165166SG-Feb2001 - February 2001 PURDUE UNIVERSITY Study...

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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. 1
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Sets of 40 practice problems for each of MA 165 and MA 166 are attached. The correct answers are given on the last page of each set. Naturally, these sets do not cover all points of the courses, but if you have no difficulty with them, you will probably do well in the exam- ination. Additional practice problems are available through the Mathematics Department webpage at www.math.purdue.edu/highSchool/collegePrep/exams-undergrad.html.
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This note was uploaded on 10/04/2010 for the course MATH 166 taught by Professor Hotlz during the Spring '08 term at HCCS.

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165166SG-Feb2001 - February 2001 PURDUE UNIVERSITY Study...

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