AP Calculus
Advanced Placement Calculus (also known as AP Calculus or AP Calc AB/BC or simply AP Calc) is used to indicate one of two distinct Advanced Placement courses and examinations offered by the College Board, AP Calculus AB and AP Calculus BC.
AP Calculus AB
AP Calculus AB is an advanced placement calculus course taken by high school students around the world, most of whom study at schools with an American curriculum. The course is traditionally taken after Precalculus, otherwise known as Introduction to Analysis, and is the first calculus course offered at most schools.
Purpose
"Calculus AB can be offered by an AP course by any school that can organize a curriculum for students with mathematical ability... 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
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
- Second derivatives
- Integrals
- Interpretations
- Properties
- Applications
- Techniques
- Numerical approximations
- Fundamental theorem of calculus
- Antidifferentation
AP Calculus BC
Purpose
"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 and/or Maclaurin series, the use of parametric equations, polar functions, including arc length in polar coordinates, calculating curve length in parametric and function (y = f(x)) equations, L'Hôpital's rule, integration by parts, improper integrals, Euler's method, differential equations for logistic growth, and using partial fractions to integrate rational functions.[4] Students in AP Calculus BC generally receive two semesters of Advanced Placement in mathematics.
AP Calculus exam
Growth
Between 1990 and 2004, the number of students taking the AP Calculus exams has increased more than threefold.[5] The exams are now taken by more than 250,000 students each year.[6] 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 and receive college credit for both in the same academic year.[7] They do not, however, bar a student from taking the two classes simultaneously; it is usually at the discretion of the individual school to label Calculus AB as the pre-requisite class for Calculus BC, although some schools do allow them as co-requisites for gifted students. However, the majority of schools require precalculus as a prerequisite to Calculus BC. In fact, the majority of students taking Calculus BC have not taken Calculus AB.
Format
The structure of the AB and BC exams is identical. Both exams are three hours and fifteen minutes long, comprising a total of 45 multiple choice questions and six free response questions.[8] They are further subdivided as follows:
| 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 | 28 | 17 | 3 | 3 |
| Time Allowed | 55 minutes | 50 minutes | 45 minutes | 45 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 I Part A during the time for Section II Part B but are NOT allowed to resume using a calculator. The Free-Response section, however, is one hour-and-a-half administration. Students are required to put away their calculators after 45 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, albeit without a calculator during the latter half.
Scoring
The multiple-choice section is scored by computer, with a correct answer receiving 1 point, an incorrect answer losing 1/4 of a point, and a blank answer receiving 0 points. 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 1-5.
Students generally receive this score report by mail in mid-July of the year they took the test.[11] 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[12]). 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
In the 2009 administration, 230,588 students took the exam. The mean score was a 2.99.
The grade distribution for 2009 was:
| Score | Percent |
|---|---|
| 5 | 23.0% |
| 4 | 18.7% |
| 3 | 17.9% |
| 2 | 15.5% |
| 1 | 24.9% |
Grade distributions for AP Calculus BC
In the 2009 administration, 72,965 students took the exam. The mean score was a 3.72.[14]
The grade distribution for the 2009 BC scores was:
| Score | Percent |
|---|---|
| 5 | 43.2% |
| 4 | 17.6% |
| 3 | 19.2% |
| 2 | 7.4% |
| 1 | 12.5% |
The grade distribution for the 2009 AB subscores was:
| Score | Percent |
|---|---|
| 5 | 56.5% |
| 4 | 19.0% |
| 3 | 12.3% |
| 2 | 6.2% |
| 1 | 6.0% |
References
- ^ a b "2006, 2007 AP Calculus Course Description" (PDF). College Board. 2005. Retrieved 2008-11-29.
- ^ "Topic Outline". Calculus AB. College Board. Retrieved 2008-11-29.
- ^ "Course Descriptions".
- ^ "Topic Outline". Calculus BC. College Board. 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).
{{cite book}}: CS1 maint: multiple names: authors list (link) - ^ "Exam Calendars". College Board.
- ^ "The Exam". Calculus AB. College Board. 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. Retrieved 2008-11-29.
- ^ "Exam Grades". College Board. Retrieved 2008-11-29.
- ^ "AP Scores - AP Grades & Reporting Services". College Board. Retrieved 2008-11-29.
- ^ http://apcentral.collegeboard.com/apc/public/repository/ap09_CalculusAB_GradeDistributions.pdf
- ^ [1]