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Bc Essay Topics

Generally speaking, the AP Calculus BC exam is more comprehensive, but not necessarily more difficult, than the AB exam. Let’s take a look at what topics you may expect to find on the BC exam.

The AP Calculus BC Exam

The material on the BC exam is the equivalent of about two semesters of calculus at the college level. The topics come from four main areas:

  1. Limits
  2. Derivatives
  3. Integrals
  4. Sequences and Series

However, these broad categories are interrelated. Any given problem on the test might require techniques from multiple areas.

Scores and Credits

Many colleges and universities award up to two semesters of calculus credit for a high score on the BC exam. If you earn at least a 4 on the exam, you could be eligible to receive about 8 credits of calculus — that’s Calculus I and II — before even setting foot on campus! In addition, some schools offer credit in lower level courses such as Precalculus if you earn at least a 3 on the test. However, schools differ in their AP policies, so check with each school that you are applying to.

List of Topics on the AP Calculus BC Exam

Mathematics builds upon itself, and calculus is no different. Because of this, think of the AP Calculus BC exam as the AB exam but with the following topics thrown in as well.


  • Derivatives of vector-valued functions, parametric functions, and functions expressed in polar coordinates.
  • Analysis of polar graphs using derivatives.
  • Velocity, speed, and acceleration for vector-valued or parametric functions.
  • Euler’s method.
  • Integrals

  • Improper integrals.
  • Integration by parts and the method of partial fractions.
  • Displacement, distance, and position of a particle moving according to a vector-valued or parametric function.
  • Areas bounded by polar curves.
  • Length of a parametric curve.
  • Logistic growth model.
  • Sequences and Series

  • Covergence and divergence.
  • Common series such as the p-series, geometric series, and harmonic series.
  • Absolute versus conditional convergence.
  • Taylor polynomials and approximation.
  • Lagrange error bound.
  • Taylor series and power series.
  • Radius and interval of convergence.


Basically, the AP Calculus BC Exam covers the same topics as the AB exam plus vector, parametric and polar functions, sequences, and series. In addition, the BC test includes more advanced techniques for finding derivatives and integrals as well as further applications of calculus not found on the AB exam.

For more information, check out What’s the Difference between that AP Calculus AB and BC tests?

More detailed descriptions of the topics covered on both the AB and BC test can be found here.

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!

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!

For years, Skidmore College included one or more short-answer questions on its supplement to the Common Application. Last year’s applicants had to respond to three prompts. One was: “Please share an example of an instance when you feel creative thought really did matter.” The answers were supposed to give Skidmore insights into applicants, says Mary Lou Bates, dean of admissions and financial aid. Yet some students and college counselors complained that the questions were too onerous. “We heard that our questions were the hardest,” she says. “And someone called them ‘the worst.’ ”

Ms. Bates has now concluded that the additional writing was not adding much to the evaluations, and the Common App essay is sufficient. “The answers felt very generic,” she says. So Skidmore removed the extra writing for students applying for the fall. After a few years of application declines, Skidmore saw a big jump this winter. The college received 8,200 applications, up from 5,700 last year. And more students (81 percent versus 75 percent) completed the application once they started it, a rise Ms. Bates attributes directly to the streamlined supplement.

The results may have as much to do with the ease of technology as with laziness. At the 11th hour, with anxious students looking for a few more colleges to apply to, those that don’t require additional writing look more appealing than those that do. “With the Common Application,” says Matthew J. DeGreeff, director of college counseling at the Middlesex School, in Concord, Mass., “you can drop 10 apps with a keystroke on Dec. 31.”

Though some students relish the opportunity to write about themselves, many view the requirement as a chore. So says Jay D. Bass, director of college counseling services at Thomas S. Wootton High School, in Rockville, Md. “Most juniors and seniors are not great writers,” he says. “Trying to figure out what colleges want to hear is stressful.”

Mr. Bass has wondered about the downside to supplemental essays. Additional requirements, he suggests, may deter low-income, first-generation applicants from applying to a particular college.

“For kids who do not have access to resources, or a parent who can sit down and help them with this,” he says, “does it impact their ability to meet what they think the college is looking for?”

Gregory W. Roberts has thought about that concern, but he says additional writing gives students more chances to make an impression. Mr. Roberts is dean of admissions at the University of Virginia, which requires two essays of about 250 words on its supplement in addition to the Common Application essay. “Asking for two short answers seems appropriate and reasonable,” he says. “Writing in a different format can give you a sense of different types of skills.” Admissions officers are looking not only at what students write, he says, but how they express themselves.

Applicants to U.Va.’s College of Arts and Sciences must describe a work of art, music, science, mathematics or literature that “surprised, unsettled or challenged” them; applicants to the schools of architecture, engineering and nursing are asked to explain their interest in those programs. All applicants must also choose one of four other prompts, including, “Discuss something you secretly like but pretend not to, or vice versa.”

Mr. Roberts recalls an essay written by an applicant from a poor family, who described her father coming home from the coal mines, his face covered in soot. In her essay, the student described why she had not participated in extracurricular activities — she had worked part-time jobs to help support her parents.

A memorable essay, Mr. Roberts says, “tells me someone knows how to write, and knows who he or she is,” and can help an applicant with middle-of-the-road test scores stand out.

Plenty of submissions fall short, however. “It’s shocking, the lack of effort we see in some essays,” he says. Yes, from time to time his staff comes across an essay that seems to have been repurposed (they know what’s being asked out there, and even a response to the quirkiest prompt can get broad after the first paragraph). He says he doesn’t really mind.

Of the four new topics presented by Boston College, the one about service to others has proved the most popular among applicants. Some responses have moved officials; the ones in which applicants recite their achievements and list their professional ambitions, not so much. “I don’t think everyone’s fully grasping the questions,” Mr. Mahoney says.

The requirement has some drawbacks. Previously, admissions officers read five applications an hour, but now they’re lucky to get through four, Mr. Mahoney says. Yet he believes the additional writing sample has helped his staff make better decisions.

“We’re trying to hear the student’s voice,” he says. And they know what they’ve heard came from applicants who were willing to type an extra 400 words.

Eric Hoover is a reporter for The Chronicle of Higher Education, covering college admissions.

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