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Explore the IB Maths AI HL syllabus
The current IB Maths AI HL syllabus combines 39 shared and 39 AHL objectives across number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. Use the five-group map to connect advanced methods to modelling decisions.
- 5
- syllabus groups
- 10
- mapped topics
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How to study IB Maths AI HL
IB Maths AI HL is not SL with a longer menu of calculator commands. Use the syllabus map to connect matrices, graph theory, advanced statistics and differential-equation methods to the decisions they enable. Define assumptions, select a model, use technology transparently, interpret parameters and output, and test sensitivity or limitations. In long problems, distinguish an invalid model from an incorrect command or unsupported inference.
Use Concept to compare models, Mastery to retrieve AHL methods and tool routines, and the Question Bank for mixed modelling and inquiry. Classify losses as assumption, method selection, algebra, technology, precision, validation or interpretation. Repair the earliest failed decision, then rebuild the complete model without copying the worked output.
Practise AHL modelling and inquiry
Connect advanced methods to modelling decisions, use technology transparently and validate conclusions across longer cross-topic problems and investigations.
Matrices and dynamic models
Matrices, eigenvalues, Markov chains and iterative processes
Define the state and transition assumptions, construct the matrix and interpret every operation. Use technology to iterate or diagonalize, then test stability, long-run behaviour and limitations of the model.
Practise matricesNetworks, vectors and optimization
Graph algorithms, vectors, routes, flows and geometric decisions
Translate the context into vertices, edges, weights or vectors before running an algorithm. Record the process, interpret the optimum and test whether real constraints make the mathematical answer feasible.
Practise networksAdvanced statistics
Nonlinear regression, confidence intervals, Poisson and sampling distributions
State the population, random variable and assumptions, then choose and execute the analysis. Interpret parameters, uncertainty and evidence without turning statistical significance or fit into an unsupported causal claim.
Practise advanced statisticsDifferential-equation modelling
Euler method, phase portraits and rates of change
Build the differential model from assumptions, use numerical or graphical technology deliberately and interpret trajectories. Compare approximate and qualitative behaviour, then evaluate sensitivity, equilibrium behaviour and important model limitations.
Practise differential modelsPaper 3 modelling inquiry
Two compulsory extended-response problem-solving questions
Parse the developing context, test cases with technology, refine the model and justify choices. Keep assumptions, output and interpretation connected, then explain limitations and how each result advances the investigation.
Practise Paper 3Where to start
Begin from one exact AHL method or use mixed modelling to locate the first failed assumption, tool choice or inference.
Choose your starting point
- Browse the HL syllabus
I know the weak area
Open the exact shared or AHL Topic and identify its prerequisites, model assumptions and technology routine.
- Open mixed HL questions
The failure is unclear
Attempt a mixed modelling problem and stop at the earliest repeated breakdown in setup, technology or validation.
Choose the right starting point
- Review a Concept
Build and justify the model
Define variables and assumptions, choose an AHL method and explain why it fits the context.
- Check Mastery
Execute and interrogate
Use technology transparently, preserve precision and examine output, parameters, residuals or numerical behaviour critically.
- Practise HL questions
Validate, generalize and repair
Test sensitivity and limitations, communicate a conclusion and rebuild from the first invalid decision after marking.
IB Maths AI HL assessment format
External assessment contributes 80% across three GDC-required papers and the exploration contributes 20%. HL preparation must add AHL model selection, validation and Paper 3 inquiry.
SourceInternational Baccalaureate Organization · Mathematics: applications and interpretation guideIB Mathematics: applications and interpretation · First assessment May 2021
IB Maths AI HL questions
HL adds 39 AHL objectives across all five topics, including matrices, graph theory, advanced statistics and differential-equation modelling. It also includes Paper 3, so revision must develop advanced model selection, technology control and validation.
The current official course gives Paper 3 one hour, 55 marks and 20% weighting. It contains two compulsory extended problem-solving questions and requires a graphic display calculator and clean formula booklet.
Practise interpreting a developing context, testing cases with technology, refining a model and justifying each choice. Keep assumptions, output, validation and interpretation connected, then explain limitations and how each result advances the investigation.
No. A graphic display calculator is required for Papers 1, 2 and 3. Availability does not replace mathematical communication: establish the model, record suitable working and explain the meaning and limitations of the output.