It’s nearing the end of the quarter for most college students and high schoolers are coming up on holiday break. That means almost every student, both in high school and college, is stressing over a massive midterm or final exam. Here are a few calculus studying tips that I didn’t necessarily follow myself in high school.
Last year, I took the AP Calculus class offered by my school, as well as the “College in the High School” course offered by the large university in the state. Essentially, this meant that I earned college credit for my work in addition to an actual grade. This differs from AP Calculus in that I do not just receive credit, but I also get a GPA on my official college transcript. While beneficial, the pressure of a grade that follows me beyond my high school years is pretty significant– if I messed up badly, I could jeopardize my admission into grad schools because the grade was recorded on my college transcript. But being a high school senior certainly made focusing difficult– after all, it is senior year, and senior-itis was beginning to kick in.
Looking back at last year, I know there are a couple of mistakes I made in my studying habits, and now that I am at a four year university where you compete with the best-of-the-best for a spot at the top of the grade curve, I realize the importance of paying attention to math in high school.
Here are my top calculus studying tips and the mistakes I made when I was in high school:
The AP class I was enrolled in was structured in a way that we didn’t ever have to do the homework. Most everyone in the class did the first assignment, figured out the teacher didn’t check work, and then stopped doing homework– myself included. This was fine for those that really had a natural ability to do calculus well, and while I, to a lesser extent than some, had this ability, ultimately I should have done the homework.
Here’s a secret that a lot of people know, but don’t necessarily realize the advantage of: many teachers take problems from homework, change a number or two, and stick it right on the test. I’ve even seen some teachers put questions on tests that are directly from the homework– completely unmodified. Sure, you could spend the time figuring the problem out when you’re taking the test, but why put yourself under that stress? By doing the homework, you’re prepared for questions that are similar– or even the exact same.
Many teachers will give out examples of past exams, especially for midterms and final exams. The teachers want you to do well– they’re not trying to fail you. Often, I’d look at the practice exams for a minute and skim over them, and without really looking at them, I’d decide I was done studying and knew how to do all of the problems.
Don’t skim them. In fact, don’t even just do the problems. Find a quiet place, allocate an hour (or however long your test actually will be), sharpen your pencil and begin. Time yourself, and if you run out of time– stop. Only use the materials you’re allowed on the actual exam– no Wolfram Alpha. By doing a trial-run of the exam, you give yourself an indication of what areas you need to improve on. Do you need to pay attention to the signs of the numbers? Do you need to go faster on a particular type of problem? By timing yourself and treating the practice like a real exam, you can diagnose problems before they become serious issues– like an “F” on your report card could be.
Even better– if you have 3, 4 or 5 or more practice tests at your disposal (if you have more than 5, you should go hug your teacher, or at least buy them a nice holiday gift) do the following:
By the time you do this a couple of times, you should be a pro and be able to ace your exam, because in reality, you’ve already taken it 4+ times.
We had a textbook that was huge and in depth, and it had answers in the back for the odd numbered problems. What more could you need?
The truth is, the textbook makes a horrible teacher. That’s why professors and teachers still have jobs– because they’re so much better and more helpful than reading a textbook. Don’t assume that because you read it in your book that you understand it. If you’re having issues, talk to your teachers, your peers, and any tutors available. Chances are, your parents may even remember some of the stuff you’re doing. If you have older siblings, then that’s even better– the math is probably even fresher in their minds.
Have someone walk you through a difficult problem. Or if no one knows, walk through a problem with someone else that’s struggling and figure it out together. Talk about why a certain method of solving a problem isn’t right, and what method is better. This is great for integrals– use the shell method or disc method, integration by parts or “u” substitution, etc. Often there may be more than one way of solving a problem, but there’s usually a “best” (easiest) way of doing so. Working with someone else will help you find the easiest way.
Eventually, when the day of the test comes, don’t panic. If you’ve taken all of the right steps, you should be able to do well and figure out all of the problems. And even if you do struggle– it’s not the end of the world. But next time, see if you can seek out additional support. There’s no shame is asking someone for help– it’s the best way to show your parents, teachers, and peers that you actually care about doing well in school.
Good luck in your next test, whether it be a small quiz or huge final, and don’t make the same mistakes I did. As for myself– now that last calculus final of my life is coming up, I will definitely be taking my own calculus studying tips seriously this time around.