AP Calculus

Last updated

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).

Contents

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 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:

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]

Score2017 [4] 2018 [5] 2019 [6] 2020 [7] 2021 [8] 2022 [9] 2023 [10] 2024 [11]
518.7%19.4%19.1%19.5%17.6%20.4%22.4%21%
418%17.3%18.7%20.9%14.1%16.1%16.2%28%
320.8%21%20.6%21.0%19.3%19.1%19.4%15%
222%22.4%23.3%24.1%25.3%22.6%21.7%23%
120.4%20%18.3%14.5%23.7%21.7%20.3%13%
% of Scores 3 or Higher57.5%57.7%58.4%61.4%51.0%55.7%58.0%64%
Mean2.932.942.973.072.772.912.993.21
Standard Deviation1.401.401.381.361.411.441.441.35
Number of Students316,099308,538300,659266,430251,639268,352273,987

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,

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]

Topic outline

AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following:

Score2017 [13] 2018 [5] 2019 [6] 2020 [14] 2021 [15] 2022 [16] 2023 [17] 2024 [18]
542.6%40.4%43.0%44.6%38.3%41.2%43.5%45%
418.1%18.6%18.5%17.6%16.5%15.6%15.9%22%
319.9%20.7%19.5%19.4%20.4%20.1%19.0%13%
214.3%14.6%13.9%14.1%18.2%16.4%15.2%15%
15.3%5.6%5.2%4.3%6.6%6.8%6.3%5%
% of Scores 3 or Higher80.6%79.7%81.0%81.6%75.2%76.9%78.5%80%
Mean3.793.733.813.843.623.683.753.87
Standard Deviation1.281.281.271.251.331.331.321.27
Number of Students132,514139,376139,195127,864124,599120,238135,458

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 1/3 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. The 5-rate is consistently over 40% (much higher than almost all the other AP exams). [ original research? ]

AB sub-score distribution

Score2017 [13] 2018 [5] 2019 [19] 2020 [20] 2021 [21] 2022 [22] 2023 [23]
548.4%48.7%49.5%N/A46.7%48.5%46.4%
422.5%20.2%23.5%N/A17.7%20.9%19.6%
314.1%15.9%13.2%N/A16.0%11.8%18.8%
210.0%9.9%9.7%N/A13.0%12.2%8.6%
14.9%5.3%4.2%N/A6.6%6.7%6.6%
% of Scores 3 or Higher85.0%84.8%86.2%N/A80.4%81.2%84.8%
Mean4.003.974.05N/A3.853.923.91
Standard Deviation1.211.231.18N/A1.311.301.26
Number of Students132,505139,376139,195N/A124,607120,276135,458

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. [24]

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. [25]

Multiple-Choice, Section I Part AMultiple-Choice, Section I Part BFree-Response, Section II Part AFree-Response, Section II Part B
# of Questions301524
Time Allowed60 minutes45 minutes30 minutes60 minutes
Calculator UseNoYesYesNo

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. [26]

The free response section is hand-graded by hundreds of AP teachers and professors each June. [27] 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.

See also

Related Research Articles

<span class="mw-page-title-main">Advanced Placement</span> American program with college-level classes offered to high school students

Advanced Placement (AP) is a program in the United States and Canada created by the College Board. AP offers undergraduate university-level curricula and examinations to high school students. Colleges and universities in the US and elsewhere may grant placement and course credit to students who obtain qualifying scores on the examinations.

<span class="mw-page-title-main">Precalculus</span> Course designed to prepare students for calculus

In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.

Advanced Placement (AP) Chemistry is a course and examination offered by the College Board as a part of the Advanced Placement Program to give American and Canadian high school students the opportunity to demonstrate their abilities and earn college-level credits at certain colleges and universities. The AP Chemistry Exam has the lowest test participation rate out of all AP Courses, with around half of AP Chemistry students taking the exam.

