IB Mathematics (AA / AI) Tutoring

Need IB Mathematics tutoring? At PY Education, this subject is taught by founder and principal tutor Tinnie. She holds an MSc in Finance and Economics from the London School of Economics (Distinction), first-class honours degrees in Accounting and Finance and in Data Science and Business Analytics from the University of London, and a BBA in Professional Accountancy from CUHK. She teaches mathematics for GCSE / IGCSE, GCE A-Level / IAL (including Further Mathematics), IBDP and AP.

This page covers the IB Diploma's Analysis and Approaches (AA) and Applications and Interpretation (AI) — four routes across HL and SL — including the HL-only Paper 3 and the exploration written for the Internal Assessment, which is worth a fifth of the grade on all four routes. IB Mathematics is one-to-one private tutoring only, 60 minutes a lesson, in Kwun Tong, online, or in another district (a surcharge applies by district). The first lesson can be a free trial.

AA and AI

Of the four routes, only AA SL and AA HL have a paper on which a calculator is not allowed — Paper 1; every AI paper assumes the candidate has a graphic display calculator in hand. In content, AA puts the weight on algebraic manipulation and proof, while AI puts more of it on statistics, probability and modelling.

A week of AA lessons: the time goes mostly into the hand — simplifying an expression, getting from one line to the next, substituting a trigonometric identity and tidying up what is left; at AA HL there are also the three steps of mathematical induction to write out in full. Practice means the same type of question again with the numbers changed, to see whether the route through the simplification goes astray.

A week of AI lessons: the time goes mostly into the data and the machine — deciding from a set of data which model to use, reading a regression result back as a sentence with units, and repeating it on the graphic display calculator to check the keystroke order. In writing, the assumptions behind the model have to be stated, along with what the result means in the context of the question.

In practice it also depends on which subjects the school offers and how the timetable is arranged. At the trial lesson we look at the student's current level and the school's arrangements together and weigh it up from there; we do not offer a recommendation before we have seen the student's own work.

HL and SL

The difference between HL and SL is written into the teaching hours, the papers and the weightings.

• SL: 150 teaching hours. Paper 1 and Paper 2 are 1 hour 30 minutes each, 40% each.
• HL: 240 teaching hours. Paper 1 and Paper 2 are 2 hours each, 30% each; there is also Paper 3, 1 hour, 20%.
• Internal Assessment: 20% on all four routes — AA, AI, HL and SL. The guide sets aside 30 teaching hours on every route for the toolkit — inquiry, investigation and modelling skills — of which at most 15 hours go to the report itself.

The five topics are the same at HL and SL; HL adds extension content on top of each topic, and Paper 3 is a paper only HL sits. Which university courses ask for HL mathematics, and whether they ask for AA or AI, is set by each institution and each programme and is revised from year to year, so check that programme's own admissions page directly; we list no grades here. HL or SL is likewise left to the trial lesson, once we have looked at the student's papers together.

Syllabus coverage

AA and AI are built from the same five topics, at different depths and weightings.

• Number and algebra
• Functions
• Geometry and trigonometry
• Statistics and probability
• Calculus

HL adds extension content to each of the five topics. The AA HL extensions include mathematical induction, complex numbers, vectors and differential equations; the AI HL extensions include matrices, eigenvalues and eigenvectors, graph theory, and numerical solutions of differential equations.

Paper 1, Paper 2 and Paper 3

No calculator is allowed on AA's Paper 1, at SL and at HL alike, while Paper 2 requires a graphic display calculator. Every AI paper assumes the candidate is using technology — two papers at AI SL, three at AI HL — and the questions are written on the basis that the machine is in hand, so AI practice does not take the calculator away, while AA practice has to keep time aside for working without one.

Paper 3 is sat by HL candidates only: 1 hour, 20%, two long questions. It is not a new topic — it joins several topics together, so that the result of one part is the material for the next. It is practised differently from the other two papers: read the whole question first and mark where it is heading, then work down part by part; if a step comes out wrong along the way, stop and see which of the marks after it can still be earned.

Keystroke order on a graphic display calculator varies by model, and the two common ones are the TI-Nspire and the Casio fx-CG50. Lessons are demonstrated on the student's own machine: regression, distributions, finding intersections and numerical integration are each run through once on the machine the student uses.

How the marks are awarded

An IB markscheme splits the marks into method marks (M), accuracy marks (A) and reasoning marks (R): an M mark is for using the correct method, an A mark for calculating correctly, and an R mark for writing the reason out. So writing out the line that sets up the calculation still stands a chance of earning the M mark, even if the numbers that follow come out wrong.

