AP Calculus Exam Multiple Choice Question Strategies

The multiple-choice questions on the AP Calculus exam count for 50% of your total score. The multiple-choice section consists of two parts: Part A contains 30 multiple-choice questions for which you are not allowed to use your graphing calculator, and Part B contains 15 multiple-choice questions for which you may (and in fact, will most likely need to) use your calculator.

Although you might not like multiple-choice questions, there’s no denying the fact that it’s easier to guess on a multiple-choice question than it is to guess the correct answer to an open-ended question. Contrast this with Section II of the AP Calculus exam, which accounts for the other 50% of your score. In that section, if you don’t know how to work a problem, you have to write down what you do know and hope to earn at least part of the available points.

Every multiple-choice question on the AP Calculus exam can be described as a “stand-alone” question. A stand-alone question covers a specific topic and is not part of a set; the question that follows it covers a different topic. Here’s a typical question:

In this question, you get some information and then you’re expected to answer the question. Where this question occurs in the test makes no difference, because there’s no patterned order of difficulty in which questions are presented on the AP Calculus exam. Tough questions are scattered between easy and moderately difficult questions.

The stand-alone questions look like a bunch of disconnected calculus questions one after the other and that’s just what they are. Because they aren’t connected to each other, there’s no reason you have to answer these questions in sequential order. The two-pass system, discussed next, should be used here. You can tweak the general idea of the two-pass system and apply it specifically to the AP Calculus exam.

If you wanted to, you could take all the AP Calculus questions and arrange them in a spectrum ranging from “fastest to answer” to “slowest to answer.” For example, questions involving a graph are often much faster to answer, as long as you can interpret the visual data correctly.

Picking out questions with graphs is not an especially critical way to analyze the exam questions, but some students do no more than that. You should realize that the more advanced your pacing system is, the more time you might have at the end of Section I to answer the questions that you find difficult. To further refine your two-pass approach before Test Day, draw up two lists of exam topics. Label one list “Calculus Concepts I Enjoy and Know About” and label the other list “Calculus Concepts That Are Not My Strong Points.”

When you get ready to begin the multiple-choice section, keep these two lists in mind. On your first pass through the section, answer all the questions that deal with concepts you like and know a lot about. If a question covers a subject that’s not one of your strong points, skip it and come back on your second pass. The overarching goal is to use the time available to answer the maximum number of questions correctly.

This refinement of the basic two-pass system should give you a clear idea about how to approach the multiple-choice section of the AP Calculus exam. Now that you’ve got an idea of the correct approach, let’s talk a bit about the correct mindset for test-taking.

Some tests are sneakier than others. A sneaky test has questions that are written in convoluted ways; they’re designed to trip you up mentally and manipulate your score by using a host of other little tricks. Students taking a sneaky test often have the proper facts, but get many questions wrong because of traps in the questions themselves.

The AP Calculus exam is not a sneaky test. It aims to see how much calculus knowledge you have. To do this, it asks a wide range of questions from an even wider range of calculus topics. The exam tries to cover as many different calculus facts as it can, which is why the questions jump from topic to topic. The test makers work hard to design the test so that it is comprehensive, which means that students who only know one or two calculus topics will soon find themselves struggling.

Understanding these facts about how the test is designed can help you to answer its questions. The AP Calculus exam is comprehensive, not sneaky; it makes questions hard by asking about hard subjects, not by using rhetorical tricks to create hard questions.

You don’t have enough time to think deeply about every tough question, so trusting your instincts can keep you from getting bogged down and wasting precious time on a problem. Some of your educated guesses are likely to be incorrect, but again, the point is not to get a perfect score. A perfect score would certainly be nice, but most people are going to lose at least some points on the AP exam (and may still get a 5). Your basic goal should be to get as good a score as you can; surviving hard questions by going with your gut feelings can help you to achieve this aim.

On other questions, though, you might have no inkling of what the correct answer should be. In that case, turn to the following key idea.

The AP Calculus exam rewards good mathematicians. It covers fundamental topics and expects you to use logical thinking and good mathematical techniques to answer questions. What the test doesn’t want is sloppy math or sloppy thinking. It doesn’t want answers that are factually incorrect, too extreme to be true, or irrelevant to the topic.

Still, bad math answers invariably appear, because it’s a multiple-choice test that includes three incorrect answer choices along with the one correct answer. So if you don’t know how to answer a question, look at the answer choices and think “Good Math.” This may lead you to find some poor answer choices that can be eliminated. Here’s an example:

Students who recall the definition of a derivative based on limits will have no problem determining that (C) is the correct answer. However, if you don’t know how to answer this question, you can use “Comprehensive, not Sneaky” and “Good Math” to give yourself a chance at guessing the right answer. The limit definition involves h approaching 0 (because it’s getting very small), so you can eliminate B right away (because h is approaching ∞). Choice A can also be eliminated, because there is nowhere to plug in 0 for h (all the terms have xs in them, but no hs). Finally, think back to Algebra I: The first coordinate in an ordered pair is x, and this function is all about x^2, so you should see a 22 in the definition, not a 42. This means you can eliminate D, leaving (C) as the only remain-ing choice.