50 Excellent IB Math IA Topic Ideas (AA and AI Streams) (Dubai 2025)
Choosing a topic for the IB Mathematics Internal Assessment (IA), or Mathematical Exploration, is often the most challenging part of the process. Students are tasked with finding a subject that balances two critical criteria: Personal Engagement (Criterion C)—a genuine interest in the topic—and Mathematical Rigor (Criterion E)—the opportunity to apply mathematics commensurate with the level of the course (HL/SL).
A poorly chosen topic can derail an exploration before it begins, while a well-defined, engaging topic can inspire a Level 7 investigation.
This guide, curated by experienced IB educators and IA moderators in Dubai, provides 50 diverse starting points for your exploration. These ideas are designed to inspire, avoid common clichés, and offer potential for rigorous mathematical analysis across both the Analysis and Approaches (AA) and Applications and Interpretation (AI) streams.
Executive Summary: Key Takeaways
Balance is Key: A successful IA topic balances personal interest with mathematical rigor appropriate for your DP level (HL/SL).
Avoid Clichés: Steer clear of overused topics (like the Fibonacci sequence in nature or the Monty Hall problem) unless you have a highly original approach.
Focus Your Aim: A broad topic leads to a superficial IA. Narrow your idea down to a focused research question or aim.
Stream Alignment: Consider whether your topic lends itself better to the theoretical approach of AA or the applied focus of AI.
Use This List as Inspiration: These ideas are starting points. You must personalize the idea and develop your own unique aim and approach.
The Criteria for an Excellent IA Topic
A Level 7 IA topic must meet several key criteria:
Focus and Clarity of the Aim: The exploration must have a precise objective, not a broad theme.
Opportunity for Genuine Personal Engagement (Criterion C): The topic should allow you to demonstrate independent thinking, creativity, or a unique perspective.
Mathematics “Commensurate with the Level of the Course” (Criterion E): The mathematical concepts and techniques used must align with the rigor of the syllabus. HL students must demonstrate greater sophistication than SL students.
Your choice of topic should align with the philosophy of your course. While there is flexibility, some topics naturally lend themselves better to the theoretical focus of Analysis and Approaches (AA) or the applied focus of Applications and Interpretation (AI). Understanding the core differences between the AA and AI streams is crucial during the selection process.
Choosing the topic is only the first step. The execution—how you research, analyze, and present your findings—is what determines your final score. Once you have an idea, consult our step-by-step guide on how to structure the IB Math IA to understand the expectations.
The Curated List of 50 Ideas
Below is a list of 50 IA topic ideas, categorized thematically, with indications for their suitability for AI or AA, and potential for HL exploration.
1. Statistics and Data Analysis (Primarily AI)
The foundation of a 7 is a profound understanding of the syllabus.a
This category is ideal for AI students, focusing on real-world data, hypothesis testing, and statistical modeling. HL students should aim for sophisticated techniques (e.g., t-tests, chi-squared, advanced regression).
Queueing Theory in a Local Context: Modeling the waiting times at a busy coffee shop or supermarket checkout and optimizing the number of servers. (AI HL/SL)
Impact of Sleep Deprivation on Cognitive Performance: Analyzing primary data collected from peers (requires ethical considerations) using hypothesis testing. (AI HL)
Analyzing Sports Performance Beyond Basic Correlation: Using advanced metrics (e.g., Expected Goals (xG) in football, WAR in baseball) to evaluate player value. (AI HL/SL)
Environmental Data Modeling: Analyzing local weather data (e.g., Dubai summer temperatures, humidity levels) to model trends and predict future patterns. (AI HL/SL; AA SL)
Analyzing the Impact of Tourism on Local Economies: Using statistical methods to quantify the economic impact of major events (e.g., Expo, Dubai Shopping Festival). (AI)
Exploring the Gini Coefficient: Analyzing income inequality in different countries and the mathematical basis of the Gini coefficient. (AI/AA)
Medical Data Analysis: Investigating the correlation between lifestyle factors and health outcomes using publicly available medical databases. (AI)
Predicting Stock Market Volatility: Using statistical models to analyze and attempt to predict trends in financial markets (e.g., DFM). (AI HL potential)
Analyzing Traffic Flow and Accidents: Using statistical analysis to identify accident hotspots and model traffic flow patterns at specific intersections (e.g., on Sheikh Zayed Road). (AI)
The Statistics of Language: Investigating Zipf’s law in different languages or texts. (AI/AA)
2. Calculus and Optimization (Primarily AA)
This category is suited for AA students who enjoy the theoretical depth of calculus, optimization, and differential equations. HL students should explore advanced techniques (e.g., integration by parts, solving differential equations).
