IB Maths IA: 60 Examples and Complete Guide
A practical guide for choosing, planning, writing and improving an IB Mathematics exploration, with 60 focused research-question examples for Analysis and Approaches and Applications and Interpretation students at SL and HL.
Bookmark this page: This updated RevisionTown guide is published at https://revisiontown.com/ib-maths-ia-60-examples-and-guidance/. Use it to narrow your IA topic, test whether your research question has enough mathematics, and connect your idea to the correct IB course level.
Quick Answer
The best IB Maths IA topics are narrow, personal and mathematically rich. A strong IA does not begin with "I want to write about calculus" or "I want to write about football." It begins with a precise research question that can be explored using appropriate mathematical methods, such as regression, optimization, probability, differential equations, graph theory, geometry, trigonometry, sequences or statistical testing.
The IB Mathematics internal assessment is an individual mathematical exploration worth 20 marks and 20 percent of the final course grade. It is used in both Mathematics: Analysis and Approaches and Mathematics: Applications and Interpretation. The criteria are the same across courses, but the expected level of mathematics should match your course and level. An AI SL student can score highly with a carefully explained statistical or modelling exploration. An AA HL student usually needs deeper analytical mathematics, such as calculus, proof, advanced functions, differential equations, complex numbers, vectors or rigorous modelling.
If you are still deciding between courses or want to understand how AA and AI differ before choosing an IA route, start with RevisionTown's IB Mathematics AA vs AI comparison guide. For broader course support, use the IB Mathematics page, the Mathematics Analysis and Approaches SL/HL page, or the Mathematics Applications and Interpretation SL/HL page.
What Is the IB Maths IA?
The IB Maths IA, officially the mathematical exploration, is a written investigation into a mathematical idea chosen by the student. It is not a standard exam answer, a textbook chapter or a long list of calculations. It is a focused piece of mathematical communication: you pose a question, explain why it matters, select methods, carry out analysis, interpret results, reflect on limitations and present a conclusion that directly answers the research question.
The word "exploration" matters. A good IA shows a journey of mathematical thinking. The reader should see why you chose the problem, how your method developed, what your calculations revealed, and how you evaluated the reliability of the result. The IA rewards accuracy, but it also rewards judgement. You need to explain why a model is appropriate, why a variable matters, why a graph supports your interpretation, and why a limitation affects the strength of your conclusion.
IB documentation describes the internal assessment as an individual exploration involving an area of mathematics. It is internally assessed by the teacher and externally moderated. This means your teacher marks the work first, but the IB can review samples to ensure marking standards are consistent. Because of that moderation process, your IA should stand on its own. A reader who does not know you should understand the aim, the mathematics, the personal choices and the reasoning.
The IA is also one of the few places in IB Mathematics where you can connect mathematics to your own interests. You can investigate sport, music, architecture, economics, environmental data, medicine, computer science, games, transport, engineering, biology, art or another subject you study. Personal interest helps, but it is not enough. The topic must still support meaningful mathematics. A beautiful personal story with shallow calculations will not score well in Use of Mathematics. A technically correct calculation with no focus or reflection will also feel weak.
Good IA question
"How accurately can a logistic model predict the growth of my school's chess club membership over two years?" This is focused, measurable and connected to modelling.
Too broad
"The mathematics of chess." This is a topic area, not a research question. It needs one problem, one method and one outcome.
Too narrow
"What is the mean score of my last five tests?" This can be answered in one calculation and does not create enough exploration.
IB Maths IA Assessment Criteria
The IA is marked against five criteria. Students often focus only on the mathematics, but the marks are distributed across presentation, communication, personal engagement, reflection and mathematical use. This is why a strong IA must be both mathematically sound and clearly written.
