Table Of Content

Second Edition Chris Monahan Laura Favata 00_Monahan_FM.indd 1 14/04/22 12:45 PM Copyright © 2022, 2019 by McGraw Hill. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-1-26-428640-9 MHID: 1-26-428640-6 The material in this eBook also appears in the print version of this title: ISBN: 978-1-26-428639-3, MHID: 1-26-428639-2. eBook conversion by codeMantra Version 1.0 All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trade- marked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringe- ment of the trademark. Where such designations appear in this book, they have been printed with initial caps. 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Contents Author’s Note ix Introduction 1 The Flashcard App 4 Putting Numbers Together and Taking Them Apart 5 The Order of Operations 6 Variables and Expressions 11 Bases and Exponents 13 Evaluating Algebraic Expressions 15 Solving Two-Step Linear Equations 18 Exercises 20 Relations and Functions 23 Cartesian Coordinate Plane 24 Relations 28 Functions 30 Function Notation 32 Exercises 35 Linear Equations 37 Solving Multistep Linear Equations 38 Solving Linear Equations with Variables on Each Side of the Equation 41 Literal Equations 44 iii 00_Monahan_FM.indd 3 14/04/22 12:45 PM iv Contents Writing Equations 47 Ratios and Proportions 51 Percent of Change 54 Weighted Averages 57 Two-Way Tables 59 Exercises 61 Equations of Linear Functions 65 Rate of Change and Slope 66 Graphing Equations in Slope-Intercept Form 74 Writing Equations in Slope-Intercept Form 78 Writing Equations in Point-Slope Form 81 Writing Equations in Standard Form 84 Graphing Equations in Standard Form 86 Parallel and Perpendicular Lines 89 Inverse Linear Functions 92 Exercises 95 Applications of Linear Functions 101 Word Problems: Coins, Geometry, and Motion 102 Coin Problems 102 Geometry Problems 105 Motion Problems 108 Direct Variation 111 Sequences 114 Arithmetic Sequences as Linear Functions 118 Arithmetic Series 121 Absolute Value 124 Exercises 129 00_Monahan_FM.indd 4 14/04/22 12:45 PM Contents v Linear Inequalities 133 Solving Inequalities with the Four Operations 134 Solving Multistep Inequalities 136 Solving Compound Inequalities 137 Inequalities Involving Absolute Value 141 Graphing Inequalities in Two Variables 143 Exercises 149 Systems of Linear Equations and Inequalities 151 Graphing Systems of Equations 152 Algebraic Solutions 155 Substitution 156 Elimination Using Addition and Subtraction 158 Solution Using Matrices 162 Applying Systems of Linear Equations 166 Currency 166 Motion 168 Mixture 171 Systems of Inequalities 173 Exercises 179 Exponents and Exponential Functions 183 Multiplication Properties of Exponents 184 Division Properties of Exponents 186 Rational Exponents 189 Scientific Notation 193 Exponential Functions 195 Growth and Decay 199 Geometric Sequences as Exponential Functions 203 00_Monahan_FM.indd 5 14/04/22 12:45 PM vi Contents Recursive Formulas 206 Exercises 211 Quadratic Expressions and Equations 215 Adding and Subtracting Polynomials 216 Multiplying a Polynomial by a Monomial 219 Multiplying Polynomials 220 Multiplying Binomials 220 Multiplying Polynomials 225 Special Products 227 Differences of Squares 228 Perfect Squares 228 Factoring Polynomials 230 First Step: Always look for a common factor. 230 Second Step: Is the polynomial one of the special polynomials? 231 Trial and Error: Part 1 233 Trial and Error: Part 2 235 Solving x2 + bx + c = 0 239 Exercises 241 Quadratic Functions and Equations 245 Completing the Square 246 Graphing Quadratic Functions 250 The Standard Form of the Parabola 250 The Vertex Form of the Parabola 255 Solving Quadratic Equations by Graphing 257 Transformations of Quadratic Functions 260 Solving Quadratic Equations by Using the Quadratic Formula 263 Special Functions 266 Exercises 273 00_Monahan_FM.indd 6 14/04/22 12:45 PM Contents vii Rational Expressions and Equations 277 Inverse Variation 278 Rational Functions 280 Simplifying Rational Expressions 282 Multiplying and Dividing Rational Expressions 284 Adding and Subtracting Rational Expressions 286 Mixed Expressions and Complex Fractions 289 Rational Equations 293 Dividing Polynomials 297 Exercises 303 Radical Functions and Geometry 309 Simplifying Radical Expressions 310 Operations with Radical Expressions 314 Radical Equations 317 The Pythagorean Theorem 320 Trigonometric Ratios 324 Exercises 332 Probability and Statistics 339 Statistics and Parameters 340 Measures of Central Tendency 341 Distributions of Data 347 Scatter Plots and Lines of Fit 361 Exercises 368 Answer Key 371 Teacher’s Guide 429 00_Monahan_FM.indd 7 14/04/22 12:45 PM This page intentionally left blank RREEAADD__TTHHIINNKK__IITTAALLIIAANN..iinndddd 22 1111//1199//2211 11::1122 PPMM Author’s Note Must Know High School Algebra continues to build on the skills and concepts learned in your middle school math classes. Much of the work done in this book concentrates on a formal process for solving equations and inequalities (including graphical approaches). In addition, you will learn about the arithmetic of polynomials, functions and function notation, solving quadratic equations, solving exponential equations, and dig a little deeper into the study of probability and statistics. As a student, I used to hate the questions that started with “Kathy has 60 coins in her purse” and then go on to ask how many coins of each type she has in her purse. I always wanted to tell Kathy to dump the contents of her purse on the table and count the coins. As a teacher, I understood the importance of learning the process of clearly defining the meaning of the variables used and the relationships described in each of the equations and inequalities written about those variables. I hope you will be patient as you work through the book’s problems and remember that they will help you understand how to analyze problems in real life. Mathematics, in general, and this book in particular are not meant for you to read only. You should always have a pencil, paper, and your calculator with you when doing math. There are plenty of examples in the book with explanations that will guide you through the steps involved. I encourage you, though, to try to do the problems before you read the explanations. This will give you a reasonable measure of how much you understand when you first read the problem. Did you get stuck at some point? That’s fine. The reason you bought this book was to help you get over whatever may have been causing you trouble. Read through the explanations. Make sure they seem logical to you. Go back and try the problem again. There are more ix 00_Monahan_FM.indd 9 14/04/22 12:45 PM