AugustEntry,
Nuke math isn't as hard as people make it out to be. If you did well enough on the ASVAB to be accepted, you probably have the ability. It wouldn't be a bad idea to brush up on your algebra, and a basic review of trig (and I mean BASIC - knowing SOHCAHTOA should suffice). If you're an MM, I don't think you'll use any trig after you finish your A-school math class - until you get to Power School, that is. If you're an EM or ET, you'll be using it more, since it applies in electrical theory. The thing people have trouble with in Nuke school math is the fact that the Navy takes basic concepts and overcomplicates them to a ridiculous extent, which will never again be applicable during your training. One simple mistake will give you an answer along the lines of "x = 1/2y + 22z/3ps - 3t/2r" when the actual answer is "x = 2". The only thing you can do is develop your attention to detail and your ability to keep your composure & think clearly during a timed exam.
As far as doing push-ups for your recruiters, I'm not sure if you have to or not. However, one thing you'll learn in the Navy is that you shouldn't pull technicalities on your seniors to try and get out of something. If you were to tell your recruiter that he can't make you do anything, you'd better pray he doesn't know or get into contact with your RDC once you go to boot camp. You would quickly realize that a few push-ups with your recruiter would be a comfortable alternative to the humiliation that would come along with constantly being singled out and beaten down in front of 80 recruits for 2 months.
As long as you stay motivated and are willing to put in the required effort, you'll make it through the training. If I were you, I would focus more on learning the things you'll need to know in boot camp. Transitioning from civilian life to boot camp is the hardest transition you'll go through, and if you go into it already knowing what you need to know, it will make it a lot easier for you. Learn the Sailor's Creed, 11 General Orders, Rank/Rate insignia, and practice doing facing movements & marching. That will give you a head start on 95% of your division. Also, there are books you can buy that teach you how to fold your clothes, make your rack, etc. Showing up to boot camp knowing all these things will probably get you extra (unwanted, although good) attention from your RDC's, but they'll like you, and they'll realize they don't need to micromanage you as much as everyone else. That little bit of slack goes a long way.
Hope this helps. Good luck to you!