IB Math Applications

What this covers

• Fitting and interpreting models: linear, quadratic, exponential, sinusoidal, logistic (HL) and piecewise — including what each parameter means in context and when a model stops being reasonable
• Statistics with the GDC: regression lines and r, Pearson's and Spearman's, chi-squared tests for independence and goodness of fit, t-tests, and stating hypotheses, p-values and conclusions in the wording IB expects
• Financial mathematics: compound interest with varying compounding periods, annuities and amortisation using the TVM solver, real vs nominal rates, depreciation
• Geometry and trigonometry in applied settings: 3D solids, bearings, non-right triangles, and Voronoi diagrams with nearest-neighbour and toxic-waste-dump problems
• Calculus for modelling: rates of change in context, optimisation, trapezoidal rule, and (HL) Euler's method, differential equations, slope fields and phase portraits
• HL extension topics: matrices and transformations, eigenvalues in Markov chains and coupled systems, graph theory including adjacency matrices and the Chinese postman and travelling salesman problems, complex numbers in AC circuits
• Exploration (IA) support: narrowing a question, sourcing real data, choosing mathematics at the right level, and meeting the reflection and communication criteria

Where learners get stuck

Doing everything by hand as if this were Analysis and Approaches

Students who transferred from AA, or who are taught alongside AA classmates, often solve equations algebraically and lose time, or give an exact surd when the mark scheme wants three significant figures from the calculator. AI rewards the efficient GDC route plus a clear statement of what was entered.

Confusing r, r² and causation, and quoting a strong correlation as proof of a relationship

The syllabus deliberately tests interpretation. Students read r = 0.92 as 'the model is correct', extrapolate far outside the data range, or describe r² as the correlation. The fix is a habit of stating strength, direction, and the limits of the data every time.

Running chi-squared tests mechanically without checking the setup

The calculator produces a p-value regardless, so students miss the degrees of freedom calculation, forget expected frequencies below 5 are a problem, or write 'we accept H0' instead of 'there is insufficient evidence to reject H0'. Marks are lost on the framing, not the arithmetic.

Sign conventions in the TVM solver

Money paid out and money received need opposite signs, and payments per year versus compounding periods per year are separate fields. A single wrong entry gives a plausible-looking loan repayment that is completely wrong, and students rarely sanity-check the magnitude.

What a session looks like

A typical session starts with you saying what topic or past-paper question is causing trouble. Evelyn talks through the modelling decision or statistical procedure step by step, asking you to say what you would enter into the calculator and why, then pushing on the interpretation sentence — what the gradient means in the context, what the p-value lets you conclude. Where a question has a diagram, network or data table, you can describe it or read the values aloud. Sessions can also be spent stress-testing an Exploration idea: whether the data is obtainable, whether the mathematics is HL or SL appropriate, and where the personal engagement and reflection marks come from.

Helpful to know first

• MYP mathematics or IGCSE/GCSE-level algebra: rearranging formulae, solving linear and quadratic equations, working with percentages
• Right-angled trigonometry and Pythagoras, plus basic area and volume formulae
• Familiarity with your own GDC (TI-84 Plus CE, TI-Nspire or Casio fx-CG50) — knowing where the statistics and graphing menus are
• For HL, comfort with SL content, since HL papers assume it throughout

Questions

What is the difference between IB Maths AI and AA?

Applications and Interpretation is built around modelling real contexts and statistics, with a calculator allowed on every paper. Analysis and Approaches is more algebraic and proof-oriented, with a non-calculator Paper 1. AI HL includes matrices, graph theory and complex numbers applied to circuits; AA HL includes more calculus techniques and proof. Universities sometimes prefer AA for engineering or maths degrees, so check course requirements.

Is AI HL actually harder than AA SL?

They are different rather than simply ordered. AI HL covers more content and includes Paper 3, a two-question extended investigation, but the algebraic demand per question is usually lower than AA HL. Students moving from AA SL to AI HL often find the volume of new topics, especially graph theory and eigenvalues, the bigger adjustment.

Can Evelyn help with the Mathematical Exploration?

Yes, for discussing scope, choosing suitable mathematics, checking that your data source and method are sound, and understanding the assessment criteria. The written work must be your own — sessions are for talking the ideas through, not producing text for you to submit.

My child keeps getting the right number but losing marks. Why?

On AI papers a large share of marks sit in interpretation and communication: stating hypotheses properly, giving units, rounding to three significant figures unless told otherwise, and explaining what a result means for the context. Sessions spend deliberate time on the sentence that follows the answer.

Which calculator topics come up most?

Regression and correlation, chi-squared and t-tests, the TVM solver for finance, numerical solving of equations, and finding maxima, minima and areas from graphs. Knowing the exact key sequence on your own model saves several minutes per paper.