A complete and detailed guide for writing, structuring, and reviewing your Mathematics Internal Assessment (IA).
What Is the Internal Assessment (IA)?
The Mathematics IA is an individual written exploration where you investigate an area of mathematics that interests you.
It allows you to demonstrate:
- Your understanding and application of mathematical concepts.
- Your ability to connect mathematics to real-world or theoretical contexts.
- Your capacity for personal engagement, reflection, and clear communication.
- Recommended time allocation: 10–15 hours of class and independent work combined.
The IA is compulsory for all SL and HL students and counts for 20% of your final IB grade.
It’s assessed internally by your teacher and externally moderated by the IB.
Length: 12–20 pages (excluding bibliography).
Format: Double-spaced, well-organized, with labeled visuals and references.
🎯 Purpose of the IA
The IA is designed to let you:
- Develop a personal insight into the nature of mathematics.
- Explore mathematical ideas independently.
- Appreciate the beauty, power, and creativity of mathematics.
- Experience the satisfaction of applying mathematical processes over time.
- Use technology appropriately as a mathematical tool.
- Reflect on your mathematical growth and thinking.
🧮 How the IA Is Graded
Your IA is assessed against five criteria, worth a total of 20 marks. Each criterion is assessed separately using descriptors.
Criterion | Description | Max Marks |
A. Presentation | Organization, structure, and coherence of your IA. | 4 |
B. Mathematical Communication | Use of notation, symbols, diagrams, and clarity. | 4 |
C. Personal Engagement | Originality, independence, and personal connection. | 3 |
D. Reflection | Depth of analysis and evaluation of results. | 3 |
E. Use of Mathematics | Level, relevance, and correctness of mathematical content. | 6 |
Total | 20 marks (20% of your final IB Math grade) |
The checklist
📘 General Requirements
Title page includes:
Title of the exploration
Candidate number
Session (e.g. May 2025)
Number of pages
12–20 pages (excluding bibliography)
Double line spacing
Page numbers included
References properly cited (APA or similar)
All sources acknowledged (no plagiarism)
Ethical guidelines followed
Work is authentic and original
Turnitin check completed
🔹 Criterion A — Presentation (4 marks)
🧩 Organization & Coherence
Clear introduction, body, and conclusion
Logical flow and structure (easy to follow)
The aim is clearly stated and addressed throughout
Graphs, tables, and diagrams are embedded, not appended
Appendices used only for supporting material (e.g. raw data)
Concise — no unnecessary repetition or irrelevant content
Each section contributes to achieving the stated aim
🔹 Criterion B — Mathematical Communication (4 marks)
📊 Clarity & Precision
Correct mathematical notation, symbols, and terminology
Key terms and variables defined when first introduced
Graphs, diagrams, and tables labeled and referenced
Logical layout for formulas and derivations
Deductive reasoning clearly set out in proofs
Multiple representations used (algebraic, graphical, tabular)
Results given with appropriate accuracy (use ≈ when needed)
Avoid calculator notation — use proper mathematical form
🔹 Criterion C — Personal Engagement (3 marks)
💡 Originality & Personal Connection
Topic chosen from genuine curiosity or personal interest
Evidence of independent or creative thinking
Mathematical ideas expressed in your own way
Clear student voice — questions, conjectures, or unique approaches
Exploration driven by curiosity (“What if…?” mindset)
Goes beyond textbook-style repetition
Perspective and initiative visible throughout the paper
🔹 Criterion D — Reflection (3 marks)
🪞 Insight & Evaluation
Reflection evident throughout, not only at the end
Each result discussed in the context of the aim
Limitations or assumptions identified
Strengths and weaknesses of methods analyzed
Implications and significance of results discussed
Connections to broader mathematics or real-world applications
“Next steps” or possible extensions mentioned
Final reflection critically evaluates your approach and learning
🔹 Criterion E — Use of Mathematics (6 marks)
📈 Relevance & Correctness (SL and HL)
Mathematics is relevant to the aim of the exploration
Mathematics is commensurate with the course level (SL/HL)
Overly complex or irrelevant mathematics avoided
Understanding is demonstrated, not just shown through results
Logical reasoning and clear steps in development
Appropriate use of technology (with understanding)
All calculations correct and justified
Results interpreted and explained clearly
📘 For HL — Sophistication & Rigour
Mathematics shows sophistication (advanced or creative use)
Reasoning and proofs show rigour (clarity, precision, justification)
Connections between mathematical ideas explored
Concepts possibly beyond the HL syllabus used meaningfully
Accurate, precise, and logically consistent mathematics throughout
🧰 Additional Checks
IA formatted neatly and consistently
Peer-edited and teacher feedback incorporated
Checked for careless or computational errors
All visuals are purposeful, labeled, and referenced
Reflection and engagement clearly visible
Mathematics is the main focus — not data, visuals, or narrative
✅ Final Pre-Submission Review
Title, rationale, and aim clearly visible in the introduction
Mathematics explored in depth and explained clearly
Communication consistent throughout
Personal engagement and reflection embedded
Exploration meets ethical and academic honesty standards
Bibliography complete and formatted correctly
The IA feels coherent, logical, and uniquely yours