| Criterion | Marks | What it rewards | How to show it in your IA |
|---|---|---|---|
| A: Presentation | 4 | Coherent structure, logical development and concise organisation. | Use a clear introduction, aim, method, analysis, reflection and conclusion. Keep graphs, tables and calculations close to the discussion that uses them. |
| B: Mathematical communication | 4 | Correct notation, terminology, diagrams, graphs, units and definitions. | Define every variable, label axes, use consistent symbols and explain formulas before applying them. |
| C: Personal engagement | 3 | Evidence that the exploration is personally meaningful and shaped by your own choices. | Explain why the question matters to you, justify decisions, show initiative in collecting data or adapting methods, and write in your own mathematical voice. |
| D: Reflection | 3 | Thoughtful evaluation of results, methods, limitations and implications. | Discuss what results mean, why limitations matter, how assumptions affect the conclusion, and what could be improved. |
| E: Use of mathematics | 6 | Relevant, accurate and appropriately sophisticated mathematics. | Choose methods that match AA or AI and SL or HL expectations. Show correct working and use the mathematics to answer the research question. |
Criterion E has the largest mark allocation, but it does not work alone. Suppose you create an excellent regression model but never define the variables, never explain the residuals and never reflect on why the model fails at the endpoints. The mathematics may be strong, but communication and reflection will hold the IA back. On the other hand, a polished essay with weak or routine mathematics cannot compensate for a shallow method.
A practical way to plan is to attach each section of your IA to a criterion. The introduction supports Presentation and Personal Engagement. The method and calculations support Mathematical Communication and Use of Mathematics. The discussion and conclusion support Reflection. The entire document supports Presentation because coherence is built through every section.
How to Choose a Strong IB Maths IA Topic
Start with a real interest, then convert it into a mathematical problem. Students often begin with a broad area: football, music, economics, climate change, medicine, architecture or computer games. That is fine for brainstorming, but it is not yet an IA. You need to narrow the area into a question where mathematics can produce an answer.
A useful topic passes five tests. First, it is focused enough to answer in a short exploration. Second, it has data, measurements, diagrams, functions or logical structures you can actually work with. Third, it uses mathematics appropriate to your course. Fourth, it allows interpretation and reflection, not just calculation. Fifth, it has a personal reason behind it.
Topic-selection test: If your research question can be answered without showing mathematical working, it is not a Maths IA question yet. If it requires a university thesis, it is too broad. The best IA question sits between those extremes: challenging enough for analysis, narrow enough for a clear conclusion.
AA vs AI topic choices
Mathematics: Analysis and Approaches usually suits topics with algebraic reasoning, proof, functions, calculus, sequences, trigonometry, complex numbers, vectors and exact methods. If you are using AA formula pages, RevisionTown's functions formulae for AA, calculus formulae for AA, and geometry and trigonometry formulae for AA can help you check the mathematical language you are using.
Mathematics: Applications and Interpretation usually suits topics involving modelling, statistics, technology, data analysis, finance, networks, optimization, probability and real-world interpretation. If your IA uses AI-style modelling, RevisionTown's statistics and probability formulae for AI, calculus formulae for AI, and geometry and trigonometry formulae for AI are natural supporting resources.
SL vs HL topic choices
SL students should not force advanced methods they do not understand. A well-explained SL-level exploration can be strong if the mathematics is accurate, relevant and reflective. HL students, however, should be careful with topics that use only basic descriptive statistics or simple linear regression. If you are in HL, ask whether the mathematical depth is enough for your level. Can you extend the model? Compare methods? Use calculus? Include proof? Analyse residuals? Investigate sensitivity? Solve a system? Use matrices, complex numbers, differential equations or more advanced probability where appropriate?
Recommended IB Maths IA Structure
Your school may give its own formatting guidance, so follow your teacher's instructions first. The structure below is a practical model that works for most explorations because it follows the logic of mathematical inquiry.
| Section | Purpose | What to include |
|---|---|---|
| Title and research question | State the investigation clearly. | A focused title, exact research question, variables or objects being studied, and the context. |
| Introduction and rationale | Show personal engagement and explain why the question matters. | Your motivation, background, scope, assumptions and a brief preview of the mathematical route. |
| Mathematical background | Prepare the reader for the methods. | Definitions, formulas, diagrams, notation and any theorem or model you will use. |
| Method and data | Explain how the investigation is carried out. | Data source, sample size, measurements, technology used, variables, units and assumptions. |
| Analysis | Develop the mathematics step by step. | Calculations, graphs, models, derivations, comparisons, interpretation and checks. |
| Reflection | Evaluate the strength of the work. | Limitations, model assumptions, accuracy, uncertainty, sensitivity and possible extensions. |
| Conclusion | Answer the research question directly. | A concise answer supported by your results, plus final comments on reliability and meaning. |
| References and appendices | Support academic integrity and keep the main text concise. | Sources, data links, large tables, extra graphs and repeated calculations if needed. |
The strongest IA structure feels like a chain. Each section leads to the next. You should not suddenly introduce a formula in the conclusion, place a huge table before explaining why it matters, or hide the main calculation in an appendix. If a graph or calculation is important enough to support the argument, it should be in the main body and explained clearly.
