.78): MC catalyst activation energies/yield or adding solid to heterogeneous equilibrium
MISS (p 0.45): Draw alkane of given molar mass plus chain isomers, name all
MISS (p 0.4): Name isomer pairs among displayed structures, 2 marks
HIT (p 0.85): MC preferred IUPAC name of branched haloalkane/amide/ketone → Q3: MC structure of 1,2-dibromopentane
PARTIAL (p 0.58): Unknown salt: outline flame test then precipitation sequence with equations → Q4: 1m MC distinguish Pb2+ from Na+
PARTIAL (p 0.5): Calibration absorbance graph: interpolate, apply dilution, convert units → Q20: 1m MC AAS calibration + dilution
PARTIAL (p 0.65): MC AAS lamp match or distinguishable flame-test pair → Q7: MC best technique to distinguish coloured complexes
HIT (p 0.55): MC particle diagram: concentrated versus dilute, strong versus weak acid → Q1: MC classify particle-diagram acid as strong/weak and concentrated/dilute
MISS (p 0.3): Amphiprotic ion: two equations showing donation and acceptance
HIT (p 0.7): MC Arrhenius base or Bronsted-Lowry acid identification with conjugate distractors → Q11: MC classify propanoic acid and amine as B-L acid/base
PARTIAL (p 0.38): Boiling-point table of alcohol/acid/ester explained via H-bonding versus dispersion → Q10: MC forces in butanoic acid; Q28(b) IMF comparison
PARTIAL (p 0.72): MC identify monomer of displayed polymer or name ester and reactant → Q16: MC polyester molar mass; Q28(a): 1m draw monomer
HIT (p 0.32): MC soap anions arranged in oil-water emulsion → Q9: MC use of saponin given hydrophilic/hydrophobic parts
0.500
Fable 5
PARTIAL (p 0.85): Late-paper 7-9 mark multi-spectra unknown structure determination chained to reaction pathway → Q36 (7m) reversed the task: predict IR/13C/1H/MS features FROM propanoic acid's structure
HIT (p 0.6): MC counting NMR signals via molecular symmetry among isomers → Q17: MC compound whose carbon environments equal proton environments
MISS (p 0.55): 2-3 mark item using 13C NMR or IR to distinguish or monitor alcohols
MISS (p 0.7): 4-5 mark ICE-table Keq calculation with unknown amount of species added
PARTIAL (p 0.65): Ksp calculation with non-1:1 stoichiometry, 3-4 mark Section II → Q20: 1m MC Ksp of silver oxalate from AAS calibration and dilution
PARTIAL (p 0.55): MC Q-vs-Ksp precipitation decision on mixing two solutions → Q32: 5m Section II Q-vs-Ksp precipitate determination
HIT (p 0.7): 5-7 mark back titration or standardisation chain ending in percent composition → Q33: 7m back titration, %CaCO3 in chalk, identify brand
PARTIAL (p 0.6): Buffer resists pH change, explain via equilibrium, 3-4 marks → Q19: 1m MC buffer pH after dilution
PARTIAL (p 0.75): MC titration or conductometric curve: pick acid-base pair or indicator → Q34(a): curve appeared as 3m Ka calculation; Q18: argentometric endpoint MC
PARTIAL (p 0.75): Calibration-curve quantification with dilution and unit conversion, 4-7 marks → Q20: 1m MC AAS calibration + dilution (used for Ksp)
PARTIAL (p 0.7): Qualitative ion testing scheme design or evaluation, 4-5 marks → Q4: 1m MC choose ion to distinguish Pb2+ from Na+
HIT (p 0.7): MC instrument principle or selectivity: AAS wavelength, overlapping spectra, flame tests → Q7: MC best technique to distinguish two coloured copper complexes
HIT (p 0.75): Sketch concentration recovery after species added plus collision-rate explanation → Q27(c): 3m sketch after ethanol added; Q35: 5m collision-theory explanation
PARTIAL (p 0.6): DeltaG and spontaneity from dH and TdS data, 3-4 marks → Q13: 1m MC signs of dH and dS for octane combustion
HIT (p 0.7): MC on temperature change and Keq with graphs → Q14: MC compare Keq and temperature across two HI experiments
MISS (p 0.75): Excess-reagent strong acid/strong base pH calculation, 3-4 marks
