In all IB Math classes, students must write a 12-20 page research paper that is commensurate with the level of difficulty of the course. You can explore the materials studied within the IB math syllabus, but it is also recommended to look elsewhere and a little beyond for inspiration.
Throughout the course, you should think about some areas in math that interest you, and how and where that math could be applied. It is highly recommended to choose a topic that is personally related, for the Personal Engagement criteria.
One of the most important parts of writing IA is to keep the level of math consistent and coherent with the SL/HL syllabus. YOU should understand every math you use in the paper, and YOUR PEERS also should be able to follow your paper fairly easily. If you don't seem like you are understanding the math, then that is worse than writing on easier math.