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 Advanced Placement (AP) is a program in the United States and Canada created by the College Board which offers college-level curricula and examinations to high school students. American colleges and universities may grant placement and course ...

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

courses and exams offered by the American nonprofit organization

College Board The College Board is an American nonprofit organization that was formed in December 1899 as the College Entrance Examination Board (CEEB) to expand access to higher education. While the College Board is not an association of colleges, it runs a ...

. AP Calculus AB covers basic introductions to

limits Limit or Limits may refer to: Arts and media * ''Limit'' (manga), a manga by Keiko Suenobu * ''Limit'' (film), a South Korean film * Limit (music), a way to characterize harmony * "Limit" (song), a 2016 single by Luna Sea * "Limits", a 2019 ...

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 In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with di ...

. 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 serie ...

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 obj ...

vector calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject ...

polar coordinate In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the or ...

functions, and curve interpolations).

AP Calculus AB

AP Calculus AB is an

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

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 technology, ...

, and graphical analysis including

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. F ...

s **Concept **At a point **As a function **

Applications Application may refer to: Mathematics and computing * Application software, computer software designed to help the user to perform specific tasks ** Application layer, an abstraction layer that specifies protocols and interface methods used in a c ...

**Higher order derivatives **Techniques *

Integrals In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with di ...

**Interpretations **Properties **

**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, or ...

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 i ...

* 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 In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series \sum_^\infty a_n. List of tests Limit of the summand If t ...

for series *

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 obj ...

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 integral In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or positive or negative infinity; or in some instances as both endpo ...

s * 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 a ...

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 rat ...

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 Free response questions or essay questions are a type of open-ended question commonly used in schools to test students' learning, as well as in entrance exams and sometimes as part of job application or screening processes. Description Free respon ...

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.

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 zh:大学先修课程#科目

AP Calculus AB

Purpose

Topic outline

AP Calculus BC

Purpose

Topic outline

AB sub-score distribution

AP Exam

Format

Scoring

See also

References

External links