PARTIAL (p 0.65): Weak-acid Ka/ICE from measured pH, or rank acid strengths → Q34(a): Ka from titration curve; Q31(b): pH from Kb
HIT (p 0.7): MC converting between pH, pOH, [H+] and [OH-] → Q6: MC pH of 0.25 mol/L HCl
PARTIAL (p 0.7): 4-6 mark lettered organic flow chart with drawn structures → Q15: 1m MC X,Y,Z reaction sequence from prop-2-en-1-ol
MISS (p 0.7): Fermentation gas-volume or combustion calorimetry quantitation
MISS (p 0.65): 2-3 mark chemical tests distinguishing alkene, alcohols, carboxylic acid
PARTIAL (p 0.7): Boiling point/solubility trend explained via hydrogen bonding versus dispersion, from graph → Q28(b): 3m Kevlar vs polystyrene IMF; Q26: trend graph but of pKa
HIT (p 0.6): Polymer item: draw section or identify condensation monomer, plus mass arithmetic MC → Q28(a): draw Kevlar's missing monomer; Q16: MC polyester molar mass
PARTIAL (p 0.6): Esterification craft: name/draw ester, justify reflux, 2-3 marks → Q25: 3m percentage yield from reflux esterification data
PARTIAL (p 0.65): Conjugate or amphiprotic 2-marker with equations → Q11: MC Bronsted-Lowry acid/base classification
MISS (p 0.5): Arrhenius vs Bronsted-Lowry model comparison, 4-5 marks
MISS (p 0.55): Enthalpy of neutralisation calorimetry with a twist
PARTIAL (p 0.55): Industrial flow-chart evaluation of design factors, 3-5 marks → Q30(b): 3m explain excess CO and catalyst in phosgene synthesis
MISS (p 0.45): Green-chemistry route comparison or 8-mark synthesis design
0.483
Gemini 3.1 Pro
HIT (p 0.85): Back titration of impure household substance, percent purity, dilution factor → Q33: 7m back titration, %CaCO3 in household chalk
PARTIAL (p 0.75): Buffer explanation via Le Chatelier with equations, 3-4 marks → Q19: 1m MC buffer pH after dilution
PARTIAL (p 0.8): Structure determination from IR, 13C, 1H and mass spectra, 7-9 marks → Q36: 7m predict spectra FROM propanoic acid's structure
PARTIAL (p 0.7): MC identify organic fragment from mass-spectrum fragmentation pattern → Q8: MC deduce reagent from molecular-ion peak shift
MISS (p 0.75): ICE-table Keq from initial plus one equilibrium concentration
HIT (p 0.7): Precipitate decision on mixing: calculate Q, compare to Ksp → Q32: 5m which precipitates form via Q vs Ksp
PARTIAL (p 0.8): Design multi-step pathway to ester/alkene from alkane with reagents and conditions → Q21: 2m single-step butane bromination with UV; Q15: 1m MC sequence
PARTIAL (p 0.65): Compare boiling points of alcohol/alkane/aldehyde via intermolecular forces → Q10: MC forces between butanoic acid molecules
MISS (p 0.75): Strong acid/strong base mixing, excess reagent, final pH
PARTIAL (p 0.65): MC pH of weak acid from concentration and Ka with assumption → Q31(b): weak-conjugate pH as 4m Section II; Q6: strong-acid pH MC
PARTIAL (p 0.8): Flowchart identifying unknown cations via HCl, H2SO4, NaOH precipitations → Q4: 1m MC distinguish Pb2+ from Na+
MISS (p 0.6): Heavy-metal water issue plus a removal method, 2-3 marks
PARTIAL (p 0.75): Compare addition versus condensation polymerisation with monomer structures → Q16: MC polyester; Q28(a): draw condensation monomer
HIT (p 0.7): Theoretical yield of ester from reactant masses, limiting reagent → Q25: 3m percentage yield of propyl butanoate from reflux data
HIT (p 0.8): Concentration-time graph disturbance explained using collision theory → Q35: 5m collision-theory explanation of cooling; Q27(c) sketch
MISS (p 0.65): Catalyst effect on forward/reverse activation energy with energy profile
MISS (p 0.7): Amphiprotic ion demonstrated with acid and base equations
MISS (p 0.6): Enthalpy of neutralisation from data plus design evaluation
0.444
DeepSeek V4
PARTIAL (p 0.9): Unknown ester C5H10O2 from four spectra, justify every feature, 7-9 marks → Q36: 7m predict spectra FROM propanoic acid's structure