Advanced Placement (AP) Computer Science A is an AP Computer Science course and examination offered by the College Board to high school students as an opportunity to earn college credit for a college-level computer science course. AP Computer Science A is meant to be the equivalent of a first-semester course in computer science. The AP exam currently tests students on their knowledge of Java.

Advanced Placement (AP) Biology is an Advanced Placement biology course and exam offered by the College Board in the United States. For the 2012–2013 school year, the College Board unveiled a new curriculum with a greater focus on "scientific practices".

Advanced Placement (AP) English Language and Composition is a course and examination offered by the College Board as part of the Advanced Placement Program.

Advanced Placement (AP) Macroeconomics is an Advanced Placement macroeconomics course for high school students that culminates in an exam offered by the College Board.

Advanced Placement (AP) Microeconomics is a course offered by the College Board as part of the Advanced Placement Program for high school students interested in college-level coursework in microeconomics and/or gaining advanced standing in college. The course begins with a study of fundamental economic concepts such as scarcity, opportunity costs, production possibilities, specialization, and comparative advantage. Major topics include the nature and functions of product markets; factor markets; and efficiency, equity, and the role of government. AP Microeconomics is often taken in conjunction with or after AP Macroeconomics.

Advanced Placement (AP) Psychology and its corresponding exam are part of the College Board's Advanced Placement Program. This course is tailored for students interested in the field of psychology and as an opportunity to earn Advanced Placement credit or exemption from a college-level psychology course. It was the shortest AP exam until the AP Physics C exam was split into two separate exams in 2006.

Advanced Placement (AP) Statistics is a college-level high school statistics course offered in the United States through the College Board's Advanced Placement program. This course is equivalent to a one semester, non-calculus-based introductory college statistics course and is normally offered to sophomores, juniors and seniors in high school.

Advanced Placement (AP) United States Government and Politics is a college-level course and examination offered to high school students through the College Board's Advanced Placement Program. This course surveys the structure and function of American government and politics that begins with an analysis of the United States Constitution, the foundation of the American political system. Students study the three branches of government, administrative agencies that support each branch, the role of political behavior in the democratic process, rules governing elections, political culture, and the workings of political parties and interest groups.

Advanced Placement (AP) Chinese Language and Culture is a course and exam offered by the College Board as a part of the Advanced Placement Program in the United States. It requires proficiencies throughout the Intermediate range as described in the American Council on the Teaching of Foreign Languages (ACTFL) Proficiency Guidelines. The course interweaves language and culture learning and is conducted mostly in Mandarin Chinese. The first AP Chinese courses were offered worldwide in the fall of 2006, followed by the exam in May 2007.

<span class="mw-page-title-main">Advanced Placement exams</span> Exams offered by College Board culminating Advanced Placement courses

Advanced Placement (AP) examinations are exams offered in United States by the College Board and are taken each May by students. The tests are the culmination of year-long Advanced Placement (AP) courses, which are typically offered at the high school level. AP exams have a multiple-choice section and a free-response section.

Advanced Placement (AP) Environmental Science is a course and exam offered by the American College Board as part of the Advanced Placement Program to high school students interested in the environmental and natural sciences. AP Environmental Science was first offered in the 1997–1998 school year.

Advanced Placement (AP) Physics C: Mechanics is an introductory physics course administered by the American College Board as part of its Advanced Placement program. It is intended to serve as a proxy for a one-semester calculus-based university course in mechanics. Physics C: Mechanics may be combined with its electricity and magnetism counterpart to form a year-long course that prepares for both exams.

Advanced Placement (AP) Physics C: Electricity and Magnetism is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to serve as a proxy for a second-semester calculus-based university course in electricity and magnetism. Physics C: E&M may be combined with its mechanics counterpart to form a year-long course that prepares for both exams.

