So I’m a DP junior and I’m ahead one math. I’ll be finishing Math II this year, so I have two options from my teacher. One is to take the SL exam this year plus the Calc AB exam, and take only BC next year. The other is to learn the HL material, and I assume do all the Further Mathematics material as well, and take that HL test at the end of next year. I’m not sure what I should do, or how difficult Further Math gets. I know it entails all the HL options plus two others, but that’s about it. What can you tell me?
Calculus BC and Further Mathematics HL are two different monsters. Yes, they are both monsters.
Mathematics HL involves learning all of Calculus BCs material, save for several topics (e.g. Length of an arc using integrative methods; Vector, Parametric, and Conic calculus; etc)
It does, however, involve learning Linear Algebra (a class you will probably have to take in Sophomore or Junior Year of college), Statistics and Probability (some say it’s very similar to AP Stats, although I cannot confirm this), Discrete Mathematics (an optional class you will take in junior or senior year of college --> It’s more math olympiad practice, I would say), and extra Geometry (things you would not even see in some college curricula).
Formally, the Further Mathematics HL curriculum involves Math HL + a Geometry Core + 4 HL Options (Sets, Groups, and Relations; Statistics and Probability; Calculus; and Discrete Mathematics)
Calculus BC is more practical. It fullfils most Calculus I and Calculus II classes in US universities, and allows you to skip them.
It involves 1 full year of learning calculus. Just pure calculus. Nothing else. You need to have solid understanding of trigonometry and other basic functions to understand Calculus BC, which I’m guessing you already have.
In the end, choosing between Calculus BC and Further Mathematics HL depends on what you want to study. Do you want to study pragmatically, finishing as much Calculus as you can in your high school years, or do you want to study Mathematics broadly, having “taste-tests” of different areas of mathematics. Choose Calculus BC for the former, and FurMath HL for the latter. 