110 IB Mathematics Extended Essay research questions, aligned with the IB EE requirements and categorized to accommodate Math AA and AI students, HL and SL, across pure and applied mathematics.

Our IB Math EE writers has focused on inquiry, analysis, and critical thinking, not just computation.

🟩 25 Simple but Interesting Math Extended Essay Topics

(accessible, with clear scope and method)

1. To what extent can the spread of a basic disease be modeled using exponential functions?
2. How accurately can linear regression predict housing prices in [city]?
3. To what extent does the golden ratio appear in the structure of human faces?
4. How effective is a linear programming model in optimizing meal plans based on cost and nutrition?
5. To what extent does temperature affect the rate of ice melting, modeled using calculus?
6. How can game theory be used to model basic decision-making in Rock-Paper-Scissors?
7. To what extent do Fibonacci sequences appear in stock market trends?
8. How does the geometry of a soccer ball relate to Euler’s polyhedron formula?
9. What is the optimal angle for maximum projectile distance in simple physics-based motion?
10. How accurate is the trapezoidal rule compared to Simpson’s rule in estimating definite integrals?
11. How can probability be used to analyze winning chances in Monopoly?
12. To what extent does the harmonic series diverge and what does that mean for convergence in real-life models?
13. How can matrices be used to model population transitions in a simple ecosystem?
14. How can parabolas be used to model the shape of suspension bridges?
15. How does the math behind RSA encryption ensure internet security?
16. To what extent can Newton’s Method be used to solve polynomial equations?
17. How can probability trees model the likelihood of certain genetic outcomes?
18. How do changes in sample size affect the accuracy of survey results in polling?
19. To what extent does traffic flow in a city follow principles of queuing theory?
20. How can statistics be used to model average IB student sleep cycles?
21. How does compound interest compare to simple interest over 10 years?
22. To what extent can mathematics model the rate of cooling of coffee using Newton’s Law of Cooling?
23. How can optimization techniques determine the best design for a cylindrical can?
24. To what extent can Pascal’s Triangle model population growth?
25. How can exponential decay model battery usage in smartphones?

🟦 25 Unique and Not Overused Maths EE Ideas

(original, creative, yet researchable)

26. How can fractals be used to model natural coastlines and why do they exhibit self-similarity?
27. To what extent can math model the spread of fake news on social media?
28. How can Voronoi diagrams be applied to determine the most efficient school district boundaries?
29. How do Markov chains model the probability of weather changes?
30. To what extent can Benford’s Law detect anomalies in election data?
31. How can non-Euclidean geometry be used to explain the curvature of space in cosmology?
32. To what extent do different card shuffling algorithms produce randomness?
33. How do power laws explain popularity distribution in music streaming platforms?
34. How does the structure of snowflakes reflect group theory and symmetry?
35. To what extent can graph theory be used to analyze airline route efficiency?
36. How can the mathematics of tiling and tessellation be used in Islamic art?
37. What is the optimal number of checkout counters to minimize wait time at a grocery store?
38. How does modular arithmetic underpin the security of digital currencies like Bitcoin?
39. To what extent can Lagrange interpolation be used to reconstruct missing image pixels?
40. How does the Mandelbrot set illustrate mathematical infinity?
41. How do simple number theory techniques help in developing Sudoku puzzles?
42. How do chaotic systems arise from small perturbations in logistic growth models?
43. How can ellipses model whispering galleries and reflect sound behavior?
44. What is the mathematical basis of optimal packing in 2D and 3D (e.g. oranges in a box)?
45. How does the Fourier Transform contribute to audio signal compression in MP3 files?
46. How can Euler circuits be used to optimize garbage collection routes in cities?
47. To what extent do irrational numbers affect the precision of GPS navigation systems?
48. How can knot theory explain molecular structures in chemistry?
49. How can voting methods be analyzed mathematically to reveal bias or fairness?
50. To what extent does game theory explain competitive behavior in online auctions?