<span class="mw-page-title-main">Mathematics education in the United States</span> Overview of mathematics education in the United States

Mathematics education in the United States varies considerably from one state to the next, and even within a single state. However, with the adoption of the Common Core Standards in most states and the District of Columbia beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level. The SAT, a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core. However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school, while seventeen states and the District of Columbia require four. A typical sequence of secondary-school courses in mathematics reads: Pre-Algebra, Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs while many complete high school without passing Calculus or Statistics. At the other end, counselors at competitive public or private high schools usually encourage talented and ambitious students to take Calculus regardless of future plans in order to increase their chances of getting admitted to a prestigious university and their parents enroll them in enrichment programs in mathematics.

Advanced Placement (AP) Physics 1 is a year-long introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a one-semester algebra-based university course in mechanics. Along with AP Physics 2, the first AP Physics 1 exam was administered in 2015.

Advanced Placement (AP) Physics 2 is a year-long introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester algebra-based university course in thermodynamics, electromagnetism, optics, and modern physics. Along with AP Physics 1, the first AP Physics 2 exam was administered in 2015.

Advanced Placement (AP) Precalculus is an Advanced Placement precalculus course and examination, offered by the College Board, in development since 2021 and announced in May 2022. The course debuted in the fall of 2023, with the first exam session taking place in May 2024. The course and examination are designed to teach and assess precalculus concepts, as a foundation for a wide variety of STEM fields and careers, and are not solely designed as preparation for future mathematics courses such as AP Calculus AB/BC.

References

  1. 1 2 "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Archived from the original (PDF) on 2008-07-20. Retrieved 2008-11-29.
  2. ↑ "Topic Outline". Calculus AB. College Board. Archived from the original on 2008-12-19. Retrieved 2008-11-29.
  3. ↑ "Course Descriptions" (PDF).
  4. ↑ College Board. "AP Calculus AB May 2017 Score Distributions" (PDF). Archived from the original (PDF) on 2018-03-26. Retrieved 2017-06-22.
  5. 1 2 3 "Student Score Distributions, AP Exams - May 2018" (PDF). The College Board. Retrieved December 24, 2022.
  6. 1 2 "Student Score Distributions" (PDF). Retrieved July 9, 2020.
  7. ↑ "Student Score Distributions" (PDF). Retrieved June 9, 2021.
  8. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  9. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  10. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  11. ↑ "2024 AP Score Distributions". Retrieved July 8, 2024.
  12. ↑ "Topic Outline". Calculus BC. College Board. Archived from the original on 2008-12-19. Retrieved 2008-11-29.
  13. 1 2 "AP Calculus AB and Calculus BC Chief Reader Report May 2017" (PDF). Archived from the original (PDF) on 2018-07-25.
  14. ↑ "STUDENT SCORE DISTRIBUTIONS". Archived from the original (PDF) on August 19, 2013. Retrieved June 9, 2021.
  15. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  16. ↑ "The 2022 AP Calculus BC scores" . Retrieved 7 July 2022.
  17. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  18. ↑ "2024 AP Score Distributions". Retrieved July 8, 2024.
  19. ↑ "STUDENT SCORE DISTRIBUTIONS – AP Exams May 2019" (PDF). College Board . Retrieved 9 July 2020.
  20. ↑ "STUDENT SCORE DISTRIBUTIONS – AP Exams May 2020" (PDF). College Board . Retrieved 20 July 2023.
  21. ↑ "STUDENT SCORE DISTRIBUTIONS – AP Exams May 2021" (PDF). College Board . Retrieved 20 July 2023.
  22. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  23. ↑ "STUDENT SCORE DISTRIBUTIONS" (PDF). Retrieved January 12, 2024.
  24. ↑ "2018 AP Exam Dates | The Princeton Review". www.princetonreview.com. Retrieved 2018-08-20.
  25. ↑ "The Exam". Calculus AB. College Board. Archived from the original on 2008-12-19. Retrieved 2008-11-29.
  26. ↑ "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Archived from the original (PDF) on 2008-07-20. Retrieved 2008-11-29.
  27. ↑ "AP: The Grade-Setting Process". College Board. Archived from the original on 2008-12-18. Retrieved 2008-11-29.

Further reading

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.