You need to be way more specific; you can't expect somebody to pick up a particular text and tick off for you "important problems" vs. "unimportant problems".
Most texts, though, DO provide their own hints of hard/advanced problems, versus routine problems.
As a general advice, you should be able to do ALL routine problems (those are typically the one given directly after the chapter, while separate problem sections will, in their last problems concentrate the truly challenging ones).
HOWEVER:
Your most important guide to which problems you MUST master are those problems which do NOT introduce new notions, but are directly asking you questions concerning the immediate text preceding them.
If a problem has a long, utterly new directions, relative to the main text, those problems are regarded as fairly advanced, and depending on the time you have at your disposal should WAIT, until you are fairly certain you master routine problems.
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Exams will, at lower levels, have a predominant focus at testing adequate competency at routine problems, in order to weed out the incompetent, whilst including a couple of "nasty ones" in order to singling out for grade praise the particularly gifted ones. If you fully master routine problems, but none of the advanced problems, you'll pass, not fail. In all probability, your professor isn't a malevolent being having a ghoulish glee at destroying the hopes of the next generation by making exam way too hard.
