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How to Survive and Thrive in AP Calculus
Monday, September 12, 2016

AP Calculus is typically considered to be one of the toughest AP courses by high school students.  There are actually two versions of the course: AP Calculus AB, and AP Calculus BC.  BC is the harder course of the two, mainly because its curriculum covers a wider range of problems.

We consulted with teachers, tutors, and recent AP Calculus students to come up with four very useful tips--two “how to survive” tips to help you achieve a score of 3 on the AP exam, and two “how to thrive” tips to help you earn a 4 or even a 5.

How to Survive in AP Calculus:

  • Memorize the various different derivation and integration formulas. Because so much of the course is centered around these ideas, the brute memorization of the different forms allows for recognition and thus the ability to solve many different problems. You should memorize these forms as soon as possible; they are central ideas of the course, so you will need to use them all the time. This task is less daunting than it seems, as the integration and derivation formulas are very similar to each other (i.e. the integral of cos(x) = sin(x) + C (a constant), and the derivative of sin(x) = cos(x)*x'). There are not that many different forms, so memorizing them won’t occupy that much time.
  • Learn the specificities of the many different formulas. There is no getting around this, as the particular details of the many rules are often the difference between going about a problem correctly or incorrectly. For example, not knowing that the shell method uses rectangles parallel to the axis of rotation or that the disc method uses rectangles perpendicular to the axis of rotation would result in the wrong answer. It is easiest to commit these nuances to memory as you learn the topics in class, so pay extra attention when your teacher talks about them as you learn new topics. Make a list of this type of rule throughout the year, so that the information is easily accessible whenever you encounter a problem that you may need to apply the rule to.

How to Thrive:

  • Constantly practice sample multiple choice questions. There is no substitute for doing this, and it will ultimately serve you well on the AP exam. After a while you begin to find patterns in the questions, so they get significantly easier. Take note: it is important to pay close attention while doing these problems, as they are oftentimes trickier than they may seem at first glance.
  • Make the effort to understand the derivation of the formulas used in this course. While merely memorizing the formulas may suffice to survive some AP Calculus courses, in order to truly thrive it is necessary to understand the proofs behind the formulas that are used every day in this class. It is easy to find these in any calculus textbook or just by searching online. While it may not seem necessary to do something that your teacher might not even be asking of you, by understanding the derivation of the formulas you will be giving yourself a much deeper understanding of the underlying ideas of the course. If you can, look at the various proofs at the same time that you are getting through material in class.

Good luck!