To me, "a sample exam" would mean a real exam, probably an old one, that people actually took and were graded on.
I don't know what "a model EXAM" would be.
For a free-form question, where you answer in your own words, a "model ANSWER" would be an example of one possible answer that would get a good grade.
Consider the question "Do you think black coffee is healthy or unhealthy? GIve your own answer. Be sure to state your reason."
A model answer might be "I think black coffee is healthy because it does not contain sugar, and sugar contributes to diabetes."
A DIFFERENT answer following the same MODEL would be "I think coffee is unhealthy because it contains caffeine, and caffeine contributes to high blood pressure."