Choosing the right IB Mathematics course is one of the most important decisions you’ll make in the Diploma Programme. The IB offers two distinct maths courses — Analysis and Approaches (AA) and Applications and Interpretation (AI) — each available at Standard Level (SL) and Higher Level (HL). The right choice depends on your strengths, your interests and, critically, what you plan to study at university. This guide breaks down the differences, explains the assessment structure, and helps you make an informed decision.
Why Study IB Mathematics?
Mathematics is compulsory in the IB Diploma — every student takes at least one maths course. But beyond the requirement, IB Maths develops analytical thinking, structured problem-solving and the ability to model real-world situations mathematically. These are skills that transfer directly to university and professional life, regardless of whether you pursue a STEM career or not.
The IB’s approach is distinctive because it emphasises mathematical inquiry and real-world application alongside formal technique. The Internal Assessment, for instance, asks you to conduct an original mathematical exploration on a topic of your choice — something no other secondary maths curriculum does in quite the same way.
IB Mathematics Course Structure: AA vs AI
The two IB Maths courses share some common content but differ significantly in emphasis, style and the types of thinking they reward.
Analysis and Approaches (AA)
AA is the more theoretical, proof-oriented course. It emphasises algebraic manipulation, calculus and formal mathematical reasoning. If you enjoy working through abstract problems, constructing proofs and developing mathematical arguments, AA is likely the better fit.
Best for: students aiming for university courses in engineering, physics, pure mathematics, computer science or economics (many of which require AA HL specifically).
Applications and Interpretation (AI)
AI focuses on using mathematics to model and solve real-world problems. It places greater emphasis on statistics, probability, data analysis and the use of technology (particularly the GDC/graphing calculator). The approach is more applied and less abstract than AA.
Best for: students heading toward business, social sciences, biology, environmental science, psychology or design-related courses.
AA vs AI at a Glance
Analysis & Approaches (AA) | Applications & Interpretation (AI) | |
|---|---|---|
Focus | Pure/theoretical maths, proof, algebra, calculus | Applied maths, modelling, statistics, technology |
Best for | Engineering, physics, pure maths, computer science, economics | Business, social sciences, biology, psychology, design |
SL exam | Paper 1 (no calculator) + Paper 2 (calculator allowed) | Paper 1 (short, technology allowed) + Paper 2 (extended, technology allowed) |
HL exam | Paper 1 + Paper 2 + Paper 3 (extended problems) | Paper 1 + Paper 2 + Paper 3 (extended problems) |
Internal assessment | Mathematical exploration (20%) | Mathematical exploration (20%) |
GDC/technology | Less emphasis — Paper 1 is non-calculator | Central to the course — both papers allow technology |
Teaching hours | SL: 150 hours | HL: 240 hours | SL: 150 hours | HL: 240 hours |
SL vs HL: Which Level Should You Choose?
Both AA and AI are offered at Standard Level (SL) and Higher Level (HL). The difference is significant — it’s not just “more of the same.”
- Standard Level (SL) covers the core syllabus in approximately 150 teaching hours. It provides a solid mathematical foundation and is sufficient for many university courses.
- Higher Level (HL) adds approximately 90 additional hours of deeper, more challenging content plus a third exam paper. HL includes topics not covered at SL — for AA HL, this means complex numbers, further calculus and proof; for AI HL, it includes further statistics, graph theory and kinematics.
The university factor: Many competitive university courses — particularly in engineering, medicine, physics and economics — require or strongly prefer Maths HL. If you’re considering any of these pathways, check your target university’s prerequisites before choosing SL. Changing from SL to HL mid-course is extremely difficult.
Quick decision guide
Choose AA HL if you need maths for engineering, physics, pure maths or competitive economics programmes.
Choose AA SL if you enjoy theoretical maths but don't need HL for your university pathway.
Choose AI HL if you're strong in applied maths and heading toward data science, business analytics or quantitative social science.
Choose AI SL if maths isn't your strongest subject and your university course doesn't require HL.
Key Topics in IB Mathematics
Both courses share five common topic areas, though the depth and emphasis differ between AA and AI:
- Number and algebra — sequences, series, logarithms, binomial theorem
- Functions — transformations, composite and inverse functions, modelling
- Geometry and trigonometry — circles, vectors, trigonometric identities and equations
- Statistics and probability — descriptive statistics, probability distributions, hypothesis testing
- Calculus — differentiation, integration, kinematics (emphasis varies: heavier in AA, more applied in AI)
At HL, additional topics are introduced. AA HL students study complex numbers, further proof techniques and advanced calculus. AI HL students study further statistics, graph theory and additional modelling techniques.