MISS (p 0.55): Why 13C NMR distinguishes propan-1-ol/propan-2-ol but MS cannot
PARTIAL (p 0.6): MC which compound gives 1H NMR with two doublets → Q17: MC environment counting, not splitting
PARTIAL (p 0.8): Ksp of PbI2 from precipitate mass, then common-ion solubility → Q32: 5m precipitation decision via Q vs Ksp
MISS (p 0.7): ICE for 2SO2+O2 after adding O2, then Keq at new temperature
PARTIAL (p 0.65): MC solubility of Ag2CrO4 in AgNO3 with common ion → Q20: MC Ksp of silver oxalate computed from data
HIT (p 0.75): Back titration of impure sodium carbonate: excess HCl, NaOH titrate, percent purity → Q33: 7m chalk CaCO3 dissolved in excess HCl, KOH back-titration, percent
PARTIAL (p 0.7): Conductivity curve NH3 vs HCl: explain shape, find equivalence, calculate → Q34: pH titration curve with Ka and pH-limit tasks
PARTIAL (p 0.6): MC suitable indicator for weak acid-strong base titration → Q18: MC argentometric endpoint colour
HIT (p 0.75): Collision-theory temperature effect on rates and exothermic equilibrium with sketch → Q35: 5m collision theory + energy profile explaining cooling shift
PARTIAL (p 0.55): DeltaG vs T graph: find non-spontaneous temperature, calculate dH and dS → Q13: 1m MC signs of dH and dS
PARTIAL (p 0.6): MC sealed NO2/N2O4 syringe compressed: colour change → Q29: 4m sealed NO2/N2O4 with argon added
PARTIAL (p 0.75): Buffer pH calculation, then pH after adding NaOH, 4-5 marks → Q19: 1m MC buffer pH after dilution
PARTIAL (p 0.65): Ka from pH and concentration, then pKa strength comparison → Q34(a): Ka from curve; Q26: pKa strength comparison graph
PARTIAL (p 0.55): MC pH after mixing equal volumes 0.1 M HCl and NaOH → Q6: MC pH of 0.25 mol/L HCl
PARTIAL (p 0.7): Pathway but-1-ene to butan-2-one with reagents; contrast butan-1-ol product → Q37: 4m deduce C5H10 alkene from hydration/oxidation evidence; Q15 MC
MISS (p 0.6): Fermentation: ethanol mass at 85% yield plus CO2 volume via gas law
MISS (p 0.55): MC reagent distinguishing butan-1-ol from 2-methylpropan-2-ol
PARTIAL (p 0.7): Anion test sequence for Cl-, SO4 2-, CO3 2- with equations → Q4: 1m MC ion-distinguishing
PARTIAL (p 0.6): Colorimetry calibration for iron: interpolate, reverse dilution, tablet mass → Q20: 1m MC AAS calibration + dilution
PARTIAL (p 0.55): MC which ion pair a flame test distinguishes → Q4: MC distinguish Pb2+/Na+ by added iodide
PARTIAL (p 0.65): Esterification lab design: reflux, catalyst, safety, purification, 5-6 marks → Q25: 3m percentage yield from reflux esterification
HIT (p 0.55): Condensation polymer section: draw the two monomers, identify linkage → Q28(a): 1m draw the missing Kevlar monomer
PARTIAL (p 0.5): MC strongest organic acid among chloroacetic acids via electronegativity → Q26: 5m construct pKa graph of haloethanoic acids and describe trend
PARTIAL (p 0.65): Compare Arrhenius and Bronsted-Lowry with HCl and NH4Cl equations → Q11: MC B-L classification only
HIT (p 0.55): MC conjugate acid-base pairs and proton-transfer direction → Q11: MC classify propanoic acid and amine as B-L acid/base
PARTIAL (p 0.5): Explain NH4Cl acidity via hydrolysis and Ka greater than Kb → Q31(b): conjugate-acid acidity as quantitative pH calculation
MISS (p 0.6): Draw and name all C4H8 alkene isomers including E/Z
HIT (p 0.55): MC IUPAC name of branched carboxylic acid → Q3: MC structure of 1,2-dibromopentane
MISS (p 0.5): Functional-group isomers of C3H6O plus distinguishing chemical test
MISS (p 0.55): Evaluate hydration versus fermentation routes to ethanol, atom economy
MISS (p 0.45): Atom economy calculation for two ethanoic acid routes
MISS (p 0.4): MC most important factor in synthesis design
0.439
Opus 5
PARTIAL (p 0.55): Ksp derived from weighed precipitate after mixing two solutions, 4-5 marks → Q32: 5m Q-vs-Ksp precipitation decision on mixing
