Integrated Algebra 1

1 AMSCO SCHOOL PUBLICATIONS, HUDSON STREET, NEW YORK, 10013 Algebra 1 AMSCO SIntegratedAnn Xavier GantertDedicationThis book is dedicated to Edward Keenan who left a profound influence on mathematics education inNew York State and on the development of Amsco Xavier GantertThis author has been associated with mathematics education in New York State as a teacher and anauthor throughout the many changes of the past fifty years. She has worked as a consultant to theMathematics Bureau of the Department of Education in the development and writing of SequentialMathematics and has been a coauthor of Amsco s Integrated Mathematicsseries, which accompanied thatcourse of :Steven BalasianoDebbie CalvinoAssistant Principal, MathematicsMathematics ChairpersonCanarsie High SchoolValley Central High SchoolBrooklyn, NYMontgomery, NYDonna GetchellSal SuteraMathematics TeacherMathematics TeacherGarden City High SchoolNew Utrecht High SchoolGarden City, NYBrooklyn, New YorkText Designer: Nesbitt Graphics, : Compset, Designer by Meghan J.

2 ShupeCover Art by Brand X PicturesPlease visit our Web site at: ordering this book, please specify:R 239 PorINTEGRATED Algebra 1,PaperbackorR 239 HorINTEGRATED Algebra 1,HardboundISBN 978-1-56765-584-1 (Paperback edition)ISBN 978-1-56765-585-8 (Hardbound edition)NYC Item 56765-584-0 (Paperback edition)NYC Item 56765-585-7 (Hardbound edition)Copyright @ 2007 by Amsco School Publications, part of this book may be reproduced in any form without written permission from the in the United States of America4 5 6 7 8 9 1011 10 09 08 07 (Paperback edition)8 9 1011 10 09 08 (Hardbound edition) Integrated Algebra 1is a new text for high school Algebra that continues theapproach that has made Amsco a leader in presenting mathematical ideas in acontemporary, Integrated manner. Over the past decades, this approach hasundergone numerous changes and refinements to keep pace with ever Amsco book uses an Integrated approach to the teaching of high schoolmathematics that is promoted by the National Council of Teachers ofMathematics in its Principles and Standards for School Mathematicsand man-dated by the New York State Board of Regents in the New York StateMathematics Core Curriculum.

3 This text presents a range of materials and expla-nations that are guidelines for achieving a high level of excellence in the studyof this book:The graphing calculatoris introduced and used throughout the book as aroutine tool in the study of mathematics. Underlying mathematical conceptsand procedures are clearly presented, stressing calculator use as a learning andcomputational real number systemis fully developed, to help students understand andcorrectly interpret technological limitations such as the calculator displays ofrational approximations. The role of precision and accuracy, in determiningacceptable computational results, is carefully explained and Algebra to the solution of problems from geometry, proba-bility, statistics, finance, and other real-world applications is developed through-out the stressed throughout the text and in the Teacher s Manualwhere multiple suggestions are given for teaching strategies, for further explo-rations of related topics, and for alternative assessment.

4 The text, as well as theManual, includes opportunities for cooperative learning, hands-on activities,extended tasks, and independent investigation. Reproducible EnrichmentActivitiesfor each chapter provide both material for review and reinforcementas well as for in-depth Exercisesare divided into three About Mathematicspro-vides questions in which students are asked to contrast, compare, evaluate, andjustify their own ideas or those of others. These questions help students incor-porate the tools of the performance indicators investigate, explore, discover,conjecture, reason, justify, explain, prove, and apply into their study of mathe-matics. These questions also provide a valuable source of material for classroomdiscussion or for inclusion in a student Skillsprovides rou-tine practice exercises that enable the student and the teacher to evaluate thestudent s ability to both manipulate mathematical symbols and understandmathematical Skills provides exercises in which the newideas of each section, together with previously learned skills, are used to solveproblems that reflect real-life understanding,procedural fluency, and problem solving, whichare the primary goals of the Core Curriculumare addressed throughout thetext.

