Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / Calc BC or simply AB / BC) is a set of two distinct
Advanced Placement calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
courses and exams offered by the American nonprofit organization
College Board. AP Calculus AB covers basic introductions to
limits,
derivatives
The derivative of a function is the rate of change of the function's output relative to its input value.
Derivative may also refer to:
In mathematics and economics
*Brzozowski derivative in the theory of formal languages
*Formal derivative, an ...
, and
integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including more advanced integration techniques such as
integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. ...
,
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor se ...
,
parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric ...
s,
vector calculus,
polar coordinate functions, and curve interpolations).
AP Calculus AB
AP Calculus AB is an
Advanced Placement calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
course. It is traditionally taken after
precalculus
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. Schools often distinguish between algebra and trigonometr ...
and is the first calculus course offered at most schools except for possibly a regular 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:
Topic outline
The material includes the study and application of
differentiation and
integration
Integration may refer to:
Biology
* Multisensory integration
* Path integration
* Pre-integration complex, viral genetic material used to insert a viral genome into a host genome
*DNA integration, by means of site-specific recombinase technolo ...
, and graphical analysis including
limits,
asymptotes
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...
, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus.
*Analysis of graphs (predicting and explaining behavior)
*
Limits of functions (one and two sided)
*Asymptotic and unbounded behavior
*
Continuity
*
Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
s
**Concept
**At a point
**As a function
**
Applications
**Higher order derivatives
**Techniques
*
Integrals
**Interpretations
**Properties
**
Applications
**Techniques
**
Numerical approximations
*
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each time) with the concept of integrating a function (calculating the area under its graph, ...
*
Antidifferentiation
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically ...
*
L'Hôpital's rule
In calculus, l'Hôpital's rule or l'Hospital's rule (, , ), also known as Bernoulli's rule, is a theorem which provides a technique to evaluate limits of indeterminate forms. Application (or repeated application) of the rule often converts an ...
*
Separable differential equations
AP Calculus BC
Purpose
According to the College Board,
Topic outline
AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following:
*
Convergence tests for series
*
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor se ...
*
Parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric ...
s
*
Polar functions (including arc length in polar coordinates and calculating area)
*
Arc length
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
...
calculations using integration
*
Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. ...
*
Improper integrals
*
Differential equations for logistic growth
* Using
partial fraction
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as ...
s to integrate
rational function
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be ...
s
AB sub-score distribution
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.
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
Multiple choice (MC), objective response or MCQ (for multiple choice question) is a form of an objective assessment in which respondents are asked to select only correct answers from the choices offered as a list. The multiple choice format is m ...
questions and six
free response questions. They are usually administered on a Tuesday morning in May.
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 half.
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.
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.
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
*
AP Physics C: Mechanics and
AP Physics C: Electricity and Magnetism
*
AP Precalculus
*
Glossary of calculus
A glossary (from grc, γλῶσσα, ''glossa''; language, speech, wording) also known as a vocabulary or clavis, is an alphabetical list of terms in a particular domain of knowledge with the definitions for those terms. Traditionally, a glo ...
*
Integration Bee
*
Math 55 at Harvard University
*
Mathematics education in the United States
*''
Stand and Deliver
''Stand and Deliver'' is a 1988 American drama film directed by Ramón Menéndez, written by Menéndez and Tom Musca, based on the true story of a high school mathematics teacher, Jaime Escalante. For portraying Escalante, Edward James Olmo ...
'' (1988 film)
References
External links
*AP Calculus AB
College Board description of the AP Calculus AB course content*AP Calculus BC
**
ttps://web.archive.org/web/20130401114413/http://www.collegeboard.com/student/testing/ap/calculus_bc/exam.html?calcbc College Board description of the AP Calculus BC examination
{{Glossaries of science and engineering
Mathematics education in the United States
Calculus
Advanced Placement
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