The Ultimate IB Mathematics IA Guide: From Planning to Submission
The Mathematics Internal Assessment is worth 20% of your final grade — a chance to demonstrate mathematical skill, creativity and analytical thinking on a topic of your choice. Whether you're in Analysis & Approaches (AA) or Applications & Interpretation (AI), HL or SL, this guide walks through the whole process: choosing a topic, structuring the exploration, and maximizing marks across every criterion.
Understanding the Mathematics IA
Your IA is evaluated on five criteria, each worth 4 marks, for a total of 20:
- Criterion A — Communication: how effectively you communicate ideas, using appropriate notation, terminology and diagrams.
- Criterion B — Mathematical presentation: logical development, justified approach, verified results.
- Criterion C — Personal engagement: genuine interest, personal significance, an exploration that is visibly your own.
- Criterion D — Reflection: evaluating the significance of your findings in various contexts.
- Criterion E — Use of mathematics: the sophistication and relevance of the mathematics relative to your course.
The IA should be 12–20 pages including diagrams (excluding appendices and bibliography), presented as a coherent report with clear sections and correct notation. Technology — a CAS, GeoGebra, Python — is encouraged where appropriate.
Choosing the Perfect Topic
Topic choice is the single most important decision. A strong topic:
- Interests you personally — you'll live with it for months.
- Allows appropriate mathematical treatment at or slightly beyond your course level.
- Has manageable scope — neither trivial nor unbounded.
- Offers personal insight — a connection to your own experiences or interests.
Inspiration for AA students
- Mathematical modeling of natural phenomena (growth patterns, population dynamics)
- Calculus explorations (real-world optimization problems)
- Number theory investigations (cryptography applications)
- Statistical analysis of real datasets (climate data, sports statistics)
- Geometric explorations (patterns in architecture)
Inspiration for AI students
- Statistical analysis of societal issues (e.g. income inequality)
- Financial mathematics (loan repayment models)
- Network theory applications (social network analysis)
- Game theory in economics or politics
- Algorithm development and analysis
Before committing, ask: Does this let me show the right level of mathematics? Can I add personal insight? Is there enough to explore? Can I actually get the data, software and references I need?
Structuring Your Mathematics IA
Introduction (1–2 pages)
Context and relevance, your personal connection to the topic, clear aims, and a roadmap of the exploration.
Main body (8–14 pages)
Background theory, methodology, the mathematical development itself in logical progression, results with analysis, and a discussion of their significance.
Conclusion (1–2 pages)
Summary of findings, honest reflection on strengths and limitations, possible extensions, and what you learned.
Bibliography and appendices
Consistent citations throughout; push large datasets, code and extra calculations to appendices so the main text flows.
Mathematics Content Requirements
For HL students: aim for mathematics at or slightly beyond the HL curriculum — advanced calculus, differential equations, sophisticated statistics or modeling. For SL students: a thorough, well-developed application of SL concepts is enough; you don't need HL-level content.
Whatever the level, show rigor: define key terms, develop ideas logically, justify your steps, verify results, and keep calculations and notation accurate.
Personal Engagement & Reflection
These two criteria separate excellent IAs from merely competent ones.
- Personal engagement: explain your motivation, take an original angle rather than reproducing a textbook example, show independent decision-making, and follow your curiosity beyond the minimum.
- Reflection: discuss the significance of findings, evaluate limitations honestly, consider alternative approaches, suggest extensions, and reflect on what the process taught you. Specific beats generic every time.
Common Pitfalls to Avoid
- Overambitious scope — a focused topic explored deeply beats a broad survey every time.
- Insufficient mathematics — context and data collection can't substitute for mathematical development.
- Lack of personal input — a rehashed textbook example scores poorly on engagement.
- Poor communication — unclear explanations, inconsistent notation, unlabeled graphs.
- Superficial reflection — generic "I learned a lot" statements earn nothing.
Technology Integration
Use technology purposefully: complex computation, visualization, pattern exploration, modeling and data analysis. Graphing calculators (TI-84, TI-Nspire, Casio fx-CG50), GeoGebra, Desmos, Python or R, and spreadsheets all have their place. Document your methods — justify the tool, show you understand the underlying mathematics, include key steps, and verify results where possible.
Final Checks Before Submission
- Introduction states clear aims and context; conclusion summarizes findings.
- Mathematics is appropriate to your level and developed, not just stated.
- Personal engagement and reflection are specific and visible throughout.
- Length is 12–20 pages; pages numbered; headings clear; notation consistent; graphs labeled and referenced.
- Bibliography complete; everything proofread; all sources cited; work is your own.
- If possible, get a peer or teacher to read it with fresh eyes.