If I could give only one piece of advice to Princeton students about preparing for exams it would be this: think of your exams as performances (e.g. a sporting event, contest, play, or recital) and prepare for them like you would for a performance.
We intuitively recognize that knowing is not the same as doing. Knowing what the technique is for solving a math problem, for instance, is not the same as using that technique effectively. To be able to do something well on demand and under pressure we need to practice regularly, and ideally, under authentic circumstances. We practice particular scenes, movements, or plays over and over again. As the performance approaches, we "go live". We scrimmage against another team or do a dress rehearsal. A coach or director gives us guidance and feedback on our performance so that we can build on our strengths and shore up our weaknesses through continued, focused practice.
Yet, how many of us put the same kind of purposefulness into our preparation and practice when it comes to academics? Students who wouldn't dream of stepping onto a stage or into a match without having practiced a lot nonetheless walk into exams without having practiced on Princeton exam-level questions under test conditions (e.g. timed, without resources like answers in the back of the book). Just as with most things, the "secret" to success is preparation. But there are less and more effective methods of preparation.
Consider how you prepare for performances and how that differs from how most people prepare for tests or exams. For performances, sure we learn the plays and formations, or memorize the music, lines and dance steps. But that's not all; in fact that's just the basics. What we do when we prepare for performances is practice what we'll be doing in the contest, on the stage, or on the field.
And, though it's almost too obvious to point out, here's what we don't do.
When getting ready for a game (let's say basketball) we don't watch a bunch of games on television and think that will be sufficient. "Hey coach, I'm ready for the big game against Harvard; I just watched the Lakers beat the Knicks (or vice versa)" is not going to cut it. When preparing to perform a piece of music, we don't simply go over the score and listen to an expert's recording of it. Notice, though, that if when preparing for an exam we simply "do" the reading or "go over" it or "look at" class notes (phrases students frequently use to describe their "studying"), that's pretty much what we're doing. We're observing how a scholar analyzes information and makes arguments when we read a text; and in lecture we merely watch as a professor or AI solves a problem. These can be passive events and learners need to ensure that they actively engage in the kinds of tasks they are going to be examined on if they expect to perform up to the rigorous expectations of Princeton faculty and at standards comparable to fellow Princeton students.
Let me spell out the mismatch. On the exam, our task is not to take the exam period to re-read a text or review course material to see what we can get out of it. We're going to be asked to do things with our knowledge, to demonstrate our expertise by performing tasks like solving complex problems or making nuanced arguments. That is, not just any tasks, but the kinds of tasks that an organic chemist or an art historian or a psychologist (depending on the course) does in their work. You're going to be asked to think like a budding expert in the field and do what they do, not simply "know" the subject. This is a key difference between high school and Princeton, and it requires that students re-think how they go about learning and that they alter their approaches to academics and adopt new learning strategies.
McGraw has assembled comprehensive advice for students on preparing for Princeton-level exams, which includes ideas on how to practice for both problem-solving exams in quantitative courses and essay exams in the social sciences and humanities.
So, here's the final two words of advice I have for you from the research on experts: “Deliberate practice. Practice Deliberately”