How Is IB Mathematics Assessed?
IB Maths is assessed through external examinations (80%) and an internal assessment (20%).
External exams
At SL, you sit two exam papers. At HL, you sit three. The papers vary between AA and AI:
- AA SL: Paper 1 (no calculator, 1.5 hours) + Paper 2 (calculator allowed, 1.5 hours)
- AA HL: Paper 1 (no calculator, 2 hours) + Paper 2 (calculator, 2 hours) + Paper 3 (extended problems, 1 hour)
- AI SL: Paper 1 (short questions, technology allowed, 1.5 hours) + Paper 2 (extended, technology allowed, 1.5 hours)
- AI HL: Paper 1 (technology, 2 hours) + Paper 2 (technology, 2 hours) + Paper 3 (extended problems, 1 hour)
Internal Assessment: The Mathematical Exploration
The IA is a 12–20 page mathematical exploration on a topic of your choice. It’s worth 20% of your final grade and is the one piece of coursework you can fully control. The IB assesses it on five criteria: presentation, mathematical communication, personal engagement, reflection, and use of mathematics.
Strong IA topics connect mathematics to something you’re genuinely interested in. Past examples include modelling the trajectory of a basketball free throw, analysing cryptocurrency volatility using statistical distributions, and exploring the mathematics of musical harmony. The key is choosing a topic where the maths is deep enough to demonstrate your skills but manageable enough to explore thoroughly.
For full details on the syllabus and assessment, see the official IB Mathematics subject page.
Tips for Succeeding in IB Mathematics
- Understand your calculator. Whether it’s a TI-84 or TI-Nspire, know its functions inside out. In AI especially, efficient GDC use can save significant time in exams.
- Start your IA early. The exploration takes longer than you think. Choose your topic by the end of Year 1 and have a draft structure before Year 2 begins.
- Practise past papers under timed conditions. The IB publishes past papers through your school. Work through them with strict time limits — exam technique matters as much as content knowledge.
- Don’t neglect the formula booklet. You’re given a formula booklet in the exam. Learn what’s in it and what isn’t — so you know what you need to memorise versus what you can look up.
- Show all working. IB examiners award method marks generously. Even if your final answer is wrong, clear working can earn you most of the marks on a question.
Benefits of Studying IB Mathematics
- Develop rigorous problem-solving skills that transfer to any discipline — from engineering to law to medicine.
- Prepare for university-level mathematics with a curriculum designed to build both conceptual understanding and technical fluency.
- Gain global recognition — the IB Diploma is accepted by universities in over 150 countries, and IB Maths HL is widely regarded as one of the strongest school-level maths qualifications available.
- See mathematics in action through the IA, which connects abstract concepts to real-world applications in a way that’s unique to the IB.
Get Expert Help with IB Mathematics
Learnmate’s research shows that 70% of students achieving ATARs of 99+ engage one or more tutors— and IB students benefit just as much from targeted support. An IB Maths tutor can help you choose between AA and AI, navigate the IA, build exam technique, and develop the confidence to aim for a 7.
FAQs
If you’re aiming for university courses in engineering, physics or pure maths, AA is usually required (often at HL). If your strengths are in applied problem-solving and you’re heading toward business, social sciences or biology, AI is typically the better fit. Check your target university’s prerequisites before deciding — this is the single most important factor.
SL covers the core syllabus in approximately 150 teaching hours. HL adds roughly 90 additional hours of deeper content plus a third exam paper. Many competitive university courses require Maths HL specifically — particularly in engineering, medicine and economics.
The IA is a mathematical exploration of 12–20 pages on a topic of your choice. It’s worth 20% of your final grade and is assessed on criteria including mathematical communication, personal engagement, reflection and use of mathematics. Choose a topic you’re genuinely interested in — the best IAs combine personal curiosity with rigorous maths.
They’re different in structure and emphasis. IB Maths AA HL is generally considered more demanding than VCE Maths Methods, covering additional topics like complex numbers and further proof. IB Maths AI SL is broadly comparable to VCE General Maths in scope, though the assessment style — particularly the IA and the emphasis on technology — differs significantly.
The IB requires a Graphing Display Calculator (GDC). The TI-84 Plus CE and TI-Nspire CX are the most commonly used models in Australian IB schools. Check with your school for their specific recommendation, as some schools standardise on one model for teaching purposes.
Switching between AA and AI is possible early in Year 1 but becomes increasingly difficult as the courses diverge. Switching from SL to HL (or vice versa) is also possible in the first few months but rarely practical after that, given the significant difference in content depth. If you’re unsure, speak to your maths teacher and an IB coordinator before the course begins.
