IB Mathematics Analysis & Approaches HL AI Tutor Playbook 2026

Target: May 2027 IB Math AA HL cohort. Goal: Markband 7 (88-100%).

The 12-Module Domain Map

The IB Math AA HL syllabus is divided into 12 compulsory modules across Number & Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, Calculus, and Linear Algebra. The AI tutor maps every Paper 1 short-response + Paper 2 long-response question to one of these modules and scores against the IB markband descriptors (1 = limited, 7 = excellent).

Modules 1–4: Algebra & Functions Foundation

1. Number & Algebra — exponents, logs, surds, binomial theorem, partial fractions
2. Functions — domain/range, composite, inverse, transformations
3. Sequences & Series — arithmetic, geometric, sum-to-infinity, sigma notation
4. Counting, Binomial, Probability — permutations, combinations, conditional probability, Bayes

Modules 5–7: Geometry, Trigonometry & Complex Numbers

1. Statistics & Probability Distributions — binomial, normal, discrete/continuous models
2. Trigonometric & Circular Functions — radians, identities, trig equations
3. Geometry — coordinate, 3D, conic sections (HL extension)

Modules 8–12: Calculus & Linear Algebra

1. Complex Numbers — i, polar form, De Moivre, roots of unity
2. Vectors — 2D/3D, dot/cross product, lines, planes
3. Differential Calculus — limits, derivatives, chain rule, implicit
4. Integral Calculus & Differential Equations — integration by parts/substitution, ODEs
5. Linear Algebra — matrices, determinants, eigenvalues/eigenvectors (HL signature)

The 3-Paper Exam Structure

Paper	Format	Duration	Weight	Marks
Paper 1	Short-response (compulsory)	2h	40%	110
Paper 2	Long-response (compulsory)	2h	40%	110
Paper 3	Investigative (2 extended questions)	1h	20%	55

Paper 1 tests breadth across all 12 modules at standard difficulty. Paper 2 tests depth — multi-step problems worth 20-30 marks each. Paper 3 — two investigative questions, often HL-extension only (complex numbers, linear algebra, differential equations).

The AI Tutor IA Exploration Workflow

The IA (Internal Assessment) is a 6-12 page mathematical exploration worth 20% of the final grade. AI tutor workflow:

1. Topic selection — identify a chapter connecting 2+ modules (e.g., "optimization using calculus and vectors in 3D geometry")
2. Personal engagement — every IA needs a "personal engagement" narrative (what sparked your curiosity, why this topic)
3. Mathematical communication — define notation, prove claims, cite theorems
4. Reflection — what you'd do differently, what you discovered

IA Markbands (5 Criteria, 0-7 Each)

Criterion	Marks	Description
Presentation	4	Structure, clarity, conventions
Mathematical communication	4	Notation, terminology, symbols
Personal engagement	4	Independence, creativity, insight
Reflection	4	Evaluation, self-critique, extension
Use of mathematics	6	Correct application, sophistication

AI tutor scores every draft against these 5 criteria — most IB Math AA HL students lose marks on Criteria B (Communication) and D (Reflection), not raw math correctness.

The 4-Gap Diagnostic

The AI tutor classifies struggling students into one of 4 gaps:

Gap 1 — Algebra Foundation

Symptom: Stuck on binomial expansion, partial fractions, complex numbers. Root: Modules 1-2 weren't mastered before HL exam prep. Fix: 4-week algebra bootcamp before calculus starts.

Gap 2 — Calculus Techniques

Symptom: Can state the rule but botches the algebra — failed u-substitution, integration by parts loop never terminates. Fix: Drill 30+ HL past-paper questions on chain rule, integration by substitution, integration by parts.

Gap 3 — Geometric Reasoning

Symptom: Vectors break down in 3D — can't visualize lines/planes intersecting, cross product becomes opaque. Fix: Whiteboard sessions, GeoGebra visualizations, 20 vector problems sequenced easy→hard.

Gap 4 — Proof Communication

Symptom: Right answer, zero markband credit — can't structure a 7-mark proof. Fix: Mark-scheme reverse-engineering — read 10 IB examiner reports and code solutions by structure (state→prove→conclude).

36-Week Workflow to 7

Weeks	Focus	Outcome
1-4	Modules 1-2 algebra	100% on binomial, logs, surds
5-8	Modules 3-4 sequences/probability	Sigma + Bayes fluency
9-12	Modules 5-6 trig	Radians + identities + equations
13-16	Modules 7-8 geometry + complex	3D + De Moivre
17-22	Modules 9-10 vectors + calculus	Vectors + differentiation
23-28	Modules 11-12 integrals + linear algebra	Integration by parts, eigenvalues
29-32	Paper 1 timed practice	80%+ on all 12 modules
33-35	Paper 2 + Paper 3 past papers	70%+ long-response
36	IA draft + revision	IA scoring 6-7

Target Universities & Programs

IB Math AA HL is the prerequisite for:

• Engineering — MIT, Stanford, Cambridge, Imperial, ETH, NUS
• Computer Science — MIT, CMU, Berkeley, Cambridge, Oxford
• Physics — Princeton, Harvard, Cambridge, UCL, Yale
• Mathematics — Cambridge, Oxford, MIT, Princeton, Berkeley
• Economics — LSE, Cambridge, Oxford, Harvard, Wharton
• Quantitative Finance — Imperial, LSE, Cambridge, NUS

Cambridge + Oxford + MIT + Caltech + Stanford + Berkeley — IB Math AA HL is the minimum entry requirement for STEM. A 7 + IA 7 is the only path that beats domestic A-Level applicants in pooled admissions.

Conclusion

IB Math AA HL is a 12-module, 3-paper, IA-intensive program where 88%+ is a 7. The AI tutor maps every question to one of 12 modules, scores against 5 IB criteria, isolates the algebra gap vs calculus gap vs geometry gap vs communication gap, and routes to drill sequences. Ship a 7. SHIP: post-203 IB Math AA HL playbook published.

Pair with: IB Physics HL (post-204) + IB Chemistry HL (post-205) + IB Math AI HL + IB Math AA SL + IB Further Mathematics.