This is the second and final (pardon the pun) article in a brief series about how to prepare for and take final exams. Here, I presented some strategies for getting ready for the final exam. And here, we saw some strategies for the time leading up to the final exam and into the first five minutes of the exam.
The first moments of a final exam are like the Big Bang — there’s lots that happens in those first few moments, and then for the remainder of the time things proceed at what we hope to be an orderly, even pace. Let’s talk now about those 115-or-so minutes that remain in the exam after the “big bang” of the first few minutes.
First: Watch the clock and stick to your time budget. I’ve mentioned how important it is to set up a quick time budget at the beginning of the exam, for example by dividing the number of minutes you have in the exam period by the point value of the exam and using that ratio to determine how much time to spend on each problem. Having done this, it’s very important to manage your time and not deviate too much from the budget. Ideally you will want to come in under the allotted time values for several of the problems so you can build up a “credit” in your time “account” as you work, which you can then “spend” on problems that turn out to be tougher than they looked. Time is a resource that is scarce, and like any scarce resource you have to budget it and manage it within the constraints of your situation, or else you’ll find it’s all gone precisely when you need it the most.
The biggest mistake I see students make apart from not budgeting their time at the beginning of the exam is simply not taking care to watch their time at all, or even to bring a watch or clock to the exam in the first place. How can you manage your time if you don’t even have a way to measure it? And don’t depend on the clock in the classroom; those somehow seem to stop working or run fast or slow just as finals week starts.
Second: Don’t waste time. As a corollary to the point above, you have to act within the exam period in an efficient way. For example, recently when giving an exam I started the exam period out by giving out some precise instructions about a particular problem on the exam, just before starting the clock. Then, about 20 minutes into the exam, a student walked all the way from the back of the room to where I was sitting and asked me, “You said ___ about this problem, right?”, wanting me to repeat my instructions. That’s 90 seconds of the exam period he will not be getting back. Maybe he’ll finish 10 minutes early and it won’t matter. But I’ve seen a of students who desperately need 2 more minutes at the end of the exam period.
And when you approach a problem, your preparation for the exam needs to be such that most of the basic mechanics of each problem are second nature to you and require little to no thinking. Calculus exams are full of these kinds of problems — there are some concepts that students must think through to set the problem up correctly and then a whole lot of derivative-taking and algebra. The latter — the mechanical stuff — needs to be so finely honed through repeated practice that these take no more time than it takes to write. The real time to be spent is in thinking through the concepts. Sadly, though, many students don’t prepare this way and end up wasting time on simple mechanics that should have become almost habitual by now.
Third: Don’t necessarily stick to working in a linear fashion. Just because the problems are numbered 1, 2, 3, etc. on an exam doesn’t necessarily mean you have to work each one in order. If you’ve done a decent job in your fly-through stage, you will know the locations of each kind of problem on the exam and can go right to the ones with the biggest point values and therefore the biggest impact on your time budget if needed. I’ve seen students get hung up on a tough problem that is numbered, say, #5 out of 10 exam problems; numbers 7 and 10 are a lot easier and well within the student’s grasp; but because the student got hung up, didn’t watch his/her time, and didn’t think to skip a problem and move on to the easier ones, s/he lost a lot more points on the exam than they needed to. Speaking of skipping problems…
Fourth: Don’t be afraid to cut your losses. Sometimes no amount of preparation will prevent an inexplicable brain fart in the middle of an exam. Every student has had this experience. You get to that problem and just can get no traction on it, no matter what. The thing to do here is know how many minutes you have in the time budget for that problem and how much time is remaining; and if you find yourself running out of time budgeted for that problem, you have to be ready to ditch it and move on, possibly never to return to it.
It’s roughly analogous to when a quarterback is in a third-and-long situation and has dropped back in the pocket to throw, and none of the receivers is open and the defensive linemen are bearing down on him. There are two options: get rid of the ball and punt on fourth down, or take the sack and punt on fourth down. Either way it’s fourth down. The rational thing to do is not give up any field position than is necessary. Likewise, the rational thing to do is save your budgeted time for problems appearing elsewhere in the exam that are more doable (and you know where those are because you’ve done a fly-through!). And who knows, perhaps in taking your mind off the troublesome problem, the solution will come to you.
Fifth: Leave nothing blank. But if you have to cut your losses on a problem, don’t just abandon it. Professors are not grading for answers but for sound thought processes. Therefore, the very least you should do on any problem is address the following: What is given? What’s the unknown? What data am I given? What ideas or concepts have I learned that could possibly connect the data and the given with the unknown? Where have I seen a problem like this before and what happened then? What would I do if I could just get unstuck? This way, you are demonstrating that, for example, even though you have blanked out on the Chain Rule, you at least understand that you are supposed to take the derivative, set it equal to zero, solve the equation, and test the results for relative extrema. Personally, I’d give a whole lot of partial credit to a student who gets turned around on the mechanics but has a very solid grasp of the idea and process.
Sixth: Budget 10 minutes for wrapping up. Endgame strategy is very important. You want to take some time, if possible, to spend at the end of the exam going through your work and making sure you have gotten the right idea on everything, and especially that you haven’t made a technical mistake such as leaving out a part of a problem or forgetting to circle your answer or the like. I would advise against making changes to your actual work unless you have verified that you made a mistake on something. It’s too easy, in the mental haze that follows a final exam, to second-guess a correct solution and start twiddling with work that is perfectly fine. Your wrap-up ought to have the same flavor as your fly-through — it’s to be done on the “macro” and not the “micro” level.
Then, before you know it, you’re done! Go out and celebrate your accomplishment and relax. That is, until your next final, which is at 2:00 the same day….
[Topmost photo by dcJohn.]