# AP Calculus

**Advanced Placement Calculus** (also known as **AP Calculus**, **AP Calc AB / AP Calc BC**, or **AP Calc**) is one of two distinct Advanced Placement courses and examinations offered by College Board in calculus: AP Calculus AB (as an introduction to derivatives, limits and integral calculus), or AP Calculus BC (with more techniques, for Taylor series, parametric equations, L'Hopital's rule, integration by parts, polar coordinate functions, and curve interpolations).

## AP Calculus AB

AP Calculus AB is an Advanced Placement calculus course taken by high school students. The course is traditionally taken after precalculus and is the first calculus course offered at most schools except for the regular calculus class. The Pre-Advanced Placement pathway for math will help 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]}

### Course content

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.
More specifically, the topics are^{[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, starting in the 2016-17 school year.
^{[4]}

Notable AP Calculus AB Teacher: Irmarie Coriano Torres (Saint John's School)

## AP Calculus BC

### Purpose

According to the College Board,

Calculus BC is a full-year 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]}

### Course content

AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as 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, L'Hôpital's rule, integration by parts, improper integrals, differential equations for logistic growth, and using partial fractions to integrate rational functions.^{[5]}

## Exam

### Growth

Between 1990 and 2004, the number of students taking the AP Calculus exams has increased more than threefold.^{[6]} The exams are now taken by more than 250,000 students each year.^{[7]} The College Board intentionally schedules the AP Calculus AB exam at the same time as the AP Calculus BC exam in order 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 pre-requisite class for Calculus BC. Some schools do this, though many others only require precalculus as a prerequisite for Calculus BC.

### 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.^{[8]} The subdivision of the multiple choice for 2017 exams and beyond are different that previously. The chart below reflects this change:

Multiple-Choice, Section I Part A | Multiple-Choice, Section I Part B | Free-Response, Section II Part A | Free-Response, 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 may work on the Section II Part A during the time for Section II Part B but are not allowed to resume using a calculator. The Free-Response section is one-and-a-half hours long. New to the exam in 2011, the calculator-required free response section contains only 2 questions, while the non-calculator section contains 4 questions. 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.

### Scoring

The Multiple-Choice section is scored by computer, with a correct answer receiving 1 point, a blank answer receiving 0 points, and an incorrect answer costing no points as a new change made by AP Central. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score.^{[9]}

The Free-Response section is hand-graded by hundreds of educators each June.^{[10]} 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.

Prior to 2013, students typically received this score report by mail in mid-July of the year they took the test.^{[11]} As of 2013, the College Board will not send the scores by mail, but instead the student taking the test will have to create a username and a password as well as input their AP code or student ID number in order to see their scores. The scores will be available sometime in July.^{[12]} Alternately, they can receive their scores by phone as early as June 27 for a fee of $8 (although the College Board only officially recognizes July 1 as the first available date to receive grades by phone^{[13]}).

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.

### Grade distributions for AP Calculus AB

The grade distributions for the AB scores since 2010 were:

Score | 2010^{[14]} |
2011^{[15]} |
2012^{[16]} |
2013^{[17]} |
2014^{[18]} |
2015^{[19]}^{[20]} |
2016^{[21]} |
---|---|---|---|---|---|---|---|

5 | 21.2% | 21.4% | 24.9% | 23.9% | 24.3% | 21.3% | 24.4% |

4 | 16.4% | 16.4% | 16.9% | 18.1% | 16.7% | 17.1% | 17.4% |

3 | 18.0% | 18.5% | 17.3% | 17.3% | 17.7% | 18.7% | 17.6% |

2 | 11.2% | 10.7% | 10.3% | 11.2% | 10.8% | 10.5% | 9.7% |

1 | 33.1% | 33.1% | 30.6% | 29.4% | 30.5% | 32.4% | 30.9% |

Mean | 2.811 | 2.826 | 2.952 | 2.956 | 2.935 | 2.844 | 2.947 |

Number of Students | 245,867 | 255,357 | 266,994 | 282,814 | 294,072 | 302,532 |

### Grade distributions for AP Calculus BC

The grade distributions for the BC scores since 2010 were:

