The AP Calculus BC exam's multiple-choice section, or Section 1, is divided into two parts: Part A, where calculator use is not permitted, and Part B, where it is allowed. This section covers all 10 course units and contributes 50% to the total exam score, with each question equally weighted.
| 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 AP Calculus BC MCQ section:
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Read the question and answer choices thoroughly
The first thing you should do on any MCQ is read it carefully. Scan through the answer choices to see the answer's form. 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.
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Annotate important information
When reading the question stem, use the highlight and notation tools available in the Bluebook App or UWorld AP Calc BC Study Guide. Focusing on key ideas helps you see the most important aspects of the question. When you encounter a vocabulary term, quickly analyze its meaning. For instance, if the question mentions 'relative maximum' or states that the 'derivative equals 0 and changes sign from positive to negative,' consider what these concepts mean in calculus.
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Answer every question
There is no difference between leaving a question blank and answering it incorrectly on the AP Calculus BC exam. If you don’t know how to solve a problem, make an educated guess. You’ll have a 25% chance of getting it right.
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Eliminate answer choices
Sometimes, you can immediately eliminate a choice because it does not fit in with what the question is asking. To cross out choices, use the Option Eliminator function by clicking the written answer choice (rather than the bubble) when using the Bluebook app or UWorld. For example, if the question specifies that you're looking for an x-value within a certain interval, you can eliminate choices outside that interval.
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Keep moving
The AP Calculus BC exam is timed, so it’s crucial to focus on answering the questions you know first. If you don’t immediately know how to solve a problem, it’s okay to guess and move on. If you want to revisit any questions later, use the Mark for Review tool. Once you’ve completed the section, return to the flagged questions and review your answers.
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Reread the Question
When you're deep into calculations, it’s easy to lose track of what the question is asking. Take a moment to reread the question to confirm what you need to calculate. Then, compare your work to ensure you haven’t overlooked any final steps. Remember that intermediary results often appear as answer choices, so arriving at one doesn’t guarantee it’s correct—always verify your final answer. For example, with the Fundamental Theorem of Calculus, if you’re finding the final value of a quantity f over an interval, given an initial value of f and its derivative f′, you’ll need to compute the definite integral of f′. But don’t forget to add the initial value at the end.
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Check before you select
Each time you answer a question, double-check your scratch paper against the Bluebook app to ensure you’re working on the correct question. Making an educated guess instead of skipping a question has an added benefit: it helps prevent misaligned answers, so you don’t lose points you might have earned.
AP Calculus BC multiple-choice examples
Here are some examples of the different AP Calculus BC multiple-choice practice questions from the UWorld QBank that you might see on the AP 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.
∫ x3 sec x tan x dx =
Below is a related-rates question from Unit 4. There are a few things to note for this one:
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If there's a word problem, 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 ft3/min, or dVdt = 8.
Sometimes, the College Board provides geometric area and volume formulas in the question stem, so memorizing anything more complicated than the area of a trapezoid is not necessary.
This is a calculator question from Part B, so answer choices are rounded to 3 decimal places. We advise that you use more than 3 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 = 13 πr 2h.)
Here's a question about the nth-term test in Unit 10. This question type gives 3 statements and asks which could be true. More than 1 statement could end 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 3 statements are true. So if you start with Statement I and determine that it’s true, you can eliminate Choices B and C, leaving you with either “I only” or “I, II, and III” as the correct option. From there, if you determine whether 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 by only analyzing 2 of the 3 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 an diverges, which of the following could be true?
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lim n→∞ an = 0;
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lim n→∞ an = 5;
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lim n→∞ an = ∞;
How Can I Practice AP Calculus BC Multiple-Choice Questions?
Effective MCQ practice for the AP Calculus BC exam doesn’t have to be expensive. UWorld’s AP Calculus BC Online Prep Course is designed to closely mimic the questions you’ll encounter on the actual exam. With an extensive range of questions covering various topics and lessons about every exam topic, the course helps you thoroughly prepare. Our detailed, step-by-step explanations ensure you understand how to solve each problem, so there are no surprises on test day.
If you are subscribing to UWorld AP Calc BC QBank, here are a few recommendations to get you started:
Reinforce key concepts
To master AP Calculus BC, create small UWorld tests with 5-10 questions from recent topics and past classes to reinforce learning. Review explanations for incorrect answers and dive into video or study guide lessons about unclear concepts to avoid repeated mistakes. Struggling with details like the constant of integration or common errors like sign mistakes? Use UWorld's notebook feature to take notes and create flashcards for formulas and tricky concepts.
Prepare for the exam
Don’t wait until you’ve covered all the topics in your AP Calculus BC class to start preparing for the exam. Begin generating UWorld tests as you progress through the course, focusing on the topics you’ve already learned. Larger tests with 10 to 30 questions can help you build stamina and simulate the length and variety of the AP Calculus exam. As you complete each test, review the questions you missed and study the detailed explanations. Create shorter, targeted tests to practice and strengthen your understanding of those areas. This ongoing practice will ensure you’re well-prepared by test day.
Frequently Asked Questions
How are AP Calculus BC multiple-choice questions graded?
A computer grades the multiple-choice questions. To ensure you get credit for all your answers, double-check that you’ve selected the correct answer choice in the Bluebook app. If you need to change an answer, update your selection carefully to avoid any mistakes.
How long is the multiple-choice section of the AP Calculus BC exam?
The MCQ section of AP Calculus BC is an hour and 45 minutes, split into two parts 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 past AP Calculus BC multiple-choice questions?
The MCQ portion of these tests is closely guarded and released only to teachers for use in the classroom. Many AP Calculus BC MCQs from past exams are available in AP Classroom, but you’ll need your teacher to assign them for practice. We provide you with the best way to access a comprehensive collection of AP Calculus BC practice multiple-choice questions that match the style and difficulty of an actual AP Calc BC exam.
References
- AP Calculus BC. (n.d.). Collegeboard.org. Retrieved December 13, 2024, from https://apcentral.collegeboard.org/courses/ap-calculus-bc
- AP Calculus AB and BC Course and Exam Description. (2020). Collegeboard.org. Retrieved December 13, 2024, from https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
- AP Calculus BC Course Overview. (2021). Collegeboard.org. Retrieved December 13, 2024, from https://apcentral.collegeboard.org/media/pdf/ap-calculus-bc-course-overview.pdf
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