IB Maths IA: ideas, topics and how it is marked
The IB Maths internal assessment, called the exploration, is worth 20% of your grade in both Analysis and Approaches and Applications and Interpretation. The best explorations start with a question you genuinely care about and use mathematics at the right level for your course.
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How the exploration works
The exploration is a piece of written mathematics on a topic you choose. It is worth 20% of the final grade at SL and HL, in both Analysis and Approaches (AA) and Applications and Interpretation (AI). Your teacher marks it and the IB moderates a sample. The IB recommends a length of about 12 to 20 pages, double-spaced.
The five criteria (20 marks)
- A. Presentation (4 marks): is it organised, coherent and concise, with a clear aim and conclusion?
- B. Mathematical communication (4 marks): correct notation, terminology, labelled graphs and defined variables.
- C. Personal engagement (3 marks): evidence that you own the exploration: your own questions, data, examples or extensions.
- D. Reflection (3 marks): critical thinking about your results, methods, limitations and what they mean.
- E. Use of mathematics (6 marks): relevant mathematics at the level of your course, used correctly and with understanding. The expectation is higher at HL.
Criterion E carries the most marks. A beautifully written exploration with only simple maths will not reach the top band, so choose a topic that lets you use the mathematics of your course.
What makes a good topic
- A narrow, clear aim, such as “to model”, “to find”, “to compare” or “to prove”.
- Mathematics from your syllabus or slightly beyond, explained in your own words.
- A personal connection: a sport you play, a place you know, data you collect yourself.
- Room to reflect: assumptions to test, limitations to discuss, extensions to try.
Ideas for Analysis and Approaches
- Modelling the shape of a bridge, arch or bottle with polynomial or trigonometric functions, then finding a volume of revolution (HL).
- Finding the optimal angle to throw a ball or kick a football, including air resistance assumptions.
- Approximating π or e with series, and investigating how fast each method converges.
- Proving and generalising a number pattern you noticed, using induction (HL).
- Using differential equations to model the cooling of tea or the spread of a rumour (HL).
- Exploring the geometry of a shape in your home, for example the area enclosed by a rangoli or kolam design.
Ideas for Applications and Interpretation
- Testing whether cricket or football scoring follows a Poisson distribution, with a chi-squared goodness-of-fit test.
- Regression on your own data: does sleep time predict reaction time among your classmates?
- Optimising a delivery route in your city using graph theory (HL).
- Modelling the growth of a city's population or of a social media account, and comparing exponential and logistic models.
- Using Voronoi diagrams to decide where a new shop or school should go (SL and HL).
- Comparing the cost of loans or savings plans with financial mathematics.
From weak idea to strong aim
Weak idea: “The Fibonacci sequence in nature.” Why is it weak, and how can it be improved?
- It is a well-worn topic that usually becomes description rather than mathematics, so criteria C and E suffer.
- Improve it by asking a question you can answer: “How closely does the ratio of consecutive spirals on a pineapple from my local market match the golden ratio, and how many spirals must I count to estimate it to two decimal places?”
- Now there is personal data, a measurable aim, an error analysis and a conclusion to reflect on.
A quick modelling example
You measure tea cooling from 90 °C to 60 °C in 10 minutes in a 20 °C room. Using Newton's law of cooling, T = 20 + 70e−kt, find k.
- At t = 10: 60 = 20 + 70e−10k, so e−10k = 40/70 = 0.5714.
- −10k = ln 0.5714 = −0.5596, so k = 0.056 per minute.
- In an exploration you would then test the model against more readings and reflect on why it fits or fails.
A simple plan
- Brainstorm three topics linked to your interests and check each against criterion E.
- Write a one-paragraph proposal with your aim and the mathematics you expect to use, and agree it with your teacher.
- Do the mathematics first, then write it up with clear notation and graphs.
- Reflect throughout, not only in the conclusion: why this method, what assumptions, what if they fail?
- Edit for length and clarity, and check every symbol is defined.
Common mistakes
- Choosing a topic only because it sounds impressive, then not understanding the mathematics.
- Using mathematics below the level of your course, which caps criterion E.
- Copying an explanation from a website instead of explaining it yourself.
- Graphs without labelled axes or units, and variables that are never defined.
- Reflection that only says “this was interesting”.
Practice questions
Try each one before opening the answer.
Q1. How many marks is criterion E worth, and why does it matter most?
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Q2. A data set of 50 goals per match has mean 2.4. Under a Poisson model, what is P(0 goals)?
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Q3. Rewrite this aim more precisely: “Investigating bridges.”
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Frequently asked questions
Is the exploration the same for AA and AI?
Yes. Both courses use the same five criteria and the same 20% weighting. Choose mathematics that fits your own course.
How long should the IB Maths IA be?
The IB recommends about 12 to 20 pages, double-spaced. Longer explorations often lose marks for conciseness under criterion A.
Can a tutor help with my maths IA?
A tutor can help you understand the mathematics, choose a workable topic and understand the criteria, but the exploration must be your own work, as the IB requires.
How much is the IB Maths IA worth?
The internal assessment (the mathematical exploration) is 20% of the final grade in both Maths: Analysis and Approaches and Maths: Applications and Interpretation, at SL and HL. It is usually 12 to 20 pages long.
Key takeaways
- 20% of the grade in AA and AI, SL and HL.
- Five criteria, 20 marks; use of mathematics is worth 6.
- Pick a narrow aim you care about.
- Use mathematics at your course's level.
- Reflect throughout, not just at the end.