AP Calculus

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. Purpose According to the College Board: AP Calculus AB is approximately equivalent to the first semester of college calculus, providing students with an opportunity to earn college credit or advanced placement. Research indicates that achieving higher scores on the exam can positively impact college completion rates by facilitating credit toward graduation requirements. Topic outline The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus. • Analysis of graphs (predicting and explaining behavior) • Limits of functions (one and two sided) • Asymptotic and unbounded behavior • Continuity • Derivatives • Concept • At a point • As a function • Applications • Higher order derivatives • Techniques • Integrals • Interpretations • Properties • Applications • Techniques • Numerical approximations • Fundamental theorem of calculus • Antidifferentiation • L'Hôpital's rule • Separable differential equations ==AP Calculus BC==

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). Purpose According to the College Board, The course is designed for students with strong mathematical ability, aiming to provide advanced placement or credit equivalent to two semesters of college calculus. Topic outline AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following: • Convergence tests for series • Taylor series • Parametric equations • Polar functions (including arc length in polar coordinates and calculating area) • Arc length calculations using integration • Integration by parts • Improper integrals • Differential equations for logistic growth • Using partial fractions to integrate rational functions It can be seen from the tables that the pass rate (score of 3 or higher) of AP Calculus BC is higher than AP Calculus AB. It can also be noted that about 1/2 as many take the BC exam as take the AB exam. A possible explanation for the higher scores on BC is that students who take AP Calculus BC are more prepared and advanced in math, often self-selecting into the course due to greater intrinsic motivation and prior achievement. The 5-rate is consistently over 40% (much higher than almost all the other AP exams). In 2025, AP Calculus BC was rated as one of the most satisfying AP exams by students, with an average satisfaction score of 8 out of 10. AB sub-score distribution == AP Exam ==

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. AP exam scores, including for Calculus, serve as strong predictors of college performance and are valued in admissions processes at institutions like the University of California system. Format 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. 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. Scoring 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. The free response section is hand-graded by hundreds of AP teachers and professors each June. 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. == History ==

There was considerable debate about whether or not calculus should be included when the Advanced Placement Mathematics course was first proposed in the early 1950s. AP Mathematics was eventually developed into AP Calculus thanks to physicists and engineers, who convinced mathematicians of the need to expose students in these subjects to calculus early on in their collegiate programs. The AP program originated in the 1950s amid Cold War concerns over educational rigor, with the first AP exams piloted in 1954 and nationally rolled out in 1956, including Mathematics as one of the original ten subjects. AP Calculus was established in 1955 as a single exam covering a full year of college-level calculus; in 1969, the AB exam was introduced for the first semester, while the original became BC. The program grew rapidly from the 1980s, with exam takership increasing fivefold by the mid-1990s, and by 2019, over 450,000 students took AP Calculus annually, representing about 20% of U.S. high school graduates. By the mid-2020s, AP Calculus AB was one of the top ten most popular AP exams. In the early 21st century, there has been demand for the creation of AP Multivariable Calculus and indeed, a number of American high schools have begun to offer "Calculus III", giving colleges trouble in placing incoming students. == See also ==