Remember that if your professor wants you to solve a new problem using knowledge you already possess, the exam question is bound to seem a bit strange at first. You will have to do a little new thinking. Now is the time to do it. Show your professor that you're answering the question. When it comes to in-class writing, students aren't the only ones pressed for time.
Most professors try to turn around exams more quickly than papers.
This has its benefits for the student. Your professor is reading quickly, so, as mentioned earlier, you can probably get away with prose that's a little looser and a little rougher. But if the professor doesn't immediately see how your answer addresses the question, you will suffer. He or she will not stop to ponder how your sixth paragraph relates to your first. In a bluebook, the pages only turn one way.