Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / BC, AB / BC Calc or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including integration by parts, Taylor series, parametric equations, vector calculus, and polar coordinate functions).
AP Calculus AB is an Advanced Placement calculus course. It is traditionally taken after precalculus and is the first calculus course offered at most schools except for possibly a regular or honors calculus class. The Pre-Advanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams.
According to the College Board:
The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity.[1] An AP Calculus AB course is typically equivalent to one semester of college calculus.[2]
| Score | 2017[3] | 2018[4] | 2019[5] | 2020[6] | 2021[7] | 2022[8] | 2023[9] | 2024[10] |
|---|---|---|---|---|---|---|---|---|
| 5 | 18.7% | 19.4% | 19.1% | 19.5% | 17.6% | 20.4% | 22.4% | 21% |
| 4 | 18% | 17.3% | 18.7% | 20.9% | 14.1% | 16.1% | 16.2% | 28% |
| 3 | 20.8% | 21% | 20.6% | 21.0% | 19.3% | 19.1% | 19.4% | 15% |
| 2 | 22% | 22.4% | 23.3% | 24.1% | 25.3% | 22.6% | 21.7% | 23% |
| 1 | 20.4% | 20% | 18.3% | 14.5% | 23.7% | 21.7% | 20.3% | 13% |
| % of Scores 3 or Higher | 57.5% | 57.7% | 58.4% | 61.4% | 51.0% | 55.7% | 58.0% | 64% |
| Mean | 2.93 | 2.94 | 2.97 | 3.07 | 2.77 | 2.91 | 2.99 | |
| Standard Deviation | 1.40 | 1.40 | 1.38 | 1.36 | 1.41 | 1.44 | 1.44 | |
| Number of Students | 316,099 | 308,538 | 300,659 | 266,430 | 251,639 | 268,352 | 273,987 | |
AP Calculus BC is equivalent to a full year regular college course, covering both Calculus I and II. After passing the exam, students may move on to Calculus III (Multivariable Calculus).
According to the College Board,
AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following:
| Score | 2017[12] | 2018 | 2019 | 2020[13] | 2021[14] | 2022[15] | 2023[16] | 2024[17] |
|---|---|---|---|---|---|---|---|---|
| 5 | 42.6% | 40.4% | 43.0% | 44.6% | 38.3% | 41.2% | 43.5% | 45% |
| 4 | 18.1% | 18.6% | 18.5% | 17.6% | 16.5% | 15.6% | 15.9% | 22% |
| 3 | 19.9% | 20.7% | 19.5% | 19.4% | 20.4% | 20.1% | 19.0% | 13% |
| 2 | 14.3% | 14.6% | 13.9% | 14.1% | 18.2% | 16.4% | 15.2% | 15% |
| 1 | 5.3% | 5.6% | 5.2% | 4.3% | 6.6% | 6.8% | 6.3% | 5% |
| % of Scores 3 or Higher | 80.6% | 79.7% | 81.0% | 81.6% | 75.2% | 76.9% | 78.5% | 80% |
| Mean | 3.79 | 3.73 | 3.81 | 3.84 | 3.62 | 3.68 | 3.75 | |
| Standard Deviation | 1.28 | 1.28 | 1.27 | 1.25 | 1.33 | 1.33 | 1.32 | |
| Number of Students | 132,514 | 139,376 | 139,195 | 127,864 | 124,599 | 120,238 | 135,458 | |
| Score | 2017 | 2018 | 2019[18] | 2020[19] | 2021[20] | 2022[21] | 2023[22] | |
|---|---|---|---|---|---|---|---|---|
| 5 | 48.4% | 48.7% | 49.5% | N/A | 46.7% | 48.5% | 46.4% | |
| 4 | 22.5% | 20.2% | 23.5% | N/A | 17.7% | 20.9% | 19.6% | |
| 3 | 14.1% | 15.9% | 13.2% | N/A | 16.0% | 11.8% | 18.8% | |
| 2 | 10.0% | 9.9% | 9.7% | N/A | 13.0% | 12.2% | 8.6% | |
| 1 | 4.9% | 5.3% | 4.2% | N/A | 6.6% | 6.7% | 6.6% | |
| % of Scores 3 or Higher | 85.0% | 84.8% | 86.2% | N/A | 80.4% | 81.2% | 84.8% | |
| Mean | 4.00 | 3.97 | 4.05 | N/A | 3.85 | 3.92 | 3.91 | |
| Standard Deviation | 1.21 | 1.23 | 1.18 | N/A | 1.31 | 1.30 | 1.26 | |
| Number of Students | 132,505 | 139,376 | 139,195 | N/A | 124,607 | 120,276 | 135,458 |
The College Board intentionally schedules the AP Calculus AB exam at the same time as the AP Calculus BC exam to make it impossible for a student to take both tests in the same academic year, though the College Board does not make Calculus AB a prerequisite class for Calculus BC. Some schools do this, though many others only require precalculus as a prerequisite for Calculus BC. The AP awards given by College Board count both exams. However, they do not count the AB sub-score piece of the BC exam.[23]
The structures of the AB and BC exams are identical. Both exams are three hours and fifteen minutes long, comprising a total of 45 multiple choice questions and six free response questions. They are usually administered on a Monday or Tuesday morning in May.[24]
The two parts of the multiple choice section are timed and taken independently.
Students are required to put away their calculators after 30 minutes have passed during the Free-Response section, and only at that point may begin Section II Part B. However, students may continue to work on Section II Part A during the entire Free-Response time, although without a calculator during the later two thirds.
The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score.[25]
The free response section is hand-graded by hundreds of AP teachers and professors each June.[26] The raw score is then added to the adjusted multiple choice score to receive a composite score. This total is compared to a composite-score scale for that year's exam and converted into an AP score of 1 to 5.
For the Calculus BC exam, an AB sub-score is included in the score report to reflect their proficiency in the fundamental topics of introductory calculus. The AB sub-score is based on the correct number of answers for questions pertaining to AB-material only.