February 2001
PURDUE UNIVERSITY
Study Guide for the Advanced Placement Exams in One-variable Calculus
Exam 1 and Exam 2 cover respectively the material in Purdue’s courses MA 165 (MA
161) and MA 166 (MA 162). These are two separate two hour examinations. Students
who pass Exam 1 will receive 4 credit hours for MA 165, and normally will be placed in
MA 173. Those who pass Exam 2 will receive 4 credit hours for MA 166, but only if they
have credit for MA 165, either by credit examination or other means, and normally will be
placed in MA 271. MA 173 and MA 271 are oﬀered in the fall semester only, but students
may also register in MA 166 or MA 162 instead of MA 173, and in MA 261 instead of MA
271.
This study guide describes brieﬂy the topics to be mastered prior to attempting these
examinations. The material can be studied from many textbooks, almost all of them
entitled
Calculus
or
Calculus with Analytic Geometry
. The textbook currently used
at Purdue is
Calculus, Early Transcendentals
,4
th
edition, James Stewart, Brooks/Cole
Publishing Company.
The topics covered on the Credit Exams are listed below. Each exam consists of 25
multiple choice problems, each worth 4 points.
Exam 1: (MA 165) (Two hours)
1. Review of functions and graphs. Trigonometric, exponential and logarithm functions.
2. Limits and continuity.
3. Deﬁnition of derivative. Rules of diﬀerentiation (sum, product, quotient). Chain rule
and implicit diﬀerentiation. Derivatives of trigonometric, exponential, and logarithmic
functions. Related rates and approximations.
4. Applications of the derivative. Maxima and minima. Mean value theorem. Exponen-
tial growth and decay. Curve sketching, concavity, asymptotes. Indeterminate forms
and L’Hˆ
opital’s Rule.
5. Deﬁnition of deﬁnite integral. Fundamental Theorem of Calculus. Indeﬁnite integrals.
Integration by substitution. Deﬁnition of logarithm.
6. Inverse functions. Exponential and logarithm functions. Inverse trigonometric func-
tions and their derivatives.
Exam 2: (MA 166) (Two hours)
1. Cartesian coordinates and vectors in space. Dot product, cross product.
2. Techniques of Integration: Integration by parts, trigonometric integrals, trigonometric
substitutions, partial fractions. Improper integrals.
3. Applications of the integral. Volumes by disks and shells. Length of a curve. Area of
a surface. Work. Moments and center of gravity.
4. Sequences and series. Convergence. Integral, comparison, ratio and root tests. Alter-
nating series and absolute convergence. Power series and Taylor series.
5. Parametric Equations. Polar coordinates. Conic sections.
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