Advanced mathematical models
Develop models from unfamiliar information, compare possible approaches, test limitations, and justify whether a result is reasonable.
IB Mathematics • HL
IB Math AI HL
Use this IB Math AI HL study guide to browse the syllabus topic structure, study materials, and practice resources.
Structured practice
IB Math AI HL Question Bank
Jump straight into grouped unit practice without losing your place in the syllabus overview.
1. Number and Algebra
1.1 Using standard form
1.2 Sequences and Sigma Notation
1.3 Geometric Sequences
1.4 Financial apps – compound interest, annual depreciation
1.5 Exponents and Logarithms
1.6 Approximating and estimating
1.7 Loan repayments and amortization
1.8 Use of technology to solve systems of linear equations and polynomial equations
1.9 Log laws
1.10 Expressions with non-integer exponents
1.11 Sum of infinite geometric sequences
1.12 Complex numbers introduction
1.13 Complex numbers continued
1.14 Introduction to matrices
1.15 Eigenvalues and eigenvectors
2. Functions
2.1 Equations of a line
2.2 Functions, domains, range, graphs
2.3 Graph of a function
2.4 Features of a graph
2.5 Modelling functions
2.6 Modelling skills
2.7 Composite functions, finding inverse function incl domain restriction
2.8 Transformations of graphs, composite transformations
2.9 HL modelling functions
2.10 Scaling large numbers, log-log graphs
3. Geometry and Trigonometry
3.1 3d space, volume, angles, midpoints
3.2 2d and 3d trig
3.3 Angles of elevation and depression
3.4 The circle, arc and area of sector, degrees only
3.5 Intersection of lines, equations of perpendicular bisectors
3.6 Voronoi diagrams
3.7 Radians
3.8 Unit circle, Pythag identity, solving trig equations graphically
3.9 Matrix transformations
3.10 Vector definitions
3.11 Vector equation of a line in 2d and 3d
3.12 Vector applications to kinematics
3.13 Scalar and vector products
3.14 Graph theory
3.15 Adjacency matrices and tables
3.16 Tree and cycle algorithms, Chinese postman, travelling salesman
4. Statistics and Probability
4.1 Introduction to Statistics
4.2 Presentation of data
4.3 Mean, median, and mode
4.4 Correlation of Data
4.5 Trial and outcome
4.6 Venn diagrams
4.7 Discrete random variables
4.8 Binomial distribution
4.9 Normal distribution
4.10 Spearman’s rank correlation coefficient
4.11 Expected, observed, hypotheses, chi squared, gof, t-test
4.12 Data collection, reliability and validity tests
4.13 Non-linear regression
4.14 Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators
4.15 Central limit theorem
4.16 Confidence intervals
4.17 Poisson distribution
4.18 T and Z test, type I and II errors
4.19 Transition matrices – Markov chains
5. Calculus
5.1 Introduction to Limits
5.2 Increasing and decreasing functions
5.3 Introduction to derivatives
5.4 Tangents and normals
5.5 Introduction to integration
5.6 Stationary points, local max and min
5.7 Optimisation
5.8 Trapezoid rule
5.9 Differentiating standard functions and derivative rules
5.10 Second derivatives, testing for max and min
5.11 Indefinite integration, reverse chain, by substitution
5.12 Areas under a curve onto x or y axis. Volumes of revolution about x and y
5.13 Kinematic problems
5.14 Setting up a DE, solve by separating variables
5.15 Slope fields
5.16 Eulers method for 1st order DEs
5.17 Phase portrait
5.18 Eulers method for 2nd order DEs
Overview
Course overview
How to study IB Math AI HL
IB Math AI HL combines practical mathematical modelling with greater technical depth. Students need to connect multiple ideas, evaluate models, work confidently with technology, and communicate conclusions precisely. This hub organises the course into a navigable revision path so you can diagnose gaps and practise demanding multi-step applications.
Statistics, probability, and networks
Build fluency across statistical inference, probability models, matrices, graph theory, and other topics that reward careful technology use.
Connected multi-step reasoning
Practise questions that combine functions, calculus, geometry, and data instead of revising every technique in isolation.
Assessment at a glance
For the current course assessed before the redesigned first-assessment-2029 syllabus, all three external papers require technology. Paper 3 focuses on extended problem solving, and the internal assessment is an individual mathematical exploration. Confirm your examination session with your school and the current IB guide.
| Component | Format | Weighting |
|---|---|---|
| Paper 1 | 2 hours; technology required; short-response questions | 30% |
| Paper 2 | 2 hours; technology required; extended-response questions | 30% |
| Paper 3 | 1 hour; technology required; extended problem-solving questions | 20% |
| Internal assessment | Individual mathematical exploration | 20% |
Sources: current IB subject guide and IB curriculum update for first assessment 2029.
Revision plan
- 1.Map each weak topic to the prerequisite skills that support it.
- 2.Alternate focused technique practice with unfamiliar modelling problems.
- 3.Record assumptions, limitations, and interpretation errors in a dedicated modelling log.
- 4.Use timed mixed sets to practise choosing methods without topic labels.
Exam strategy
Plan multi-step questions before reaching for technology. Define variables, state assumptions, preserve unrounded values during working, and evaluate whether the final answer is sensible within the model and context.
Practise IB Math AI HL questionsReview Christos Math AA & AI notes and exercisesFrequently asked questions
What is the focus of IB Math AI HL?
IB Mathematics: Applications and Interpretation HL combines modelling, statistics, technology, and advanced mathematical techniques. HL students need to connect ideas across topics, justify assumptions, and evaluate the usefulness and limitations of models.
Is technology allowed in IB Math AI HL exams?
For the current course assessed before the redesigned first-assessment-2029 syllabus, technology is required in all three Math AI HL examination papers. Students should confirm the approved calculator rules for their examination session.
How is the current IB Math AI HL course assessed?
Paper 1 and Paper 2 each last 2 hours and are each worth 30%. Paper 3 lasts 1 hour and is worth 20%, while the individual mathematical exploration is worth 20%. Technology is required in all three papers.
What is the difference between IB Math AI HL and AI SL?
AI HL studies the course with greater breadth and depth, includes additional higher-level content, and has a third external paper focused on extended problem solving. Students should use the page matching their registered level.