IB Mathematics

IB Math: Applications & Interpretation

Your modern toolkit for mastering IB Math AI — clear study guides, interactive tools, and topic-by-topic resources for SL and HL.

5 Topics
27 Study Guides
SL+HL Coverage
1

Number & Algebra

Core skills: rounding, sequences, finance, complex numbers, matrices, systems.

Number Skills

Approximation, rounding, decimals, significant figures, scientific notation, errors.

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Sequences & Series

Arithmetic & geometric sequences, sums, infinite series, sigma notation.

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Financial Mathematics

Compound interest, loans, depreciation, annuities, finance calculator.

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Complex Numbers

Cartesian, polar form, powers, Argand diagrams, applications.

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Matrices

Operations, determinants, identity/inverse, systems, eigenvalues.

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Systems of Linear Equations

Simultaneous, quadratic, cubic equations, applications.

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2

Functions

Function forms, applications, properties, transformations.

Linear Equations & Graphs

Forms of lines, gradients, intercepts, perpendicular bisector, parallel lines.

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Applications of Functions

Linear, exponential, sinusoidal, logistic, piecewise, direct/inverse variation.

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Properties of Functions

Domain & range, finding/interpreting composite & inverse functions.

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Transformations

Translations, reflections, stretches with scale factors, composite transformations.

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3

Geometry & Trigonometry

3D geometry, trigonometry, diagrams, vectors, transformations, graph theory.

Geometry of 3D Shapes

Surface area, volume, spheres, cones, prisms, pyramids.

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Trigonometry

Triangles, sine/cosine rule, arcs/sectors, radians, non-right triangles.

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Voronoi Diagrams

Sites, edges, vertices, interpolation, bisectors, applications.

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Trigonometric Functions

Unit circle, identities, solving trig equations, trig graphs.

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Geometric Transformations

Transformation via matrices, reflections, stretches, rotations, translations.

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Vectors

Vector equations, product, angle between, kinematics applications.

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Graph Theory

Walk/trail, Euler/Hamilton graphs, Chinese Postman, Traveling Salesman.

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4

Statistics & Probability

Statistics, regression, probability, distributions, hypothesis testing, estimation.

Descriptive Statistics

Mean, median, mode, IQR, histograms, box plots, cumulative frequency.

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Bivariate Statistics

Scatter plots, correlation, regression, coefficient of determination.

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Probability

Tree/Venn/sample space diagrams, Markov chains, transition matrices.

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Distributions

Binomial, normal, Poisson, combinations of random variables.

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Hypothesis Testing

Significance levels, p-values, critical values, chi-square, t-tests, Type I/II errors.

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Estimation & Confidence Intervals

Data reliability, central limit theorem, confidence intervals.

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5

Calculus

Differentiation, integration, kinematics, differential equations.

Differentiation

Product/chain/quotient rules, tangents/normals, optimization, related rates.

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Integration

Antidifferentiation, areas, trapezoidal rule, substitution, volumes of revolution.

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Kinematics

Displacement, velocity, acceleration, graphs, total distance traveled.

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Differential Equations

Slope fields, separable equations, Euler's method, phase portraits.

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📚 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 in social sciences, natural sciences, medicine, statistics, business, and more.

This toolkit makes revision and exam practice efficient. Each card links to a focused guide for concept mastery and study strategies. Navigate through the topics to build confidence in applying mathematics to real-world contexts.

🛠️ Useful Tools & Resources

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May 2026 IB Exam Schedule

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