Even though the AP Calculus exam is months away, students are already beginning to stress about staying on top of the demanding course load needed to pass the test. But, by following these six tips, students can maximize their potential in class and conquer the exam.
1) Read a good textbook.
If your teacher is not providing you with the best notes, find a good textbook, like James Stewart’s Single Variable Calculus or Jon Rogawski’s Calculus. These textbooks are written in a way so you can follow along on the thought process without getting lost in the math. While you are reading the textbook you should always write study guides by highlighting key terms, formulas and theorems. In addition, it’s helpful to redo example problems from the textbook. After all, you have the solutions and explanations right there, so don’t be afraid to try it on your own!
2) Learn the concepts, procedures, and methods
: The AP exam emphasizes concepts more than plug-and-chug type problems. Understand why a theorem exists and what you can do with it. Then, learn to do the algebra, arithmetic, and graphing. Be methodical! Work neatly, carefully, and consistently so you can remember the steps to a basic problem and extend it to a difficult one.
3) Look for patterns.
As you read through the book and look at more examples, see if you can spot what the author is doing over and over. Math—and especially calculus—is based on logical thinking and if you can follow the logic for one problem, chances are you can extend that logic to any problem the AP exam throws at you.
4) Practice, and practice it again.
Even after your teacher assigns homework problems, do the next one over (e.g., if he or she assigns #4, do #5 on your own). Do every problem in the review section of the textbook—most often textbooks will provide you with all the review answers. Redo the problems you missed on the homework or quiz. The more times you do a problem, the more likely you are to see the pattern that you can extend to other problems, like those on an exam.
5) Do practice Free Response Exams.
The College Board—the folks who make the AP Exam—has an extensive list of practice free response questions for you to practice. You will notice that every year there is a pattern of questions that show up, over and over. So make sure you know how to do those types of problems! For example, they like to test on infinite sums and series—I would make 110% sure that I know how to do those. Especially since FRQs are free and accessible to everyone, you’ll be able to see what sorts of concepts show up over and over again and you can hone-in your studying topics. (Hint: Look out for those integration by parts, 1st and 2nd fundamental theorems of calculus, volumes, and Taylor series).
6) Know how to take advantage of your calculator.
Although many teachers will not allow you to use it on an in-class exam, a TI-89 is allowed for the AP exam. Use it to your advantage: Understand when to use a calculator (e.g., to solve for an unknown, to graph a function, etc.) and how to use it. Write out all your steps to get partial credit in case you do something wrong.
If you think you need an extra boost in AP Calc BC, consider dropping in on my AP Companion Course. Revolution’s AP Companion Courses are designed to give students weekly tutoring sessions on advanced topics. Every week I instruct a couple Companion Courses- you can call Revolution at (877)738-7737 to set up a free session in my class.