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The Expert's Guide to the AP Calculus BC Exam

Posted by Ashley Robinson | Apr 8, 2020 5:00:00 PM

Advanced Placement (AP)

 

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Taking the AP Calc BC exam can feel like a lot of pressure: you want to earn college credit for your AP class, but the test is pretty tough! 

But there are a few things you can do to make the AP Calculus BC exam a little easier, like understanding the exam's format, the topics it covers, and how it's scored. Knowing what to expect before you take the AP Calc BC exam can help you earn a higher score! 

To give you all the inside information you need about the AP Calculus BC Exam, we’ll explain the following in this article: 

  • What the AP Calculus BC Exam is, including who should take it
  • The AP Calculus BC Exam format and topics
  • How the exam is scored
  • 5 tips for scoring well on the exam

The regularly scheduled date for the AP Calc BC exam is May 5th at 8:00 a.m., so you'll want to start preparing as early as possible. (Good thing this article has you covered, huh?) 

So let’s get started!

 

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What Is the AP Calculus BC Exam?

The AP Calculus BC exam assesses high school students’ ability to apply the content and skills learned in the AP Calculus course. The content of the AP Calculus BC exam is pulled straight from the study units that students learn in the AP Calculus BC course: 

Unit 1: Limits and Continuity 
Unit 6: Integration and Accumulation of Change
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 7: Differential Equations 
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions 
Unit 8: Applications of Integration 
Unit 4: Contextual Applications of Differentiation
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions 
Unit 5: Analytical Applications of Differentiation
Unit 10: Infinite Sequences and Series 

 

So how is the AP Calculus BC exam different from the AP Calculus AB exam? 

The difference between the tests isn't difficulty, it's content. If you're taking the AB exam, you'll be tested over content from the first eight units. The BC exam tests you on all ten! Both tests are about on par in terms of difficulty. If you're curious about what makes an AP test "hard," be sure to check out our breakdown of the hardest AP tests.

 

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The AP Calculus BC Exam Format

How long is the AP Calculus BC exam? It lasts three hours and 15 minutes, but how is that time divided up? 

During the three hour and 15 minute testing period, exam takers will complete the two sections of the AP Calc BC exam: Section 1, which is the multiple choice section, and Section 2, which is the free response section. 

Let's take a closer look at each BC Calculus section below. 

 

Section 1: The Multiple-Choice Section

Section 1 of the AP Calculus BC exam is comprised of 45 multiple choice questions that are divided up into two parts: Part A and Part B. Here's how the two parts of the exam break down: 

Exam Part
Time
Number of Questions
Graphing Calculator
Part A
60 minutes
30 questions
Not allowed
Part B
45 minutes
15 questions
Allowed

 

In terms of content, both Part A and Part B of Section 1 include algebraic, exponential, logarithmic, trigonometric, and general types of functions, as well as analytical, graphical, tabular, and verbal types of representations.

 

Section 2: The Free-Response Section

Section 2 of the BC Calculus exam gives you one hour and 30 minutes to answer six free response questions. Just like Section 1, this section of the AP Calc BC exam is also divided into a Part A and Part B. Here's how those parts break down: 

Exam Part
Time
Number of Questions 
Graphing Calculator
Part A
30 minutes
2 questions
Allowed
Part B
1 hour 
4 questions 
Not allowed

 

Now, if you’re thinking that six questions doesn’t sound like much to get done in an hour and 30 minutes, you should know that each of the six free response questions has multiple parts. In fact, it’s common for the free response questions to consist of three or four sub-questions, usually labeled with letters, like (a), (b), and (c). 

You’ll have to answer all of the parts of each free response question in order to get full points on this section of the exam. 

So how are the free response questions graded? Students will be assessed based on their ability to implement mathematical processes, connect representations, provide justification, and provide communication and notation. You'll also need to be able to work these problems in context since at least two free response questions will incorporate a real-world context or scenario into the question.

 

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The nice part about the AP Calculus BC exam is that the test topics follow the units of the AP class. So if you're paying attention in class and staying on top of your work, you should have a good grasp on the test concepts already. 

 

The AP Calculus BC Exam Topics

Like we mentioned earlier, the AP Calculus BC exam topics are based on the material that is taught in the AP Calculus BC course. The exam assesses your knowledge of content from the three “Big Ideas” of the AP Calculus BC course. These three big ideas are change, limits, and analysis of functions. 

The three big ideas that the AP Calc BC course is built around are divided up across ten units of study, and you'll have to demonstrate knowledge and skills from each of these ten units on your AP Calculus BC exam.