Useful Mathematical Tools and Formulas for the Maths IA
The right method depends on your research question. Do not choose a formula first and then force a topic around it. Instead, decide what your question asks: prediction, comparison, optimization, measurement, proof, uncertainty, pattern, rate of change or relationship. Then choose the mathematical tool that fits that purpose.
Regression and model fit
Regression is useful when you want to model a relationship between variables. A linear model has the form:
where \(a\) is the intercept and \(b\) is the gradient. A residual measures the difference between an observed value and a modelled value:
For model comparison, students often use the coefficient of determination:
Do not simply state that a high \(R^2\) is good. Reflect on residual patterns, outliers, data quality, sample size and whether the model makes sense in context.
Statistics and uncertainty
Statistical topics work well when you have real data and a question about variation, association or prediction. The sample mean and sample standard deviation are common starting points:
If your IA relies on standard deviation, check RevisionTown's standard deviation formulas. For quick checking and exploration, the statistics calculator can help, but your IA should still explain the mathematics rather than outsourcing the reasoning to technology.
Optimization
Optimization asks for a maximum or minimum. In calculus-based explorations, a common route is to define a function \(f(x)\), find critical points and test them:
Optimization topics are strong when the constraint is realistic. For example, optimizing the dimensions of a package for fixed volume is better than optimizing a random shape with no context. The reflection should discuss whether the constraints match the real situation.
Growth models
Exponential and logistic models are useful for population, finance, disease, social media, cooling, decay and growth topics. A basic exponential model is:
A logistic model introduces a carrying capacity \(K\):
For related review, see RevisionTown's exponential growth and decay page.
Differential equations
Differential equations are appropriate for many AA HL and some AI HL explorations because they model rates of change. A simple separable model may begin with:
More advanced models, such as SIR disease modelling, use systems:
If you choose this route, your IA must explain the meaning of each parameter. RevisionTown's differential equations page can help you review the background before writing.
Sequences, series and binomial methods
Sequences can support investigations into recursion, finance, population, algorithms, games and number patterns. A geometric sequence has:
For topic support, use Sequences or Binomial Expansion when those methods appear naturally in your exploration.
60 IB Maths IA Examples and Research Questions
The examples below are not titles to copy. They are starting points that show how broad interests can become focused research questions. Adapt the context, data and method to your own situation. A strong IA should feel personal, not generic.
| No. | Research-question idea | Possible mathematics | Best fit |
|---|---|---|---|
| 1 | How does changing the iteration rule affect the visual complexity of a fractal generated from a simple recursive process? | Recursion, self-similarity, scale factor, box-counting dimension and logarithmic relationships. | AA HL, AA SL extension |
| 2 | Can a recursive sequence model the growth of a savings plan better than a simple explicit formula? | Arithmetic and geometric sequences, recurrence relations, compound interest and limiting behaviour. | AA SL, AI SL |
| 3 | How accurately does Newton's law of cooling model the temperature drop of my preferred hot drink? | Exponential decay, differential equations, curve fitting, residuals and parameter interpretation. | AA HL, AI HL |
| 4 | At what parameter values does the logistic map change from stable behaviour to chaotic behaviour? | Iteration, fixed points, bifurcation diagrams, sensitivity to initial conditions and graphical analysis. | AA HL |
| 5 | What is the most efficient delivery route between a fixed set of local destinations near my school? | Graph theory, distance matrices, nearest-neighbour algorithm, route comparison and optimization. | AI SL, AI HL |
| 6 | How would changing the infection rate affect the peak number of infections in a simple disease model? | SIR model, systems of differential equations, parameter changes, graphs and interpretation. | AA HL, AI HL |
| 7 | Which geometric container shape minimizes surface area for a fixed volume of 500 ml? | Surface area, volume, differentiation, constraints and comparison between cylinders, prisms and cones. | AA SL, AA HL |
| 8 | What launch angle gives the greatest projectile range for a ball under measured local conditions? | Quadratic functions, trigonometry, projectile equations, regression and experimental error. | AA SL, AI HL |
| 9 | How closely can a simplified gravitational model predict the orbit path of a selected planet or moon? | Conic sections, inverse-square relationships, parametric equations and model limitations. | AA HL |
