Writing is always more difficult when you are racing against the clock. Write a Rough Draft - your paper always improves between drafts. Have your professor or TA read your draft over - if the person grading the paper feels like he or she helped work on it, then they are more likely to give you a good grade. Use quotes from lecture - this shows that you were paying attention in class, and a professor is less likely to dispute his or her own ideas. Write in a quiet place where you can concentrate.
Good writing requires concentration.
Proofread you paper out loud. This is a good way to catch mistakes and awkward sentences. Also, have a friend or class mate read over your paper. If possible, choose a topic for your paper which you will be able to reuse in another class.