There are many possible topics that you can write about for a math Internal Assessment (IA) in the International Baccalaureate (IB) program. Some possible topics could include:
Exploring patterns in number sequences: You could investigate the properties of a particular number sequence, such as the Fibonacci sequence, and try to find patterns or trends in the sequence.
Analyzing real-world data: You could use mathematical techniques to analyze data from a real-world situation, such as analyzing the distribution of ages in a population or the performance of a stock market index over time.
Modeling real-world phenomena: You could use mathematical models to describe and analyze real-world phenomena, such as the spread of a disease or the motion of a projectile.
Investigating geometric concepts: You could explore the properties of geometric shapes and figures, such as triangles, circles, or polygons, and try to find relationships between different geometric concepts.
Examining the properties of functions: You could investigate the properties of different types of functions, such as linear, quadratic, or exponential functions, and try to find trends or patterns in the behavior of these functions.
Applying mathematical techniques to solve practical problems: You could use mathematical techniques to solve practical problems, such as finding the optimal route for a delivery truck or designing an efficient irrigation system.
These are just a few examples of the many topics that you could explore for a math IA. Ultimately, the best topic for your IA will depend on your interests and the resources that are available to you.