| 10 | Why do parabolas, ellipses and hyperbolas appear in real optical or orbital systems? | Conic equations, focus-directrix properties, transformations and applications to reflectors or orbits. | AA SL, AA HL |
| 11 | What is the optimal release angle for improving my basketball free-throw success rate? | Projectile motion, trigonometry, quadratic modelling, measurement uncertainty and comparison of trials. | AA SL, AI SL |
| 12 | How can probability be used to compare penalty-kick strategies in football? | Conditional probability, expected value, two-way tables, decision trees and sample bias. | AI SL, AI HL |
| 13 | Can linear or nonlinear regression predict running performance from weekly training distance? | Regression, correlation, residuals, outliers and comparison of linear, exponential or logarithmic models. | AI SL, AI HL |
| 14 | How does drag affect swimming speed over short and long distances? | Proportionality, power functions, regression, rates of change and physical assumptions. | AA HL, AI HL |
| 15 | Does my heart-rate recovery after exercise follow an exponential decay model? | Exponential functions, half-life, curve fitting, residual analysis and health-data limitations. | AI SL, AA SL |
| 16 | How can exponential decay model caffeine concentration in the body after different drinks? | Half-life, exponential decay, parameter estimation and comparison of scenarios. | AI SL, AA SL |
| 17 | How do logarithms explain musical intervals and equal temperament tuning? | Logarithms, frequency ratios, geometric sequences and percentage error between tuning systems. | AA SL, AA HL |
| 18 | Can a Markov chain model the chord transitions in a song or playlist I enjoy? | Transition matrices, probabilities, steady states and data coding. | AI HL |
| 19 | How can Fourier-style thinking explain the shape of a simple sound wave? | Trigonometric functions, periodicity, harmonic components, regression and technology-supported modelling. | AA HL |
| 20 | How different are just intonation and equal temperament for a chosen musical scale? | Ratios, logarithms, cents, geometric sequences and error analysis. | AA SL |
| 21 | Which function best models the arch shape in a local bridge, gate or building? | Quadratic, catenary, trigonometric or exponential models, regression and residual comparison. | AA SL, AA HL |
| 22 | Is a suspension cable closer to a parabola or a catenary in a real bridge photograph? | Coordinate modelling, transformations, hyperbolic cosine, residuals and scale estimation. | AA HL |
| 23 | What dimensions minimize packaging material for a product box with a fixed volume? | Optimization, differentiation, constraints, surface area and real design limitations. | AA SL, AI HL |
| 24 | What solar-panel angle maximizes estimated sunlight exposure in my city? | Trigonometry, angle of elevation, seasonal data, sine models and approximation. | AI SL, AA SL |
| 25 | How accurately can trigonometry estimate the height of a school building from shadow measurements? | Right-triangle trigonometry, error propagation, repeated measurement and reflection on accuracy. | AA SL, AI SL |
| 26 | Does smartphone battery percentage decrease linearly or exponentially during a fixed task? | Regression, exponential decay, residuals, data collection and model comparison. | AI SL |
| 27 | Can logistic growth model the follower count of a school club or public account over time? | Logistic functions, carrying capacity, parameter estimation and long-term prediction limits. | AI HL |
| 28 | Do arrivals at my school cafeteria fit a Poisson model during lunch? | Poisson distribution, mean rate, goodness of fit, data collection and queue implications. | AI HL |
| 29 | How reliable is my bus or train route based on arrival-time data? | Mean, standard deviation, box plots, normal modelling, probability and schedule interpretation. | AI SL |
| 30 | How can traffic-light timing be adjusted to reduce waiting time at a simple intersection? | Optimization, piecewise functions, rates, simulation, expected waiting time and assumptions. | AI HL |
| 31 | Is the average temperature in my city changing linearly over the past 20 years? | Time-series data, regression, moving averages, residuals and correlation limits. | AI SL |
| 32 | Can rainfall probability be modelled from historical monthly rainfall data? | Probability distributions, mean, variance, seasonal grouping and prediction uncertainty. | AI SL, AI HL |
| 33 | How can integration estimate the volume of water passing through a stream cross-section? | Numerical integration, area under a curve, trapezoidal rule and measurement limitations. | AA SL, AI HL |
| 34 | Which model best describes the growth of atmospheric carbon dioxide over a selected period? | Regression, exponential and quadratic models, residuals, extrapolation and ethical interpretation. | AI HL, AA SL |
| 35 | Can a transition matrix model changes in age groups within a small population over time? | Matrices, population vectors, transition probabilities and long-term projections. | AI HL |
