@“sh.elite” What math are you taking this year? It’s a little unclear because of some of your previous posts.
Calc AB this year supplemented with 18.01 MIT OpenCourseware would be good preparation, and you can note that in the “additional notes” part of your application. If your math teacher has previously taught AP Calc BC, you might ask them about some work on the side so that you will cover all the material.
Over the summer before freshman year, Caltech provides incoming students with an online class called Math 0. It is a good introduction to proofs that prepares students for taking the freshman math sequence at Caltech. Many incoming students do not have much prior experience with proofs.
You can state on your Caltech application that you plan to take the Calc BC test. But, if you do that, Caltech will expect you to actually take the test and send the scores in July. Yes, this is despite the fact that they don’t offer any credit based on AP tests. It’s an Honor Code thing. You’ll need to read up on Caltech’s Honor Code anyway if you are applying, because there is an essay about that.