Practice Exams
Practice Final Exams
Math 1031 



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Math 1142 



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Math 1151 



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Math 1155 



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Math 1271 



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Math 1272 



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Math 1281 



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Math 2263 



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Course Notes
Math 1151 / 1271 Course Notes
Trigonometric Identities  Starting from the Pythagorean Identity, these notes show how the most often useful trigonometric identities are derived.
Math 1271 Course Notes
Math 1271 Course Notes  All Section references are to Stewart, Calculus: Early Transcendentals, 6th Edition
Functions These are some notes that were written in the fall of 2007 on topics from Chapter 1 and early in Chapter 2.
The Elementary Functions and some of their PropertiesThis is a summary reference of the basic mathematical functions that were used in this course sequence.
Limits at Infinity for Rational FunctionsThis is an elaboration of some of the material in Section 2.6, based on an earlier handout and posting.
Derivations of Some Differentiation Rules  These notes provide some supplementary discussion of the differentiation rules presented in the first half of Chapter 3 in Stewart. The Product Rule, Quotient Rule, and Chain Rule are derived; alternative proofs of the trigonometric limits are shown, leading to the derivation of the derivatives of the sine and cosine functions; and a variant proof for the derivative for the general exponential function is shown.
Trigonometric Limits This is a set of solutions for Problems 3948 in Section 3.3. While we will learn a more powerful method of calculating such limits in Section 4.4, you may find the solutions worth studying for techniques of problemsolving.
Derivative Tests This is a summary of the First and Second Derivative Tests. There is a reference table which collates the results for the derivative tests applied to a function.
Optimization Problems Here are some additional problems worked out from Section 4.7.
November 25, 2009 Lecture This is a set of notes for a lecture given on Thanksgiving Eve, mostly covering Section 5.2 of Stewart, on Riemann sums and the definition of definite integrals, with some worked examples.
November 26, 2008 Lecture This is a set of notes for a lecture given on Thanksgiving Eve on the Net Change Theorem (Section 5.4 of Stewart), with a leadin to the "substitution method" for integration (Section 5.5).
Math 1272 Course Notes
all Section references are to Stewart, Calculus: Early Transcendentals, 6th Edition
Integrals of Power of Triginometric Functions This is a "handout" written in 2003, which he revised slightly and to which he added a summary. It covers cases beyond what is discussed in Section 7.2 of Stewart and includes many examples.
Weierstrass’ “HalfAngle” SubstitutionThis is an additional integration "trick" that has been taught by some instructors for this course in the past. It is not essential to the course, but it may be helpful for you to know about it.
Strategy for Integration This is a summary of the methods of integration we have learned in Chapters 5 and 7 and the circumstances in which they might be applied.
ptest for Improper Integrals This is another "handout" from 2003 on a useful convergence test for improper integrals, which was discussed in Section 7.8. This concept will also be of use to us in Chapter 11.
March 13, 2009 Lecture These are the notes for the lecture given on the Friday before Spring Break, covering arc length and area for polar curves (Section 10.4), including examples and some cautions.
Lecture for 12 March 2010 There is a fair amount of overlap between the topics of this lecture and the Spring Break eve lecture from last year. Some other problems were worked out this time, so you may wish to read both sets of notes, as the 2009 lecture is referred to for additional details on certain points.
Conic Sections and Polar Coordinates  The material covered in Sections 10.5 and 10.6 of Stewart is discussed with an emphasis on deriving the equations of the curves in both rectangular and polar coordinates and demonstrating the unity underlying them.
Convergence Tests for Infinite Series This is a summary of the tests studied in Sections 11.2 to 11.6, along with some guidance on their use.
Space Curves  The topics in Sections 13.2 and 13.3 of Stewart are discussed, along with calculations of all the properties presented there for a particular curve given in one of the problems; these notes may also be of interest to students in Math 2263.
Math 1272 Course Notes
all Section references are to Stewart, Calculus: Early Transcendentals, 6th Edition
Mixing Problems I  This is the first part of notes of the mixing problems discussed in Section 9.3 of Stewart, where the differential equation for the model is separable; the model is also dealt with early on in a first differential equations course.
Mixing Problems II  The second part of these notes investigate the mixing problems found in Section 9.5 of Stewart, where the differential equation must be solved using an "integrating factor"; this method also appears early on in a first differential equations course.
Course Reviews
Math 1031 
Problems+Answer Key 
Solution Set 
Math 1051 
Problems+Answer Key 
Solution Set 
Math 1151 

Math 1271 

Math 1272 

Physics 1201 







Physics 1301 