| 36 | How well does an Elo-style rating system predict outcomes in my chosen sport or game? | Probability, logistic functions, iterative updates, prediction accuracy and model limitations. | AI HL |
| 37 | Can a binomial model estimate the probability of winning a tennis game from serve success rate? | Binomial probability, expected value, tree diagrams and assumptions about independence. | AI SL, AA SL |
| 38 | How can run-rate data predict the final score in a cricket innings? | Regression, moving averages, residuals, piecewise models and uncertainty. | AI SL |
| 39 | What launch angle and speed maximize the distance of a baseball or softball hit? | Projectile equations, trigonometry, optimization and sensitivity analysis. | AA SL, AA HL |
| 40 | What pacing strategy minimizes total marathon time for a runner with measured fatigue data? | Functions, regression, optimization, rates of change and constraints. | AI HL, AA HL |
| 41 | Do examination scores in a class follow a normal distribution closely enough for percentile prediction? | Normal distribution, z-scores, standard deviation, histograms and goodness-of-fit reflection. | AI SL |
| 42 | Is there an association between study time and self-reported exam confidence in my year group? | Scatter plots, correlation, regression, chi-square test or rank correlation. | AI SL, AI HL |
| 43 | How can queueing theory estimate waiting time at a school cafeteria line? | Arrival rates, service rates, expected waiting time, simulation and Poisson assumptions. | AI HL |
| 44 | How well does a normal model describe height variation in a sample of students? | Mean, standard deviation, normal curves, z-scores and sampling limitations. | AI SL |
| 45 | Which probability distribution best models human reaction time in a simple online test? | Histograms, skewness, normal or log-normal models, standard deviation and outlier treatment. | AI HL |
| 46 | How does the frequency of compounding affect the future value of a student savings plan? | Compound interest, exponential functions, limits and comparison of annual, monthly and continuous compounding. | AA SL, AI SL |
| 47 | How do interest rate changes affect total mortgage repayment over a fixed term? | Geometric series, annuity formula, amortization tables and sensitivity analysis. | AI SL, AI HL |
| 48 | Can an inflation model explain the changing price of a common food item over several years? | Index numbers, exponential growth, regression and purchasing-power interpretation. | AI SL |
| 49 | How volatile is a selected asset compared with a market index over a fixed period? | Percentage change, standard deviation, variance, correlation and risk interpretation. | AI HL |
| 50 | How sensitive is an option-pricing model to changes in volatility? | Normal distribution, logarithms, exponential functions, partial sensitivity and model assumptions. | AA HL, AI HL |
| 51 | How accurately does a logarithmic function approximate the number of primes below \(n\)? | Prime counting, logarithms, ratios, percentage error and numerical investigation. | AA HL |
| 52 | How does modular arithmetic make a simplified RSA encryption example work? | Prime numbers, modular arithmetic, Euler's theorem, inverse operations and worked examples. | AA HL |
| 53 | Does a real financial or population data set follow Benford's law? | Logarithmic probability, frequency tables, chi-square comparison and data authenticity. | AI HL, AA HL |
| 54 | How can graph colouring help create a conflict-free timetable for a small set of classes? | Graph theory, vertices, edges, chromatic number and scheduling constraints. | AI HL |
| 55 | How many valid arrangements are possible in a simplified Sudoku-style puzzle? | Combinatorics, constraints, permutations, counting cases and proof structure. | AA HL |
| 56 | What is the shortest path through a network of school buildings or campus locations? | Weighted graphs, Dijkstra-style algorithm, distance matrices and route interpretation. | AI HL |
| 57 | How can matrices transform or compress a simple grayscale image? | Matrices, transformations, pixel arrays, approximation and error measurement. | AA HL, AI HL |
| 58 | How do Bezier curves create smooth shapes in fonts or digital design? | Parametric equations, polynomial functions, control points and curvature. | AA HL |
| 59 | How can exponential decay model medicine concentration after repeated doses? | Exponential decay, recurrence, steady state, half-life and safety assumptions. | AI HL, AA HL |
| 60 | How can linear programming allocate limited resources between competing school projects? | Inequalities, feasible regions, objective functions, vertices and sensitivity analysis. | AI SL, AI HL |
The original version of this article listed ten broad ideas, such as fractals, recursive sequences, differential equations, chaotic systems, route optimization, infectious disease modelling, geometry, projectile motion, gravitational modelling and conic sections. Those are still useful starting points, but the improved list above makes each idea more IA-ready by adding a research-question direction, mathematical route and course fit.