Score | 2010^{[22]} |
2011^{[23]} |
2012^{[24]} |
2013^{[17]} |
2014^{[18]} |
2015^{[17]}^{[20]} |
2016^{[21]} |
---|---|---|---|---|---|---|---|

5 | 50.1% | 47.6% | 50.4% | 45.8% | 48.3% | 44.6% | 48.8% |

4 | 15.4% | 15.9% | 16.1% | 16.1% | 16.8% | 16.9% | 15.5% |

3 | 18.0% | 16.7% | 15.8% | 17.9% | 16.4% | 18.5% | 17.6% |

2 | 5.8% | 5.9% | 5.4% | 5.7% | 5.2% | 5.4% | 5.9% |

1 | 11.4% | 13.9% | 12.3% | 14.4% | 13.3% | 14.6% | 12.6% |

Mean | 3.856 | 3.764 | 3.87 | 3.73 | 3.816 | 3.715 | 3.832 |

Number of Students | 78,998 | 85,194 | 94,403 | 104,483 | 112,463 | 118,707 |

#### AB subscore distribution

Score | 2010 | 2011 | 2013 | 2014 | 2015 |
---|---|---|---|---|---|

5 | 51.0% | 55.1% | 56.0% | 55.0% | 56.1% |

4 | 19.4% | 17.9% | 19.9% | 16.8% | 16.3% |

3 | 14.2% | 13.2% | 11.3% | 12.9% | 12.8% |

2 | 5.7% | 4.9% | 5.4% | 6.3% | 5.5% |

1 | 9.7% | 8.9% | 7.4% | 9.1% | 9.4% |

Mean | 3.96 | 4.05 | 4.16 | 4.02 | 4.04 |

## 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 non-AP students or AP Calculus students who did not take their course's AP test.^{[25]} This led the authors to state that AP participation "... is not beneficial to students who merely enroll in the courses ..."^{[25]}^{:p. 414}

## References

- 1 2 "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Retrieved 2008-11-29.
- ↑ "Topic Outline".
*Calculus AB*. College Board. Archived from the original on 19 December 2008. Retrieved 2008-11-29. - ↑ "Course Descriptions" (PDF).
- ↑ "AP Calculus AB, BC Updates Taking Effect in Fall 2016".
*AP Calculus AB and BC*. College Board. Archived from the original on 22 May 2015. Retrieved 2015-05-22. - ↑ "Topic Outline".
*Calculus BC*. College Board. Archived from the original on 19 December 2008. Retrieved 2008-11-29. - ↑ "Chapter 1: Elementary and Secondary Education, Student Coursetaking in Mathematics and Science, Participation in AP Testing".
*Science and Engineering Indicators 2006*. National Science Board. 2006-02-23. - ↑ Robinson, M.; Fadali, M.S.; Malisa, M.; Johnson, W.; Batchman, T.
*AP mathematics and science courses as a gateway to careers in engineering*(PDF). - ↑ "The Exam".
*Calculus AB*. College Board. Archived from the original on 19 December 2008. Retrieved 2008-11-29. - ↑ "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Retrieved 2008-11-29.
- ↑ "AP: The Grade-Setting Process". College Board. Archived from the original on 18 December 2008. Retrieved 2008-11-29.
- ↑ "Exam Grades". College Board. Archived from the original on 1 December 2008. Retrieved 2008-11-29.
- ↑ "Online Scores for Students". College Board. Archived from the original on 6 May 2013. Retrieved 2013-05-07.
- ↑ "AP Scores - AP Grades & Reporting Services". College Board. Archived from the original on 4 December 2008. Retrieved 2008-11-29.
- ↑ 2010 Calculus AB score distribution
- ↑ 2011 Calculus AB score distribution
- ↑ 2012 Calculus AB score distribution
- 1 2 3 2013 AP Exam Score Distribution
- 1 2 2014 AP Exam Score Distribution
- ↑ 2015 AP Exam Score Distribution
- 1 2 2015 AP Student Score Distribution
- 1 2 Registration, Total. "2016 AP Exam Score Distributions".
*www.totalregistration.net*. Retrieved 2016-07-01. - ↑ 2010 Calculus BC score distribution
- ↑ 2011 Calculus BC score distribution
- ↑ 2012 Calculus BC Score Distributions
- 1 2 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.

## External links

- AP Calculus AB
- AP Calculus BC