IB Maths AI Notes (SL & HL)

IB Maths AI is a course about using mathematics: building models, reading data, choosing the right test and explaining what an answer means in context. The GDC is allowed on every paper, so the marks go to setting up the problem correctly and interpreting the result. These notes follow the Applications and Interpretation syllabus topic by topic, with SL and HL in one note and HL-only content clearly tagged. Every worked example shows the M1 and A1 marks, every Paper skill comes with GDC steps, and topics leaving the course in May 2029 are flagged.

What every note gives you

• SL and HL in one note. HL-only parts carry an HL ONLY tag, so SL students can skip them.
• GDC steps for every skill, because AI allows the calculator on every paper.
• Marked like the markscheme. Worked examples show the M1, A1 and R1 marks, including the "interpret in context" marks.
• Formula booklet tags, so you know what is given and what you must learn.
• 2029 syllabus status. Topics that leave the course in May 2029 are flagged, so you know what you still need.
• Modelling and IA ideas, because AI rewards real-world thinking.

Notes ready now

1. 1Approximation, standard form and errorsStandard form and calculator E-notation, rounding to decimal places and significant figures, upper and lower bounds of measurements and calculations, estimation, and percentage error, all set in the real contexts IB Maths AI uses.~6 min read · SL
2. 1Sequences and financial mathematicsArithmetic and geometric sequences and series in context, sigma notation, compound interest, depreciation and inflation, and loans, amortisation and annuities with the GDC finance (TVM) solver, plus the sum to infinity for HL.~8 min read · SL + HL
3. 1Exponents, logarithms and equationsLaws of exponents, an introduction to logarithms with base 10 and e, log scales such as pH and decibels, solving systems of linear equations and polynomial equations with the GDC, and for HL: the laws of logarithms and rational exponents.~6 min read · SL + HL
4. 1Complex numbersHL complex numbers for Maths AI: Cartesian form and the Argand diagram, modulus and argument, polar and Euler forms, multiplying and dividing, solving quadratics with complex roots, and adding sinusoidal waves (phasors) with complex numbers.~6 min read · HL
5. 1Matrices and eigenvaluesHL matrices for Maths AI: order, addition and multiplication, the identity and zero matrices, determinants and inverses, solving systems with AX = B, and eigenvalues, eigenvectors, the characteristic polynomial, diagonalisation and powers of a matrix.~6 min read · HL
6. 2Lines, functions and graphsGradients and equations of straight lines, parallel and perpendicular lines, what a function is, domain and range, inverse functions as reflections, and using the GDC to find the key features of a graph: intercepts, maxima, minima, asymptotes and intersections.~6 min read · SL
7. 2Modelling with functionsThe modelling cycle and the families of models IB Maths AI uses: linear and piecewise, quadratic, exponential growth and decay, direct and inverse variation, cubic and sinusoidal models, finding parameters from data, and for HL: logistic, natural logarithm and further piecewise models.~8 min read · SL + HL
8. 2Composites, transformations and linearising dataHL functions for Maths AI: composite functions, inverses with restricted domains, translations, stretches and reflections of graphs, and linearising data with semi-log and log-log graphs to decide between exponential and power models and find their parameters.~7 min read · HL
9. 3Trigonometry, 3D geometry and Voronoi diagrams3D distance, midpoint, volume and surface area, right-angled trigonometry with angles of elevation and depression, the sine and cosine rules, area ½ab sin C, bearings, arcs and sectors in degrees, perpendicular bisectors, and Voronoi diagrams with the toxic waste dump problem.~8 min read · SL
10. 3Radians, vectors and matrix transformationsHL geometry for Maths AI: radians, arcs and sectors, the unit circle and Pythagorean identity, solving trig equations, geometric transformations with 2 × 2 matrices, vectors and the scalar product, vector equations of lines, vector kinematics with closest approach, and the vector product.~8 min read · HL
11. 3Graph theoryHL graph theory for Maths AI: vertices, edges and degrees, simple, complete, weighted and directed graphs, Eulerian and Hamiltonian paths, adjacency matrices and counting walks, minimum spanning trees with Kruskal and Prim, the Chinese postman problem and the travelling salesman problem with upper and lower bounds.~8 min read · HL
12. 4Statistics, correlation and regressionSampling methods and bias, presenting data with histograms, cumulative frequency and box plots, mean, median, quartiles, standard deviation and outliers, scatter diagrams, Pearson’s r, the regression line, Spearman’s rank correlation, and for HL: designing data collection, reliability and validity, and non-linear regression with R².~8 min read · SL + HL
13. 4Probability, binomial and normal distributionsProbability rules, expected numbers of outcomes, Venn, tree and sample space diagrams, conditional probability and independence, discrete random variables and fair games, the binomial distribution, and the normal distribution with inverse normal calculations, all with GDC methods.~6 min read · SL
14. 4Chi-squared and t-testsHypothesis testing for IB Maths AI: null and alternative hypotheses, significance levels and p-values, the χ² test for independence with contingency tables and degrees of freedom, the χ² goodness of fit test, and the two-sample t-test with one- and two-tailed alternatives, all with GDC steps and conclusions in context.~6 min read · SL
15. 4Estimation, Poisson, hypothesis tests and Markov chainsHL statistics for Maths AI: linear combinations of random variables, unbiased estimates, the central limit theorem, confidence intervals for a mean, the Poisson distribution, hypothesis tests with binomial, Poisson and normal distributions, Type I and Type II errors, and Markov chains with transition matrices and steady states.~8 min read · HL
16. 5Differentiation and optimisationThe derivative as a rate of change and a gradient, differentiating axⁿ, increasing and decreasing functions, tangents and normals, stationary points, and optimisation in context, plus for HL: derivatives of sin, cos, tan, eˣ and ln x, the chain, product and quotient rules, related rates and the second derivative.~8 min read · SL + HL
17. 5Integration, areas and kinematicsIntegration as anti-differentiation, boundary conditions, definite integrals and areas with the GDC, the trapezoidal rule for data and functions, and for HL: integrating sin, cos, eˣ and 1/x, integration by inspection, areas between curves and the y-axis, volumes of revolution, and kinematics with displacement and distance.~7 min read · SL + HL
18. 5Differential equations and phase portraitsHL differential equations for Maths AI: setting up models from rates of change, slope fields, separation of variables, Euler’s method for single and coupled equations, coupled linear systems solved with eigenvalues and eigenvectors, phase portraits and their stability, and second-order equations written as systems.~8 min read · HL

