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Friday, June 29, 2018

AP Calculus BC - Lagrange Error Bound - YouTube
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Advanced Placement Calculus (also known as AP Calculus, AP Calc, or simply AB / BC) 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, integration by parts, polar coordinate functions, and curve interpolations). The College Board has administered the calculus exam since its inception (originally titled Mathematics). When Mathematics split into Calculus AB and Calculus BC in 1969, problems fell into three categories: A (precalculus concepts), B (first-year calculus concepts), and C (second-year calculus concepts). Before 2000, A topics could be on the exam, but now, all concepts are strictly calculus-based.


Video AP Calculus



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.

Course content

The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus. More specifically, the topics are

  • 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.

Maps AP Calculus



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.

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
  • Integration by parts
  • Improper integrals
  • Differential equations for logistic growth
  • Using partial fractions to integrate rational functions

AP Calculus ab | The Frederick Douglass Academy
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AP Exam

Growth

Between 1990 and 2004, the number of students taking the AP Calculus exams increased more than threefold. The exams are now taken by more than 250,000 students each year. 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. The AP awards given by Collegeboard do count both exams. However, they do not count the AB subscore piece of the BC exam.

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. The subdivision of the multiple choice for 2017 exams and beyond differs from that in previous years. The chart below reflects this change:

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.

The Free-Response section is hand-graded by hundreds of educators each June. 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. 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. 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).

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:

Grade distributions for AP Calculus BC

The grade distributions for the BC scores since 2010 were:

AB subscore distribution


AP Calculus AB & AP Calculus BC 2016 Exam FRQ #5 - YouTube
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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. This led the authors to state that AP participation... is not beneficial to students who merely enroll in the courses ...":p. 414


Why AP Calculus is the Scariest AP Test of All | Straighterline
src: www.straighterline.com


See also

  • Calculus
  • Glossary of calculus
  • Stand and Deliver

AP Calculus BC 2016 Exam FRQ #6 - YouTube
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References


D11 - AP Area & Volume Practice - AP Calculus: To Infinity & Beyond!
src: wowmath.org


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


Source of article : Wikipedia