AP Calculus.html



Advanced Placement Calculus (also known as AP Calculus or 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. It's 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 are³

• 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.

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:

The two parts of the Multiple-Choice section are timed and taken independently; students may not work on the Section I Part A during the time for Section II Part B or vice-versa. 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 phone¹²). 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 2007 administration, 211,693 students took the exam from 11,819 schools. The mean score was a 2.94.¹³

The grade distribution for 2007 was:

Grade distributions for AP Calculus BC

In the 2007 administration, 64,311 students took the exam from 4,672 schools. The mean score was a 3.71.¹⁴

The grade distribution for 2007 was:

Composite score range

The College Board has released information on the composite score range (out of 108) required to obtain each grade (note that this changes annually): ¹⁵

References

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

• ti89.com - Step by Step Calculus