Your IB Math IA is a personal mathematical exploration — a chance to showcase your ability to apply math to real-world contexts or theoretical problems. While creativity is encouraged, a clear structure and rigorous mathematical communication are essential for scoring highly.
1. Cover Page
Include:
- Title (clear and reflective of your topic)
- IB Candidate Number
- Course & Level (e.g., Math AA HL)
- Date of Submission
- Session (e.g., May 2025)
- Page count (IA must be 12–20 pages)
- School name & code
- Your full name
- Optional: Abstract (100–150 words summarizing aim, method, and findings)
- Optional: Declaration of Authenticity (if school requires)
2. Introduction
This section should:
- Explain why you chose the topic (personal engagement).
- Clearly state the aim of your exploration.
- Provide background context (definitions of key terms, theories).
- Outline how you will approach the IA (methods or models used).
- If applicable, state any assumptions made in modelling.
➡ Think of this as: Why → What → How → Then How (your plan of action)
- Main Body (Theory & Calculations)
This is the core of your IA and where most marks are won.
Theory:
- Introduce only relevant mathematical theory.
- Explain why a certain method is used.
- Ensure clarity for someone not familiar with the topic.
Calculations & Application:
- Show step-by-step derivations, not just results.
- Use appropriate notation, graphs, tables, and explain them.
- Highlight assumptions, sample calculations, and interpretations.
- Maintain logical flow between sections.
4. Reflection and Conclusion
Conclusion:
- Re-state the aim and summarize whether it was achieved.
- Explain key findings and their mathematical implications.
- Use this to wrap up your investigation clearly and concisely.
Reflection:
- Should appear throughout the IA, not just at the end.
- Reflect on:
- Strengths and weaknesses of your method.
- How the math deepened your understanding.
- Limitations and assumptions.
- Suggestions for future work or extensions of your topic.
IB guidance: A high-level reflection is crucial, deciding, or deeply insightful and helps develop the exploration.
5. Bibliography
- Use a consistent referencing style (MLA, APA, etc.)
- Include all resources: websites, books, journal articles, textbooks, etc.
- Reference any formulas, theories, or data sources used.
IB Rubric Breakdown (Key Criteria)
| Criterion | Marks | Tips |
| Mathematical Presentation | /4 | Clear structure, logical flow, good use of math notation/symbols |
| Personal Engagement | /3 | Make it personal — choose a topic you care about and reflect that |
| Reflection | /3 | Reflect critically throughout, not just in conclusion |
| Use of Mathematics | /6 | Use appropriate, accurate math with clear explanations |
| Mathematical Communication | /4 | Present all work coherently; diagrams, graphs, and notation matter |
Mathematical communication
- This rubric assess the student’s ability to organize his research and findings in a coherent manner. The fluency of the mathematical language used is assessed via the following ways:Notation
- Symbols (choose universally accepted ones)
- Terminology (All key terms and variables must be defined appropriately when first introduced)
Personal Engagement
A unique part of this IA is the personal engagement. This rubric assess a student’s ability to make the Mathematics his/her own – Infusing creativity in the exploration of ideas from multiple angles. The student must develop his or her own independent understanding of the topic he/she is exploring. For example, you could write in the first person why you have decided to pursue your interest in Fourier series. You could link it with your interest in understanding heat conduction. You discuss the challenges you encountered during your research, discuss how you felt, and emphasize the mathematical concepts you have learned during the investigative process.
Use of Mathematics
This rubric assesses how well a student uses the Mathematics in the exploration. Simplicity is encouraged, and the level of difficulty should be pegged at the level of the course. The Mathematics must be precise, and exhibiting a clear logical structure. Note the difference between receiving a 6/6 for the use of mathematics rubric for HL/SL according to the IB:
SL – “Relevant mathematics commensurate with the level of the course is used. The mathematics explored is correct. Thorough knowledge and understanding are demonstrated.”
HL – “Relevant mathematics commensurate with the level of the course is used. The mathematics explored is precise and demonstrates sophistication and rigour. Thorough knowledge and understanding are demonstrated.”
In both cases you should use mathematics of a similar level to what you are studying in your respective studies. However, in HL, the mathematics that is explored must be precise and shows sophistication and rigour. Students must show the mastery and use of complex concepts, be able to see the Mathematical problem from various viewpoints, and see the ways to link different areas of Mathematics.
E.g., use of mathematics carries a weighting of up to 6/20 while reflection carries a weighting of up to 3/20. Hence, you should expect to spend more pages on calculations than your reflection.
