A Brief Overview of the AP Calculus Exams

The AP Calculus exam will test your student’s knowledge of the mathematical concepts that they’ve covered in class, as well as cumulative knowledge of algebra, trigonometry and pre-calculus concepts. In addition to solving equations, students will also select and use the proper formulas for each calculation. They will also need to show the procedures they used to find the answer, using correct notations in their work.

This coursework is challenging, and the exam can be intimidating. However, it can also open new doors of opportunity for your student. In particular, it’s a chance to demonstrate readiness for more challenging coursework. The AP Calc exams are also an opportunity to earn college credit! For those reasons, it’s smart for your student to take the exam, even if it seems daunting.

Is the AP Calculus exam hard?

To paraphrase, knowing is half the battle. Before your teen dives into AP Calculus test prep, help them take the time to understand the test itself. Learn the format and timing of the exam and how it’s scored. They should also set a realistic score goal based on the data.

It’s harder to get a 5 on the most popular AP exams

In general, it’s hardest to get a top score of 5 on the most popular AP exams. That’s hardly surprising, if you think of it statistically. Specialized exams, such as AP Computer Science, attract fewer students because they have pre-requisites. What’s more, exams such as AP Physics C seem intimidating. That further deters students.

As a result, students taking lower-enrollment exams tend to be highly motivated. Further, they often have experience with previous AP exams. In contrast, the most popular AP exams attract a wide range of students. And many of them may be taking the first or only AP course of their high school career.

The AP Calculus AB Exam Attracts Twice as Many Students as Calculus BC

In 2021, 249,762 students took the AB Calculus exam. In contrast, only 124,335 students braved the BC exam. Among all 38 exams, AB Calc comes in as the 7th most popular test, while BC Calc ranks 15th.

There are a number of reasons for this number. Fewer schools offer a BC Calculus course. In fact, AB Calculus is the most advanced math class at many high schools. Secondly, the BC Calculus exam tests some topics not covered on the AB exam. Finally, it explores other topics in greater depth, and AP exam questions on similar topics may be more challenging.

All that said, taking AB vs BC Calculus isn’t a reflection on your student’s math mettle. Nor does it pre-determine their prospects for college admissions.

But it does mean that the scores on the AB and BC exams differ slightly.

Results of the AP Calculus AB Exam in 2021

In 2021, 19% of students scored a five on the AB Calculus test. At the same time, 51% of students received a passing score of three or higher.

Compared to other AP exams, those stats mark BC Calculus as one of the easier exams on which to get a five.

Among 38 exams, only 10X offered a higher likelihood of achieving a five. In contrast, there were six AP exams on which fewer than 10% of students garnered the top score.

That said, it’s getting harder to pass the AP Calculus AB exam in recent years. While just over half of students passed the AB exam in 2021, that figure represents a ten-year low. In comparison, nearly 60% of students passed in four of the preceding ten years.

Results of the AP Calculus BC Exam in 2021

Unsurprisingly, the results of the BC Calculus exam track with the overall trend among lower-enrollment courses. That is, when an AP course is perceived as hard, or requires more pre-requisites, AP results trend higher.

In 2021, fully 38% of students got a five on the AP exam! Even better, 75% of students passed with a three or higher.

As with the AB Calc test, the results for BC Calculus mark a decade-long low point. 2021 was the only year in the past decade when fewer than 80% of students passed the BC exam. As for the top score, the 2021 results were also singularly low. Between 2012 and 2020, an average of 45% of students received a 5.

AP Calculus Exam Scores in 2021 May Have Skewed Lower Because of COVID-19 and Unusual Testing Conditions

It remains to be seen whether AP Calculus scores will rebound to earlier levels. It’s possible that two factors slightly depressed scores in 2021.

First, online learning and COVID-related disruptions in school may have set some students back. The College Board standards don’t change from year to year. That means the AP exam questions were just as rigorous in 2021 as they were in previous years.

What changed was students’ level of preparation. Many students missed units in precalculus in the spring of 2020. In other instances, teachers had to compress the AP Calculus course because of missed instructional time. Finally, online learning didn’t work well for many students. Taken together, students may simply have struggled more on AP Calculus exams that didn’t change to reflect their unusual circumstances.

