<p>Like others, I’m inclined to make my first question, “Why such a hurry?” If you’re that good at math, and you like math, and you’d be bored in a class with sophomores and juniors (and maybe seniors) who are slogging through trig plus whatever else is in your precalc syllabus (it can vary a lot), then OK, I guess. If you’re doing this just as a kind of trophy-collecting, it isn’t going to end very well (but I’m not going to be able to talk you out of it, either).</p>
<p>Before you begin studying calculus, you’ll need to know trigonometry pretty well. Not just the SOHCAHTOA they taught you in Geometry, but a bunch more besides. On the other hand, if you’re a gifted math student, you absolutely can learn trig over the summer.</p>
<p>If you’re that gifted a math student, however, you might need to stop thinking in terms of course titles and start thinking instead in terms of course content. If your high school’s precalculus class is mostly stuff from Algebra II (rational equations and functions, logarithmic and exponential equations and functions) and trig, then maybe you would be bored and restless in it, and you should skip it. On the other hand, if it also includes a lot of new topics (e.g., matrices, vectors in 2 and 3 dimensions, polar coordinates and polar form of complex numbers), then you should take it. Because if you keep hurtling through your high school’s math curriculum, some day you will take a class where it’s assumed you know that stuff. As I said, precalculus classes vary a lot. This is because, mathematically, there isn’t any such thing as “precalculus”; “precalculus” is just a kind of catch-all term we use to name the class where we teach a hodgepodge of topics that we want students to know before they start learning calculus. So before I could say whether I thought it was a good idea to skip precalc, I’d have to know what the content of the course would be.</p>
<p>But if you are so talented a math student that you really should skip precalc and take calculus, I agree with goodgig about the AB curriculum. If you’d be bored and unhappy taking precalculus, taking AB calculus isn’t going to make you very much happier. You’ll think it takes a long time to get where it’s going. If you should skip precalculus at all, you should do it to take BC calculus, and (contrapositively) if you shouldn’t take BC calculus, then you shouldn’t skip precalculus.</p>