A CS degree at any decent university will require calculus I and II and linear algebra, and probably also discrete mathematics (or some CS-department replacement). It's 50/50 whether it will require differential equations and/or calculus III. This is the voice of experience looking up CS degree plans at many different universities.
abge is also correct about what the academic field of computer science is. Phil and Draug are partially right about what it is as practiced. As both have mentioned, of course, there are actually many CS jobs where the math IS used, though somewhat rarely to the same extent that it is used by (say) electrical engineers.
(Some fields, though, like graphics or audio processing, are going to be very math-intensive, and at a level somewhat beyond calculus. On the other hand, sometimes it's possible just to use the algorithms that others have developed without fully understanding them).
@CM, abge is completely right. Math is not a course that has anything to do with memorization. The one and only way to study it is to work a great number of problems until they are second nature to you. There is no other alternative. By "great number of problems," I mean, say, all the problems in the book (if you have a book). If you get stuck, go to your teacher for help.