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What is the Math IA?
The IB Math Internal Assessment (IA) is a mathematical exploration — a written piece of 12–20 pages in which you investigate a mathematical topic of your choosing. It is worth 20% of your final IB Math grade and is assessed by your teacher, then moderated by IB examiners.
The IA is an opportunity to demonstrate genuine mathematical curiosity. Unlike exams, you have months to develop, refine, and polish your work. Students who invest time in choosing a good topic and writing it well can score 18–20/20.
IA submission timeline (typical): First draft to teacher by December/January of Year 2. Final submission to IB by March/April. Your teacher can provide one round of feedback on your draft — use it wisely.
Marking Criteria
| Criterion | Description | Marks |
|---|
| A — Presentation | Clear structure, appropriate diagrams, consistent notation, relevant title | 4 |
| B — Mathematical Communication | Correct notation, appropriate level of detail in working | 4 |
| C — Personal Engagement | Evidence of genuine curiosity, personal investigation, independent thought | 3 |
| D — Reflection | Discussion of limitations, extensions, what you would do differently | 3 |
| E — Use of Mathematics | Correct and sophisticated mathematics relevant to your course level | 6 |
Criterion E (6 marks) is the highest-weighted criterion but also the most misunderstood. IB describes three levels: "Adequate" (uses mathematics from the course), "Correct" (accurate, no errors), and "Sophisticated" (demonstrates deeper understanding). To reach "Sophisticated," your mathematics must go beyond routine calculations and show insight.
Choosing Your Topic
Topic choice is the single most important decision. The right topic should satisfy three conditions:
- It genuinely interests you. Assessors can identify authentic curiosity vs. generic exploratory work. Personal engagement (Criterion C) is nearly impossible to fake.
- It allows you to use mathematics at the right level. For AA HL, your topic should naturally involve HL mathematics (calculus, complex numbers, vectors). For SL, the mathematics should be substantial but not necessarily HL-exclusive.
- There is a clear mathematical question to investigate. The best IAs have a focused research question: "How does the damping constant affect the period of oscillation in a spring system modelled by a differential equation?" — not "I will explore calculus."
Topic Ideas
Strong AA HL topics
- Modelling disease spread using differential equations (SIR model)
- Exploring Fourier series convergence for different periodic functions
- Using complex numbers to prove trigonometric identities and de Moivre extensions
- Mathematical modelling of projectile motion with air resistance
- Investigating the convergence of different numerical integration methods (Riemann, Simpson, trapezoid)
- Fractal dimension and iterative functions (Mandelbrot or Julia sets)
Strong AI HL topics
- Statistical analysis of a personal data set (sports performance, environmental data)
- Network analysis of social connections using graph theory
- Markov chains and long-run probability predictions
- Game theory analysis of a strategic decision (prisoner's dilemma variants)
- Logistic growth modelling of population data
Avoid overused topics: The Golden Ratio, Fibonacci sequences (without novel angles), Pascal's Triangle, basic modelling with linear regression, and simple probability card games are seen hundreds of times per year and rarely score highly on Criterion C (Personal Engagement).
How to Structure Your IA
- Introduction (1–2 pages): State your topic, explain why you chose it, and state your specific research question. Make your personal motivation clear — not "I chose this because it's interesting" but "I play piano and wondered whether the mathematics of harmonics could explain why certain chord combinations sound discordant."
- Mathematical Background (2–3 pages): Introduce any necessary theory, notation, and definitions. This is where you establish the mathematical foundations your investigation will use.
- Investigation / Exploration (6–10 pages): The core of your IA. Carry out your mathematical work, present calculations and proofs clearly, use graphs and tables to support your findings. Show genuine exploration — including dead ends and revisions.
- Conclusion (1–2 pages): Summarise your findings. Address your original research question directly.
- Reflection (1 page): Criterion D. Discuss limitations (e.g., assumptions in your model), what surprised you, and what you would investigate further if you had more time or data.
Common Mistakes
Mistakes that cost marks:
- No clear research question — the IA describes mathematics but doesn't investigate anything
- Mathematics is too routine — just applying formulas without insight (fails Criterion E "sophisticated")
- No reflection section, or reflection is only one sentence
- Notation errors — undefined variables, inconsistent use of symbols
- Word count too short (<12 pages) or too long (>20 pages) — both are penalised by Criterion A
- Copying investigation structure from online examples without genuine personal engagement
IB Math IA Tutoring
Our tutors help you choose a strong topic, develop your research question, and guide you through the mathematical exploration. We also review drafts for all 5 criteria before final submission.
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