Hi Holly,
I don't have much help for you...I'd have to dig out dusty old books with that sheet of paper with all the formulas crammed onto it to do that...but I do have lots of sympathy to offer, if that helps. It sounds like you have a truly evil prof. I had a physics lab once, a long time ago, taught by a TA who did evil things like that...I wonder if he's now your prof. He doesn't happen to have a funny French Canadian accent, does he? His quizzes always had questions completely unrelated to anything in lecture or lab. I have this vivid recollection of a quiz that asked us what color an electron was. I also recall answering "sky blue pink" because that answer seemed as logical as the question.
As for the whole formula issue, yes, you do need formulas to solve physics questions, at least a few basic ones that you already seem to have. Your professor's approach is a good one for a few lectures, just to get your thinking cap on and make sure you do intuitively understand the problems you're solving. It will help you catch mistakes when you use the formulas if you have some sense of what direction to expect something to change. However, to never give you any formulas and then expect you to solve problems that require formulas is completely unreasonable. The problem is, once you get beyond a few very basic formulas, deriving the rest of the formulas you'd need does require calculus. I'm not fond of physics courses that don't require calculus as a prerequisite. That just makes no sense because you really can't understand what you're being taught and do end up needing to rely on a memorized list of formulas you don't really understand.
It's true what others have told you that you need to write your very own list of formulas. Just the process of writing them all down will help you remember a lot of them. Besides, it's an age-old tradition among Freshmen to locate the pencil with the thinnest lead, sit down with your one sheet of paper and cram every formula imaginable onto it in your smallest handwriting , writing upside-down, sideways, along the edges, until there is no white space left on the paper. Every physics course I've ever heard of has allowed one sheet of paper with anything you want on it to be brought to the exam. Then the students all arrive at the exam and spend half their time trying to find the right formula amid that sea of scribble. Here's a trick everyone can benefit from. Don't bother cramming every formula onto it. Get the basics down...standard velocity, acceleration formulas, free energy, entropy, enthalpy, etc. Write those large enough so you can read them, and know how to derive the remaining formulas from them. Then, use the rest of the space to write sample problems with the solutions...put on the toughest homework solutions, the ones that if you can solve those, you can solve anything (assuming you are explicitly told you can write ANYTHING on the paper, and not just formulas...don't want to encourage cheating). Afterall, the formulas are useless if you don't know how to use them.