5 General concepts and principles are fully addressed and developed indetail, then further explored in the examples and exercise sections. TheProceduresthroughout the text explain how to perform both arithmetic andgeometric processes. The Examplesgiven in each section demonstrate problemsolving approaches, often presenting alternative strategies for solution. Bothroutine and non-routine problems are material in this text is intended to present basic Algebra and its rela-tionship to other branches of mathematics. The text aims at developing mathe-matics as a unified whole in which each branch of mathematics is integrallyrelated. Many of the concepts presented in this text have been introduced inprevious mathematics courses. The text provides the opportunity for students toreview familiar material that is the foundation for the development of new top-ics, and presents all the material needed to develop the skills and achieve thegoals suggested in the New York State Core Curriculumfor Integrated intent of the author was to make this text of greatest service to the aver-age student.

6 However, the materials for reinforcement and for enrichment thatthe text contains make it appropriate for varying abilities. Specifically:Concepts are carefully developed using appropriate language and mathe-matical principles and procedures are stated clearly and solved examples serve as models for students, with detailed step-by-step and varied exercises develop skills and test enrichment activities challenge the most capable text is offered so that teachers may effectively continue to help stu-dents to comprehend, master, and enjoy vCONTENTSC hapter 1 NUMBER SYSTEMS11-1 The Integers21-2 The Rational Numbers111-3 The Irrational Numbers171-4 The Real Numbers251-5 Numbers as Measurements28 Chapter Summary34 Vocabulary34 Review Exercises35 Chapter 2 OPERATIONS AND PROPERTIES372-1 Order of Operations382-2 Properties of Operations452-3 Addition of Signed Numbers542-4 Subtraction of Signed Numbers592-5 Multiplication of Signed Numbers642-6 Division of Signed Numbers682-7 Operations with Sets712-8 Graphing Number Pairs75 Chapter Summary81 Vocabulary82 Review Exercises83 Cumulative Review85viCONTENTSC hapter 3 ALGEBRAIC EXPRESSIONS AND OPEN SENTENCES883-1 Using Letters to Represent Numbers893-2 translating Verbal Phrases into Symbols913-3 Algebraic Terms and Vocabulary953-4 Writing Algebraic Expressions in Words983-5 Evaluating Algebraic Expressions1003-6 Open Sentences and Solution Sets1043-7 Writing Formulas107 Chapter Summary111 Vocabulary111 Review Exercises111 Cumulative

7 Review114 Chapter 4 FIRST DEGREE EQUATIONS AND INEQUALITIES IN ONE VARIABLE1164-1 Solving Equations Using More Than One Operation1174-2 Simplifying Each Side of an Equation1224-3 Solving Equations That Have the Variable in Both Sides1284-4 Using Formulas to Solve Problems1344-5 Solving for a Variable in Terms of Another Variable1424-6 Transforming Formulas1434-7 Properties of Inequalities1464-8 Finding and Graphing the Solution Set of an Inequality1514-9 Using Inequalities to Solve Problems157 Chapter Summary161 Vocabulary162 Review Exercises162 Cumulative Review164 Chapter 5 OPERATIONS WITH ALGEBRAIC EXPRESSIONS1675-1 Adding and Subtracting Algebraic Expressions1685-2 Multiplying Powers That Have the Same Base1735-3 Multiplying by a Monomial1775-4 Multiplying Polynomials1835-5 Dividing Powers That Have the Same Base1865-6 Powers with Zero and Negative Exponents1885-7 Scientific Notation1915-8 Dividing by a Monomial197 CONTENTSvii5-9 Dividing by a Binomial200 Chapter Summary202 Vocabulary202 Review Exercises203 Cumulative Review204 Chapter 6 RATIO AND PROPORTION2076-1 Ratio2086-2 Using a Ratio to Express a Rate2126-3 Verbal Problems Involving Ratio2146-4 Proportion2166-5 Direct Variation2226-6 Percent and Percentage Problems2276-7 Changing Units of Measure234 Chapter Summary238 Vocabulary239 Review Exercises239 Cumulative Review242 Chapter 7 GEOMETRIC FIGURES, AREAS, AND VOLUMES2457-1 Points, Lines.

