Course hub · Mathematics: Applications and Interpretation HL

IB Maths AI HL: free cheatsheets, paper analysis and study guides

Everything for IB Maths AI HL in one place: a free cheatsheet for each of the 26 topics, the marks-weighted analysis of every recent paper, the guidebook, IA help and predicted papers.

  • 26 topics
  • 3 exam papers
  • IA worth 20%
  • Free to read

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Free26 topic cheatsheetsEvery formula, method and common trap. FreePast-paper analysisWhere the marks have gone since 2021. GuidebookIB Maths AI HL e-bookEvery question type, with a free chapter. IA helpMaths IA guideCriteria in plain words, ideas and outlines. Set 1 freePredicted papersFull papers with markschemes.

All 26 IB Maths AI HL topics

Grouped by theme. Each one opens its free cheatsheet.

Number & Algebra

The largest AI HL theme — sequences and financial maths through matrices, Markov chains and complex numbers. The AHL matrix and eigenvalue work is Paper 3 gold.

Topic 01Sequences & SeriesArithmetic & geometric sequences and series, sum to infinity, sigma notation, and growth problems on the GDC.Topic 02Exponents & LogarithmsIndex laws, fractional & negative indices, exponential equations, logarithms, change of base and log scales.Topic 03Loans & AnnuitiesCompound interest, depreciation, annuities, loan repayments and amortisation with the GDC finance solver.Topic 04Approximation & ErrorRounding, significant figures, standard form, percentage error, and upper & lower bounds.Topic 05MatricesMatrix arithmetic, products, determinants, inverses and solving AX=B — all on the GDC.Topic 06Eigenvalues & Markov ChainsEigenvalues & eigenvectors, transition matrices, n-step states and long-run steady states.Topic 07Complex NumbersCartesian, polar & Euler forms, modulus-argument, De Moivre, roots, AC phasors and complex eigenvalues.

Functions

Function notation, domain and range, and the modelling toolkit: fitting and using linear, exponential and power models.

Topic 08FunctionsDomain & range, composite & inverse functions, and quadratic, exponential and piecewise models.Topic 09Non-Linear ModellingFitting linear, exponential and power models, r and R², and using a model to predict.

Geometry & Trigonometry

Trigonometry and its graphs, Voronoi diagrams, vectors, graph theory and matrix transformations — the most application-heavy, 'AI-flavoured' theme.

Topic 10TrigonometrySOHCAHTOA, the sine & cosine rules, area, sectors, bearings and 3-D trigonometry.Topic 11Trigonometric GraphsAmplitude, period and phase of sinusoidal models — tides, Ferris wheels — and solving in a range.Topic 12Voronoi DiagramsPerpendicular bisectors, nearest-site regions, Voronoi vertices and the toxic-waste-dump problem.Topic 13VectorsMagnitude, unit vectors, the dot product & angle, vector lines and particles that meet.Topic 14Graph TheoryAdjacency matrices, walks via matrix powers, spanning trees, Dijkstra and the travelling-salesman problem.Topic 15Affine Transformations2×2 matrix transformations, enlargements, rotations, reflections, area factor |det| and compositions.

Statistics & Probability

The heart of AI — summarising data, correlation and regression, probability, distributions, confidence intervals and hypothesis testing, all on the GDC.

Topic 16Univariate StatisticsCentral tendency & spread from the GDC, grouped data, outlier fences, box plots and ogives.Topic 17Bivariate StatisticsScatter diagrams, correlation r, R², the least-squares regression line and prediction.Topic 18ProbabilitySample spaces, complements, unions, independence, two-way tables, tree diagrams and Bayes.Topic 19Probability DistributionsExpected value, the binomial and normal distributions, inverse normal and Poisson.Topic 20Confidence IntervalsStandard error, margin of error, confidence-interval limits, width and required sample size.Topic 21Hypothesis Testingχ² tests, expected frequencies, degrees of freedom, t-tests and the decision rule.

Calculus

Differentiation and integration for real-world optimisation and kinematics, plus differential equations and coupled systems on Paper 3.

Topic 22DifferentiationThe power rule, tangents & normals, stationary points and applied optimisation on the GDC.Topic 23IntegrationReverse power rule, definite integrals, area under a curve, the trapezoidal rule and kinematics.Topic 24Kinematics & ProjectilesDisplacement, velocity & acceleration by calculus, at-rest points and projectile motion.Topic 25Differential EquationsExponential & Newton-cooling models, separable DEs and Euler's method.Topic 26Coupled Differential EquationsTrace–determinant phase behaviour, eigenvalue portraits, Euler on systems and second-order reduction.

The exam

How IB Maths AI HL is assessed

  • Paper 1 Calculator allowed. Shorter questions across the course.
  • Paper 2 Calculator allowed. Longer, structured questions.
  • Paper 3 Calculator allowed. Two extended modelling and problem-solving questions (HL only).
  • Internal assessment 20% of the grade. Read the IA guide.

See how the marks are spread across topics in recent papers.

The guidebook

Mathematics Applications and Interpretation HL for the IB Diploma

Two volumes and 24 chapters for the full Higher Level course, with Paper 3 modelling and exam technique.

See the book

HL Paper 3 guidebook · Free sample chapters

IB Maths AI HL questions

How many topics are in IB Maths AI HL?

This hub covers 26 topics, grouped into the course's five themes. Each has its own free cheatsheet.

Which papers do IB Maths AI HL students sit?

Paper 1: Calculator allowed. Shorter questions across the course. Paper 2: Calculator allowed. Longer, structured questions. Paper 3: Calculator allowed. Two extended modelling and problem-solving questions (HL only). The internal assessment makes up the rest of the grade.

Is the formula booklet allowed in every paper?

Yes, the IB provides its formula booklet in every maths paper. Each cheatsheet flags the results that are not in it and must be learned.

Are the cheatsheets free?

Yes, every cheatsheet and the paper analysis are free to read without signing in.

Who writes these pages?

Ejaz Ahmad and the Photon Academy team, IB teachers since 2015. Every example and question is original.

In Singapore?

Learn IB Maths AI HL live

The same teachers run small classes in Singapore. See live classes at Photon Academy in Singapore.