Must Know High School Algebra

450 Pages·2022·35.074 MB·English

by  Christopher Monahan, Laura Favata

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.
McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in
corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com.
TERMS OF USE
This is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work
is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the
work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit,
distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent. You
may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to
use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED “AS IS.” McGRAW-HILL EDUCATION AND ITS LICENSORS MAKE NO GUARANTEES
OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED
FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA
HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUD-
ING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR
PURPOSE. McGraw-Hill Education and its licensors do not warrant or guarantee that the functions contained in the work will
meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill Education nor its licensors
shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages
resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work.
Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive,
consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of
the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or
cause arises in contract, tort or otherwise.
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