The good news is that these questions are pretty basic, so there are plenty of books covering them. Ask your lecturer if he/she can recommend another book or maybe even if he/she can loan you a copy. If you are allowed to access the stacks in the library, go to the place where the recommended book is supposed to be (books are grouped by topic) and look at the books nearby that cover the topics in question: Boolean algebra, counting principles, basic probability and basic liner algebra. Look up the recommended book or something like "Discrete Mathematics and Its Applications" by Rosen on Amazon and see related books there. And, of course, feel free to ask any specific questions on this forum. It is recommended to limit the number of question to two per thread. Questions about the first part should be asked in the Discrete Math subforum, and the ones from the second part (vectors, matrices, planes, etc.) should probably go to the Advanced Algebra subforum.

You can definitely prepare for an exam like this in the time remaining.