1
Calculus
Description of the Examination
The Calculus examination covers skills and concepts
that are usually taught in a one-semester college
course in calculus. The content of each examination
is approximately 60% limits and differential calculus
and 40% integral calculus. Algebraic, trigonometric,
exponential, logarithmic, and general functions are
included. The exam is primarily concerned with an
intuitive understanding of calculus and experience
with its methods and applications. Knowledge of
preparatory mathematics, including algebra, plane
and solid geometry, trigonometry, and analytic
geometry is assumed.
Students are not permitted to use a calculator during
the CLEP Calculus exam.
The examination contains 45 questions to be answered
in 90 minutes. Any time candidates spend on tutorials
and providing personal information is in addition to
the actual testing time.
Knowledge and Skills Required
Questions on the exam require candidates to demon-
strate the following abilities:
• Solving routine problems involving the techniques
of calculus (about 50% of the examination)
• Solving nonroutine problems involving an
understanding of the concepts and applications
of calculus (about 50% of the examination)
The subject matter of the calculus examination is
drawn from the following topics. The percentages
next to the main topics indicate the approximate
percentages of exam questions on those topics.
5%
Limits
•
Statement of properties, e.g., limit of a
constant, sum, product, or quotient
•
Limits that involve inﬁ
nity, e.g.,
lim
x
x
→
0
1
is nonexistent and
lim
sin
x
x
x
→∞
=
0
• Continuity
55% Differential Calculus
The Derivative
• Deﬁ
nitions of the derivative,
e.g.,
′
=
−
−
→
fa
fx
xa
( )
lim
()
and
′
=
+−
→
fx h
h
h
( )
lim
(
)
0
•
Derivatives of elementary functions
•
Derivatives of sum, product, and quotient
(including
tan
x
and
cot
x
)
•
Derivative of a composite function (chain
rule), e.g.,
sin
,
, ln(
)
ax
b
ae
kx
kx
+
( )
•
Derivative of an implicitly deﬁ ned function
•
Derivative of the inverse of a function
(including Arcsin
x
and Arctan
x
)
•
Derivatives of higher order
•
Corresponding characteristics of graphs
of
ff
f
,,
′′
′
and
•
Statement (without proof) of the Mean
Value Theorem; applications and
graphical illustrations
•
Relation between differentiability
and continuity
•