IB Math AA HL Paper 3 Predicted Questions 2026
The investigation themes most likely to anchor the 2026 session Paper 3 — backed by frequency analysis of past HL Paper 3 sessions. Paper 3 is two long extended-response problem-solving questions, and a GDC is required throughout.
Stop hoping the right investigation comes up.
Know exactly which extended problem to drill — and how to build it.
Paper 3 rewards students who can sustain one long investigation, and the HL question setters keep returning to the same engines: optimisation of function families, polynomial roots via the factor and remainder theorems, and proof, with differential equations and sequences close behind. We drill those high-frequency threads as full extended-response builds, not isolated short questions.
- High-frequency investigation walkthroughs: optimisation, polynomial roots, proof, differential equations, sequences.
- Extended-response method drills with the GDC required — the exact problem-solving stamina Paper 3 tests.
- How to structure a two-question investigation: conjecture, justify, generalise, and prove.
- Worked HL builds that connect calculus, algebra and proof into one sustained answer.
Most likely Paper 1 focus areas
Based on frequency analysis across past HL Paper 3 investigation sessions
- 1Families of functions — stationary points, inflexion and optimising across a parameter (39 question parts in 11 sittings since 2021)
- 2Polynomials — using the factor and remainder theorems to pin down roots in an extended investigation (33 question parts in 8 sittings)
- 3Proof — direct, contradiction and induction arguments built into the question (30 question parts)
- 4Sequences and series — spotting and justifying a pattern across an investigation (29 question parts)
- 5Differentiation rules and tangents — chain, product and quotient rules, then tangent and normal lines (26 question parts)
- 6Differential equations — modelling and solving within a sustained problem (23 question parts)
- 7Quadratics and the discriminant — conditions on roots inside a longer argument (13 question parts in 9 sittings)
How to use these Paper 3 predictions
- 1Start with optimisation of function families — it anchors the most Paper 3 investigations, so practise carrying a parameter all the way through.
- 2Drill the factor and remainder theorems until finding and verifying polynomial roots is automatic under time pressure.
- 3Rehearse a complete proof out loud — direct, by contradiction or by induction — because Paper 3 wants the full argument, not a sketch.
- 4Practise stringing differential equations, sequences and differentiation into one sustained, GDC-supported answer rather than as separate short questions.
Ready to walk in confident on Math AA HL Paper 3?
Turn these predicted investigation themes into practised, exam-ready method. The crash course walks you through full HL extended-response builds on the highest-frequency Paper 3 topics — with the GDC work shown at every step.
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