How to Study Calculus

So I just finished my Calc 2 class with the highest marks in the class and I wanted to put together a “guide” on how to study for calculus. It doesn’t matter if you are taking AP Calculus or Calculus in college, this guide should be a general overview but I will mention some specifics to AP Calc. 

General Tips

• Buy the AP CALC review books. Regardless of whether you are in college calculus or actually in AP Calculus, the review books are great in condensing materials and having good examples. 
• Create your own cheat sheet. Every time you learn a new formula or theorem, write it down in a cheat sheet. This forces you to recall the information constantly.
  • Know your common derivatives and common integralslike the back of your hand.
  • Fundamental Theorem of Calculus, Part I & II? Yeah, it’s fundamental. Need to know that. 
  • Common limits? Yep, that too. 
• Know your pre-calc and algebra by heart. The hardest thing about calculus is not the formulas and theorems, but recalling past materials to solve a problem. If you could easily recognize trigonometric identities, you would be well set for the class.
  • Know what trig graphs look like and what they approach, etc. 
• Learn how to do the math without a calculator. Some professors don’t let you use calculators on the tests and when you are become too dependent on the calculator, you tend to forget how to do simple addition/subtraction and multiplication/division. Also, there is a non-calculator portion to the AP Calculus Exam, so don’t make your calculator your crutch.
• Practice every day + do your homework. A little practice everyday goes a long way and doing your homework (even if it doesn’t count as a grade) can be a drastic way of improving your grades because chances are, your teacher knows you probably aren’t going to do the homework and will have test questions very similar to the homework questions. 
  • Show all your work. Write all the steps out. If you make a mistake mentally, your whole answer will be wrong. To decrease the chances of loosing points for careless errors, label everything, even if it tedious. Also, work shown can count towards partial credit on tests. 
  • Practice the problems from your textbook + problems outside your textbook.
• Understand and review old tests. When you get your tests back, redo the whole test on another sheet of paper. Try to understand where you went wrong. Was it a simple math calculation error? Did you do the derivative wrong? Was the theorem wrong? Did you forget a step like checking for conditions to apply L’hopitals Rule or Alternating Series Test for Convergence? Whatever it is, go through the entire test (yes, even the ones you got right) and re-do it. 
• Ask for help when you don’t understand something. Solving tough calculus problems are easier when working with a group on a white board because you get a fresh set of eyes and a new mindset/approach to a problem. If you cannot tackle a problem, regardless of how many ways you have tried, it’s best to ask someone who already knows how to do it. 

Resources for AP Calc

• Buy review books. Honestly, this is self-explanatory. I usually would go with a Barron review book, but hey, what ever works with you. 
• Do the previously released AP Calc exams. If you are a BC student, do the release exams for both AB and BC for more practice. 
  • Previously released AB Exams
  • Previously released BC Exams
  • Step-by-step explanations for free response questions release
  • AB Study Guide

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Cheat Sheets + Other ResourcesI advise you to print out the cheat sheets and place it in the front of your calculus binder/notebook or where it can be easily accessed. 


Cheat Sheets

• AP Calculus Stuff You Must Know Cold 
  • This 2-page cheat sheet is honestly god gifted and I advise you to print it out and laminate or something and put it in the front of your calc binder/notes. Will definitely save your life. 
• Algebra Cheat Sheet 
• Trigonometric Cheat Sheet
• Calculus Cheat Sheet
• Derivatives and Limits
• Integrals

Online Tutorials + Videos

• Khan Academy
  • Differential Calculus
  • Integral Calculus
• Paul’s Online Math Notes
• HippoCampus

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Online Calculators

• Symbolab’s Calculus Calculator
  • The most beautiful thing to ever exist when you are checking your answers or looking for the steps on how to do a problem.
  • Don’t rely on it too much. Actually learn how to do it. 
• Wolfram Alpha
  • Implicit Differentiation Calculator
• Desmos Online Graphing Calculator
  • Bet you don’t know how to graph an x-function on that TI-84 without solving it out for y. But it’s cool, neither do I. That’s why I rely on Desmos’ Online Graphing Calculator.

​Source: studygene