Nov 2025 TZ1
Most recent sitting. Tests the rising DE signal (logistic + Gompertz) in the current 75-minute regime — the highest-weight prior for the next paper.
Math · AA HL · Paper 3
An honest forecast.
Built from 14 past sittings (May 2022 → Nov 2025), three independent prediction models and two audits. A grounded prior — not a leaked paper.
14papers coded
28questions
3models
2audits
The forecast
If you only do three past papers
May 2025 TZ3
Induction in the new 75-minute format. Locks in the markscheme-stable Q1 template under the regime that now applies.
Nov 2024
The only paper that hits both the most-likely (induction) and most-overdue (palindromic polynomials, complex roots) content in a single sitting.
All 14 papers + markschemes → /math/p3/
Drill these three techniques
1
The induction template
6 / 14 papers
Always in Q1, always 6–8 marks. The markscheme idioms are 100% stable across all 14 sittings: explicit n=1, "assume true for n=k", conclusion R1.
Always in Q1, always 6–8 marks. The markscheme idioms are 100% stable across all 14 sittings: explicit n=1, "assume true for n=k", conclusion R1.
2
DE methods
rising signal
Separable, homogeneous y=vx, integrating factor, Euler's method. Three of the last seven sittings carried one. Most often in Q2.
Separable, homogeneous y=vx, integrating factor, Euler's method. Three of the last seven sittings carried one. Most often in Q2.
3
Complex roots (Vieta)
most overdue
Sum/product of roots, conjugate-pair theorem, palindromic polynomials. Last seen Nov 2024 — longest gap of any non-trivial genre.
Sum/product of roots, conjugate-pair theorem, palindromic polynomials. Last seen Nov 2024 — longest gap of any non-trivial genre.
What carries the paper
Calculus
75%
Number & Algebra
43%
Functions
25%
Stats & Prob
18%
Geometry / Vectors
14%
Complex numbers
11%
Q1 vs Q2 — typical content
Q1 — the opener
23–28 marks · investigate / generalise
- Induction proof6/14
- Parameter-family curve4/14
- Probability investigation3/14
- Geometric construction2/14
Q2 — the closer
27–32 marks · technique-driven
- Differential equation4/14
- Functional construction5/14
- Series / approximation3/14
- Vectors / 3D geometry1/14
More detail (optional)
The 14-paper table ›
Every paper coded by topic + genre. Rows sorted oldest → newest. The dashed line marks the May 2025 format change (60 min → 75 min, 55 marks unchanged).
| Session | Q1 | Q2 |
|---|---|---|
| May 2022 TZ1 | Sequences + induction | Calculus · l'Hôpital |
| May 2022 TZ2 | Family of curves y²=x³+ax+b | Vieta · complex roots |
| Nov 2022 | Log graphs / functions | Surface of revolution |
| May 2023 TZ1 | xⁿe⁻ˣ + induction | AM-GM max product |
| May 2023 TZ2 | Sequences + induction | Polynomial roots (real surds) |
| Nov 2023 | Cubic family · 4a³b+27b²<0 | Orthogonal trajectories · DE |
| May 2024 (a) | Geometric-distribution prob | Quartic inflexion · golden ratio |
| May 2024 (b) | Novel (fg)' = f'g' · DE | Random-quadratic discriminant |
| Nov 2024 | Recurrence + induction | Palindromic polynomials · complex |
| — format change: 60 min → 75 min — | ||
| May 2025 TZ1 | Stats · PGF | Calculus · curvature |
| May 2025 TZ2 | Rational curve → homogeneous DE | Vectors · spherical geometry |
| May 2025 TZ3 | Self-composite + induction | Open-box optimisation |
| Nov 2025 TZ1 | Normals to y=k²/x | Logistic + Gompertz · DE |
| Nov 2025 TZ3 | Iterated sin compositions | Maclaurin arctan · π approximation |
The three confidence tiers ›
Locked (>99%) — rule-based, 14/14 of all sittings. Paper format, mark counts, the "In this question you will investigate / explore / examine..." opener.
Likely (data-driven) — count out of 14 sittings, with a Wilson 95% confidence interval. N=14 is small; the interval is wide on purpose. Treat the interval as the truth, not the point estimate.
Speculative / overdue — the data is silent (or near-silent) but the syllabus is loud. Includes content that should be tested by IB design logic but hasn't appeared. The asymmetric cost of skipping these (a whole question's worth of marks) justifies preparing them even at low data signal.
Top 5 must-rehearse techniques ›
- Induction template — explicit base case, hypothesis wording, conclusion R16 / 14
- DE recipes — separable, homogeneous y=vx, integrating factor, Euler's method3–4 / 14
- Vieta + conjugate-root theorem — sum / product of roots, polynomial root algebra3 / 14
- Implicit differentiation + 2nd derivative — for curvature, inflexion, classification4 / 14
- Geometric series manipulation — finite & infinite, differentiation of series7 / 14
Runners-up: l'Hôpital, integration by parts, Maclaurin series for arctan / e^x / sin x, polynomial division, cross product, partial fractions.
What NOT to cram ›
- Matrices, hypothesis testingoff-syllabus for P3
- De Moivre / polar / roots of unity (light pass, not deep)0 / 14
- R-form trig identities, sum-to-product0 / 14
- Newton-Raphson0 / 14
- Routine binomial / normal distribution (P2 turf)covered by SL prep
If they sit Nov 2026 vs May 2027 ›
Nov 2026 — DE bumped to ~60%, complex content overdue (now 4 sittings since), induction ~40–50%. The N25 papers are the highest-weight prior.
May 2027 — same DE signal, slightly less "due" pressure on complex (May 2026 papers would have filled in by then), induction roughly unchanged.
Both sessions: the 75-min format is now the regime; older 60-min papers are weighted down.
How the forecast was built ›
Five-phase pipeline. Phase 1: four agents coded the 14 papers in parallel — topic, genre, sub-part skeleton, techniques, mark distribution. Phase 2: three cross-cuts — recurrence (with due-scores), a canonical 7-genre taxonomy, and a technique frequency catalogue. Phase 3: three independent prediction models (pure frequency, recency-weighted exponential decay, Bayesian with syllabus prior). Phase 4: methodology audit + a ground-up re-audit re-deriving every count from the raw PDFs.
The re-audit caught three over-counts: induction 6 / 14 (not 7 or 8), DE 3–4 / 14 (not 5.5 — one question was wrongly bucketed), complex 3 / 14 (not 4 — one paper's "roots" were real surds). The figures on this page are the corrected ones.
The 14 papers are downloadable at /math/p3/.
Why this might be wrong. N = 14 is small. The May 2025 format change (60 min → 75 min) means only the last 5 papers are in the current regime. The friends' session isn't confirmed; recency-sensitive calls split Nov 2026 vs May 2027. Single-observation genres (Maclaurin, AM-GM, spherical vectors) are noise, not signal. None of the probabilities on this page are physics — they're calibrated guesses with their CI shown. The structural near-certains are different — those are rules, not estimates.