I could be wrong about the possibility of not getting any exemption. But I was told to take one... even though I earned 90s on all my regents... weird. I didn't take AP calculus, only regular calculus in my senior year.
If you received letter to take the math placement exam, and your counselor tells you don't worry about it, then don't take it.
Yes. I took it before orientation. I go to City for engineering.