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The reason we professors give exams is to find out how much you have learned. Professors need to know that in order to assign grades at the end of the term. You also need to know it so as to assess whether you are mastering the knowledge and skills you paid all this money to go to college to get. (Another reason for exams is motivational. There's nothing quite like the prospect of a good or bad grade to keep one's mind focused during the boring bits.)
In general, as I develop exam questions, I want to identify three things: (1) Has the student studied the material of the class? (2) Has the student understood it? (3) Has the student thought about it well enough to manipulate it? These three questions probably underlie all exams, regardless of the discipline, but since I am an anthropology professor, I will talk about anthropology exams and exams that are like anthropology exams.
Some professors prefer a very narrow sample of the student's understanding and make an exam with only one or two questions that are to be answered at some length, often by composing an essay on a set problem. The logic is that they are concerned to see how well you can reason with the material presented. The disadvantage is that with only one or two questions, there is the risk of them falling into or outside of the student's particular strength, so the exam results are heavily influence by luck.
Others (including me) prefer to get a broader sampling of what you know, using more questions on more topics, and necessarily requiring less time per question. Sometimes this can be done with multiple-choice or true-false formats or variants on them. Sometimes the responses are written into spaces on the exam. Nearly always at least some of the questions on an exam require brief written responses. The disadvantage is that such exams require astonishing effort to create, and are always at risk of turning into mere memory dumps.
In theory, if you have kept up with everything, you should not need to do any extra study for an exam. That turns out to be an overstatement, however. "When a man's knowledge is not in order, the more he has of it the greater will be his confusion," wrote Herbert Spencer. He was probably thinking about anthropology exams. The problem, then, is not just to increase knowledge, but to reduce confusion, that is, to organize what you know.
In preparing for an exam, you should review each of the readings and each of the lectures, first alone, then perhaps with a fellow-student.
Questions of Fact. In introductory courses, most professors ask quite a lot of straight questions of fact. Not obscure facts, but facts that figure in the course in some meaningful way. Admittedly this is partly just to be sure you have been there and been paying attention. Partly it is to find out whether you understand the situation.
For example, the interpretation of fossil life forms depends very much upon their sequence in time. You probably won't remember the details a year after you study them, and you may well mix up the names shortly after the course ends, but at the time you are studying them, you should have a sense of a series of reasonably linked changes in them, and when you go into an exam, names like Homo habilis should still be fresh in your mind so that you are in a position to talk about them. It therefore makes sense for the instructor to check your ability to do that.
Assuming that you have read everything and attended the lectures, and that you have reviewed it all and have basic control over the facts, you should be able to answer these kinds of mechanical questions, whether they are in very short answer form (true-false, matching, &c.) or are in the form of questions requiring short paragraphs of explanation.
Questions of Interpretation. The next issue is being able to be able to reason some about these issues and to link them to each other. This is more challenging. It requires not only recall at the time of the exam, but the ability to draft a coherent statement with little time to plan it and no possibility of revision. Four rules of thumb may help you to write good essays under these circumstances:
Exception: It sometimes happens that a professor asks a question that doesn't seem to make any sense or that misses the point in some way. Sometimes it may even be a trick question (although that is rare). You can always ask whether it is a typo or other mechanical error, but assuming the professor thinks the question is what was intended, what are you going to do with it? The best approach is to begin by stating the real question, and then answering that.
For example, a question in a paleontology course might ask you to describe Neanderthal specimens from China. The problem is that no forms in China are properly described as Neanderthal, even though that is what the question assumes. The best approach is therefore to explain that no Chinese fossils have been identified as "Neanderthal" in the way that the term is used for European forms, and then, if you know more than that, go on to say that some Chinese forms are more or less contemporary with European Neanderthals, and appear to be morphologically intermediate between Homo erectus and modern humans, and that they include Maba, Dingcun, Liujiang, or whatever other examples you can think of.
Finally of course you can also always invoke the ghost of your college patron — Aunt Eleanor, Big Earl, Thumpin' Thurgood, or whoever. Rumor has it that this works, and indeed Aunt Eleanor seems almost pathetically grateful for chocolate chip cookies placed before her statue in the ERC administration building. There have even been unconfirmed reports of all sorts of exam miracles associated with cookie-sacrifice.
I don't encourage this, since, although it is not cheating, it is superstitious to give statues cookies, right up there with wearing a lucky exam shirt or rolling your eyes and muttering "Wiggle, wiggle, whip!" before you start to write. Even assuming it works brilliantly, you wouldn't want to be superstitious just to get a higher grade, would you? (Well ... would you?!)