🟥 25 Complex and Challenging Questions for IB Math EE

(advanced modeling, pure math, or abstract ideas — for strong HL students)

51. To what extent can Galois theory explain the solvability of polynomial equations?
52. How does the concept of measure zero apply to the construction of the Cantor set?
53. To what extent does eigenvalue decomposition simplify complex systems of linear equations?
54. How can the Fourier series be used to model periodic electrical signals?
55. To what extent can elliptic curves be used in modern cryptographic systems?
56. How does the concept of fractal dimension apply to the Sierpinski triangle and similar sets?
57. What is the mathematical basis of error correction codes in digital communication?
58. To what extent can topology be used to distinguish between a coffee cup and a donut?
59. How does calculus of variations lead to solutions in physics, such as brachistochrone curves?
60. How does the Riemann zeta function relate to prime number distribution?
61. To what extent can optimization techniques solve real-world logistics problems like the traveling salesman problem?
62. How does the convergence of infinite series affect the approximation of functions?
63. How can the Fast Fourier Transform (FFT) algorithm be used to analyze musical signals?
64. To what extent can discrete mathematics model blockchain structures?
65. How does the use of Laplace transforms simplify complex differential equations?
66. To what extent does the Banach-Tarski paradox challenge conventional mathematical logic?
67. How can integral transforms model heat distribution in materials over time?
68. How do Hilbert spaces contribute to quantum mechanics?
69. To what extent do probability distributions model fluctuations in financial markets?
70. How can the Navier-Stokes equations be simplified for basic fluid dynamics problems?
71. How does dynamic systems theory explain nonlinear population fluctuations in ecology?
72. How can matrices be used to model and analyze social network influence?
73. To what extent can real analysis rigorously define continuity and differentiability?
74. How does the Cauchy-Schwarz inequality underpin various mathematical proofs?
75. How does spectral graph theory analyze complex communication networks?

🟨 25 IB Mathematics EE Current and Up-to-Date Questions

(using recent tech, trends, or relevant modern issues)

76. To what extent can machine learning models be evaluated using statistical error analysis?
77. How accurate are predictive models for COVID-19 case growth using logistic and exponential functions?
78. How does data normalization affect AI prediction in online recommendation systems?
79. To what extent can math be used to optimize delivery routes for companies like Amazon or Uber Eats?
80. How is linear algebra used in AI image recognition software (e.g. face detection)?
81. How can regression analysis be used to detect salary inequalities in real-world datasets?
82. To what extent can math model voter behavior based on demographic data?
83. How are heatmaps and probability used in football player movement analysis?
84. How does blockchain technology rely on modular arithmetic and prime numbers?
85. How can simple statistical tools detect bias in AI-generated content?
86. How can probability models predict the spread of misinformation on social media?
87. To what extent can calculus be used to optimize renewable energy output from wind turbines?
88. How does the geometry of smartwatches influence battery design and space efficiency?
89. To what extent does graph theory support COVID-19 contact tracing networks?
90. How can statistics model and reduce dropout rates in online learning platforms?
91. How can calculus be used to model and minimize carbon emissions in supply chains?
92. How is optimization used in vaccine distribution networks?
93. How does the Poisson distribution apply to analyzing traffic flow through intersections?
94. To what extent do algorithms for ad targeting rely on mathematical clustering methods?
95. How can math evaluate fairness in algorithmic credit scoring models?
96. How do motion tracking systems use vector calculus in sports analytics?
97. To what extent can network modeling predict global supply chain delays?
98. How do AI models use matrices in natural language processing tools like ChatGPT?
99. To what extent can geometry improve drone path optimization in agricultural mapping?
100. How do financial institutions use statistical confidence intervals in market forecasts?

🟪 10 Fun and Unusual Questions for Your Maths Extended Essay

(playful, surprising, still math-based)

101. How does math determine the optimal strategy in Pokémon battles?
102. To what extent do TikTok algorithmic trends follow mathematical patterns of virality?
103. How can number theory help crack escape room puzzles?
104. What is the probability of winning the lottery if you buy a ticket every day for 10 years?
105. How can trigonometry determine the best seat in a circular concert venue?
106. What is the math behind the optimal slicing of pizza (more than 8 ways)?
107. To what extent do palindromic numbers follow predictable patterns in base-10?
108. How can geometry explain why bees build hexagonal honeycombs?
109. How does the probability of “shiny Pokémon” compare across generations and methods?
110. What is the maximum number of M&Ms that can fit in a standard jar, mathematically?