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IB Maths AA HL Study Guide & Review

Connect proof, advanced algebra, calculus and multiple representations, then develop sustained inquiry-style mathematical reasoning for the current IB Maths AA 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 AA HL syllabus

The current IB Maths AA HL syllabus contains SL and AHL content across number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. Use the five-group map to connect 32 AHL objectives to their 51 SL foundations.

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 AA HL

IB Maths AA HL requires connected reasoning, not an isolated list of advanced techniques. Use the syllabus map to link AHL content to its SL foundation across all five topics. For each problem, state definitions and assumptions, choose a useful representation, test simple cases, build the algebra or proof and interpret the result. In long solutions, verify each transition so a weak premise is separated from a later execution error.

Use Concept to compare methods and proofs, Mastery to retrieve exact relationships, and the Question Bank for mixed, multi-stage work. Classify losses as concept, proof logic, algebra, representation, technology, communication or interpretation. Repair the earliest failed decision, then solve the complete problem without reopening the worked solution.

Practise HL connections and inquiry

Integrate proof, advanced techniques, representations and technology across topics, then practise sustaining a justified argument beyond routine exercises.

Proof and advanced algebra

Induction, contradiction, complex numbers, De Moivre and polynomial structure

Start from precise definitions and identify what must be proved. Separate numerical evidence from justification, make each logical implication visible and test whether the conclusion covers every required case.

Practise proof and algebra

Functions, vectors and geometry

Rational functions, inverse trigonometry, vectors, lines and planes

Switch deliberately among symbolic, graphical and geometric representations. State restrictions, choose parameters or coordinates carefully, and interpret intersections, orientation and distance rather than treating the algebra as the final answer.

Practise representations

Probability and continuous models

Bayes, continuous random variables and distribution reasoning

Define events or variables before calculating, justify the model and connect density, cumulative probability and expectation. Interpret conditions and results in context, then test independence and boundary behaviour.

Practise probability

Advanced calculus

Integration techniques, differential equations and Maclaurin series

Identify the structure before choosing a technique, preserve constants and domains, and verify by differentiation or substitution. Connect local approximation or differential behaviour to the wider function and model.

Practise advanced calculus

Paper 3 inquiry

Two compulsory extended problem-solving questions

Read the developing context, test manageable cases, form a conjecture and justify or generalize it. Keep a connected written argument and explain how each result advances the investigation.

Practise Paper 3

Where to start

Start from one precise AHL weakness or use mixed problems to locate the first failed premise, representation or proof decision.

Choose your starting point

  1. I know the weak area

    Open the exact SL or AHL Topic and identify its definitions, prerequisites and connected representations.

    Browse the HL syllabus

  2. The failure is unclear

    Attempt a mixed problem and stop at the earliest repeated breakdown in setup, proof, algebra or interpretation.

    Open mixed HL questions

Choose the right starting point

  1. Build the mathematical structure

    State assumptions, choose a representation and connect the advanced method to its underlying definition or theorem.

    Review a Concept

  2. Reconstruct the argument

    Retrieve exact relationships, derive transitions visibly and test special cases before trusting the general result.

    Check Mastery

  3. Explore, justify and repair

    Solve a connected problem, locate the first unsupported step and repeat the full argument after repair.

    Practise HL questions

IB Maths AA HL assessment format

External assessment contributes 80% across three papers and the exploration contributes 20%. HL preparation must separate no-calculator proof, GDC-supported interpretation and Paper 3 inquiry.

Paper / componentQuestionsTime% of grade
Paper 1110 marksSection A short-response and Section B extended-response questions; calculators are not permitted.How to prepare: Practise exact forms, algebraic control, diagrams, proof and complete supported working without relying on calculator output.2 hours30%
Paper 2110 marksSection A short-response and Section B extended-response questions; a graphic display calculator is required, although not every question needs it.How to prepare: Set up the mathematics first, use technology deliberately, record relevant output and interpret the result with appropriate accuracy and notation.2 hours30%
Paper 355 marksTwo compulsory extended-response problem-solving questions; a graphic display calculator is required.How to prepare: Practise exploring cases, forming conjectures, justifying patterns and communicating one connected argument under time pressure.1 hour20%
Mathematical exploration20 marksOne individual mathematical report, internally assessed and externally moderated; the mathematics is judged at the appropriate level.How to prepare: Choose a focused question, show personal mathematical decision-making and ensure interpretation, reflection and communication support the mathematics used.Approximately 15 course hours20%

SourceInternational Baccalaureate Organization · Mathematics: analysis and approaches guideIB Mathematics: analysis and approaches · First assessment May 2021

IB Maths AA HL questions

HL adds 32 AHL objectives across all five topics and expects deeper proof, algebra, calculus and connected reasoning. It also includes Paper 3, so preparation must develop inquiry and sustained problem solving rather than only harder routine exercises.

Practise exploring unfamiliar contexts: test simple cases, organize observations, form a conjecture and justify or generalize it. Keep a connected argument and explain why each calculation or representation advances the investigation.

No. Calculators are not permitted on Paper 1. A graphic display calculator is required for Papers 2 and 3, although not every individual question or part necessarily requires calculator use.

Do not record only the final error. Find the first unsupported premise, representation or algebraic transition, repair that step and redo the entire solution without looking. This separates conceptual failure from later execution mistakes.