Secondly, the College Board shifted gears in 2021 and offered three separate administrations of all AP exams. That means they needed to harmonize student scores across three distinct AP Calculus exams: two paper-based exams and a third online-only exam. Unusual testing circumstances, combined with some students unease with an online AP testing format, may also have pushed scores down slightly.

All that said, it’s important to note that colleges only compare students with others in their cohort. So a lower pass rate on any AP exam in 2021 or any other year is not cause for alarm. Instead, look at it simply as a baseline to manage your student’s expectations and AP study plan.

AP Calculus Exams: What To Expect

Coronavirus upended even the best laid AP study plans in 2020 and 2021. In 2020, the AP tests were online only in May. Then, in 2021, the College Board offered three separate administration periods for the tests in May and June.

When thinking about their AP Calculus study schedule, students should plan for all contingencies. Are they ready to take a paper-based test in school? An online test? Will they test in June rather than May?

Make sure your student’s teacher is keeping them up to date on the latest news from the College Board. More importantly, encourage them to check the College Board’s AP Calculus AB or BC course page for any updates on test dates and status.

Testing Timeframes

If your student is currently enrolled in AP Calculus, they will have the opportunity to take the AP exam on Monday, May 10 at 8am local time. Students take either the AB Calc or BC Calc exam (not both). In fact, that’s why the exams run concurrently.

Each year, AP exams straddle the first two weeks in May. In 2022, the AP Calculus exams will be held on the first day of the second week.

On the one hand, a Monday exam is a plus. It gives students the weekend to study intensively. Moreover, they can arrive on AP exam day fresh and alert.

On the other hand, AP Calc kicks off the second week of exams. Students facing a mountain of AP exams may already be tired. Worse, they may have a second exam on the same day.

Does your student have multiple AP tests that could cut into studying time for the AP Calc test? Are they a night owl that will struggle with an 8am start time?

Take note of the AP testing calendar and help them build an individualized study plan that guarantees they’ll do their best.

Will the AP Calculus exams be online in 2022? 

The College Board has stated that it will monitor health conditions and adapt its testing schedule accordingly. Whatever the outcome, the College Board’s stated goal is to ensure all students who want to take an AP test can do so. For that reason, you don’t need to worry that your child’s AP Calculus exam will be canceled. You can expect that there will be options to accommodate the widest range of school and student needs.

AP Calculus Exam 2021: 3 Separate Test Administrations

A look at the 2021 AP exam schedule could shed light on what we might see in 2022.

In 2021, the College Board broke exam dates into three Administration periods.  Administration 1 and Administration 2 dates were offered in-person, in school. Students tested via paper format only. In contrast, Administration 3 dates were digital, online exams offered either in school or at home.

In 2021, the dates for the AP Calculus exams were as follows. Both AB and BC exams were offered on the same day.

  • Administration 1: Tuesday, May 4, 2021
  • Administration 2: Monday, May 24, 2021
  • Administration 3: Wednesday, June 9, 2021

Individual schools were free to use any of the testing options. So it’s important to check with your teen’s teacher or school’s AP coordinator to understand how, when, and where the test will take place.

In 2021, the paper and digital versions of the AP Calculus exams were comprehensive and full-length. While the questions varied from one administration to the next, the format and scoring rubric were identical.

AP Calculus Test Length and Format

Both AP Calculus exams last three hours and 15 minutes. There will be 45 multiple-choice questions as well as six free-response questions. Here’s a more detailed breakdown.

  • Time and Date of 2022 exam: May 10, 8am local time
  • Test Length: 3 hours 15 minutes
  • Section 1: Multiple Choice
    • 45 Questions
    • 1 hour 45 minutes
    • 50% score
  • Section 2: Free Response Questions
    • 6 Questions
    • 1 hour 30 minutes
    • 50% of score

Multiple-Choice Questions

The multiple-choice portion of the AP Calculus exam is divided into two sections. They include:

  • Part A: 30 questions: 33.3% of total exam weight, 60 minutes
  • Part B: 15 questions: 16.7% of total exam weight, 45 minutes

Your student will not be able to use a graphing calculator to complete Part A of the multiple-choice questions. They are required to use it in Part B.

