How to Prepare for the AP Calculus AB Free Response Questions
Updated: May 7, 2019
I have a lot of students who are preparing for AP Calculus exams right now, so I thought I'd cover some helpful tips to prepare. The best thing you can do is practice. You want to be constantly doing previous year's free response questions.
But here's the most important tip for the free response questions (FRQ): they are fairly predictable. For the most part, the types of questions used on the AP Calculus Exam are similar each year. Below I included a picture of all the FRQs from the previous years. I split it into two tables so you could see somewhat more recent exams versus a longer period of time, but the trend is the same.
Your goal is to be a master of the top 7 types of questions here. That's why I organize my AP Calculus YouTube playlists by these topics so that you can practice a lot of those topics that you may be struggling with.
Rate problems usually are describing the rate of something happening in a word problem. Typical rate problems will talk about flowing in and flowing out and you're given an equation describing the rate of change. Here's an example of the 2018 free response question on rates:
You want to make sure you understand a few basic concepts to answer this question:
The integral of the rate of change is the amount. In this example, the rate r(t) is people per second who enter the elevator, so the integral of this rate is the number of people who enter the escalator.
There's usually a flow-in rate and a flow-out rate. In this problem, r(t) is the number of people who enter per second, which is the flow-in rate. The flow-out rate is 0.7 people per second because that is the rate people are leaving the escalator. The net rate of change of people on the escalator is the flow-in rate minus the flow-out rate.
This is a favorite for AP Calculus AB. I would definitely expect one of these types of questions on your AP Calculus Exam. This kind of problem requires you to find information about a function by knowing a graph of its derivative. Thus, the normal techniques for finding derivatives and integrals analytically won't be of any use. Instead, you have to understand the physical interpretation of derivatives of integrals. Here's an example from the 2018 AP Calculus exam.