Keep reading to learn more about what topics you can expect to see on each section of the AP Calc BC exam.

 

Multiple-Choice Section

To make studying a little easier, we've broken everything you need to know about the multiple-choice portion of the exam into an easy-to-read table. We've listed the major concepts from each unit along with the percentage of multiple choice questions that deal with those skills and ideas: 

Unit Name
Major Unit Topics
Weighted Percentage of Exam Score on Multiple-Choice Section
Unit 1: Limits and Continuity
  • How limits help us handle change at an instant
  • Definition and properties of limits in various representations
  • Definitions of continuity of a function at a point and over a domain
4% - 7% of exam score
Unit 2: Differentiation: Definition and Fundamental Properties
  • Applying limits to define the derivative
  • Determining derivatives
  • Connecting differentiability and continuity
4% - 7% of exam score
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
  • Use of the chain rule
  • Implicit differentiation
  • Differentiation of general and particular inverse functions
  • Determining higher-order derivatives
4% - 7% of exam score
Unit 4: Contextual Applications of Differentiation
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
  • Applying understandings of differentiation to problems involving motion
  • Local linearity and approximation
6% - 9% of exam score
Unit 5: Analytical Applications of Differentiation
  • Mean Value Theorem and Extreme Value Theorem
  • Derivatives and properties of functions
  • How to use the first derivative test, second derivative test, and candidates test
  • Sketching graphs of functions and their derivatives
  • How to solve optimization problems
  • Behaviors of Implicit relations
8% - 11% of exam score
Unit 6: Integration and Accumulation of Change
  • Apply limits to define definite integrals
  • How the Fundamental Theorem connects integration and differentiation
  • Apply properties of integrals and practice useful integration techniques
17% - 20% of exam score
Unit 7: Differential Equations
  • Solve differential equations
  • Apply knowledge of how to solve differential equations to understand exponential growth and decay and logistic models
6% - 9% of exam score
Unit 8: Applications of Integration
  • Solve problems involving net change over an interval of time
  • Find lengths of curves, areas of regions, or volumes of solids defined using functions
6% - 9% of exam score
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
  • Solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration
  • Deepen understanding of straight-line motion to solve problems involving curves
11% - 12% of exam score
Unit 10: Infinite Sequences and Series
  • Explore convergence and divergence behaviors of infinite series
  • Learn how to represent familiar functions as infinite series
  • Learn how to determine the largest possible error associated with certain approximations involving series
17% - 18% of exam score

 

This probably feels like a lot to take in, but if you think about how long the AP Calculus BC course lasts (a whole school year!), you’ll realize that there’s plenty of time to learn and practice each of the skills listed above!

 

Free-Response Questions 

Let’s talk next about how the topics from the AP Calc BC course will appear in the free-response questions. 

Most of the free-response questions on the BC Calculus exam will state a scenario and ask you to respond to it, in writing, in several steps. To help you get a better idea of what to expect from the questions on the free-response section of the exam, here are some common “task verbs” that are used in the wording of the free-response questions: 

  • Approximate
  • Calculate/Write an expression
  • Determine
  • Estimate
  • Evaluate
  • Explain
  • Identify/Indicate
  • Interpret (when given a representation)
  • Justify
  • Represent
  • Verify


All of these “task verbs” are asking you to show your work in a specific way.
Knowing the difference between what it means to estimate an answer versus explain an answer will help ensure you're answering each free response question in the right way! 

On the free-response section of the exam, you’ll be provided with ample blank space in your exam booklet to show the process of how you arrived at a certain answer. Doing so clearly and correctly will is also crucial to doing well on this portion of the exam!

 

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(Nick Youngson/The Blue Diamond Gallery)

 

How the AP Calculus BC Exam Is Scored

Like all AP exams, the AP Calculus BC exam is scored on a scale from 1 to 5, with 1 being the lowest score, and 5 being the highest score. But how do exam scorers arrive at your number score, and how are the different parts of the exam figured into your overall AP exam score? 

There are two sections on the AP Calculus BC exam, and each section accounts for 50% of the weight in your overall score on the exam. The weighted percentage of the exam sections can be broken down even further, like this:

Section of AP Calc BC Exam
Percentage of Overall Score
Section 1, Part A
33.3%
Section 1, Part B
16.7%
Section 2, Part A
16.7%
Section 2, Part B
33.3%

 

Earning points on the multiple choice section of the exam is pretty simple: if you select the correct answer, you receive a certain number of points. If you select the wrong answer, you don’t receive points. That means there is no penalty for guessing, so make sure you try to answer every question on the exam! 

