First, think about what your professor wants. In each class you are taking the professor as well as an exam. Does your professor play hide the ball or not? Give hopelessly long fact patterns? Find this out if you haven't already done so. Take some practice exams if the professor has any on file. Attend any review session the professor might offer. Ask questions about your professor's approach to exams.
Second, get plenty of sleep the night before the exam. I didn't always do this, and I could tell a difference in my exam performance. If you haven't mastered the material by the night before the exam, you aren't going to. So get some rest and at least be mentally sharp for the exam.
Third, carefully read the questions. Make sure you identify the issues presented by (or imbedded in) the question. Sort the relevant facts from the irrelevant ones.
Fourth, outline your answer. Take the time to do this. Invariably students do not follow this advice, since outlining reduces the time they have to write their answers. But outlining makes you think about the entire question and how to answer it. You'll be less likely to miss issues, and more likely to organize your answer well--both of which mean a higher score.
Fifth, cite to relevant sources of law on the exam--cases, statutes, regulations, doctrines. You may have the general concepts down, but if you can cite to the relevant cases or statutes, that shows me both that you were paying attention and that you have the gist of how to take law from a particular source and apply it to a new fact pattern. Which is largely what law school exams (and the practice of law) are about.
Sixth, in citing to relevant sources of law, paraphrase. Don't rewrite enormously long quotes on the exam. Use of key legal terminology and a brief paraphrase of a rule or principle will serve just as well, and in fact is better. I personally do not care if you can accurately produce a key paragraph from Judge Learned Hand's opinion in such-and-such a case. I do care whether you understand the principles involved. Use of key terms and a paraphrased summary actually demonstrates your level of understanding better than a long quote.
Seventh, in answering the question, be a lawyer, not a politician. A lawyer asked a question by a client should do her best to answer it. In contrast, all too often a politican asked a question during a debate gives the answer to the question he wishes had been asked. That gets you zero points on a law school exam.
Eighth, when the exam is over, walk away! Don't dwell on what you think you missed. Unless you have a time machine, you cannot do anything about it. Law school exams are complex, and you almost never get to identify or address everything on them. An "A" grade on my exams is often about a 70% score--which means 30% of the points were left on the table. So let it go.
And whatever you do, DO NOT call your professor to discuss how you think you screwed up on the exam. Not only is that enormously unprofessional, the fact is that we grade exams anonymously. Telling me how you answered a question undermines that system, and does far more to harm you than help you.
You might agree or disagree with some of my advice--but if you are in my classes, you'll do far better by heeding these suggestions. So good luck.
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Some of my previous posts regarding how to take law school exams can be linked to here (How Law Professors Write Exams), here (How to Improve Your Law School Exam Grades), and here (More About Law School Grades).