Advanced Placement Calculus (also known as AP Calculus, AP Calc, or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by College Board. AP Calculus AB covers limits, derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including more integration techniques such as integration by parts, Taylor series, parametric equations, polar coordinate functions, and curve interpolations).
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.
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 half.
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 educators 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.
AP Calculus AB
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 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. 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
- Derivatives Concept At a point As a function Applications Higher Order derivatives Techniques
- Integrals Interpretations Properties Applications Techniques Numerical approximations
- Fundamental theorem of calculus
- L'Hôpital's rule, starting in the 2016-17 school year.
AP Calculus BC
According to the College Board,
AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following:
- Convergence tests for series
- Taylor series
- The use of parametric equations
- Polar functions (including arc length in polar coordinates)
- Calculating curve length in parametric and function equations
- Integration by parts
- Improper integrals
- Differential equations for logistic growth
- Using partial fractions to integrate rational functions
Independent research on the academic benefits of the Advanced Placement Calculus course indicates that not all students receive academic benefits from participating in the course. In a study with a sample size of over 90,000, the authors found that students who took the AP Calculus course did not receive any increase in academic achievement unless they also prepared for and took the AP test. The authors controlled for over 70 intervening variables and found that AP students who took and passed the AP Calculus AB or BC exam had ACT scores that were 1.8 points higher than non-AP students or AP Calculus students who did not take their course's AP test. This led the authors to state that "AP participation... is not beneficial to students who merely enroll in the courses ...":p. 414