IB Math Internal Assessment

The IB Math Internal Assessment is a mathematical exploration that counts for 20% of your final grade. This comprehensive resource hub provides everything you need to excel in your IA, from topic selection and research methodology to mathematical communication and assessment criteria. Get expert guidance for all IB Math LA courses (AA SL, AA HL, AI SL, AI HL) with step-by-step tutorials and proven strategies.

IB Math Internal Assessment Criteria

4/4

Criterion A

Presentation

4/4

Criterion B

Mathematical Communication

3/3

Criterion C

Personal Engagement

3/3

Criterion D

Reflection

6/6

Criterion E

Use of Mathematics

Presentation

Mathematical Communication

Personal Engagement

Reflection

Use of Mathematics

Criterion A: Presentation 4/4

Organization, coherence, and conciseness of the exploration

What This Criterion Assesses

This criterion evaluates the structure and organization of your exploration. It measures how well your introduction, body, and conclusion connect to each other. Strong mathematics can lose marks if the IA is unclear or poorly structured. This is not about mathematical complexity but about how clearly you present your work.

The Top Mark Standard

To achieve full marks, your exploration must be coherent, well organized, and concise.

Coherent: Your work is logically developed and easy to follow. It reads well and effectively meets its stated aim.

Well Organized: Your IA contains a clear introduction stating the aim, a body with logical flow, and a conclusion. Graphs, tables, and diagrams are integrated into the text where they are discussed, not dumped in appendices.

Concise: Your work contains no irrelevant material or unnecessary repetitive calculations. Every page adds value to the investigation.

The Difference Maker

The critical distinction between a good IA and an excellent one is conciseness. Your work may be coherent and well organized but still fail to achieve top marks if it includes repetitive calculations or irrelevant descriptions that do not support your aim. The examiner should not have to work through unnecessary material to find your mathematical argument.

Required Structure

Title Page: Include a clear title and total page count.
Length: 12 to 20 pages, double-spaced, excluding bibliography and appendix.
Page Numbers: Required. Recommended placement is bottom-right.
Introduction: State your topic and investigation clearly. Include your aim and rationale.
Aim: Direct, precise, and focused on mathematical purpose. Example: "Apply calculus to model water flow efficiency in cylindrical tanks."
Rationale: Explain why you chose this topic. Make it personal but brief.
Plan: Outline how you will achieve your aim. Describe methods and mathematical approaches.
Body: Present your mathematics with logical flow. Use headings and subheadings to guide the reader.
Conclusion: Summarize findings clearly and link directly to your aim. Avoid vague statements.

Use of Visuals

Placement: Place graphs, tables, and diagrams near the text where they are discussed. Do not relegate essential visuals to appendices.
Labels: All visuals must be labeled and referenced in the text.
Introduction: Introduce each visual with a short sentence. Example: "Figure 3 shows population growth over 10 years."
Formulas: Center-align all equations and calculations.
Large Tables: Move extensive raw data to the appendix, but include summary tables in the main body.

Citations and References

Cite all data sources, tools, and models not covered in the IB syllabus. Reference any definitions, theories, or explanations beyond IB curriculum. Acknowledge software such as Desmos, GeoGebra, Excel, or Python. Include a complete bibliography at the end.

Appendix Use

The appendix is optional. Use it only for raw data, extended graphs, or lengthy calculations that would disrupt the flow of your main argument. Do not place essential graphs or tables in the appendix. The examiner should be able to understand your work without consulting the appendix.

✓ Do

Include a clear rationale and aim in the introduction
Use headings to create logical flow
Place all essential graphs in the main body
Keep work concise and relevant
Link your conclusion back to your aim

✗ Don't

Attach relevant graphs or diagrams as appendices
Show repetitive manual calculations
Include irrelevant material
Write vague or general summaries
Exceed 20 pages without strong justification

Criterion B: Mathematical Communication 4/4

Clarity, correctness, and consistency of mathematical language

What This Criterion Assesses

This criterion evaluates the clarity and effectiveness of your mathematical language. It assesses your use of notation, symbols, and terminology, as well as your ability to present mathematics in multiple forms such as formulae, diagrams, tables, and graphs. Poor mathematical communication can undermine strong mathematical work.

The Top Mark Standard

To achieve full marks, your mathematical communication must be relevant, appropriate, and consistent throughout.

Consistent: Notation and symbols are used correctly every single time. Not most of the time. Every time.

Appropriate: You use deductive methods correctly and set out proofs logically. You choose the right mathematical tools for your investigation.

Relevant: Your mathematical communication directly supports your aim. You do not include excessive or irrelevant notation.

