How to Prepare for the AP Calculus Exam – Part 4

You hung on to the last AP Calculus blog post. You’re on your way to a 5, but first…The Free-Response Section. For most students, this is probably the most intimidating part of the test, but if you’re solid with basic derivative and integral topics, you can survive this section and complete your solid score.

Before we dive into specific topics, let’s discuss the format of the Free-Response Section. The section consists of six questions that you will have 90 minutes to complete. These six questions are broken down into two parts: Part A and Part B. Part A has two questions, which are worth a total of 24 points, while Part B has four questions, which are worth a total of 56 points.

A few things to remember about these questions:

  • Each question will have multiple components, and the number of components may vary
  • You will be expected to show your work and provide clear explanations for your answers
  • Some questions may require you to sketch graphs or diagrams to illustrate your solutions

Now, let’s talk about the topics that you should focus on for the Free-Response Section. The questions will cover a range of calculus concepts, including limits, derivatives, integrals, differential equations, and applications of integration. You should be comfortable with both the algebraic and graphical representations of these concepts.

In particular, make sure you are solid on the following topics:

Derivatives: You should be able to find derivatives using the power rule, product rule, quotient rule, chain rule, and implicit differentiation. You should also be able to use derivatives to find critical points, determine concavity, and sketch graphs.

Integrals: You should be able to find integrals using the power rule, and trig antiderivatives. You should also be comfortable with using integrals to find areas, volumes, and average values.

Differential Equations: You should be able to solve first-order differential equations using separation of variables, as well as understand how to fill out slope fields.

Applications of Calculus: You should be comfortable applying calculus concepts to real-world problems, such as optimization, related rates, and motion problems.

Just like the rest of this exam, you don’t have to get 100% to get a 5. Use the twice through method we talked about last time. Go through the free-response questions (FRQs) and do the quickest and/or easiest problems first. Then, go back and attempt the more time consuming and/or difficult ones.

Remember to show all of your work here! You will get points for setting up the problem correctly even if you make a mistake getting the answer or are unable to get all the way to the answer. Cleaning up on the easy problems and getting a few parts of the harder ones is all you need to get a 5 here.

The cool thing about the content here is that it’s very repetitive. I mentioned this all the way back in Part 2 of this series, but I’ll say it again: the College Board has every FRQ from the previous 25 years on their website for both the AB and BC tests. Take advantage of this. Get familiar with these questions, what they want to see for work shown and brush up on the ideas they cover.

Congrats on making it through the AP Calculus Blog series! With your newfound knowledge and some good study time, you’re ready to perform on the AP Calculus test. Don’t hesitate to reach out to your teacher or a tutor for some help with the core concepts. Some directed studying goes a long way!

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