How Hard Is the AP Calc BC Exam?

Many students are unsure whether they should take the AP Calculus AB or AP Calculus BC exam. On the one hand, the AP Calculus BC exam can help you get more course credit going into college if you get a high score. On the other hand, the AP Calculus BC exam covers more material than the AB exam, and may be harder to get a high score on. So, just how hard is the AP Calculus BC exam? This guide will help you consider all the relevant factors when deciding which test to take.

What Makes the AP Calculus BC Exam Difficult?

What makes the AP Calculus BC exam more difficult than the AP Calculus AB exam is that it covers significantly more material. While AP Calculus AB is meant to correspond to one semester of introductory college-level mathematics, AP Calculus BC is meant to cover two semesters. That means that not only is there more material to know, but also that the additional material is more advanced.

To refresh yourself on the 8 units covered on the AP Calculus AB test, take a look at this blog post. According to the College Board, the AP Calculus BC test covers all material on the AB test, as well as these additional topics:

1. In unit 6: additional techniques of integration such as integration by parts and determining improper integrals
2. In unit 7: Euler’s method and logistic models with differential equations
3. In unit 8: arc length and distance traveled along a smooth curve
4. Two additional units:
   1. Unit 9: parametric equations, polar coordinates, and vector-valued functions. This unit covers topics such as:
      1. Finding the derivatives of parametric and vector-valued functions
      2. Determining the position, velocity, speed, and acceleration of a particle moving along a curve
      3. Finding derivatives of functions written in polar coordinates
      4. Finding the area of regions bounded by polar curves
   2. Unit 10: infinite sequences and series, including Taylor and Maclaurin series. This unit covers topics such as:
      1. Applying limits to understand convergence of infinite series
      2. The main types of series: geometric, harmonic, and p-series
      3. Tests for divergence and convergence of infinite series
      4. Approximating sums and error bounds of convergent infinite series
      5. Determining an infinite series’ radius of convergence
      6. Representing a function as a Taylor or Maclaurin series

Is it Easy to Get a 5 on AP Calc BC?

At first glance, it may appear that it is easier to get a 5 on the AP Calculus BC exam than on the AP Calculus AB exam. In 2021, for example, about 38% of Calculus BC test-takers received a 5 on the exam, whereas only 18% of Calculus AB test-takers received a 5 that same year.

That being said, it’s important to remember that not only is the material on the AP Calculus BC exam more advanced, but also that the group of students taking the exam is a self-selecting group of highly motivated and mathematically successful students.

Additionally, the AP Calculus AB exam is significantly more popular than the AP Calculus BC exam. In 2021, only about half as many students took the AP Calculus BC exam as took the AP calculus BC exam. So, while more students (as a percentage) may be getting a 5 on the BC test, this is probably out of a more competitive group of students, and reflects fewer students overall.

What Score Is a 5 on the AP Calc BC Exam?

You’ll typically need to get a 4-5 on the BC test in order to receive college credit, so it’s important to know what raw scores you need in order to achieve a high score on the test.

The test is comprised of 54 points for 45 multiple-choice questions (your score here is the number of questions you answer correctly, multiplied by 1.2), and 54 points for 6 free-response questions (each of which is worth 9 points in total, but often contain 3-4 subparts which can grant you partial credit).

Your raw score, out of 108, is a sum of these scores, so that the multiple-choice and free-response sections each account for 50% of your raw score.

While the formula to translate raw scores into the scaled 1-5 score varies from year to year, a good rule of thumb is to aim for at least 70 points out of 108 for a score of 5, and at least 60 points out of 108 for a score of 4 or higher.

What Should I Do to Prepare for the AP Calculus BC Exam?

The most important thing you can do to prepare is to practice! Previous years’ AP Calculus BC tests are a great resource to check your understanding of the core topics. If you’re currently taking a calculus class in school, it’s a good idea to review past homework, quizzes, and tests.

When it comes to practice, it’s not just enough to know how to solve the problems: you also want to practice explaining why some answers are correct. The free-response section will often ask you to justify your response, so being able to do so is crucial for getting a high score. We highly recommend reviewing the “Task Verbs Used in Free-Response Questions” page of this guide written by the College Board (page 227) to better understand what these kinds of free-response questions are looking for.

You’ll also want to make sure that you have key formulas and equations memorized: unlike the SAT, the AP Calculus exams don’t include any equation sheet. A good rule of thumb is that any formula, theorem, or equation that you use regularly (either in class or while doing practice problems) is probably something you’ll want to have memorized.

When is the AP Calculus BC Exam in 2023?

The AP Calculus BC Exam will take place on Monday, May 8, 2023.

What to Bring to the AP Calculus BC Exam

You should bring the following items to the AP Calculus BC Exam:

• two sharpened No. 2 pencils with erasers (for the multiple-choice section)
• two black or blue ink pens (for the free-response section)
• a graphing calculator (see here for the offical AP calculator poilcy)
• a government-issued of school-issued photo ID (if you are not taking the exam somewhere other than your school)
• a watch (but not a smart or Apple watch)
• College Board SSD Eligibility letter, if you have approved testing accomodations

Looking for AP Calculus BC Exam Practice?

Officially, only one full AP Calculus BC exam has been released by the College Board: this one, from 2012. While this test isn’t particularly recent, it’s still good practice to help you get used to the format, timing, and content on the exam.

The College Board also has more recent past free-response questions on their website here. They also include sample responses with commentary, so you can get a sense for how the answers are scored. These official questions are a great resource because they are the most accurate representation of what kinds of questions you should expect to be asked.

Although the official College Board resources are limited, Khan Academy has partnered with the College Board to develop their own study resources. These resources will not only help you by providing practice problems, but will also explain concepts that you may be struggling with.

For an extra boost, see one of our experienced AP Calculus tutors to help you get your ideal score!