Advanced Placement
From Wikipedia, the free encyclopedia
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 credit to students who
obtain high scores on the examinations. The AP curriculum for each of the various subjects is
created for the College Board by a panel of experts and college-level educators in that field of
study. For a high school course to have the designation, the course must be audited by the
College Board to ascertain that it satisfies the AP curriculum. If the course is approved, the
school may use the AP designation and the course will be publicly listed on the AP Course
Ledger.[1]
AP Calculus
From Wikipedia, the free encyclopedia
(Redirected from Advanced Placement Calculus)
Advanced Placement Calculus (also known as AP Calculus, AP Calc, or simply AB / BC) is a
set of two distinct Advanced Placement calculus courses and exams offered by the American
not-for-profit organization College Board. AP Calculus AB covers basic introductions to limits,
derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional
topics (including more advanced integration techniques such as integration by parts, Taylor
series, parametric equations, vector calculus , polar coordinate functions, and curve
interpolations).
AP Calculus AB[edit]
AP Calculus AB is an Advanced Placement calculus course. It is traditionally taken
after precalculus 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[edit]
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.[5]
Topic outline[edit]
The material includes the study and application of differentiation and integration, and graphical
analysis including limits, asymptotes, and continuity.[6] An AP Calculus AB course is typically
equivalent to one semester of college calculus.[7]


Analysis of graphs (predicting and explaining behavior)
Limits of functions (one and two sided)




Asymptotic and unbounded behavior
Continuity
Derivatives
o Concept
o At a point
o As a function
o Applications
o Higher Order derivatives
o Techniques
Integrals
o Interpretations
o Properties
o Applications
o Techniques
o Numerical approximations
AP Calculus BC[edit]
Purpose[edit]
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.[5]
Topic outline[edit]
AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as the following:









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[11]