The free response section is a little different. AP Exam scorers work from a rubric to score the free response answers. The scorers are going to be looking to see that you addressed one or more key ideas that are associated with each free response question in the grading rubric. You will receive points for each idea that you address clearly and accurately on each free response exam question. 

For example, there might be three total points associated with one part of a free response question. Exam scorers would be instructed to award you one point for considering a function, one point for identifying the correct answer, and one point for justifying your answer. If you fail to justify your answer but correctly fulfill the other two requirements, you’d earn two out of three points for that part of the free response question. 

We know that sounds tricky, but luckily, the CollegeBoard provides in-depth information about scoring the exam. To look at more examples of how AP Calculus AB free response questions are scored, check out the Scoring Guidelines on the CollegeBoard website.

 

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Our five tips will help you ace the AP Calculus BC exam...and when you do, you'll have a great reason to celebrate. (We recommend confetti. Lots of confetti.)

 

5 Tips for Scoring Well on the AP Calculus BC Exam

The AP Calc BC exam is tough, but you’ll be ready to tackle those equations if you follow our top tips for acing the test! 

 

Tip 1: Pay Attention in Class

The most important thing you can do to prepare for the AP Calc BC exam is to show up and pay attention in class! Your teacher is going to dedicate class time to working hard to help you learn the material you need to know in order to do well on the AP Calc BC exam. Also, the course is designed to help you progress from easier concepts to harder ones, especially since mastering foundational math skills is a key component to working difficult problems. 

During class, your teacher will explain and demonstrate new concepts and talk you through using your graphing calculator to solve equations. They’ll also go over homework assignments, quizzes, and tests—all of which will most likely mimic the format of the AP Calc BC exam and include questions that are on-par with the difficulty level of the exam. 

Basically, a major goal of the AP Calc class is to help prepare you for your AP exam. If you really want to do well on the AP Calc BC exam, you need to show up to class, pay attention, take notes, and ask questions.

 

Tip 2: Show up for Tutoring Sessions

Many schools have free tutoring programs for students who are taking math classes. These can be offered through the school, but sometimes teachers have special tutoring hours specifically for their students. Make sure you check into the tutoring opportunities available at your school and take advantage of them if you need extra help! Getting one-on-one tutoring can help you master calculus concepts that are giving you a hard time. 

If your school doesn't have tutoring programs, don't worry. There are probably other services available in your community! And if not, there are excellent online tutoring programs you can use, too.  

 

Tip 3: Form a Study Group 

Trying to solve difficult calculus problems by yourself, especially when you're not exactly sure how to do them, can be discouraging. Working on equations together with a group of classmates can boost morale and give you the opportunity to get a better handle on core skills and concepts.

Study groups can be a good alternative to one-on-one tutoring, especially if it's not available at your school. They give you the opportunity to compare notes, help one another master difficult concepts, and can even give you new techniques to solve complex problems. 

 

Tip 4: Take Practice AP Calc BC Tests

Knowing the concepts on the AP Calc BC exam and being comfortable with taking the exam are two different things. For some students, the pressure of a timed exam can affect their overall performance (and unfortunately, their exam score). 

A good way to conquer your test jitters is to use practice exams to familiarize yourself with the test format. A good way to practice with these materials might be to time yourself on completing the practice materials so you can get a feel for what it will be like attempting to select and articulate correct, coherent answers on the real exam.

 

Tip 5: Get Familiar With Your Graphing Calculator

If you’ve taken a calculus course, you already know that a graphing calculator is essential to solving certain equations--two parts of the exam state that a graphing calculator is required! 

When you take your AP Calc BC course, you should get a lot of practice with using your graphing calculator to solve equations and perform functions. If you struggle with any aspect of using your graphing calculator, talk to your teacher so you can get the help you need. It’s important to fully understand how to use the different functions and capabilities of your graphing calculator before you have to use it on the exam!

 

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What's Next? 

Are you thinking about taking the AP Calculus AB exam, too? Be sure to check out our expert guide to that exam as well!

Calculus has a reputation for being a tough test, but is it the hardest? Check out this list of the hardest AP classes to find out. (And if you're looking to take easy AP classes, we have a list for that, too.)

Are you curious about how your AP scores stack up to those of your classmates? Here's a rundown of the average AP scores for every single AP exam. 

 

Want to improve your SAT score by 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

Get eBook: 5 Tips for 160+ Points

Raise Your ACT Score by 4 Points (Free Download)

 

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Ashley Robinson
About the Author

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.



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