AP® Calculus BC Multiple-Choice Questions
The AP® Calculus BC exam consists of two major sections: multiple choice questions (MCQs) and free response questions (FRQs). In this guide, we’ll focus on the first section - MCQs. First, we’ll break down the format of the AP Calculus BC multiple choice questions, then give you tips to maximize your points on the MCQs, and finally provide a few practice questions that you might see on the exam. We will also teach you how to practice the MCQs as you prepare for your AP Calculus BC exam.
Format of AP Calculus BC Multiple-Choice Section
The MCQs on the AP Calculus BC exam, collectively called Section I, are split into two parts, A and B. Part A consists of 30 questions on which you are not allowed to use a calculator, and you are given an hour to complete it. Part B consists of 15 questions for which a calculator is allowed, and 45 minutes is allotted for this section.
The entire Section I accounts for 50% of the total points on the exam. Each question is weighted the same regardless of whether it is in Part A or B. The questions cover all ten units of the AP Calculus BC course. The table below is a summary of the MCQ section of the AP Calculus BC exam.
Section I | Part A | Part B |
---|---|---|
No. of Questions | 30 MCQs | 15 MCQs |
Exam Weight | 33.3% | 16.7% |
Time Allotted | 1 hour | 45 minutes |
Calculator Usage | Not Permitted | Permitted |
How to Approach AP Calculus BC Multiple-Choice Questions?
Here are some tips for approaching the MCQ section of the AP Calculus BC exam:
- Read the question and answer choices thoroughly
The first thing you should do on any MCQ is carefully read the question. Then scan through the answer choices to see what form the answer will be in. For example, sometimes the question will include an integral and the answers will be numbers, requiring you to calculate the result of the integral. Other times, the answers will be in integral notation, so computing the integral will waste time.
- Underline important information
When reading through the question stem, underline (or highlight when using UWorld AP Calc BC QBank Practice Tests) things like vocabulary, given values, function definitions, and the actual quantity the question is asking for. This will help you key in on the important aspects of the question. When you hit a vocabulary word, stop and analyze what that means. For example, if the question says “relative maximum,” take a moment to think about what that means in calculus, like “derivative equals 0 and changes sign from positive to negative,” “second derivative is negative,” and so on.
- Eliminate answer choices
Sometimes you can immediately eliminate a choice because it does not fit in with what the question is asking. Cross out any such choices in your test booklet (or click on the answer choice when using UWorld). For example, if the question specifies that you’re looking for an x-value within a certain interval, you can eliminate choices that are outside that interval.
- Keep moving
If you do not immediately know how to solve a problem, it’s OK to skip it and come back later. The AP Calculus BC exam is a timed test. Therefore, it is crucial to not waste time on questions you do not know until you’ve made sure to answer the ones you do know. Fold the corner of the page in your question booklet to mark the pages you need to come back to (UWorld provides a drop-down menu at the top of the screen that allows you to quickly navigate to unanswered questions). You can even mark the ones you answered but aren’t sure of by folding the corner of the page. Then, if there is time, at the end of the exam, revisit all of the pages you marked to either try to answer the question or double-check your answer, unfolding the page corners as you revisit them.
- Read the question again
Sometimes, when you get into the thick of computing things, you tend to forget the gist of the question. Before answering, reread the question to find what you are supposed to calculate (if you underlined, it should be easy to find). Then compare it to help you ensure that you haven’t forgotten the final steps. One common example is the fundamental theorem of calculus. If you’re looking for the final value of a quantity f over an interval given an initial value of f and the derivative f ′, you’ll need to compute the definite integral of f ′. But don’t forget to add the initial value at the end. The results of intermediary steps are often answer choices, so just because you arrive at an answer choice doesn’t mean it’s the right one.
- Check before you bubble
Every time you answer a question, compare your answer sheet to the test booklet to make sure you’re answering the right question. This is especially important if you skip a question that you don’t know how to answer, but it is good practice regardless. If your answer sheet gets misaligned with the test booklet, you may end up missing points that you otherwise would have gotten.
- Answer every question
Last but not least, remember that, on the AP Calculus BC exam, there is no difference between leaving a question blank and answering it incorrectly. So if you don’t know how to solve a problem, take a guess and you’ll have a 25% chance of getting it right. You can also try to eliminate a few answer choices to increase your odds of guessing correctly. If you are running out of time, spend the last couple of minutes making sure you’ve filled in an answer for every question that you couldn’t get to.
If you take a full-length AP Calculus practice exam before the actual exam but don’t have answer sheets to use, make your own by listing out the numbers 1-30 and 76-90 on a piece of paper before starting the test. This will allow you to practice skipping over questions and comparing them to the booklet before answering.
AP Calculus BC Multiple-Choice examples
Here are some examples of AP Calculus BC multiple-choice practice questions from the UWorld QBank to illustrate different kinds of questions you may experience on the exam.
The question below is the simplest type of question you’ll see where you are given an expression and asked to compute it. In this question from Unit 6, you are given an indefinite integral and asked to find the corresponding antiderivative. The challenge is to find the appropriate technique that will allow you to integrate, which in this case is integration by parts. Sometimes the answer choices might give you clues for how to solve the problem. For example, B and C still resemble the general form of integration by parts.
