IB Math Analysis

What this covers

• Paper 1 exact-value technique: surds, exact trig values from the unit circle, logarithm and exponent laws, and rationalising rather than reaching for a decimal
• Proof methods on the AA syllabus — direct proof, proof by mathematical induction for sums, divisibility and derivatives, and (HL) proof by contradiction and counterexample
• Sequences, series, the binomial theorem with fractional and negative indices (HL), and sigma-notation manipulation
• Functions and transformations: composite and inverse functions, domain restrictions, rational functions and their asymptotes, and the graph relationships between f(x), f'(x) and 1/f(x)
• Calculus in AA style: implicit differentiation, related rates, optimisation with justification, integration by substitution and by parts (HL), volumes of revolution, and separable differential equations
• HL-only strands: complex numbers in Cartesian, modulus-argument and Euler form with De Moivre's theorem; vectors, lines and planes in three dimensions; Maclaurin series and l'Hôpital's rule
• Reading the command terms — 'show that', 'hence', 'justify', 'find the exact value' — and writing enough working to earn method marks

Where learners get stuck

Writing an induction proof that never uses the inductive hypothesis

Students learn the ritual (base case, assume n = k, prove n = k + 1) before they see that the whole point is substituting the assumed statement into the k + 1 expression. The result is a proof that quietly assumes what it is trying to show, which loses most of the marks even when the algebra is correct.

Losing the dy/dx factor in implicit differentiation and related rates

Two years of differentiating y = f(x) trains the hand to write 2y for the derivative of y². Once y is an unknown function of x or of t, every y-term needs a chain-rule factor, and the omission is invisible to the student because the resulting equation still looks solvable.

Treating Paper 1 as Paper 2 without a calculator

Practice at home is usually done with a GDC in reach, so exact trig values, log laws and surd arithmetic never become automatic. Under exam conditions this shows up as decimal answers where an exact form was required, or as a stall at the first line of an otherwise routine question.

Confusing the argument of a complex number with arctan(b/a) (HL)

The calculator's inverse tangent only returns angles in two quadrants, so points in the second and third quadrants come out with the wrong argument — and the error then propagates through every De Moivre or Euler-form calculation built on it.

What a session looks like

You bring a question — a past-paper item, a textbook exercise, a topic you did not follow in class — and talk through it aloud. Evelyn Tutor asks what you have tried, works from your line of reasoning rather than restarting, and stops at the step where the mistake actually occurred. For proof and 'show that' questions it will ask you to state the argument in words before writing it, since that is where AA marks are won or lost. Sessions can be aimed at SL or HL, and at Paper 1 or Paper 2 conditions.

Helpful to know first

• Comfort with IGCSE / MYP-level algebra: expanding, factorising, solving quadratics and rearranging formulae
• Right-angled and non-right-angled trigonometry, and familiarity with radian measure
• Index and logarithm laws, and function notation including f(g(x)) and f⁻¹(x)
• For HL calculus and complex number work, a first course in differentiation and integration of polynomials, trigonometric and exponential functions
• Access to a graphic display calculator (TI-84, TI-Nspire or Casio fx-CG) for Paper 2 style work

Questions

What is the difference between IB Math AA and AI, and which one does this cover?

This topic covers Analysis and Approaches (AA), the course built around algebraic technique, calculus and formal proof. Applications and Interpretation (AI) is a separate topic and leans towards modelling, statistics and technology-based methods. If your school report or timetable says 'AA SL' or 'AA HL', this is the right one.

Can it help with Higher Level topics like complex numbers and vectors?

Yes. HL-only content — De Moivre's theorem, Euler form, vector equations of lines and planes, Maclaurin series, integration by parts and l'Hôpital's rule — is included, and you can say at the start of a session whether you are working at SL or HL so the level of the examples matches.

Will it write or check my Internal Assessment exploration?

It will not write any part of it. It can talk through whether a topic idea has enough mathematics in it for the criteria, explain a technique you want to use, and help you understand the assessment criteria — but the exploration must be your own work, and IB academic honesty rules apply to any AI assistance.

My child can do the questions with a calculator but freezes on Paper 1. Can this help?

Yes, and it is a common pattern. Sessions can be run in non-calculator mode, where the tutor insists on exact forms and works on the specific gaps — unit-circle values, log manipulation, surd arithmetic — that make Paper 1 feel harder than it is.