Racing to calculus in high school so that you can repeat it in college?

However, Caltech’s math courses are theory/proof based, so that regular college math courses or AP courses do not cover the material in the same depth. Caltech expects entering frosh to have taken regular calculus while in high school before starting there (and regular multivariable calculus while in high school would also be a bonus before taking the Caltech theory/proof based version).

I.e. the Caltech math situation is quite a bit different from that of a student with an 5 on AP calculus BC who repeats a regular calculus course at a college that allows that AP score to give advanced placement.