IB Maths tuition, AA and AI at SL and HL

Specialist one-to-one support for students who want to understand the mathematics clearly, work accurately under pressure and turn what they know into marks. I teach all four routes: Analysis and Approaches (AA) and Applications and Interpretation (AI), each at Standard and Higher Level. Available online internationally and in person in London.

Supporting students in the UK, Switzerland, the UAE and internationally.

Analysis and Approaches or Applications and Interpretation?

Course choice is usually made before the Diploma Programme begins, taking account of prior attainment, school guidance, timetable constraints and university plans. For tuition, the key is to understand the demands of the student’s chosen route.

Analysis and Approaches (AA)

AA is the more algebraic and analytical of the two. Its strongest emphasis falls on functions, algebra and calculus, and it asks for exact algebraic work, proof and formal mathematical reasoning. Students are expected to construct and justify an argument, not only to produce an answer. Real contexts appear, but the character of the course is abstract.

AA is also the only route with a non-calculator paper. Paper 1 is sat without technology at both Standard and Higher Level, so students must be able to carry out procedures by hand and work confidently with fractions, surds, logarithms, π and exact trigonometric values. That single fact shapes much of how I prepare AA students.

Applications and Interpretation (AI)

AI is the more applied and contextual course. Statistics, modelling and the use of technology carry greater weight, data interpretation is far more prominent, and the mathematics is consistently set in real situations. Formal algebraic manipulation matters less. Deciding which model suits a situation, and explaining what a result means, matters more.

Technology is central to AI rather than supplementary. Every paper requires a graphic display calculator, at both levels. Students need real fluency with it, covering regression, distributions, graphing, numerical solutions and statistical tests, along with the judgement to recognise that calculator output is not yet an answer until it has been interpreted and evaluated.

My lessons are tailored to each student’s needs—whether that means revisiting foundations, explaining a full topic, tackling difficult questions or practising topic-based past-paper problems. Teaching also reflects the course: AA places greater emphasis on algebraic development and mathematical reasoning, while AI focuses more on modelling, calculator use and interpretation. Students progress best when the teaching matches both their course and their individual needs.

Official IB Maths resources

A few of the IB’s own pages are worth knowing about. They are the authoritative source on what the courses contain and how they are assessed, and they are more reliable than the summaries that circulate online. Unlike the sciences, mathematics is covered by a single IB course page for both AA and AI.

• IB Mathematics course page — the IB’s own overview of both courses at SL and HL, with the official subject briefs.
• IB sample and specimen exam papers — examples showing the format and style of the current examinations.
• IB educational resources and publishing — the IB’s official publications and resources for schools.
• Follett IB Store — the IB’s official store for guides, exam papers and other materials.
• IB Questionbank — the IB’s official practice-question tool (a paid subscription, with a free demo available).

Official past papers and mark schemes are provided to schools, so your school is usually the best place to ask for them. Where a resource must be purchased, the links above lead to the IB’s own store.

Support with the exploration and the Extended Essay

The exploration is the internally assessed part of every IB Mathematics course, worth 20% of the final grade, and it is a piece of independent mathematical writing rather than a laboratory investigation. Most of the difficulty arrives at the beginning. An initial idea is often too broad to finish, too narrow to develop, or not mathematical enough to be assessed, and students who keep changing direction lose weeks they cannot recover. I help a student settle on a question early and shape it to a scope that can be completed in the time available. The explorations that go best are usually rooted in something real to the student: an intended university course, a career they are moving towards, a family business, a sport or an interest they already understand. The purpose is not only to complete the task. It is to see where the mathematics of the course genuinely applies, and to go further into its theoretical basis than the syllabus itself goes.

Selecting mathematics at the right level is the next difficulty. It should sit at or a little beyond the level of the course, and it should be developed rather than quoted. The exploration needs a clear aim and a line of reasoning that holds from beginning to end, and a common weakness is work that computes without explaining, where results appear but the thinking behind them does not. AA students sometimes lean on calculator or software output where analytical development and justification are wanted. AI students can use technology more extensively, but they still have to explain the method, interpret the output and evaluate the model rather than reproduce what the screen showed. Notation should be correct and consistent throughout.

Personal engagement is widely misunderstood. It is not demonstrated by choosing a topic the student happens to find interesting. It is shown in the decisions they make: testing a prediction, adapting a method when it does not work, considering an alternative approach, and allowing their own choices to shape the direction of the work. It also asks for critical reflection on results, assumptions and limitations as the exploration develops, rather than saved up for the conclusion.

Referencing matters more than students expect. Data sources, formulae, methods, graphs, diagrams, images and ideas all need to be acknowledged clearly and consistently. Students often overlook this because the work is mathematical rather than written, but weak referencing raises questions about authenticity, and those questions are entirely avoidable.

The same applies to the Extended Essay in mathematics, where the demands are similar and the scale is larger. I mentor: helping a student find a workable question, plan the structure, choose and develop appropriate mathematics, and sustain a coherent argument across a much longer piece of writing. All of this support stays within the IB’s academic integrity requirements. I help a student think more clearly and improve their own work. I do not write any part of a submission for them, and there is good reason for that: the understanding a student builds by doing this work themselves is exactly what the examination will test.

Urgent one-off session

Occasionally a student needs help immediately rather than as part of ongoing tuition. If that is your situation, I keep limited availability for single sessions.