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'Advanced Placement Calculus', (also known as 'AP Calculus' or 'AP Calc'), is the name 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 some United States high school students. It traditionally follows Precalculus, which is 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.
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, vector calculus, polar functions, including arc length in polar coordinates, calculating curve length in parametric and function (y = f(x)) equations, L'Hôpital's rule, improper integrals, 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
Since 1990, 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].
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[7]. They are further subdivided as follows:
| Multiple-Choice, Part I | Multiple-Choice, Part II | Free-Response, Part A | Free-Response, Part B | |
|---|---|---|---|---|
| # of Questions | 28 | 17 | 3 | 3 |
| Time Allowed | 55 minutes | 50 minutes | 45 minutes | 45 minutes |
| Calculator Use | No | Yes | Yes | No |
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[8].
The free-response section is hand-graded by hundreds of educators each June[9]. No points are subtracted for guesswork or incorrect answers on this portion of the exam. 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[10]. Alternately, they can receive their scores by phone as early as June 27 for a fee of $8. 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.
Grade distributions for AP Calculus AB
In the 2006 administration, 197,181 students took the exam from 11,526 schools. The mean score was a 3.03[11].
The grade distribution for 2006 was:
| Score | Percent |
|---|---|
| 5 | 22.3% |
| 4 | 20.5% |
| 3 | 18.6% |
| 2 | 15.5% |
| 1 | 23.2% |
Grade distributions for AP Calculus BC
In the 2006 administration, 58,602 students took the exam from 4,371 schools. The mean score was a 4.13[12].
The grade distribution for 2006 was:
| Score | Percent |
|---|---|
| 5 | 41.9% |
| 4 | 19.7% |
| 3 | 19.7% |
| 2 | 6.4% |
| 1 | 12.3% |
AP Calculus in popular culture
★ The AP Calculus exam was prominently featured in the film ''Stand and Deliver''.
★ In House episode Poison, House's patient was taking his AP Calculus exam when he collapsed.
References
1. http://collegeboard.com/prod_downloads/ap/students/calculus/ap-cd-calc-0607.pdf
2. http://collegeboard.com/student/testing/ap/calculus_ab/topic.html?calcab
3. http://collegeboard.com/prod_downloads/ap/students/calculus/ap-cd-calc-0607.pdf
4. http://collegeboard.com/student/testing/ap/calculus_bc/topic.html?calcbc
5. http://www.nsf.gov/statistics/seind06/c1/c1s2.htm#sb3
6. http://ieeexplore.ieee.org/iel5/8925/28283/01264690.pdf
7. http://collegeboard.com/student/testing/ap/calculus_ab/exam.html?calcab
8. http://www.collegeboard.com/prod_downloads/ap/students/calculus/ap-cd-calc-0607.pdf
9. http://www.collegeboard.com/student/testing/ap/exgrd_set.html
10. http://collegeboard.com/student/testing/ap/exgrd.html
11. 2006 Calculus AB Grade Distribution
12. 2006 Calculus BC Grade Distribution
External links
★ AP Calculus AB
★
★ College Board description of the AP Calculus AB course content
★
★ College Board description of the AP Calculus AB examination
★ AP Calculus BC
★
★ College Board description of the AP Calculus BC course content
★
★ College Board description of the AP Calculus BC examination
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