How to Improve a Maths IA Research Question
Most first-draft IA questions are too broad. The fix is not to make the wording more complicated. The fix is to define the object, variables, method and outcome. A strong question tells the reader what is being studied and what mathematics will help answer it.
| Weak version | Problem | Stronger version |
|---|---|---|
| The mathematics of music | Too broad and no method is clear. | How do logarithms and frequency ratios explain the difference between equal temperament and just intonation for a C major scale? |
| Football and probability | The context is clear but the mathematical question is missing. | How can conditional probability be used to compare left, right and centre penalty-kick strategies from a data set of professional penalties? |
| Climate change | Too large for an IA and not specifically mathematical. | Which regression model best represents the trend in annual mean temperature for my city from 2000 to 2025? |
| Optimization of cans | Better, but still generic unless the constraints are defined. | What cylinder dimensions minimize surface area for a 330 ml drink can, and how close are common commercial cans to this optimum? |
| Disease modelling | Too broad and potentially unrealistic without a specific model. | How does changing the transmission parameter \(\beta\) affect the infection peak in a simplified SIR model for a closed population of 1,000 people? |
A good question also creates room for reflection. If the answer is exactly one number, the reflection may become thin. If the answer involves model choice, assumptions, reliability, limitations or comparison, you have more opportunity to discuss the quality of your work. For example, "What is the standard deviation of bus arrival times?" is a calculation. "How reliable is my bus route, and does a normal model represent its arrival-time variation well enough for practical prediction?" is an investigation.
Drafting Workflow for a Strong Maths IA
A strong IA is not written in one sitting. It develops through testing, narrowing and revising. The workflow below is practical because it prevents the two most common problems: choosing a topic that has no mathematical depth and writing a long report before discovering that the data does not support the question.
| Stage | Task | Checkpoint before moving on |
|---|---|---|
| 1. Brainstorm | List 5 to 10 personal interests and possible mathematical links. | At least three ideas can be turned into measurable or investigable questions. |
| 2. Feasibility test | Find data, measurements, diagrams or theoretical material for each idea. | You can access reliable data or create your own valid data collection plan. |
| 3. Method test | Try a small sample calculation or graph before committing. | The method produces enough results to analyse and reflect on. |
| 4. Research question | Write a precise question with variables, context and expected method. | The question is narrow, mathematical and appropriate to your course level. |
| 5. Outline | Plan sections, formulas, graphs and reflection points. | Every section has a purpose linked to the research question. |
| 6. Draft | Write the exploration with calculations, graphs and explanations integrated. | The reader can follow the mathematical reasoning without guessing missing steps. |
| 7. Review against criteria | Check Presentation, Communication, Engagement, Reflection and Use of Mathematics. | You can point to clear evidence for each criterion in the draft. |
| 8. Final edit | Remove repetition, label figures, correct notation and refine the conclusion. | The IA is concise, readable and directly answers the research question. |
When drafting, write the mathematics and interpretation together. Do not place ten pages of calculations followed by one paragraph saying what they mean. After each major calculation, explain why it was done and what it suggests. This habit improves Mathematical Communication and Reflection at the same time.