Multiple-choice questions will test your child’s knowledge of different types of functions. These include:

  • General
  • Algebraic
  • Logarithmic
  • Exponential
  • Trigonometric

Students will be required to showcase their skills in employing a variety of mathematical practices to solve a given problem. These practices are broken down as:

  • Applying mathematical processes: 53% to 66% of total exam weight
  • Connecting representations: 18% to 28% of total exam weight
  • Justification: 11% to 18% of total exam weight

Note that calculator restrictions only apply to students taking the paper-based AP Calculus exam. Graphing calculators are permitted on all sections of the digital exam.

Free-Response Questions

Free-Response Questions - learn more by Tungsten Prep

Likewise, there are two sections of free-response questions. They include:

  • Part A: 2 questions: 16.7% of total exam weight, 30 minutes
  • Part B: 4 questions: 33.3% of total exam weight, 60 minutes

Your student is required to use a graphing calculator to complete Part A of the free-response questions. If they’re taking a paper test, then they are not allowed to use it in Part B. The free-response questions will be equally divided between procedural and conceptual types. Your student should also expect at least two questions that present course subjects in a real-world scenario.

All three of the mathematical practices covered in the multiple-choice questions are also tested in the free response section, though the weights are different. There’s also an extra fourth practice. In the free-response portion of the test, these breakdowns apply:

  • Applying mathematical processes: 37% to 55% of total exam weight
  • Connecting representations: 9% to 16% of total exam weight
  • Justification: 37% to 55% of total exam weight (Calculus AB), 37% to 59% (Calculus BC)
  • Communication and notation: 13% to 24% of total exam weight (Calculus AB), 9% to 20% (Calculus BC)

Units Covered 

The specific units covered in the exam will depend on whether your child is currently enrolled in AP Calculus AB or AP Calculus BC. Note that they cannot take both exams in the same testing period. The AP exam for students in AP Calculus AB will cover eight course units, while the exam for AP Calculus BC will cover 10 course units. Let’s take a closer look at each unit, and the exam weight it carries.

Units 1-8: Both Calculus AB and BC

The following eight units are covered in the exams for both Calculus AB and Calculus BC. However, they’re weighted differently for each course type. Here’s the breakdown:

  • Unit 1: Limits and Continuity: 10% to 12% for AB, 4% to 7% for BC
  • Unit 2: Differentiation (definition, basic rules): 10% to 12% for AB, 4% to 7% for BC
  • Unit 3: Differentiation (composite, implicit, inverse functions): 9% to 13% for AB, 4% to 7% for BC
  • Unit 4: Differentiation (contextual applications): 10% to 15% for AB, 6% to 9% for BC
  • Unit 5: Applying derivatives: 15% to 18% for AB, 8% to 11% for BC
  • Unit 6: Change integration and accumulation: 17% to 20% for AB, 17% to 20% for BC
  • Unit 7: Differential equations: 6% to 12% for AB, 6% to 9% for BC
  • Unit 8: Applications of integration: 10% to 15% for AB, 6% to 9% for BC

Units 9 and 10: Calculus BC Only

Calculus BC expands on the topics covered in Calculus AB. As such, the exam for this course includes two more units. These are:

  • Unit 9: Parametric equations, polar coordinates, vector-valued functions: 11% to 12%
  • Unit 10: Infinite series, sequences: 17% to 18%

Tips to Help Your Student Prepare

Before your child takes the AP Calculus exam, there are a few study tips that can help them go into test day with the utmost confidence. Here are a few of our top suggestions.

Practice Task Verbs

In the Course and Exam Description (CED) for AP Calculus AB and BC, you’ll find a list of key task verbs that The College Board typically looks for in free-response questions. By learning this list, your student can make sure their answers respond precisely to the question that is asked.

A few of the ones to remember include:

  • Approximate
  • Calculate
  • Determine
  • Estimate
  • Indicate
  • Interpret
  • Justify
  • Represent
  • Verify

A question that asks a student to represent the answer might require a graph or drawing of a geometric shape, while a question that calls for the student to justify will warrant a written explanation supported by a proof or other steps that use relevant equations or techniques. By incorporating these varied mathematical techniques into their responses, students can demonstrate mastery in the subject and reveal their depth of test preparedness.

