Types of Calculus Questions Found on the AP Calculus Exam

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Shaun Ault

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What types of calculus questions show up on the AP Calculus AB and BC tests? In this article we’ll discuss the AP question format and see a few examples of actual test questions.

Types of Calculus Questions Found on the AP Calculus Exam
Be prepared for the types of AP calculus questions you will encounter on the test.

What is the Format of the Test?

Both the Calculus AB and Calculus BC exams have the same basic format.

There are two main section, multiple choice (MC) and free response (FR).

Within each section there is a part that requires a calculator and a part in which calculators are not permitted.

Section / Part Type of questions Number of questions Time Limit Calculator permitted?
IA Multiple Choice 30 60 minutes No
IB Multiple Choice 15 45 minutes Yes
IIA Free Response 2 30 minutes Yes
IIB Free Response 4 60 minutes No

Example: Multiple Choice

A typical MC question states a problem and shows four answer choices below it. Here’s an example.

If f(x) is the function given by f(x) = e3x + 1, at what value of x is the slope of the tangent line to f(x) equal to 2?

(A) -0.135

(B) 0.231

(C) -0.366

(D) 0.693

Snail with glasses.
Choose. But choose wisely!

Your calculus knowledge tells you that the derivative measures the slope of a curve. So just find the derivative of f, set it equal to the give slope 2, and solve for x.

derivative slope example

Example: Free Response

The FR questions are more substantial. For one thing, each FR question has three to five parts. You may skip parts if you have to, however the later parts often depend on the results from previous parts, so tread carefully!

AP Calculus exam? Challenge accepted!

Here’s an example.

Oil is draining at the rate of 12π ft3/sec from the vertex at the bottom of a conical tank. The diameter of the tank at its base is 36 ft and its height is 48 ft.

(a) Find an expression for the volume of water (in ft3) in the tank in terms of its radius at the surface of the oil.

(b) At what rate (in ft/sec) is the radius of the oil in the tank decreasing when the radius is 8 feet?

(c) How fast (in ft/sec) is the height of the oil in the tank dropping at the instant that the radius is 8 feet?

AB Free Response
Get your pencil and paper ready.

Keep in mind, you must show your work to receive credit for the FR questions.

Where Can I Find Out More?

For more information about the multiple choice questions, check out: AP Calculus: Tips to Answering Multiple Choice Questions

For more tips on Free Response section, check out the following helpful resource. Understanding AP Calculus Free Response Questions

Author

  • Shaun Ault

    Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music — almost as much as math! — and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!

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