The Difference Maker

The distinction between partial credit and full marks is consistency. Minor errors are acceptable only if they do not impair communication. However, repeated notation mistakes, inconsistent variable definitions, or unclear terminology will restrict your score. Examiners expect flawless execution of basic notation and terminology.

Mathematical Language

Notation: Use correct mathematical notation, symbols, and terminology throughout your IA.
Equation Editor: Present equations using proper mathematical formatting. Calculator notation such as y = x^2 or * for multiplication is not acceptable unless it appears in a direct software screenshot.
Consistency: If you define a variable as t for time, use t consistently. Do not switch to T or "time" without explanation.
Formal Language: Use "substitute" instead of informal phrases like "plug in" or "put in."

Variables and Terms

Define Immediately: Define all variables when you first introduce them. Example: "Let v represent velocity in meters per second."
Units: Provide units where appropriate. Do not write "The distance is 50." Write "The distance is 50 meters."
Key Terms: Clearly explain key terms relevant to your investigation, especially if they are beyond the IB syllabus.

Visuals

Label Everything: Label all graphs, tables, and diagrams clearly. Include titles, figure numbers, and axis labels with units.
Reference in Text: Refer to visuals appropriately in your text. Example: "As shown in Figure 2, the relationship is linear."
Unlabelled Graphs: Unlabelled or poorly labelled graphs can restrict your score to 1 mark. This is a common and costly error.

Accuracy and Rounding

Rounding: Round values to a suitable degree of accuracy. State your level of precision. Example: "All values are rounded to 3 significant figures."
Consistency: Apply the same rounding standard throughout your IA. Do not round to 2 decimal places in one section and 4 in another without justification.

⚠ Critical Mistakes That Cost Marks

Using calculator notation (x^2, sqrt, *) in written work
Unlabelled or poorly labelled graphs and tables
Inconsistent variable definitions
Missing units on numerical answers
Informal language like "plug in" or "times by"

✓ Do

Define all variables immediately
Use equation editors for all mathematics
Label all graphs with titles, axes, and units
Use formal mathematical language
Maintain consistent notation throughout

✗ Don't

Use calculator notation in written work
Leave graphs or tables unlabelled
Use informal phrases like "plug in"
Switch variable definitions mid-IA
Omit units from numerical answers

Criterion C: Personal Engagement 3/3

Independent thinking, creativity, and ownership of the mathematics

What This Criterion Assesses

This criterion evaluates the extent to which you engage with the topic and make the mathematics your own. It measures independent thinking, creativity, and the presentation of ideas in a unique way. This is not a measure of effort. Engagement must be demonstrated through the work itself, not through statements of interest.

The Top Mark Standard

To achieve full marks, there must be evidence of outstanding personal engagement.

Outstanding: Engagement is authentic and drives the exploration forward in a creative way. It is not forced or artificial.

Ownership: You leave the impression that you have developed a complete understanding of the topic through your specific approach. The IA is clearly your work, not a reproduction of a textbook example.

The Difference Maker

The distinction between significant engagement and outstanding engagement is both quality and frequency. Significant engagement is evident on several occasions and helps the reader understand your intentions. Outstanding engagement occurs in numerous instances and is of high quality. Most importantly, it drives the exploration forward creatively. Statements like "I have always loved calculus" are insufficient. Engagement must be demonstrated through your actions, decisions, and the mathematics itself.

How to Show Personal Engagement

Explain Your Motivation: Clearly explain why you chose this topic. Keep your introduction and rationale personal but concise.
Ask Your Own Questions: Ask curious and relevant questions within your IA and provide answers later. Do not simply follow a textbook structure.
Use First Person: Use "I decided," "I realized," "I wondered" to highlight your decision-making process and personal ownership.
Create Original Examples: Develop your own examples or models rather than using textbook data. Collect your own data where possible.
Make Conjectures: Form and test hypotheses. Show how your thinking changed as the investigation progressed.
Connect to Real-World Applications: Link your mathematics to real-world situations that matter to you.

Making Your IA Unique

Original topics show strong engagement, but common topics can also demonstrate personal engagement by using unique or local datasets, deriving your own models, adding original interpretations, or exploring the topic from multiple perspectives (mathematical, social, economic, scientific).

Optional Ways to Demonstrate Engagement

Collect and analyze your own data
Learn and apply a new mathematical concept at the appropriate IB level
Derive your own model or formula from the data
Use new tools such as GeoGebra, Desmos, or Excel in creative ways
Compare different models for the same situation and evaluate which works better

✓ Example of Outstanding Engagement

Common Topic: Trajectory of a ball

Unique Twist: Adding the Magnus effect to model spin. Collecting real data from filming basketball free throws at different spin rates. Comparing theoretical predictions to actual measurements and discussing discrepancies.