Exam special notes

Built from the IB examiners' subject reports: where students actually lose marks, and how to stop it.

1. ★IB Maths AI Grade Boundaries (May 2025 & Nov 2024)Every grade boundary for IB Maths AI from the IB subject reports: May 2025 time zones 1–3 and November 2024, SL and HL, overall and paper by paper, and what it takes to get a 7.~5 min read · Grade boundaries
2. ★IB Maths AI Exam Traps: Mistakes Examiners FlaggedThe mistakes IB examiners flagged in the November 2024 and May 2025 Maths AI subject reports, grouped by topic, each with the fix, plus a last-week checklist.~11 min read · Exam traps
3. ★IB Maths GDC Guide: TI-84 Plus CE and Casio fx-CG50The calculator skills IB examiners say students under-use, with menu paths for the TI-84 Plus CE and the Casio fx-CG50: solving, graphs, calculus, statistics, distributions, finance, tests, matrices and complex numbers.~13 min read · GDC guide
4. ★IB Maths AI Answer Templates: Interpret, Justify, ConcludeFill-in-the-blank model answers for the IB Maths AI questions where examiners say students lose reasoning marks: hypothesis tests, interpreting parameters, regression, comparing data, Voronoi, finance and model limitations.~9 min read · Answer templates
5. ★IB Maths IA Guide: How to Score Highly on the Exploration (AA & AI)A practical guide to the IB Maths exploration for AA and AI, SL and HL: what each criterion rewards, how to choose a topic with enough mathematics, a structure that works and the mistakes moderators flagged in the 2024–25 reports.~8 min read · IA guide
6. ★IB Maths Command Terms and Markscheme Codes (M1, A1, R1, AG, FT)What every IB Maths command term asks for, and how examiners award marks: M1, A1, R1, AG, FT, implied marks, misreads, "hence" vs "hence or otherwise", accuracy and the presentation rules that cost students marks.~9 min read · Command terms & marks
7. ★IB Maths AI Formula Booklet: What Is Given and What to MemoriseWhat the IB Maths AI formula booklet (SL and HL) contains and the facts it leaves out, from Voronoi diagrams, sinusoidal models and outliers to χ² degrees of freedom, eigenvalues and graph theory, plus tips for using it in the exam.~7 min read · Formula booklet guide

Full syllabus map

Practise any topic with full mark schemes in the free IB Paper Generator.

Frequently asked questions