AP Calculus
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 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 more advanced integration techniques such as integration by parts, Taylor series, parametric equations, vector calculus, polar coordinate functions, and curve interpolations).
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 PreAdvanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams.
Purpose
According to the College Board:
An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning. The AP Program includes specifications for two calculus courses and the exam for each course. The two courses and the two corresponding exams are designated as Calculus AB and Calculus BC. Calculus AB can be offered as an AP course by any school that can organize a curriculum for students with advanced mathematical ability.^{ [1]}
Topic outline
The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity.^{ [2]} An AP Calculus AB course is typically equivalent to one semester of college calculus.^{ [3]}
 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
Score  2017^{ [4]}  2018^{ [5]}  2019^{ [6]}  2020^{ [7]}  2021 

5  18.7%  19.4%  19.1%  19.5%  
4  18%  17.3%  18.7%  20.9%  
3  20.8%  21%  20.6%  21.0%  
2  22%  22.4%  23.3%  24.1%  
1  20.4%  20%  18.3%  14.5%  
% of Scores 3 or Higher  57.5%  57.7%  58.4%  61.4%  
Mean  2.93  2.94  2.97  3.07  
Standard Deviation  1.40  1.40  1.38  1.36  
Number of Students  316,099  308,538  300,659  266,430 
AP Calculus BC
Purpose
According to the College Board,
Calculus BC is a fullyear course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics...Students who take an AP Calculus course should do so with the intention of placing out of a comparable college calculus course.^{ [1]}
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^{ [8]}
Score  2017^{ [9]}  2018^{ [5]}  2019^{ [6]}  2020^{ [10]}  2021 

5  42.6%  40.4%  43.0%  44.6%  
4  18.1%  18.6%  18.5%  17.6%  
3  19.9%  20.7%  19.5%  19.4%  
2  14.3%  14.6%  13.9%  14.1%  
1  5.3%  5.6%  5.2%  4.3%  
% of Scores 3 or Higher  80.6%  79.7%  81.0%  81.6%  
Mean  3.79  3.73  3.81  3.84  
Standard Deviation  1.28  1.28  1.27  1.25  
Number of Students  132,514  139,376  139,195  127,864 
AB subscore distribution
Score  2017^{ [9]}  2018^{ [5]}  2019^{ [11]} 

5  48.4%  48.7%  49.5% 
4  22.5%  20.2%  23.5% 
3  14.1%  15.9%  13.2% 
2  10%  9.9%  9.7% 
1  4.9%  5.3%  4.2% 
% of Scores 3 or Higher  85%  84.8%  86.2% 
Mean  4  3.97  4.05 
Standard Deviation  1.21  1.23  1.18 
Number of Students  132,505  139,376  139,195 
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 subscore piece of the BC exam.^{ [12]}
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 Tuesday morning in May.^{ [13]}
MultipleChoice, Section I Part A  MultipleChoice, Section I Part B  FreeResponse, Section II Part A  FreeResponse, Section II Part B  

# of Questions  30  15  2  4 
Time Allowed  60 minutes  45 minutes  30 minutes  60 minutes 
Calculator Use  No  Yes  Yes  No 
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 FreeResponse 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 FreeResponse time, although without a calculator during the later half.
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 multiplechoice score.^{ [14]}
The free response section is handgraded by hundreds of educators each June.^{ [15]} The raw score is then added to the adjusted multiple choice score to receive a composite score. This total is compared to a compositescore scale for that year's exam and converted into an AP score of 1 to 5.
For the Calculus BC exam, an AB subscore is included in the score report to reflect their proficiency in the fundamental topics of introductory calculus. The AB subscore is based on the correct number of answers for questions pertaining to ABmaterial only.
Benefits
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 nonAP students or AP Calculus students who did not take their course's AP test.^{ [16]} This led the authors to state that "AP participation... is not beneficial to students who merely enroll in the courses ..."^{ [16]}^{:p. 414}
See also
References
 ^ ^{a} ^{b} "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Archived from the original (PDF) on 20080720. Retrieved 20081129.
 ^ "Topic Outline". Calculus AB. College Board. Archived from the original on 20081219. Retrieved 20081129.
 ^ "Course Descriptions" (PDF).
 ^ College Board. "AP Calculus AB May 2017 Score Distributions" (PDF). Archived from the original (PDF) on 20180326. Retrieved 20170622.
 ^ ^{a} ^{b} ^{c} https://securemedia.collegeboard.org/digitalServices/pdf/research/2018/StudentScoreDistributions2018.pdf
 ^ ^{a} ^{b} "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved July 9, 2020.
 ^ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved June 9, 2021.
 ^ "Topic Outline". Calculus BC. College Board. Archived from the original on 20081219. Retrieved 20081129.
 ^ ^{a} ^{b} "AP Calculus AB and Calculus BC Chief Reader Report May 2017" (PDF). Archived from the original (PDF) on 20180725.
 ^ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved June 9, 2021.
 ^ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved July 9, 2020.
 ^ "2018 AP Exam Dates  The Princeton Review". www.princetonreview.com. Retrieved 20180820.
 ^ "The Exam". Calculus AB. College Board. Archived from the original on 20081219. Retrieved 20081129.
 ^ "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Archived from the original (PDF) on 20080720. Retrieved 20081129.
 ^ "AP: The GradeSetting Process". College Board. Archived from the original on 20081218. Retrieved 20081129.
 ^ ^{a} ^{b} Warne, Russell T.; Larsen, Ross; Anderson, Braydon; Odasso, Alyce J. (2015). "The impact of participation in the Advanced Placement program on students' college admissions test scores". The Journal of Educational Research. 108 (5): 400–416. doi: 10.1080/00220671.2014.917253. hdl: 10.1080/00220671.2014.917253. S2CID 146577291.