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What are some good study techniques for Calculus?

  1. Feb 22, 2012 #1
    I'm a freshman in college and thinking of majoring in Math and maybe Chemistry (Don't really know yet, as I've never taken high school Chem). I took Calculus 1 (Differentiation) last quarter and managed to get an A+ (94.79%) for the overall course despite not doing so well on the first midterm. I got 86% on Midterm 1 (worth 25% of overall grade), 100% on Midterm 2 (worth 25% of overall grade), and 97% on the Final (worth 40% of overall grade) and homework was done online with unlimited attempts so everyone manages to get the remaining 10%.

    BUT for this quarter in Calc 2 (Integration), I had a professor who gave out the following weight distribution of assessments:
    Midterm 1(worth 30% of overall grade)
    Homework (worth 20% of overall grade) Again it's done online, so full marks is guaranteed.
    Final Exam (worth 50% of overall grade)

    For the first Midterm, despite the fact that I had studied, I only managed to get 47/60 = 78.33%. So I calculated that even if I did get full marks on the Final which is highly unlikely, my overall course percentage will still be 93.5%. To make matters worse, my friend told me that his TA said that their class average for Midterm 1 was about 85%. That would mean that my 78% would be a C grade...plus if they managed to get the same grade as me in the Final, then it wouldn't change anything.

    I know what's done is done and I can't change the past. So, how can I prepare myself for the Final that is 4 weeks from now? Right now, my approach of studying Math is to do a lot of problems from the Textbook (Single Variable Calculus 6 Ed. by James Stewart) after he had taught us the relative section of the chapter. E.g. He goes through Section 7.1 today, I go back home tonight and do problems in 7.1.

    Or should I try a different approach? Perhaps I should read, learn and do the problems from the Textbook ahead of his teaching schedule, so that it would be a lot easier for me to understand his lectures? I also have another Calculus textbook from a different school, should I get extra practice from that book as well so I can be more familiar with solving different types of problems? I'm going to be really dedicated right now on improving myself since I have practically failed my only Midterm, so please give me some suggestions on how to study. I would really appreciate some help from the experts. I haven't got my Midterm back yet, I had only seen my scores online, so I'm not 100% sure what mistakes I have made.

    Sorry for making this so long. But one of the main difficulties I face in Math is forgetting how to do stuff. It is really frustrating that I would forget how to do solve some types of problems such as finding Volumes using Cylindrical Shells or Proof of the FTC after not doing them for 1-2 weeks. My speed would dramatically decrease. So before the exams, I always had to re-do nearly all of those problems in the book to familiarize myself again. Is there a way to decrease the rate of this from happening?
  2. jcsd
  3. Feb 22, 2012 #2


    Staff: Mentor

    i used to make little diagrams on my test when I first sat down to help me remember things maybe you could do the same.

    I would also study the problems I lost points on to see if there was a common thread to my mistakes. Spend more time on these problems but not so much time that you forget the others.

    You could try standing up and teaching it to another student on the whiteboard and then see where you get stuck.

    What are the key things you forget, write them down and carry them with you. At test time, write them down on your test for fast lookup. Find a simple version of the volumes of revolution problems, replay them in your mind so you'll have something to latch on to.

    Sometimes, you can use the test to help you remember. You don't have to start at problem 1 and work your way to the end. Scan the test front to back then do the problems you know and your test anxiety will drop and you'll remember better. Its the anxiety that's making you forget.
  4. Feb 22, 2012 #3
  5. Feb 22, 2012 #4
    Like fauboca said all you need is practice and determination.
  6. Feb 22, 2012 #5


    User Avatar
    Science Advisor

    there are two things involved in problem-solving:

    understanding (the theory and methods behind the solution), and execution.

    the first is the most important, because without it, you can't do the second part. if you don't understand "why", it's going to be hard to focus on the "how". errors of the second kind are: arithmetic mistakes, sign errors, algebraic errors, etc. these things can be remedied by practice, but practicing something 100 times if you don't understand what it is you're practicing, won't make you understand it any better.

    it's hard to say, without knowing what gave you trouble (which questions you missed, and why) which kind of trouble you are having. but from your later remarks about how "things don't stick", makes me suspect you are glossing over the theory, and concentrating too hard on the methods.

    when you really understand something, you don't forget it. the knowledge becomes a part of you, it's not like you can "forget you have a hand", or "how to say hello". sometimes repetition CAN help, because some of the mystery "goes away" through familiarity, but it doesn't always work like that.

    to mention an example you gave as something you "forgot": the cylinder (shell) and disk (washer) methods of finding volumes of solids of revolution depend on a key idea:

    we can find areas of "round" things (the disks/cylinders) easily using known formulas. so the only thing is: do we want to integrate parallel to the axis of revolution (disks), or perpendicular to it (cylinders). are we stacking pancakes, or assembling the rings on a tree? once the underyling "picture" is clear in your mind, the rest is just calculation. i've long-since forgotten the formula for the shell method, and the washer method. it doesn't matter, if i need them, i can re-derive them at will, because i understand why they work (which makes the "how" obvious).

    but i cannot tell you how to "understand things better". studying alone is no guarantee. not that studying and practice and homework is bad, on the contrary, they are like doing warm-up exercises so that you are limber for the game, and are recommended. sometimes the teacher, or the text are partly to blame, but these things are usually beyond your control.

    i would ask myself: why is (some topic) giving me trouble? where do i lose the thread, and how far back is it to firm ground? seeing other texts "may" help. discussing the problems you missed with your instructor is also a good idea.

    the goal is not to "get an A". the goal is to learn calculus, so that you own it, like a car you get to drive wherever you want to. at some point, it will be assumed that you have indeed learned it, future classes that build on calculus will not give any more than a cursory review.

    one thing i might suggest, is: instead of just "doing the problems" in the text, read the theorems (and their proofs, ofc). the theorems are what you're actually supposed to understand, the problems are just exercises to see if you actually do. they are the "tools of the trade", problems are just the "jobs you use the tools on".
  7. Feb 25, 2012 #6
    Do as many practice problems of as many kinds as you can, especially hard ones. Don't just reread the book, but apply what it teaches.
  8. May 30, 2013 #7
    A very useful learning technique is making mistakes. Do multiple problems sets and illustrate the areas of misconception. Once you have mastered learning from your mistakes, your brain will adhere to catching blunders before they occur.
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