Math 151      Study Guide for Hour Quiz #2       C.S.Davis

You are responsible for the subject matter in the sections below. The following topics are the most important. Typical exercises from Precalculus, 5th edition, by Stewart, Redlin & Watson are assigned at the end of each objective. Work additional exercises if you need more practice. The answers to the odd numbered problems are in the back of the text.  These exercises are for practice and are not graded.  The problem sets found on the PreCalculus Welcome Page are graded in class.  See the Semester Plan for the current dates for the grading of the problem sets and taking of the hour quizzes.
3.1          Use of the properties below along with a graphing calculator assures a graph showing all of the important characteristics of the polynomial.
1. Analyze and graph polynomials in expanded form or factored form.
a.  Give the general shape for that degree polynomial.
b.  Give the maximum number of possible humps.
c.  Draw the graph by plotting points and/or with the aid of your calculator.   P262#5-10,13,17,21,27,28,33,37,39,41,45,51,59,65,67
2. Solve an extreme value word problem involving polynomials.   P264#77,79
3.2          Finding roots of polynomials is a crucial step in optimization problems in calculus.
1. Use long division on polynomials to give an example of  the division algorithm.  P270#11 
2. Use the remainder theorem and synthetic division to evaluate polynomials and test for roots.   P270#7,11,15,27,31,45,68
3.3          Finding rational roots leads to solving linear homogeneous differential equations.
1. Use the rational zeros theorem to find all possible rational roots (zeros) of a polynomial, use synthetic division repeatedly to find the rational roots and use the quadratic formula to find any remaining irrational roots.   P279#9,11,17,23
3.4          The reactance of an electric circuit is a quantity whose measure is a complex number.
1. Do arithmetic with complex numbers.   P289#11,17,29,33,41,45,51
2. Solve a quadratic equation with complex roots (zeros).   P290#59,67
3.5          Finding all roots of a polynomial is critical in differential equations, the branch of mathematics which is usually studied following calculus.
1. Find all roots of a polynomial.  (Find the possible rational roots, then check for the actual rational roots by synthetic division, then find remaining irrational or complex roots using the quadratic formula.)   P298#25,41,49,51,59,61
2. Find a polynomial having integer coefficients with given real and complex roots.   P298#31,35,37,39
3.5           Rational functions model examples in calculus wherein quantities grow very slowly as time passes. 
1. For rational functions, find all intercepts and asymptotes and draw the graphs.   Check by graphing with the calculator.   P313#25,29,41,53,61
11.5          Mathematical induction is used to prove theorems where direct proofs are not applicable.
1. Use mathematical induction to prove that a formula is true.   P859#2,4,7 
11.6         We've already used the binomial theorem for small exponents.
1. Expand a binomial expression 
   a.  using Pascal's triangle;   P868#5,9       b.  using the factorial notation.   P868#25,29,43