An essay examination tests not only your knowledge and understanding
  of the subject but also your skill in reading and writing.  It tests
  your skill in reading in that it requires you to find out exactly what
  the questions mean, not approximately what they are concerned with.
  It tests your skill in writing in that, if you are to be successful, you
  must make your meaning unequivocally clear, you must employ a
  reasonable organization with sufficient thought development, and
  you must make every word count.  And all this you must accomplish
  in what is essentially a first draft.  No wonder, then, that it is difficult
  to write a good essay examination.

             Glorfield, Lauerman, Stageberg, A Concise Guide for Student Writers

Some tips for writing successful essay exams are:

1.  Read the entire exam carefully before plunging in to answer question I.  Note the amount of credit given to various questions, e.g. I= 20%, II=80%, and allot your time accordingly.

2.  Note the verb used in the exam question; for example, contrast suggests a quite different rhetorical method than define or attack.  Be sure you understand all the terms used in the question, and use a dictionary if you’re in doubt.  Be watchful for vague words like democracy or religious, which require a clear definition before you use them in your essay.

3.  Five minutes devoted to making an outline or rough list of topics you intend to cover are five minutes well spent.  You want to avoid digression or repetition.  Clear organization and sharp focus are especially important in an in-class essay.
 
4.  Be sure you answer the question!  All the information you’ve gathered in preparation for this exam is of little use if not applied to the assigned question.

5.  It’s a good idea to indicate your answer to the question, your argument, in your introductory paragraph.  You may have time for a strong conclusion, but you may not.  You want to avoid writing an exam that is filled with specific information but never addresses the question directly.