My school offers (only AP wise):
AP Calculus
AP Calculus AB
AP Calculus BC
They all seem the same, though AB seems to cover more than just AP Calculus and BC seems to cover Calc I and Calc II in both years.
Would it be doable going from precalculus to AP Calculus BC?
Yes because AB and BC both start from the same point, right after precalculus. It’s just that BC moves faster and covers all the AB material as well as extra topics, so stronger math students tend to take BC.
I think you may be mistaken, there is no ap exam just called ap calculus. Whether your school offers a course called that is a different story, but, to answer your question, yes it’s doable. BC is about 60% AB 40% new stuff.
I went from Pre-Calc to BC, so it’s completely manageable. AB and BC are almost the same, but BC has a few extra topics (Taylor Series, convergence, divergence, etc.).
One of the things I regret the most is taking AB before BC (I’m a junior currently in BC and took AB last year and precalculus as a freshman). For someone who did well in precalc and likes math, AB was way too easy. If you’re doing well in precalc and are willing to have hard math for a year, go ahead and take BC.
I never stated an exam in AP Calculus. My school offers that as a separate course.
In general, it’s not AP without an exam.
You must talk to your own school. Some schools teach BC after precalc. Others expect AB as a prereq. Do not go by what happens in another school. Ask your GC and the BC teacher.