The markscheme also allows follow through: if an earlier part is answered wrongly, later parts that use that wrong value with a correct method can still earn their marks, provided the later steps are actually written out. And unless a question says otherwise, numerical answers are to be given exactly or to three significant figures — that line of instruction is printed on every IB mathematics paper.

When we mark past papers, we go through them against the IB's published markschemes point by point, and name which step misses the method mark, which step misses the accuracy mark, and which step was simply never written down.

The Internal Assessment: we do not write it

The Internal Assessment is a mathematical exploration on a topic the student chooses, written at school, and it is worth 20% of the final grade on all four routes — AA, AI, HL and SL. The guide sets aside 30 teaching hours on every route for the toolkit — inquiry, investigation and modelling skills — of which at most 15 hours go to the exploration itself. We do not write it, and we do not rewrite a student's draft. What we do is this.

• Choosing the topic. Too broad is the commonest case — "music and mathematics" is not a topic; "using regression to compare how the tempo changes across two pieces of music" is. We start from something the student is actually interested in and narrow it to a question that can be calculated and can reach a conclusion.
• Whether the mathematical depth matches the route. An HL exploration that only uses SL-level mathematics will not score well on Use of mathematics in the criteria; equally, importing a method the student cannot explain earns nothing either, because the criteria ask the student to say what they are doing.
• Structure. How much space goes to the question, the method, the calculations, the results and the reflection, and where the graphs and the equations sit in the text.
• How graphs and calculations are presented. Axis labels, units, significant figures, and which tool produced each result all have to be stated.
• Aligning to the assessment criteria. The five criteria in the current guide are Presentation, Mathematical communication, Personal engagement, Reflection and Use of mathematics; we go through the student's draft criterion by criterion and point out which ones it has not met yet.
• Demonstrating how to revise. We take one section and show how it would be revised, and the student does the rest — the write-up has to be the student's own work, which is an IB academic integrity requirement.

Moving into IB from IGCSE or a local curriculum

Coming up to IB from IGCSE, the gap usually sits in two places. One is calculus: a student who took Additional Mathematics (0606) has already met differentiation and integration, while one who did not starts from limits and the definition of the derivative, and that is the first thing to establish in the opening lessons. The other is fluency in algebraic manipulation — AA HL questions assume that the laws of indices, the laws of logarithms, factorisation and the trigonometric identities are already at the student's fingertips, and test the step that comes after them.

For a student moving across from a local curriculum, the content in fact overlaps a good deal; what takes adjusting is how an answer is written and the English terminology. An IB answer sets the reasoning out — which theorem was used, why this step is allowed — rather than handing over a final number alone. In the opening lessons we take questions the student has already done and go through them line by line: which reasons have to be written out, which can be compressed. We also put together a Chinese–English glossary of the terms that come up most.

Which guide we teach

This page describes the current Analysis and Approaches and Applications and Interpretation subject guides — first taught in 2019, first assessed in 2021. These two subjects replaced Mathematical Studies SL and the former Mathematics SL and Mathematics HL, whose topic lists no longer apply; Further Mathematics HL was discontinued in the same change, with no successor course.

The IB has announced that both subjects are being revised: the new Analysis and Approaches and Applications and Interpretation guides are both released in February 2027, first taught in August 2027, and first assessed in May 2029. The revision reduces content rather than adding new topics. In other words, a student enrolling now and sitting the November 2028 session or earlier sits the current guide in either subject.

What the first four lessons cover

We bill every four lessons, and the first four are scoped like this. Lesson one confirms the route (AA or AI, HL or SL), the school's schedule, and the most recent school test or mock paper — working back from the questions that went wrong to find which of the five topics the break sits in. Lessons two and three deal with that topic itself: if calculus stops at the chain rule and implicit differentiation, for instance, we pick those up together with the laws of indices and the trigonometric identities they rest on. Lesson four uses a timed Paper 1 or Paper 2 question to redo the same question type with the numbers changed, to see whether the break really has been joined up. If the Internal Assessment is already under way, one of the four lessons goes to the topic choice or to the draft.

Lesson arrangements

• 60 minutes a lesson.
• One-to-one private tutoring only; there is no group option for IB Mathematics.
• HK$800 per hour, billed every four lessons, so HK$3,200 for four; the rate is the same for AA and AI, HL and SL.
• Where lessons are held: Kwun Tong, online, or in another district (a surcharge applies by district).
• The first lesson can be a free trial.

The trial lesson starts by confirming whether the student is on AA or AI, HL or SL, then looks at the most recent paper and at where the Internal Assessment stands, and from there we talk through which topic to start with. Nobody is asked to sign up on the spot.