Technology is allowed and often useful, but it must be transparent. If you use a graphing calculator, spreadsheet, Desmos, GeoGebra, Python or another tool, state what it was used for. If the tool produces a regression equation, explain what the parameters mean. If the tool solves an equation numerically, describe the equation and why a numerical solution is reasonable.
Common IB Maths IA Mistakes to Avoid
Choosing a topic before checking the mathematics
A topic may be interesting but mathematically weak. Test the method before you commit.
Using formulas without explanation
Define variables, explain why the formula applies, and interpret the result in context.
Relying on one graph
A graph can support analysis, but it should be accompanied by calculation, interpretation and reflection.
Writing generic reflection
"More data would improve accuracy" is weak unless you explain how and why the current data limits the conclusion.
Forgetting units and definitions
Undefined variables, missing units and unlabelled axes are avoidable communication losses.
Using mathematics below course level
This is especially risky for HL students. The method should be appropriate for the course and level.
Another common mistake is treating the IA like an Extended Essay. The IA is not meant to be an enormous literature review. Background context matters, but mathematics should drive the document. If a paragraph does not help the reader understand the research question, method, result or reflection, it may not belong in the main body.
Students also lose clarity by overloading the IA with too many methods. Comparing two models can be excellent. Using seven unrelated techniques usually weakens the flow. Choose enough mathematics to answer the question properly, then go deep. Depth is usually more valuable than a scattered display of formulas.
IB Maths IA FAQs
How many pages should my Maths IA be?
Follow your teacher's instructions. Many schools guide students toward a concise exploration rather than a very long report. The practical target is enough space to explain the question, mathematics, analysis and reflection without padding.
Can I use statistics for a Maths IA?
Yes. Statistics can work very well, especially for AI students, but it must go beyond basic averages. Include clear data collection, appropriate statistical measures, graphs, interpretation and reflection on sample size, bias and uncertainty.
Can I use calculus for a Maths IA?
Yes. Calculus is a strong route when the question involves optimization, rates of change, area, volume, motion, growth or modelling. It should be used because the problem requires it, not because it sounds impressive.
Can my IA be on a topic outside the syllabus?
It can, but you must understand the mathematics well enough to explain it clearly. Out-of-syllabus work can show engagement, but it can also become risky if the method is copied without understanding.
Should I collect my own data?
Personal data collection can strengthen engagement, but it must be reliable and ethical. Public data can also work if you choose it carefully and explain why it is suitable for your question.
What is the difference between personal engagement and reflection?
Personal engagement is about your ownership of the exploration: why you chose it, how you shaped it and what decisions you made. Reflection is about evaluating the mathematics, results, assumptions and limitations.
Can I use AI tools to write my Maths IA?
You must follow your school's academic integrity policy and IB expectations. The IA must be your own work. Tools may help with planning or checking, but the mathematical thinking, writing, data decisions and explanations must be authentically yours and properly acknowledged where required.
What is the safest way to choose between two IA ideas?
Run a mini-test for both. Collect a small sample of data or complete one sample calculation. Choose the idea that produces clearer mathematics, better reflection opportunities and a more personal connection.
Final Advice for a High-Quality Maths IA
A strong IB Maths IA is not built around a topic that sounds impressive. It is built around a focused question, appropriate mathematics and honest reflection. Start with something you genuinely care about, but make the mathematics central. Define variables carefully. Show enough working for the reader to follow. Explain graphs and calculations in words. Evaluate limitations specifically. End by answering the research question, not by summarising the whole essay vaguely.
Before submitting, read your IA as if you are an examiner seeing it for the first time. Can you identify the aim within the first page? Are the methods justified? Are formulas rendered clearly? Are graphs labelled? Does the conclusion answer the research question? Is the personal engagement visible throughout the exploration rather than only in one paragraph? If those answers are yes, your IA will be much stronger than a generic topic list with calculations attached.
Official References Used
This guide was source-checked on July 9, 2026 against public IB information about the Mathematics internal assessment and course structure. Always follow your own teacher's instructions and the assessment materials provided by your school.
