Skipping Precalculus

I took a summer precalc class, though it only gives credit for the first semester of the course. The class itself had a very ambitious teacher who actually covered basically all of the course curricula except for series ( learned it in algebra 2, so it should be review for me), polar coordinates, and parametric equations. We also didn’t go over limits as much as we should have, we covered the basics of the topic. Both the teacher and the tutor recommend me to just skip the course once I go back to school and jump directly into AP Calc AB. The tutor gave me some review material of the algebra stuff that is needed for calc. I have about three weeks left to review some of the essential material before school starts up for me again. Is it doable for me to jump straight into calc ab without doing the full precalculus course again?

Yes

Yes. Go for it!
But make sure to map out your math sequence through senior year, adjusting based in the major you are interested in.

Make SURE you know limits and parametrics. Both will play heavily into calc and you’ll be expected to know them.

Is the class through your school? I know our high school would not accept it if they hadn’t approved the class ahead of time nor would they approve of anyone skipping a level without taking the full course (self studying, taking a test etc isn’t allowed).

Yeah, my school doesn’t do the self-study thing either. You get credit by passing the courses that we offer, period.

http://math.buffalo.edu/rur/rurci3.cgi may help you determine your actual readiness for calculus (as opposed to whether your school will accept your summer course as a prerequisite).

Sounds like you’ve covered the topics to be ready for Calc AB. Limits is actually the first topic, at least in my D’s coursework, in AB. Neither that nor parametric equations nor polar coordinates were covered in pracalc.

Understanding sequence/series is important - our school also had it in Alg 2, but covered more in pre-calc. I’d learn/review that, and move on to AB.