# 125 - Copyright January 2007 by Stanley Ocken. No part of...

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Copyright © January 2007 by Stanley Ocken. No part of this document may be copied or reproduced in any form whatsoever without express permission of the author. Math Review for Algebra and Precalculus Stanley Ocken Department of Mathematics The City College of CUNY Copyright © January 2007 1

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Copyright © January 2007 by Stanley Ocken. No part of this document may be copied or reproduced in any form whatsoever without express permission of the author. Table of Contents Part I: Algebra Notes for Math 195 Introduction……………………………………. ...................... 3 1. Basic algebra laws; order of operations…………………. .. 4 2. How algebra works…………………………….……….… 12 3. Simplifying polynomial expressions………………………29 4. Functions…………………………………………………. .. 41 5. When to use parentheses…………………………………. .. 55 6. Working with fractions…………………………………… 61 7. Adding fractions…………………………………………. ..76 2
Copyright © January 2007 by Stanley Ocken. No part of this document may be copied or reproduced in any form whatsoever without express permission of the author. Math Review for Precalculus and Calculus Part I: Algebra Introduction Algebra is the language of calculus, and calculus is needed for science and engineering. When you attack a real-world problem, you want to represent the problem using algebra expressions. When you read technical books, you want to be comfortable deciphering and working with these expressions. Computers can’t do either of these tasks for you. Algebra used in undergraduate mathematics involves three main activities: rewriting expressions, solving equations, and solving inequalities. You need to perform these somewhat mechanical activities quickly and accurately. It’s very difficult to achieve this goal unless you understand how algebra works. Algebra is a symbolic language that allows communication between people who don’t know each others’ spoken language. The grammar of the language involves three main components: expressions, identities, and equations. An expression involves numbers, variables, parentheses, and algebra operations. Basic types of expressions are integers, variables, monomials, polynomials, and so forth. We’ll deal mostly with expressions in one variable, such as the polynomial . 4 3 + x x An identity between two expressions, written with an equals sign, is a statement that each expression can be obtained by rewriting the other. A simple example is 1 1 2 + + = + x x . With rare exceptions, substituting numbers for variables turns an identity into a true statement about numbers. For example, setting x to 4 yields . 1 4 1 2 4 + + = + An important part of algebra is using identities to rewrite expressions.

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## 125 - Copyright January 2007 by Stanley Ocken. No part of...

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