Foreword:
Strictly speaking, this article is tailor-made for the Calc 1 sections that I’m TA’ing this semester (taught by Prof. Mancera). But of course, its main ideas also apply to any other calculus classes taught by other professors. Note that for midterms, different professors have different exam problems while the exam date is the same (Nov 4, Friday) for all Math 125 sections. The final exam, though, will use the same set of problems for all calculus sections. ☺
First and foremost, we have enough reason to believe that the following midterm exam will be extremely similar to the problems on the sample and practice midterm exams based on our first midterm. If you do not have time to review your homework problems again, please review all the sample- and practice- midterm problems. Again, these two sets of problems are the BEST resources for our review. First, try to solve them on your own; then figure out those hard problems you didn’t manage to solve through the solutions that Professor and I provide in lectures and discussions. There are only 8 of them on the two sample exams, so I’m sure, with solutions, you can finish reviewing within 2~3 hours. (Mancera said he’d publish them to Blackboard this weekend.)
Both quizzes and midterms are composed by Prof. Mancera for our course, so the next review I recommend is going over all the quiz problems that you didn’t get right on Tuesdays. First, since you put a lot of effort (at least 20 minutes, right?) into doing them, it will maximize the efficiency of the effort you put in if you run over them again. Second, I have shown you all the detailed solutions in Thursday’s discussions, so reviewing them won’t take too long. Also, if you haven’t already, please take a look at my Gradescope comments on your quizzes since many of my comments there are quite insightful and can give you more information than your mistakes.
Next, our textbook exercises serve as a source of problems for new exams. Hence, be sure to take a look at your homework problems and complete all of Thursday’s discussion questions (problems in red). As there are not a lot of homework problems in our course and we’ve discussed most of them together in Thursday’s discussions, I am sure you can finish reviewing within a few hours as well. Here is Prof. Mancera’s homework and discussion list (the same as what he published in Blackboard). And I have sorted out all these problems here, along with the solutions I provided.
Math is about unchained creation, while unfortunately timed math exams are chained and only about solving problems. (As a result, “how to prepare for calculus exams” and “how to learn calculus” are two very different topics in my opinion.) Thus, once you have finished all the above reviews, you can practice further by going to the past final exams and doing as many problems as you can. (Obviously, you only need to do the problems on the materials we’ve covered so far.) Remember, to nail Calculus exams, volume is the key! However, don’t be pressured; fully understanding all problems on both sample midterms and all quiz problems should already be enough.
An important rule is: even if you know how to solve a problem well, practice it nonetheless. Relatively constant practice will enable you to avoid careless mistakes and to solve all similar problems (covering similar materials) without the assistance of textbooks or the internet. In this process, be sure to pay attention to two things: (1) how long it takes you to do each problem, and (2) how you write your solution up so it clearly explains what you are doing and why.
Moreover, try to write as much as possible on your exam paper, because your grade usually will depend more on your ability to explain how you reached your conclusion rather than your final answer. Incidentally, my design philosophy is “simplicity is the utmost sophistication” (less is more), but unfortunately, this rule does not apply to our exams. Instead, more writing can usually earn you more points as long as your idea is correct. (As I described on my “Design” page, famous mathematician Riemann believed in his teacher Gauss’s motto “few, but ripe”. Therefore, I guess Riemann would not necessarily get a better score than you on our Calc 1 exams.) So, again, avoid doing work in your head, and do not skip steps on your exam.
Last, but not least, please be meticulous on your exam! I assure you that your score will exceed your expectations if you can avoid all careless computational blunders on exam day. They are so avoidable and avoiding them doesn’t take us much effort. So I’m very confident that you can do it. And I am very confident that you will succeed on the exam!
Ivan Zhanhu Feng
October 28, 2022
At my office in KAP Hall, USC