Can I take an AP exam even though my school does not offer this specific AP course? And if my AP exam score is from 3-5, can I report it to colleges that accept AP credit (this is even when I don’t get school credit)?
The challenge may be finding a teacher at your school, or another school, that will offer the test for you. Unlike the SAT, there aren’t generic “test centers” where one can just sign up to test. I don’t think CB has any specific prohibition against it, though I do seem to recall that “self study” testing became more difficult this year.
If you do take a test, and meet the scoring criteria for credit/placement for a specific college, I don’t see why you wouldn’t receive the credit/placement.
I would caution about this though - “self study” AP scores mean nearly nothing in college admissions, and doing well on a 2-3 hour test typically doesn’t provide the real learning that an entire year of coursework does.
If you want credit for a Gen Ed, off-major, history or psychology class, that’s probably fine. Cramming from a book to squeak out the minimum score for credit on a Physics test and then jumping into 2nd year Physics as a STEM major at a challenging school is likely a bad idea.