Hey, first of all you shouldn't need or use a calculator on the test. However, you will have to do some calculation. The calculations can usually be done, however, by rounding off physical constants and stuff like that. Question #91 (if I remember right) in GR8677 is typical of this kind of problem.
Also, you are right - you won't be able to learn all of the material on the exam in a month. In fact, you wouldn't be able to given a year. There's always some random questions that you can't predict. So, what you should do is get good at recognizing questions that are out of your league and then skipping them. It's an essential strategy.