⚠ What Does NOT Count as Engagement

Simply stating "I have always been interested in calculus" or "I chose this topic because it is important." These are empty claims. Engagement must be evident in the mathematics and your approach, not in your introduction.

Critical Reminder

Textbook-style explorations are unlikely to achieve high scores. If your IA looks like it could appear in a standard textbook, it lacks the personal engagement required for top marks. Even if your mathematics is correct, without genuine engagement, you cannot achieve full marks in this criterion.

Criterion D: Reflection 3/3

Critical evaluation and analysis of the exploration

What This Criterion Assesses

This criterion evaluates your ability to review, analyze, and evaluate the exploration. It focuses on the evaluation of findings, not just the description of results. Reflection should be present throughout the IA, not only in the conclusion.

The Top Mark Standard

To achieve full marks, there must be substantial evidence of critical reflection.

Critical Reflection: This involves considering implications, discussing strengths and weaknesses of techniques, comparing different mathematical approaches, and linking results back to the aim.

Substantial Evidence: Reflection must be present throughout the exploration, not just in the conclusion. One exceptional final reflection is not sufficient unless it is of exceptionally high quality.

The Difference Maker

The distinction between meaningful reflection and critical reflection is depth and insight. Meaningful reflection links to the aim or comments on what has been learned. Critical reflection goes deeper by analyzing why a method worked or failed, discussing the implications of results on your understanding, or comparing the effectiveness of different approaches. Simply describing results is limited reflection and will not achieve high marks.

How to Reflect Effectively

Comment on Results: Are the results what you expected? If not, why?
Identify Limitations: Discuss limitations in your methods or assumptions. Be specific.
Suggest Improvements: What could be done better? How would you extend this work?
Analyze Implications: What do your results mean mathematically and in the real world?
Evaluate Methods: Compare different approaches. Which worked better and why?
Show Evolution of Thinking: Explain how your understanding changed as the investigation progressed.

💡 Reflective Questions to Include

"How reliable are my models given the assumptions made?"
"What would happen if I changed this variable or condition?"
"Are there alternative methods that could improve accuracy?"
"Does the data suggest a pattern I did not anticipate?"
"Why did this method fail in certain cases?"
"What are the practical implications of my findings?"

Strategies for Strong Reflection

Compare Predictions to Outcomes: Did your model accurately predict real-world behavior? If not, analyze why.
Evaluate Different Approaches: If you tested multiple models, discuss which was most effective and why.
Highlight Sources of Error: Identify where errors came from and explain their effect on results.
Suggest Extensions: Propose how the investigation could be taken further.
Use Mathematical Reasoning: Support your reflections with mathematical justification, not just opinions.

✓ Example of Critical Reflection

Weak: "The linear model worked well."

Strong: "The linear model achieved R² = 0.94, but residual analysis revealed systematic errors at high values. This suggests a non-linear relationship that a quadratic model might capture more accurately. Testing this would require additional data points in the upper range where the linear model shows greatest deviation."

⚠ What Does NOT Count as Reflection

Simply describing your results ("I found that the correlation was 0.85") or stating obvious facts ("More data would improve accuracy") does not demonstrate reflection. Reflection requires analysis and evaluation, not description.

Location of Reflection

Include reflection at multiple points throughout your IA, not only at the end. Each major section can include brief reflective comments. Show how your thinking evolved. If reflection appears only in the conclusion, achieving full marks is very difficult unless that final reflection is exceptionally insightful.

Tips to Maximize Marks

Reflect throughout the IA, not only in the conclusion
Be specific and concise. General statements do not earn full marks
Connect reflection to your aim and research question
Show personal understanding of the topic and the mathematics involved
Evaluate the validity and reliability of your methods

Criterion E: Use of Mathematics 6/6

Relevance, correctness, sophistication, and understanding of mathematics

What This Criterion Assesses

This criterion evaluates the relevance, correctness, and understanding of the mathematics used in your exploration. It assesses whether your mathematics supports the aim and is appropriate for your course level (SL or HL). This is the most heavily weighted criterion.

The Top Mark Standard

The descriptors for SL and HL differ significantly at the top end.

Standard Level (SL)

The mathematics must be relevant, commensurate with the level of the course, correct, and demonstrate thorough knowledge and understanding.

Higher Level (HL)

The mathematics must be precise and demonstrate sophistication and rigour. Sophistication means using challenging concepts or examining problems from multiple perspectives. Rigour means clarity of logic and language in mathematical arguments and proofs.

