1. Survey the landscape. When you first get the test, look over the whole thing. Figure out what the tasks are, paying special attention to how many essays you're asked to write (be sure to note any choices offered) and, most important, how much time you're supposed to devote to each. You'd be amazed at how many students make a mistake about the basic instructions.
2. Budget your time. Craft each essay around the time you have available. Professors who allot one hour expect longer and more detailed essays than ones who ask you to write for 20 minutes. Don't have a one-size-fits-all approach to essay questions. (By the way, it wouldn't hurt to take a working watch to the exam. Not all professors want to track the time for you.)
3. Scan (in your mind) all the resources. Before you start writing your answer, think through what elements of the course might be relevant for your answer. Most students are primed to think first about the lectures that bear on the topic. But if you can bring in materials from the reading or discussion sections, and if they're relevant, your answer is likely to be stronger.
4. Don't waste time. Some students begin an essay exam by writing elaborate outlines—so elaborate that they run out of time after writing a sentence or two of the actual answer. If you need to jot down a few notes before you start, that's fine, but you need to spend most of your time writing the answer, not preparing to write it.
5. Don't survey. If you're asked a specific question, answer that specific question. Don't dump everything you know about a topic into your response. No matter how nervous you are, you need to attend to what's being asked. Professors usually craft their essay questions carefully, so if you compare when you were asked to contrast, or list reasons but don't assess them, it will be noticed when the grading rolls around.
6. Don't introduce. Essay exams are not the time to give lengthy introductions or "setups" to the topic. Usually the time is budgeted tightly, and there's not time for this. Begin your answer in the very first sentence. Nailing the main point down right up front puts your essay on track for an A.
7. Don't gesture. Some students think the answer is so obvious—and the professor knows it, after all—that they only need to wave their hands at the answer (rather than wasting all that ink to spell it out). But the prof is looking for you to demonstrate your knowledge and understanding of the material, which can only be done if you take the time to make explicit your points. Be sure your answers can be understood by a reasonably intelligent person, not one who is previously familiar with the material (like the professor).
8. Write quickly and neatly. More detail equals a better grade (usually). Legible handwriting equals a better grade (usually).
9. Keep it real. Answer in simple, clear language. Avoid fillers, and eliminate irrelevant material. When an instructor is reading 70 essays on the same topic, information not related to the topic really stands out like a sore thumb. Some graders just ignore it, but others take off for it.
10. Don't be afraid to go back. It's OK to go back to a previous essay to fill in some important point you just thought of. Just draw an arrow to the margin or to the top of the paper and add in your latest brainstorm. In many cases, these later additions tip the scales from a B to an A.
Question in mulitple parts. If the question has specific subparts or subtasks, it's often best to do them separately, and to "letter" your parts (Part A, Part B, Part C, etc.). That way the grader will be able to see that you've answered each of the parts and assign you the points to which you're entitled.
Running out of time? If you find yourself running out of time on a question, at least sketch out how you would answer the part you've left out. Usually you will get at least some credit for this and won't have to take the full hit for material left unanswered.
One of the most common questions we get asked is what you can do to turn your B essay into an A essay. Though each course is different, here are seven things you might think about to turn a good essay into an excellent one:
Offer a more nuanced thesis, not the most obvious one.
Probe the relations between the parts or issues treated in the question.
Give more examples or illustrations.
Draw distinctions if they are relevant to the question(s) asked.
Bring in materials from the readings or the discussion section (if relevant).
Use the methods, techniques, and analytic tools of the field (like the ones the professor or TA used in the lectures).
Borrowed from: https://www.usnews.com/education/blogs/professors-guide/2009/11/18/top-10-tips-for-taking-essay-tests