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.

## 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 byf(x) =e^{3x}+ 1, at what value ofxis the slope of the tangent line tof(x) equal to 2?

(A) -0.135

(B) 0.231

(C) -0.366

(D) 0.693

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*.

### 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!

Here’s an example.

Oil is draining at the rate of 12π ft

^{3}/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 ft^{3}) 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?

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

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##### About 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!

### 2 Responses to “Types of Calculus Questions Found on the AP Calculus Exam”

### Leave a Reply

**Magoosh blog comment policy:** To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!

So I am looking to further my knowledge and education. Have take other majors in IT and Electronics Technology, but currently looking into Areonautics and astroauntics. Found out I will be required bto take AP Calculus plus AP Physics C, considering I have never taking any course above geometry and CP algebra I want to know how hard it is. These questions were surprisingly easy, unfortunately I am not able to show my work but knew the answer to the questions. Is there anywhere I can find more? I would really like to learn more before attempting to study at a college for the specified degree. Thank you in advance.

Hi Corey,

I’d definitely recommend looking at the official AP materials for the Calculus AB exam! That will give you a good idea of what to expect on the exam 🙂