The Difference Maker

The distinction between partial credit and full marks is demonstrated understanding. Getting the correct answer is not sufficient. You must explain why steps are taken. Merely substituting values into a formula does not demonstrate understanding. Your mathematics must be commensurate with your course level. Mathematics based solely on prior learning (material learned before IB) will not achieve top marks.

Key Components for Full Marks

Correctness: All calculations, formulas, and derivations must be accurate. Avoid careless errors. Double-check your results.

Appropriateness: Use mathematics that is suitable for your topic. Examples include calculus for rates of change, statistics for data analysis, or algebra for modelling.

Variety and Sophistication: Include more than one type of mathematical method where appropriate. Examples include differentiation and integration for modelling curves, regression and correlation for data analysis, or matrices and sequences for structured calculations.

Demonstrated Understanding: Present all work clearly using proper notation, symbols, and terminology. Explain your reasoning. Show why steps are necessary, not just that they produce correct answers.

Use of Technology

Tools: Use Desmos, GeoGebra, Excel, Python, or other appropriate tools to support your mathematics.
Explanation Required: Clearly show how technology is applied. Software-generated answers without explanation demonstrate limited understanding.
Citation: Cite any external models or functions you use.

Strategies for Maximizing Marks

Apply mathematical methods at a level appropriate for HL or SL
Integrate different techniques to explore your research question
Demonstrate logical progression in calculations and derivations
Include interpretation of results, linking mathematics back to the aim
Highlight novel applications or extensions beyond routine exercises
Explain and justify every step. Do not assume the examiner knows your reasoning

Commensurate with the Course

To score highly, your mathematics cannot be based solely on prior learning. It must be at the level of the IB syllabus (SL or HL) or slightly beyond. Using only basic algebra or arithmetic from earlier years will restrict your score. For HL students, sophistication means using challenging concepts, examining problems from different perspectives, or applying SL mathematics in complex ways beyond SL expectations.

Relevance

Overly complicated mathematics used where simple mathematics would suffice is considered irrelevant and will lower your score. Do not include regression or correlation simply for the sake of it. Ensure the mathematics directly answers your research question. Quality over quantity.

⚠ Common Problems to Avoid

Using only basic or superficial mathematical techniques
Mathematical errors that undermine your argument
Failing to show steps or reasoning behind results
Overloading with irrelevant calculations
Relying on prior learning without applying IB-level mathematics
Using complex mathematics you do not fully understand

Final Advice

It is better to use a few elements of syllabus mathematics well than to use many advanced topics poorly. Demonstrate understanding through clear explanations and justifications. If you use technology, explain what it does and why you chose it. Your mathematics must be correct, relevant, and appropriately sophisticated for your course level.

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Frequently Asked Questions

Get answers to the most common questions about IB Math Internal Assessment

What is the IB Math Internal Assessment?

The Internal Assessment is a mathematical exploration that counts for 20% of your final IB Math grade. It's a 12-20 page investigation where you explore a mathematical topic that interests you, using appropriate mathematical techniques and demonstrating personal engagement with the subject. The IA is assessed on five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, and Use of Mathematics.

How do I choose a good IA topic?

Choose a topic that genuinely interests you and connects to your personal experiences or hobbies. Ensure it allows for mathematical exploration at your course level (SL or HL) and isn't too complex or too simple. Good topics often involve real-world applications, patterns in nature, sports analysis, or mathematical modeling. Avoid overused topics like the golden ratio in art or simple probability calculations.

What mathematical level should I aim for in my IA?

Use mathematics appropriate to your course level that goes beyond basic curriculum content. For SL students, this might involve extending topics like calculus applications or statistical analysis. HL students should demonstrate more sophisticated mathematical techniques. The key is using relevant mathematics correctly rather than including complex math for its own sake. Quality over complexity is essential.

How important is personal engagement in the IA?

Personal engagement is worth 3 out of 20 marks and demonstrates your genuine interest in the mathematical exploration. Show this through your choice of topic (personal connection), independent thinking in your approach, and evidence of mathematical curiosity throughout your investigation. Explain why the topic matters to you and what insights you gained during the exploration process.

What should I include in my IA reflection?

Your reflection should go beyond summarizing what you did. Critically evaluate your mathematical processes, discuss unexpected findings, consider limitations of your approach, and suggest improvements or extensions. Reflect on what you learned about mathematics and your problem-solving process. This shows mathematical maturity and earns marks in the Reflection criterion worth 3 points.

IB Math Internal Assessment