∫ x^{3} secx tanx dx =
- ^{1}⁄_{4} x^{4 } secx + C
- 3x ^{2} secx – ∫ x^{3} secx dx
- x^{3} secx – 3∫ x^{2} secx dx
- x^{3} secx + ^{1}⁄_{4} x^{4 } secx tanx + C
- There’s a context (word problem), so you’ll need to carefully read the question and pick out key information. For example, “water flows into the container at a constant rate of 8 cubic feet per minute” means that the volume of water is increasing by 8 ft^{3}/min, or dV/dt = 8.
- Sometimes the College Board gives geometric area and volume formulas in the question stem, so it’s not necessary to memorize anything more complicated than the area of a trapezoid.
- This is a calculator question (Part B), so answer choices are rounded to three decimal places. We advise that you use more than three decimal places in your calculations to eliminate round-off errors.
Water flows into a container in the shape of an open right circular cone, as shown above. The container has a radius of 5 feet at the top and its height is 15 feet. If water flows into the container at a constant rate of 8 cubic feet per minute, how fast in feet per minute is the water level rising when the height of the water is 9 feet? (The volume of a cone with radius r and height h is V = ^{1}⁄_{3} πr^{ 2}h.
- 0.094
- 0.283
- 0.424
- 1.273
Here’s a question about the nth term test in Unit 10. This question type gives three statements and asks which could be true. For this type of question, there could be more than one statement that ends up being true, so it may be necessary to calculate multiple things. However, it’s sometimes possible to strategize.
For example, in this particular question, all three statements are true. So if you start with Statement I and determine it is true, you can eliminate Choices B and C, leaving you with “I only” and “I, II, and III” as correct options. From there, if you determine if either Statement II or Statement III is true, the answer must be D, and if either is false, the answer must be A. Therefore, you can arrive at the correct answer while only analyzing two of the three statements. It’s not always possible to strategize this way, but if you eliminate answer choices as you go, you may save yourself some work.
if series Σ∞n=1 a_{n} diverges, which of the following could be true?
- ^{lim} _{}n →∞ a_{n} = 0
- ^{lim} _{}n →∞ a_{n} = 5
- ^{lim} _{}n →∞ a_{n} = ∞
- I only
- II only
- II and III only
- I, II, and III
How can I practice AP Calculus BC Multiple-Choice questions?
A good MCQ practice for the AP Calculus BC exam won’t cost you much. Direct College Board resources like AP Classroom require teacher involvement, and other free options do not do a good job of emulating test questions.
Fortunately, UWorld is a low-cost QBank that perfectly mimics the questions on the AP Calculus BC exam. We provide a wealth of questions across various topics in the course to prepare you well for the test. Our questions span all of the different ways that the College Board presents information, and our in-depth explanations show you step-by-step how to solve the problems, so you won’t see any curveballs on test day.
If you are subscribing to UWorld AP Calc BC QBank, here are a few recommendations to get you started :
Learning the course material
If you are still learning the AP Calculus BC course material, create small UWorld tests covering the topic(s) that you learned in your last class. It may be a good idea to also include topics you learned in the previous one or two classes to cement those ideas as well. Small tests of 5-10 questions targeting recently learned concepts is a good idea to start with. Read through our explanations for any questions you answer incorrectly. This will help you learn from your mistakes. It may also be helpful to read the explanations for other questions that you may not fully understand, even if you were able to get the question right.
Students tend to repeat the same mistakes if they aren’t aware of where they went wrong. Having a log of all the mistakes can help you review them later and identify if there are any patterns you tend to fall into. Do you frequently forget small details like the constant of integration C for indefinite integrals? Do you tend to make sign errors like dropping a negative or not distributing correctly? Do you often forget what the question is asking and stop a step or two early? Take advantage of UWorld’s notebook feature to take notes of your mistakes as you work through our QBank. Not only that, if you’re struggling to remember a formula, you can add it to a flashcard as well.
Preparing for the exam
After you have covered all of the topics in the AP Calculus BC class, it’s time to prepare for the exam. Start generating UWorld tests covering all of the topics. Larger tests of 10-30 questions spanning the entirety of the course will simulate the length and variety of the AP Calculus exam. When you have finished the test, identify the questions you answered incorrectly and read through the explanations. Then create shorter tests over those topics specifically to help you practice and learn from your mistakes.
Frequently Asked Questions
How are AP Calculus BC multiple-choice questions graded?
On the AP Calculus BC exam, a machine grades the multiple-choice questions. To make sure you get credit for all your answers, fill in the bubbles in the answer sheet completely but try not to mark outside the lines. If you have to change an answer, make sure to erase your original answer as completely as possible.
How long is the multiple choice questions section of the AP Calculus BC Exam?
The MCQ section of AP Calculus BC is an hour and 45 minutes long, split into two parts of 30 questions (1 hour) and 15 questions (45 minutes). You have an average of 2 minutes per MCQ in Part A and 3 minutes per MCQ in Part B.
Where can I get the AP Calculus BC past exam released multiple-choice questions?
Many MCQs from past exams are released in AP Classroom, which will require a teacher to assign them to you if you want to practice with them. Some tests are closely guarded and released only to teachers for use in the classroom. At UWorld we provide you the best way to access enough AP Calculus BC practice multiple-choice questions that match the style and difficulty of an actual AP Calc BC exam.
Read more about the AP Calculus BC Exam
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