IB Math — Analysis and Approaches HL
IB Math AA HL tutor for the most demanding course in the Diploma
Renzo Diaz is an IB Math AA HL tutor working one-to-one, online, from Milan with students worldwide. Application-only. He helps HL students move from surviving the pace to actually commanding it — proof, Paper 3, the HL Exploration — with diagnosis-first tuition built around their own wrong answers.
AA HL is the point where IB mathematics stops rewarding execution and starts demanding proof. Your child can follow every worked example in class and still freeze when Paper 3 hands them an unfamiliar three-page scaffold. That is not a knowledge gap, and more explanation will not close it. It is a reasoning gap — and it has an exact location.
That is how I work as an AA HL tutor online. Every week opens with the questions you got wrong last week — not a fresh topic, not a lecture. We locate where your argument collapsed: an unproven claim in an induction step, a substitution chosen because it was the only one you knew, a vector problem set up in the wrong plane. Then we rebuild that step until it holds under exam conditions. This page covers AA HL; the other three courses sit under IB Math tutoring. I am based in Milan and teach students worldwide, one-to-one, on application. If that sounds like what HL actually requires, read on.
The IGCSE-to-HL gap: top of the class before, surviving rather than learning now.
HL hits with pace and depth at the same time. The syllabus does not pause for consolidation — one week is further calculus, the next is complex numbers. Students who cruised through prior courses by being fast find that speed no longer compensates, because HL questions resist the obvious first method. The diagnosis is usually not "weak at maths" but "no selection layer": you have many procedures and no way to choose between them under time pressure.
Proof and "show that" questions: they feel like a different subject entirely.
AA HL is the first course where you must build an argument rather than execute one. Proof by induction, proof by contradiction, the careful "show that" derivations in Paper 1 — these are marks awarded for the structure of your reasoning, not the final line. Many strong students lose their first HL marks here because nobody has ever taught them what a valid argument is. We work on it directly: claim, justification, conclusion, in that order, until it becomes reflex.
Paper 3: the unseen-problem paper that undoes you.
The HL-only paper is two extended problems built on unfamiliar scaffolding — notation you have never seen, a guided investigation that later asks you to leave the scaffolding behind. Students who are excellent at Papers 1 and 2 still freeze in Paper 3 because they trained on recognisable question types, and Paper 3 is designed to have none. Preparing for it means practising reasoning with a GDC inside unfamiliar structures, not memorising more types. See the FAQ below for what makes it different.
The university-requirement doubt: you chose HL for it, and now you're not sure.
Maths, physics, engineering and economics at competitive universities frequently require or strongly prefer AA HL. Some students take it for the transcript rather than the love of the subject, then find DP1 brutal. That is a legitimate position — but the answer is rarely to drop mid-course. It is to make HL tractable: identify which of the five syllabus strands is actually losing you marks, and repair that one first. If you are genuinely weighing SL against HL, the intake conversation is the right place to decide it properly. If your real choice is between AA HL and AI HL, that comparison deserves its own page — and if AI at Standard Level is genuinely on the table too, it belongs in the same conversation, not a separate one later.
The HL Exploration: stalled, with no clear way to restart it.
The Mathematical Exploration is worth 20% of the final grade, and HL markers expect mathematics commensurate with the course — differential equations, advanced trigonometric modelling, complex analysis applied to something real. Most stalled explorations share one problem: a topic chosen for the title, not for the maths it contains. IB AA HL IA help here means stress-testing your topic and your level of mathematics before you write, not editing a draft at the end.
Coverage
The full AA HL syllabus, taught to HL depth
I am an IB maths Analysis and Approaches HL tutor, not a generalist. Every topic below is taught at HL depth — meaning not just how to perform the method, but when to select it and how to justify the choice, because that is where HL marks live. Coverage follows the current syllabus (first assessment 2021), across all three papers and the internal assessment. The syllabus itself is published on the IB's mathematics courses page.
- Proof and reasoning: proof by induction across all four classic forms (sum identities, divisibility, inequalities, general induction), contradiction and counterexample; the logic behind every "show that" mark in Paper 1
- Functions and trigonometry at HL depth: composite and inverse functions, transformations, reciprocal and inverse trig functions, compound-angle identities and their use in integration
- Complex numbers: modulus–argument form, de Moivre's theorem, roots of unity, polynomial roots and the conjugate root theorem, geometric interpretation in the Argand plane
- Vectors in three dimensions: scalar and vector product, equations of lines and planes in 3D, intersections and angles — the single most mismarked HL topic
- Further calculus: implicit and parametric differentiation, L'Hôpital's rule, integration by parts and by substitution (including the judgement of which to reach for), separation of variables and integrating factors for differential equations, and Maclaurin series with their radius of convergence
- Counting, probability and distributions: permutations and combinations, Bayes' theorem, normal and binomial distributions, and HL-only continuous probability density functions
- Paper-specific preparation: Paper 1 without a calculator (exact values, algebraic stamina), Paper 2 with the GDC (using it to check, not to think), and Paper 3's two extended, multi-part problems (30 minutes each, later parts building on earlier ones)
- The HL Mathematical Exploration: topic selection at genuine HL level, structure, and the mathematical communication criteria that decide the top bands
The method
Diagnosis first. Then a fixed weekly rhythm.
Before any teaching plan, I diagnose the exact step where your reasoning breaks — in a proof, in a Paper 3 part (c), in a calculus set-up. Then we work to a fixed weekly rhythm: every session opens with last week's wrong answers, because a mistake that is not revisited is a mistake you will repeat in May. Sessions run on Zoom with a shared Excalidraw whiteboard, and every session is recorded, summarised and archived into a searchable library you keep — so by exam season you own a personal archive of every error you ever made and how it was repaired.
Documented, not promised
What AA HL students say after the exams
Yuval Rossen studied IB Maths HL and Physics HL with me from Ireland across the full two-year Diploma. His words from August 2022: "Renzo has been helping me with physics and math throughout the 2-year course of IB… having solved so many past paper questions in our classes and independently, I was very well prepared for both exams." He went on to study applied physics at university — a course for which AA HL-level mathematics is the entry ticket — and chose to continue lessons with me through his degree. The review is public on Google.
Leandro Iñiguez, based in Bulgaria, took IB Physics SL and Maths HL, sat his finals in the May 2022 session, and finished with a 7 in Physics and a 5 in Maths HL — one mark away from a 6. "Having had 1 or 2 classes per week with him helped me to stay on track and feel extremely prepared for my exams to the point where I was quite calm as I went through them." Calm in an AA HL exam hall is not a personality trait. It is what preparation feels like from the inside. Public Google review.
HL does not need more explanation. It needs a diagnosis.
AA HL is the course that decides whether a mathematically capable student gets into the programme they want — and it is unforgiving of vague preparation. If you are surviving rather than commanding it, the next step is a conversation, not a commitment. Two free conversations, a reply within 48 hours, and an honest assessment either way. That is the whole offer.