<p>I would just point out that it is a lot more work for Caltech to develop and administer its own placement exams. They have their own standards, and as Ben notes, assume that most students enter having the equivalent of an AP course anyway. If you really want to take courses that are widely available in high school, you may be missing the point of Caltech. The few people I know who got 5’s on calculus are very glad they did not try to skip Math 1. It was much deeper and more theoretical than their high school courses.</p>