Optimizing Container Shapes: Investigating the most efficient shape for packaging (e.g., soda cans, Pringles tubes) to minimize material usage while maximizing volume. (AA)
Modeling Physical Phenomena with Resistance: Exploring projectile motion considering air resistance, which introduces differential equations. (AA HL potential)
The Brachistochrone Problem: Exploring the curve of fastest descent between two points under gravity. (AA HL)
Calculus in Architecture: Analyzing the mathematical design of complex architectural structures (e.g., the curves of the Museum of the Future or the Burj Khalifa). (AA)
Modeling Cooling Processes: Investigating Newton’s Law of Cooling and its application (e.g., forensics, food safety). (AA/AI)
Optimization in Logistics: Determining the most efficient delivery routes (related to the Traveling Salesman Problem). (AA/AI)
Modeling Population Dynamics: Using differential equations to model predator-prey relationships (Lotka-Volterra equations). (AA HL/AI HL)
The Mathematics of Music Harmony: Exploring Fourier analysis and the mathematical basis of musical harmony and sound waves. (AA)
Optimizing Renewable Energy Placement: Using calculus to determine the optimal placement or angle of solar panels. (AA/AI)
Volumes of Revolution: Calculating the volume of irregular shapes (e.g., a vase, a piece of fruit) using integration techniques. (AA)
3. Pure Mathematics, Proofs, and Geometry (Primarily AA)
This category appeals to students interested in abstract reasoning, number theory, and the foundations of mathematics. It is ideal for AA HL students.
Exploring Different Voting Systems: Investigating the mathematics of social choice theory, such as Arrow’s Impossibility Theorem. (AA)
Fractal Geometry: Exploring the mathematics behind fractals (e.g., the Mandelbrot set, Koch snowflake) and calculating their dimensions. (AA)
Complex Numbers and Transformations: Investigating the application of complex numbers in modeling physical systems or generating geometric patterns. (AA HL)
Non-Euclidean Geometry: Exploring spherical or hyperbolic geometry and how they differ from traditional Euclidean geometry. (AA HL)
Number Theory: Investigating prime numbers, modular arithmetic, or Diophantine equations. (AA HL)
The Mathematics of Origami: Exploring the geometric principles behind paper folding and optimization in origami designs. (AA)
Topology and the Möbius Strip: Investigating the properties of topological surfaces. (AA HL)
Exploring Different Proof Techniques: Comparing proof by induction, contradiction, and direct proof through a specific mathematical problem. (AA HL)
The Four-Color Theorem: Investigating the mathematics behind map coloring. (AA)
Knot Theory: Exploring the mathematical classification and properties of knots. (AA HL)
4. Modeling, Algorithms, and Networks (AI/AA Crossover)
This category integrates concepts from both streams, focusing on dynamic systems, algorithms, and network analysis. It offers strong potential for HL explorations in both AI and AA.
Graph Theory in Transport Networks: Using graph theory to analyze the efficiency of transport systems (e.g., optimizing the Dubai Metro map or flight networks). (AI HL/AA HL)
Modeling Infectious Diseases (Beyond Basic SIR): Developing sophisticated epidemiological models (e.g., SEIR models) and analyzing the impact of vaccination strategies. (AI HL/AA HL)
Markov Chains: Using Markov chains to model dynamic processes (e.g., weather patterns, stock movements, board games). (AI HL)
Cryptography and RSA Algorithm: Exploring the mathematics (number theory, modular arithmetic) behind modern encryption systems. (AA HL/AI HL)
Game Theory: Analyzing strategies in games or economic scenarios using mathematical models (e.g., the Prisoner’s Dilemma). (AI/AA)
Modeling Cellular Automata: Investigating systems like Conway’s Game of Life and the complex patterns that emerge from simple rules. (AA/AI)
Machine Learning Algorithms: Exploring the mathematics behind a simple machine learning algorithm (e.g., linear regression, k-means clustering). (AI HL/AA HL)
Modeling Traffic Flow: Using mathematical models to simulate traffic jams and analyze the impact of road design. (AI/AA)
The Mathematics of GPS: Investigating the geometry and algebra involved in global positioning systems. (AA/AI)
Modeling the Spread of Information/Virality: Using networks to model how information spreads through social media. (AI HL)
5. Applications in Finance, Business, and Games (Primarily AI)
This category focuses on the practical application of mathematics in economic and recreational contexts, ideal for students interested in business and finance.