AP Calculus Practice Exams: Use Them to Assess Readiness

There is no better way to study for the AP Calculus exam that with official practice tests. Fortunately, the College Board releases free response questions going back to 1998! What’s more, it offers sample student free response answers. Study these carefully to learn what it takes to achieve the maximum 9 points on each question. Equally, you’ll discover the pitfalls that lead to a lower score.

AP Calculus AB Practice Tests: Lots of Free Response Resources, Few Multiple Choice Questions

The College Board maintains an archive of free response questions from each AP Calculus AB exam going back to 1998.

Unfortunately, the College Board has released a scant 22 official multiple choice questions. You can find them starting on page 228 of the CED.  That’s typical of most AP exams. The test-makers reuse or repurpose questions, so they prefer to keep them under wraps for future use.

Many teachers keep paper-based copies of past AP Calculus exams. So your student might still have low-tech resources at their fingertips.

AP Calculus BC Practice Tests: Take Advantage of Free Response Questions Going Back to 1998, but Be Aware of Changes to the Test

Equally, you can also find more than two decades of AP Calc BC free response questions on the College Board’s BC Calculus exam page.

For both the AB and BC exams, take note of changes in the exam after 2016. Starting with the AP Calc tests in 2017, the College Board added several topics to both the AB and BC curriculum. So, you won’t see any questions on L’Hopital’s rule on AB Calc tests before 2017. Nor will you see questions on Calculus BC prior to 2017 that cover the limit comparison test, absolute and conditional convergence, and the alternating series error bound.

Fortunately, the test-makers did not remove any topics from the AP Calculus exams from 2017. So, as long as your child recognizes that a few select topics are missing from earlier practice tests, by all means use them as a realistic gauge for exam day.

How to Incorporate AP Practice Tests Into Their Study Plan

For the multiple choice section, you can also find any number of unofficial sample test questions online. In fact, one website has collated multiple choice questions on all AP Calculus exams from 1969 to 1998. Or you can invest in a paper-based study guide, which typically includes unofficial practice tests.

But don’t fret. Even unofficial practice tests will ready your child for the types of questions and topics they’ll see on test day. They’ll also refine several key test-taking skills. Namely, you’ll learn to efficiently manage your time and familiarize yourself with the pace and format of the AP exam itself. Further, they’ll also develop a list of which topics feel easy and which require additional practice and review.

Take Advantage of Digital Practice

Is your student planning to take the exam online in June? If so, they can see what test day will be like via The College Board’s Digital Practice page. This is a new feature rolled out to help students become more acclimated to taking the test in a virtual environment.

With this tool, they can preview the different types of questions on their exam (both multiple-choice and free-response). They can also learn all of the pre-exam steps they need to complete, as well as the directions and tools to follow. This is also a great time for them to check and make sure their technology is working as it should!

If they can’t access the extensive Digital Practice library, students can log into the shorter App Demo. The demo covers the same concepts but includes fewer practice questions.

Get AP Test Prep 

Some parents want extensive, year-long support for their child as they navigate their AP Calculus course. Others simply want dedicated, short-term test prep as they gear up for the AP Calculus exam. Either way, our team is here to help. Our AP Test Prep services were designed with the ambitious student in mind.

If a subject doesn’t come easily for your child, you may notice that they’re spending an inordinate amount of time on their homework, lab assignments or school projects. While there will undoubtedly be assignments that require substantial work and time to complete, it could be a sign that they’re stuck on a particular topic and can’t work past it. When this happens, a tutor can help break even the most difficult calculus topics into approachable segments that are easier to learn and retain. This way, they’ll be able to approach their work in a more easily digestible manner that will help them require less time studying.

Not only do we know the content, format, and scoring methodology, but we can also help your student learn other skills to improve their testing performance. For instance, we’ll cover how to self-pace to ensure adequate time during the test. We’ll work one-on-one with your child to make sure they understand exactly what to expect on the big day. We’ll cover the concepts to learn so they can demonstrate college readiness throughout the exam.

Help Your Student Ace the AP Calculus Exam

The AP Calculus exams might look a little different this year, but it’s still critical for your student to prepare as early as possible. If they’ve persevered through a year of studying, homework, and  test-taking, then it’s smart to take exam prep seriously.

At Tungsten Prep, we take test prep seriously too.

We offer extensive AP test prep services on a variety of subjects, and we’d love to help your student succeed. Book a free consultation today to learn more about the services that we can provide.