MISS (p 0.5): ICE-table Keq: solve algebraically for unknown amount added
PARTIAL (p 0.7): MC molar solubility of non-1:1 salt from data-sheet Ksp → Q20: MC computes Ksp (reverse direction) inside an AAS wrapper
PARTIAL (p 0.8): Anchor 7-9 mark four-spectra unknown ester/ketone, draw and justify → Q36: 7m predict spectra FROM propanoic acid's structure
MISS (p 0.5): 2-3 mark 13C NMR distinguishing isomers or monitoring a conversion
HIT (p 0.7): MC spectrum-to-compound match via IR bands or M/M+2 pair → Q8: MC deduce addition reagent from molecular-ion peaks 70 to 90 m/z
HIT (p 0.6): 5-7 mark back or double titration with outlier and dilution factor → Q33: 7m back titration, %CaCO3 in chalk
PARTIAL (p 0.5): 3-4 mark titration/conductivity curve explained via ions present → Q34(b): 2m explain why final pH never reaches 13
PARTIAL (p 0.4): Working Scientifically critique of a defective titration procedure → Q23: 3m justify improvements to gravimetric sulfate procedure
MISS (p 0.55): Strong acid mixed with strong base, excess reagent pH via pOH
HIT (p 0.5): Weak acid/base ICE from concentration plus Ka/pKa, calculate missing quantity → Q31(b): 4m pH of 0.20 mol/L N2H5+ using Ka.Kb=Kw
MISS (p 0.4): Two acids same pH: show incomplete dissociation, rank strength
HIT (p 0.6): 3 mark collision-theory explanation after a disturbance → Q35: 5m collision theory + energy profile on cooling; Q29: 4m argon addition
PARTIAL (p 0.5): Gibbs free energy computation and spontaneity from data or graph → Q13: 1m MC signs of dH and dS
HIT (p 0.45): 2 mark sketch of concentration/rate curves after imposed disturbance → Q27(c): 3m sketch ethanol concentration after extra ethanol added
PARTIAL (p 0.55): 4-6 mark reaction-pathway flow chart, draw lettered products → Q15: 1m MC identify X, Y, Z in sequence
MISS (p 0.5): Alcohol calorimetry q=mcdT to molar enthalpy
MISS (p 0.45): 3 mark distinguish alcohol classes with oxidant colour change and equations
PARTIAL (p 0.55): 4-5 mark evaluate a failing qualitative ion-test sequence → Q4: 1m MC distinguish Pb2+ from Na+
PARTIAL (p 0.55): 4-5 mark calibration-curve interpolation, dilution reversal, unit conversion → Q20: 1m MC AAS calibration + dilution
PARTIAL (p 0.4): 4 mark gravimetric calculation from dried precipitate mass → Q23: gravimetric procedure critique, no calculation
HIT (p 0.7): MC branched drawn structure to preferred IUPAC name → Q3: MC pick structure of 1,2-dibromopentane
MISS (p 0.5): 2-3 mark isomer naming or drawing item
MISS (p 0.5): Homologous-series boiling point trend via dispersion forces
PARTIAL (p 0.45): Classify substances under both Arrhenius and Bronsted-Lowry, 4-5 marks → Q11: MC Bronsted-Lowry classification only
MISS (p 0.45): Calorimetry of neutralisation/dissolution with mass correction
MISS (p 0.45): 2 mark acid plus metal/carbonate/base products and equation
HIT (p 0.55): Draw addition-polymer section or identify condensation monomer → Q28(a): 1m draw Kevlar's missing monomer; Q16: MC polyester
PARTIAL (p 0.5): Esterification: identify acid/alcohol, reflux conditions and reasons, 3-4 marks → Q25: 3m percentage yield of propyl butanoate
PARTIAL (p 0.4): Compare boiling points of two series via H-bond electronegativity → Q28(b): IMF comparison Kevlar/polystyrene; Q10: MC forces in butanoic acid
PARTIAL (p 0.45): 3-4 mark industrial flow-chart design factors: catalyst, recycling feed → Q30(b): 3m explain excess CO and catalyst, no flow chart
MISS (p 0.3): Green-chemistry comparison of two routes with atom economy data
0.438
Chemistry (2025):
one dot per question-level prediction —
hit ,
partial , grey miss; the figure at right is
the weighted hit rate (hits + ½·partials) / predictions. Hover any dot for the
prediction and what actually appeared.