Exploring the Black-Scholes Model: Investigating the mathematics behind option pricing (requires advanced calculus and statistics). (AI HL/AA HL)
Optimizing Investment Portfolios: Using mathematical modeling (e.g., Modern Portfolio Theory) to balance risk and return. (AI HL)
The Mathematics of Gambling: Analyzing probabilities and expected values in casino games (e.g., poker, blackjack) and evaluating strategies. (AI/AA)
Modeling Business Growth: Using logistic functions or other models to analyze the growth trajectory of companies. (AI)
The Mathematics of Ranking Systems: Exploring the algorithms used to rank sports teams (e.g., Elo rating system in chess) or websites (e.g., Google’s PageRank). (AI/AA)
Financial Mathematics: Deep dive into amortization, annuities, and the modeling of loans and investments. (AI)
Actuarial Science and Insurance: Investigating the mathematics used to calculate insurance premiums and assess risk. (AI HL)
Modeling Supply Chains: Using mathematical optimization to improve the efficiency of supply chains. (AI HL)
The Mathematics of Board Games: Analyzing the strategy and probability involved in complex board games (e.g., Settlers of Catan, Risk). (AI/AA)
Behavioral Economics and Mathematical Modeling: Exploring how mathematical models are used to understand human decision-making. (AI HL)
Scaling the Scope: HL vs. SL Considerations
Remember that Criterion E requires the mathematics to be “commensurate with the level of the course.”
How to Increase Complexity for HL: An SL topic can often be adapted for HL by introducing more sophisticated techniques:
From Correlation (SL) to Hypothesis Testing (HL): Instead of just calculating a correlation, perform a t-test or chi-squared test.
From Basic Modeling (SL) to Advanced Modeling (HL): Use matrices, graph theory, or differential equations instead of simple linear or quadratic models.
From Basic Calculus (SL) to Advanced Techniques (HL): Utilize integration by parts, volumes of revolution, or optimization with multiple variables.
It is crucial to understand the specific demands of your level. We recommend reviewing the detailed comparisons of the difficulty gaps for both the Analysis and Approaches (AA) stream and the Applications and Interpretation (AI) stream to ensure your chosen mathematics aligns with the expectations.
Overused Topics That Examiners Are Tired Of
While it is possible to score well with a common topic if the approach is highly original, we strongly advise against the following clichés. Examiners have seen these hundreds of times, making it very difficult to demonstrate genuine Personal Engagement.
Fibonacci sequence and the Golden Ratio in nature/art.
The Monty Hall Problem.
The Birthday Paradox.
Basic correlations (e.g., GDP vs. life expectancy, BMI vs. exercise).
Golden Ratio in facial beauty.
Choosing an overused topic makes it extremely difficult to demonstrate genuine personal engagement and originality, which is one of the most frequent pitfalls. Before committing to a topic, review our analysis of the common mistakes students make on the IB Math IA.
What to Do After You Choose Your Topic
Refine the Aim: Narrow your chosen topic into a focused research question or aim. (e.g., instead of “Math in Basketball,” aim for “Modeling the optimal shot trajectory considering air resistance”).
Preliminary Research: Ensure the necessary mathematical tools are within your grasp and that data (if needed) is available.
Consult with Your Supervisor: Discuss your refined aim and proposed methodology with your teacher to ensure it is viable.
Once you have selected a compelling topic, the challenge lies in the execution—developing the mathematical analysis, ensuring rigor, and communicating your findings effectively. Our expert IB Math IA support and guidance provides personalized mentorship throughout the exploration process, from refining the aim to the final draft.
Conclusion: Your Mathematical Journey
The IB Math IA is a unique opportunity to move beyond the textbook and explore an area of mathematics that genuinely interests you. Embrace the challenge, be creative, and let your curiosity drive the exploration.
The IB Math IA is an opportunity to explore mathematics beyond the textbook. If you need guidance selecting a topic or support throughout your IB mathematics journey, our team of specialized math tutors in Dubai is here to help.
Frequently Asked Questions
If your IA is statistics-based (common in AI), look for publicly available datasets from government databases, international organizations (e.g., World Bank, WHO), sports analytics websites, or scientific repositories. You can also collect your own primary data through surveys or experiments, but ensure your methodology is rigorous.
Yes, you can explore mathematics beyond the syllabus. This is often encouraged, especially for HL students, as it demonstrates strong Personal Engagement and mathematical curiosity. However, you must ensure that you thoroughly understand the mathematics you are using and that the level of rigor is commensurate with the course. The majority of the mathematics should still be grounded in the DP level.
It is very important (Criterion C, 3 marks). Personal Engagement is about making the exploration your own—showing independent thinking, creativity, and genuine curiosity. It is often the differentiator between a good IA and an excellent one.
AA (Analysis and Approaches) topics tend to focus more on pure mathematics, theoretical concepts, proofs, or the analytical application of calculus and algebra. AI (Applications and Interpretation) topics typically focus on applied mathematics, statistics, data modeling, and the use of technology to solve real-world problems. However, there is flexibility, and crossover is possible.
Your aim should be highly focused and specific. A broad topic (e.g., “Math in Climate Change”) leads to a superficial exploration. A focused aim (e.g., “Using the Weibull distribution to model wind speeds in Dubai”) allows for deep mathematical analysis and reflection.