Free Sample Lessons

Free IB Math Sample Lesson — Diagnostic Assessment Before You Commit

Before any student starts paid tutoring with me, I offer a free diagnostic assessment. This is not a marketing session — it is a real piece of work that tells me exactly where to begin and tells you exactly what your child needs help with. No obligation, no commitment to a package, no pressure.

What the Free Diagnostic Involves

When a family contacts me, the first thing I send is a short set of past-paper questions — typically 15 to 20 minutes of work — tailored to the student’s course and year group. These questions are chosen to cover the topics where IB Math students most commonly lose marks: the areas where a gap in understanding will cost marks across multiple question types in the real exam.

The student completes the questions and sends them back. I mark them against the IB mark scheme and identify:

  • Which topics have solid understanding and which have gaps
  • Whether the errors are conceptual (the student does not understand the topic) or procedural (the student understands the topic but makes technique errors under time pressure)
  • Which topics to prioritise in the first four to six lessons
  • A realistic grade trajectory given the current level and the time before exams

This diagnostic is the starting point for every student I work with. It means the first paid lesson is immediately targeted at the highest-priority gap — not spent on a general overview of what the course covers.

Diagnostics by Course

I tailor the diagnostic questions to the student’s course. Here is what each diagnostic focuses on:

AA HL Diagnostic

For Analysis & Approaches HL students the diagnostic covers: integration (the most common source of lost marks on Paper 1), complex numbers (where gaps often emerge in Year 12), and functions (graph sketching and inverse functions). These three areas together account for a large proportion of Paper 1 and Paper 2 marks at HL.

AA SL Diagnostic

For Analysis & Approaches SL students the diagnostic covers: calculus (differentiation and integration), probability (tree diagrams and conditional probability), and trigonometry (the unit circle and solving trig equations). These are the topics where AA SL students most often have gaps that are not visible in classroom performance but emerge under exam conditions.

AI HL Diagnostic

For Applications & Interpretation HL students the diagnostic covers: hypothesis testing (stating H₀ and H₁, interpreting the p-value correctly), Markov chains (setting up transition matrices), and regression (choosing and justifying the correct regression model). These topics appear frequently in Papers 2 and 3 and require both GDC skill and written interpretation.

AI SL Diagnostic

For Applications & Interpretation SL students the diagnostic covers: financial mathematics (compound interest, loan repayments), hypothesis testing at SL level (chi-squared and t-tests on the GDC), and geometry and trigonometry (surface area, volume, and triangle problems). These are the areas where AI SL students most frequently underperform in May and November exams.

What Happens After the Diagnostic

After I review the diagnostic, I send the family a short summary of what I found and what I recommend. This typically includes:

  • The two or three topic areas to prioritise immediately
  • Whether the student needs regular ongoing sessions or intensive exam preparation
  • Which tutoring package I would recommend given the time before exams and the gap between the current level and the target grade
  • A suggested schedule for the first block of lessons

At this point the family decides whether to proceed. There is no obligation and no pressure. Many families have the diagnostic done two or three months before exams to understand where things stand, then book lessons when the schedule allows.

What the Free Sample Lesson Includes

For some students, rather than (or in addition to) the diagnostic, I offer a free 20-minute introductory session — either online or in person — where we work through one of the diagnostic questions together. This gives the student a sense of how I teach and whether my approach suits the way they learn.

In this session I typically work through one multi-step past-paper question from the student’s course, showing exactly how to read the question, identify the relevant techniques, set out the working to earn method marks, and check the answer. This 20 minutes is more useful than any amount of reading about my tutoring approach — it shows directly whether the student responds well to how I explain things.

How to Request a Free Diagnostic

To request a free diagnostic, contact me via WhatsApp with your child’s:

  • Current year group (Year 12 or 13)
  • IB Math course (AA HL, AA SL, AI HL, or AI SL)
  • Current predicted or actual grade
  • The date of their IB exams (May or November session)

I will send the diagnostic questions within 24 hours. Once I have the student’s responses, I will send my assessment within 48 hours.

You can also browse the free resources on this site while you decide: the question banks, past papers, formula booklets, exam tips, and mock exams are all available without booking a session. These resources alone give a good indication of the level of specificity and structure I bring to IB Math preparation. Contact me to request your free diagnostic →