Topics to spur interest (note these topics are not developed but are included to stimulate your own more developed aims):
| Algebra and number theory | Geometry | Calculus/analysis and functions |
| Modular arithmetic
Goldbach’s conjecture Probabilistic number theory Applications of complex numbers Diophantine equations Continued fractions General solution of a cubic equation Applications of logarithms Polar equations Patterns in Pascal’s triangle Finding prime numbers Random numbers Mersenne primes Magic squares and cubes Loci and complex numbers Matrices and Cramer’s rule Matrices and coding/decoding Image rotations using rotational matrices Divisibility tests Egyptian fractions Complex numbers and transformations Euler’s identity: ei_ + 1 = 0 Chinese remainder theorem Fermat’s last theorem Natural logarithms of complex numbers Twin primes problem Hypercomplex numbers Diophantine application: Cole numbers Odd perfect numbers Euclidean algorithm for GCF Palindrome numbers Factorable sets of integers of the form ak + b Algebraic congruences Inequalities related to Fibonacci numbers Combinatorics – art of counting Boolean algebra Graphical representation of roots of complex numbers Roots of unity Fermat’s little theorem Prime number sieves Recurrence expressions for phi (golden ratio) Physical, biological and social sciences Radiocarbon dating Gravity, orbits and escape velocity Mathematical methods in economics Mathematical modelling in Biology Modelling in Geography: Gini’s coefficient Modelling of average monthly temperature Biostatistics Genetics Crystallography Computing centres of mass Elliptical orbits Logarithmic scales – decibel, Richter, etc. Fibonacci sequence and spirals in nature Predicting an eclipse Concepts of equilibrium in economics Mathematics of the ‘credit crunch’ Branching patterns of plants Column buckling – Euler theory |
Non-Euclidean geometries
Cavalieri’s principle Packing 2D and 3D shapes Ptolemy’s theorem Hexaflexagons Minimal surfaces and soap bubbles Tesseract – a 4D cube Map projections Tiling the plane – tessellations Penrose tiles Morley’s theorem Cycloid curve Symmetries of spider webs Fractal tilings Euler line of a triangle Fermat point for polygons and polyhedra Pick’s theorem and lattices Properties of a regular pentagon Conic sections Nine-point circle Geometry of the catenary curve Regular polyhedra Euler’s formula for polyhedra Eratosthenes – measuring earth’s circumference Stacking cannon balls Ceva’s theorem for triangles Constructing a cone from a circle Conic sections as loci of points Consecutive integral triangles Area of an ellipse Mandelbrot set and fractal shapes Curves of constant width Sierpinksi triangle Squaring the circle Polyominoes Reuleaux triangle Architecture and trigonometry Spherical geometry Gyroid – a minimal surface Geometric structure of the universe Rigid and non-rigid geometric structures Tangrams Numerical analysis Linear programming Fixed-point iteration Methods of approximating π Applications of iteration Numerical methods solving of equations Numerical methods of Integration Estimating size of large crowds Generating the number e Descartes’ rule of signs Numerical Methods for solving differential equations |
Mean value theorem Torricelli’s trumpet (Gabriel’s horn)
Integrating to infinity Applications of power series Newton’s law of cooling Fundamental theorem of calculus Brachistochrone (minimum time) problem Second order differential equations L’Hôpital’s rule and evaluating limits Hyperbolic functions The harmonic series Time series Torus – solid of revolution Projectile motion Why e is base of natural logarithm function Statistics and modelling Traffic flow Logistic function and constrained growth Modelling growth of tumours Modelling epidemics/spread of a virus Modelling the shape of a bird’s egg Correlation coefficients Central limit theorem Modelling change in record performances for a sport Hypothesis testing Modelling radioactive decay Least squares regression Modelling the carrying Modelling the carrying capacity of the earth Regression to the mean Modelling growth of computer power past few decades Modelling of time series Probability and probability distributions Monte Carlo simulations Random walks Insurance and calculating risks Poisson distribution and queues Determination of π by probability Bayes’ theorem Normal distribution and natural phenomena Medical tests and probability Probability and expectation Logic and sets Codes and ciphers Set theory and different ‘size’ infinities Mathematical induction (strong) Proof by contradiction Zeno’s paradox of Achilles and the tortoise |
Key Reminders
- Stick to 12–20 pages (double-spaced).
- Use proper section headings (e.g., Introduction, Analysis, Reflection).
- Your classmates should be able to understand your IA without extra help.
- Always connect back to your aim.
- Try to keep a personal tone, especially in reflections.
In conclusion, a well-structured layout is crucial for a successful Math IA, including an introduction, main body, analysis, and conclusion. Meeting the rubric requirements is also essential for a high grade, which includes criteria such as presentation, communication, and reflection. By following these guidelines, you can write an engaging and informative Math IA.
