IB Mathematics: AI
Your modern toolkit for mastering IB Math Applications & Interpretation — clear study guides, interactive tools, and topic-by-topic resources for SL and HL.
Topic 1 · Number & Algebra
Core skills: rounding, sequences, finance, complex numbers, matrices, systems.
Number Skills
Approximation, rounding, decimals, significant figures, scientific notation, errors.
Sequences & Series
Arithmetic & geometric sequences, sums, infinite series, sigma notation.
Financial Mathematics
Compound interest, loans, depreciation, annuities, finance calculator.
Complex Numbers
Cartesian, polar form, powers, Argand diagrams, applications.
Matrices
Operations, determinants, identity/inverse, systems, eigenvalues.
Systems of Linear Equations
Simultaneous, quadratic, cubic equations, applications.
Topic 2 · Functions
Function forms, applications, properties, transformations.
Linear Equations & Graphs
Forms of lines, gradients, intercepts, perpendicular bisector, parallel lines.
Applications of Functions
Linear, exponential, sinusoidal, logistic, piecewise, direct/inverse variation.
Properties of Functions
Domain & range, finding/interpreting composite & inverse functions.
Transformations
Translations, reflections, stretches with scale factors, composite transformations.
Topic 3 · Geometry & Trigonometry
3D geometry, trigonometry, diagrams, vectors, transformations, graph theory.
Geometry of 3D Shapes
Surface area, volume, spheres, cones, prisms, pyramids.
Trigonometry
Triangles, sine/cosine rule, arcs/sectors, radians, non-right triangles.
Voronoi Diagrams
Sites, edges, vertices, interpolation, bisectors, applications.
Trigonometric Functions
Unit circle, identities, solving trig equations, trig graphs.
Geometric Transformations
Transformation via matrices, reflections, stretches, rotations, translations.
Vectors
Vector equations, product, angle between, kinematics applications.
Graph Theory
Walk/trail, Euler/Hamilton graphs, Chinese Postman, Traveling Salesman.
Topic 4 · Statistics & Probability
Statistics, regression, probability, distributions, hypothesis testing, estimation.
Descriptive Statistics
Mean, median, mode, IQR, histograms, box plots, cumulative frequency.
Bivariate Statistics
Scatter plots, correlation, regression, coefficient of determination.
Probability
Tree/Venn/sample space diagrams, Markov chains, transition matrices.
Distributions
Binomial, normal, Poisson, combinations of random variables.
Hypothesis Testing
Significance levels, p-values, critical values, chi-square, t-tests, Type I/II errors.
Estimation & Confidence Intervals
Data reliability, central limit theorem, confidence intervals.
Topic 5 · Calculus
Differentiation, integration, kinematics, differential equations.
Differentiation
Product/chain/quotient rules, tangents/normals, optimization, related rates.
Integration
Antidifferentiation, areas, trapezoidal rule, substitution, volumes of revolution.
Kinematics
Displacement, velocity, acceleration, graphs, total distance traveled.
Differential Equations
Slope fields, separable equations, Euler’s method, phase portraits.
About this Course:
IB Mathematics: Applications & Interpretation (AI) emphasizes mathematical modeling, real-world data, and practical applications. Both SL and HL develop skills in technology integration and mathematical communication, preparing students for diverse pathways.
This toolkit makes revision and exam practice efficient. Each card links to a focused guide for concept mastery and study strategies.
Useful Tools & Schedules
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May 2026 IB Exam Schedule
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