Just about every exam I had at university involved solving/proving at least one novel problem that we'd never seen before. For example we might have seen the proof of a statement under certain conditions, but on the exam you where asked if it was also true for a slight different condition. That isn't something you could do just through memorizing the proofs you'd been shown in class.

Memorizing and 'regurgitating' would most of the time get you a passing grade, but never a top grade.