IB maths tutors for AA, AI, SL and HL

The International Baccalaureate Diploma Programme offers Mathematics: Analysis and Approaches (AA) and Mathematics: Applications and Interpretation (AI), each at Standard Level (SL) and Higher Level (HL). Students take one of these four options. Tell a prospective tutor the full course name and your examination session.

Both routes include number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. HL extends the breadth and depth of study. Choose support for the mathematical demands of your course, including its additional HL content where relevant.

A learner may know how to differentiate but stop before answering the question. This constructed SL example shows the missing reasoning. A derivative describes a curve’s slope; a stationary point has slope zero.

For f(x) = x³ − 3x, differentiating gives f′(x) = 3x² − 3. Setting this equal to zero gives x = −1 and x = 1. These are candidates for a maximum or minimum; solving that equation alone has not classified them.

The derivative is positive when x < −1, negative between −1 and 1, and positive when x > 1. The curve therefore rises, falls, then rises again. At x = −1 the slope changes from positive to negative, giving a local maximum of f(−1) = 2. At x = 1 it changes from negative to positive, giving a local minimum of f(1) = −2. A complete answer identifies the points (−1, 2) and (1, −2) and explains those sign changes.

A useful follow-up is f(x) = x³. Its derivative, 3x², is zero at x = 0 but stays positive on either side. The horizontal tangent is not a turning point. Explaining this difference shows more understanding than repeating the first calculation.

At AA HL, a further calculus task is integration by parts. For the constructed integral ∫ x e^x dx, choose u = x and dv = e^x dx, so du = dx and v = e^x. Then ∫ x e^x dx = x e^x − ∫ e^x dx = (x − 1)e^x + C, where C is a constant. Stopping at x e^x misses the subtraction: differentiating it gives e^x + x e^x. Differentiating the complete answer cancels that extra term. That check is a practical habit to build into HL working.

Consider a constructed example in which a culture has masses of 20 g, 30 g and 45 g on days 0, 1 and 2. The increases are 10 g and 15 g, so a fixed increase of 10 g per day does not describe all three values. The ratios are both 1.5, suggesting 50% growth per day.

An exponential model is N(t) = 20 × 1.5^t, where t is time in days and N(t) is mass in grams. It predicts N(3) = 20 × 1.5³ = 67.5 g. This is a prediction for day 3, not another measured value. It assumes that the same proportional growth continues. Three measurements do not establish that the culture can keep growing at that rate indefinitely.

Useful AI working explains the starting mass, growth factor and units alongside the calculator result. A follow-up task is to plot the measurements and the model together, then explain what an additional measurement would tell you about the model’s suitability.

At AI HL, logistic models introduce a growth limit. Take a separate illustrative model, L(t) = 100 / (1 + 4e^(−0.5t)), again measuring mass in grams and time in days. At t = 0 it gives 100 / 5 = 20 g. As time increases, the exponential term tends to zero, so L(t) approaches 100 g. That is the model’s carrying capacity, or limiting mass. Sharing the first measurement does not establish that this second model fits the original data; its other predictions would also need checking.

The details below are checked against the 2026 examination sessions. In all four courses, the mathematical exploration contributes 20% and the written papers together contribute 80%. For a learner sitting in 2027 or 2028, confirm their session instructions with the school before setting timed practice.

For AA, practise presenting methods by hand as well as working with technology. For AI, make calculator practice part of explaining a model or statistical result: a screen output still needs a mathematical interpretation.

The revised AA and AI courses begin teaching in August/September 2027, with first assessment in May 2029. For those new courses, HL Paper 3 is 60 minutes and still contributes 20%. The exploration also has revised assessment criteria shared by SL and HL.

Match textbooks, specimen papers and exploration guidance to the learner’s examination course. A page or resource labelled “new IB maths” may describe the 2029 course rather than the one the learner is currently studying.

The mathematical exploration, often called the maths IA, must remain the student’s own work. Support can focus on understanding an underlying technique through separate practice questions, such as interpreting a growth parameter or checking an integral. The student’s submitted calculations, reasoning and writing must reflect their own effort.

Before seeking help on an assessed draft, check the permitted scope with the school teacher. The IB’s allowance for a teacher to advise on one draft does not give a private tutor the same feedback permission. A request to write the analysis, repair the calculations for submission or rewrite the conclusion would cross that boundary.

Keep the school’s exploration brief, assessment criteria and internal deadlines together. These give the learner a clearer starting point for planning independent work than collecting finished explorations to imitate.