Not necessarily past exams, but practice tests with worked solutions would help. Actively discourage students from just memorizing the answers at the last minute.
Look at MCAT prep. It's basically all practice testing. If you took the SAT or ACT or AP exams, did you take practice tests?
Here are several reasons to provode practice exams.
Practice testing helps students learn. Students are quite literally practicing the things you would like them to know.
Practice tests help students gauge their level of understanding. How many times have you heard a student say, "I thought I was going to do better on that test?" That would not be as likely to happen if they took a practice test or two well in advance.
It is more effective than other studying techniques. A lot of students, if they don't have questions to practice with, will reread the book, flip through their notes, and say they get it. They could be fooling themselves because they don't know if they can answer questions about the subject.