Roughly half of all question-level predictions recognisably appeared —
against a question space where naive guessing lands far lower. The stories behind the dots:
five of six models called the 7-mark chemistry back-titration almost exactly; Fable's 3-mark
series induction “whose step needs factorisation, not expansion” landed verbatim.
And the misses teach the same lesson every time: all six models staked the chemistry flagship
on identify-the-unknown-from-spectra — NESA inverted it (given the structure,
predict the spectra). Content bullseye, format twist. That's why every subject page pushes
skill chains over memorised questions.
The caveats, verbatim:
The 2025 papers may appear in the models' training data — leakage-guarded packs reduce but cannot eliminate this, so backtest numbers are a ceiling, not a guarantee.
Two pilot subjects only; the other thirteen inherit the method, not the measured hit rate.
November 2026 — predictions locked before the papers exist — is the true test.
The full backtest verdict (calibration tables, per-model Brier scores)
Holdout backtest verdict — predicting 2025 blind, scored against the real papers
Six models predicted the 2025 HSC Chemistry and Maths Ext 1 exams from
2019/2020–2024 evidence only (leakage-guarded packs verified free of 2025/2026
content), then were scored against the actual papers via the official
marking-guideline mapping grids.
Calibration (Brier scores; lower is better)
Topic-examined is saturated — both 2025 papers touched every taxonomy
topic; all models' p≥0.9 calls hit (37/37 across the panel). This dimension
validates the pipeline but cannot separate models.
Topic-substantial (≥4-mark item) separates them:
model
Chemistry Brier(subst)
Ext 1 Brier(subst)
gpt-5.6-sol
0.179
0.325
opus
0.192
0.187
grok
0.200
0.259
deepseek
0.217
0.389
gemini-3.1-pro
0.251
0.512
fable
0.281
0.285
in-sample base-rate bar
0.248
0.16
Chemistry: four of six beat the bar. Ext 1: nobody beat it — the paper
concentrated its ≥4-mark questions in just two topics (vectors, binomial) and
the whole panel over-predicted breadth. Opus is the most consistently
calibrated; the panel as a whole runs overconfident on "substantial".
Question-level hits (strict grading: form must match, not just topic)
Weighted hit rate = (hits + 0.5·partials) / predictions.
model
Chemistry
Ext 1
gpt-5.6-sol
0.600
0.571
fable
0.483
0.648
grok
0.500
0.558
gemini-3.1-pro
0.444
0.528
opus
0.438
0.517
deepseek
0.439
0.375
Roughly half of all question-level predictions recognisably appeared —
against a question space where naive guessing would land far lower.
The stories
Biggest collective hit : the 7-mark chemistry back-titration (Q33) —
five of six called it, DeepSeek nearly verbatim.
Sharpest single hit : Fable's Q12 3-mark series induction "whose step
needs factorisation not expansion" — Q12(c) (Σk·k! = (n+1)!−1) is exactly
that; its p=0.4 tan-addition/polynomial-roots fusion landed almost verbatim
as Q14(e).
Most instructive partial : all six staked their chemistry flagship on
identify-the-unknown-from-spectra; NESA inverted it (Q36: given the
structure, predict the spectra). Content bullseye, format twist.
Biggest collective misses : the ICE-table Keq calculation (6/6 predicted,
absent) and, in Ext 1, two broken streaks — pigeonhole and the
vector-geometry proof (5/6 each, neither appeared).
Format migration tax : several content-correct calls were downgraded
because questions moved to multiple choice (|2x−3|≥5 → MC Q1;
cos2x+sinx=0 → MC Q5; the substitution integral shrank to transform-only MC Q3).
DeepSeek's breadth backfired in Ext 1: 18 of 36 predictions missed,
many in off-taxonomy topics it invented.
What this means
The method's strength is what gets examined and which question
families recur; NESA's freedom lives in format twists and streak-breaking
— exactly the uncertainty the probabilities express. Marketing claims
should be calibration-shaped, not oracle-shaped.
The ensemble is justified: different models win different dimensions
(Sol: chemistry calibration + hits; Opus: substantial calibration;
Fable: question-level sharpness in maths, but overconfident on breadth).
2026 implications now carry backtest support: the spectra capstone
"reversion" call and the Keq "due after resting" call are strengthened by
2025's observed absences/inversions.
Caveats, stated plainly: the 2025 papers may sit in these models' training
data (instructed-against but unverifiable), the in-sample base-rate bar is
itself hindsight, and one year × two subjects is a small sample. The
November 2026 scoring — truly out-of-sample — is the real test, and this
harness is exactly what will run it.