IB Maths AI HL Study Guide & Review

Integrate advanced modelling, technology, statistics and numerical methods, then develop model validation and sustained inquiry for the current IB Maths AI HL course and Paper 3.

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  1. 01Learn concepts
  2. 02Practise questions
  3. 03Review mistakes

Syllabus knowledge tree

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

Preview the course map

Explore the course units and topics. Sign in to open the full mastery workspace and see your progress.

1 Number and algebra
1.1 Number and algebra - SL content
1.2 Number and algebra - AHL content
2 Functions
2.1 Functions - SL content
2.2 Functions - AHL content
3 Geometry and trigonometry
3.1 Geometry and trigonometry - SL content
3.2 Geometry and trigonometry - AHL content
4 Statistics and probability
4.1 Statistics and probability - SL content
4.2 Statistics and probability - AHL content
5 Calculus
5.1 Calculus - SL content
5.2 Calculus - AHL content

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 matrices

Networks, 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 networks

Advanced 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 statistics

Differential-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 models

Paper 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 3

Where 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

  1. I know the weak area

    Open the exact shared or AHL Topic and identify its prerequisites, model assumptions and technology routine.

    Browse the HL syllabus
  2. The failure is unclear

    Attempt a mixed modelling problem and stop at the earliest repeated breakdown in setup, technology or validation.

    Open mixed HL questions

Choose the right starting point

  1. Build and justify the model

    Define variables and assumptions, choose an AHL method and explain why it fits the context.

    Review a Concept
  2. Execute and interrogate

    Use technology transparently, preserve precision and examine output, parameters, residuals or numerical behaviour critically.

    Check Mastery
  3. Validate, generalize and repair

    Test sensitivity and limitations, communicate a conclusion and rebuild from the first invalid decision after marking.

    Practise HL questions

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.

Paper / componentQuestionsTime% of grade
Paper 1110 marksCompulsory short-response questions; a graphic display calculator and clean formula booklet are required.How to prepare: Practise rapid model selection, concise supported working, accurate technology use and contextual interpretation across the full syllabus breadth.2 hours30%
Paper 2110 marksCompulsory extended-response questions; a graphic display calculator and clean formula booklet are required.How to prepare: Sustain one context across connected parts, carrying assumptions, precision, output and interpretation consistently through the full response.2 hours30%
Paper 355 marksTwo compulsory extended-response problem-solving questions; a graphic display calculator and clean formula booklet are required.How to prepare: Practise exploring with technology, refining a model, justifying choices and communicating one connected conclusion with limitations.1 hour20%
Mathematical exploration20 marksOne individual written mathematical investigation, internally assessed and externally moderated; mathematics must be appropriate to the level.How to prepare: Choose a focused context, make modelling decisions visible and ensure technology, interpretation, reflection and communication support the mathematics.Part of the 30-hour toolkit and exploration allocation20%

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.