8 And Planes2467-2 Pairs of Angles2507-3 Angles and Parallel Lines2587-4 Triangles2627-5 Quadrilaterals2727-6 Areas of Irregular Polygons2797-7 Surface Areas of Solids2827-8 Volumes of Solids286 Chapter Summary293 Vocabulary294 Review Exercises294 Cumulative Review297 Chapter 8 TRIGONOMETRY OF THE RIGHT TRIANGLE3008-1 The Pythagorean Theorem3018-2 The Tangent Ratio3078-3 Applications of the Tangent Ratio313viiiCONTENTS8-4 The Sine and Cosine Ratios3178-5 Applications of the Sine and Cosine Ratios3238-6 Solving Problems Using Trigonometric Ratios327 Chapter Summary331 Vocabulary332 Review Exercises332 Cumulative Review334 Chapter 9 GRAPHING LINEAR FUNCTIONS AND RELATIONS3379-1 Sets, Relations, and Functions3389-2 Graphing Linear Functions Using Their Solutions3469-3 Graphing a Line Parallel to an Axis3529-4 The Slope of a Line3559-5 The Slopes of Parallel and Perpendicular Lines3639-6 The Intercepts of a Line3669-7 Graphing Linear Functions Using Their Slopes3709-8 Graphing Direct Variation3749-9 Graphing First-Degree Inequalities in Two Variables3789-10 Graphs Involving Absolute Value3829-11 Graphs Involving Exponential Functions387 Chapter Summary393 Vocabulary394 Review Exercises394 Cumulative Review399 Chapter 10 WRITING AND SOLVING SYSTEMS OF LINEAR FUNCTIONS40110-1 Writing An Equation Given Slope and One Point40210-2 Writing an Equation Given Two Points40410-3 Writing an Equation Given the Intercepts40710-4 Using a Graph to Solve a System of Linear Equations41010-5 Using Addition to Solve a System of Linear Equations41610-6 Using Substitution to Solve a System of Linear Equations42210-7 Using Systems of Equations to Solve Verbal Problems42610-8

9 Graphing the Solution Set of a System of Inequalities431 Chapter Summary436 Vocabulary436 Review Exercises436 Cumulative Review439 CONTENTSixChapter 11 SPECIAL PRODUCTS AND FACTORS44211-1 Factors and Factoring44311-2 Common Monomial Factors44711-3 The Square of a Monomial44911-4 Multiplying the Sum and the Difference of Two Terms45011-5 Factoring the Difference of Two Perfect Squares45211-6 Multiplying Binomials45411-7 Factoring Trinomials45711-8 Factoring a Polynomial Completely461 Chapter Summary464 Vocabulary464 Review Exercises465 Cumulative Review466 Chapter 12 OPERATIONS WITH RADICALS46912-1 Radicals and the Rational Numbers47012-2 Radicals and the Irrational Numbers47612-3 Finding the Principal Square Root of a Monomial48212-4 Simplifying a Square-Root Radical48412-5 Addition and Subtraction of Radicals48712-6 Multiplication of Square-Root Radicals49112-7 Division of Square-Root Radicals494 Chapter Summary496 Vocabulary497 Review Exercises497 Cumulative Review499 Chapter 13 QUADRATIC RELATIONS AND FUNCTIONS50213-1 Solving Quadratic Equations50313-2 The Graph of a Quadratic Function50813-3 Finding Roots from a Graph52213-4 Graphic Solution of a Quadratic-Linear System52513-5 Algebraic Solution of a Quadratic-Linear System529 Chapter Summary533 Vocabulary534 Review Exercises534 Cumulative Review536xCONTENTSC hapter 14 ALGEBRAIC FRACTIONS.

10 AND EQUATIONS AND INEQUALITIES INVOLVING FRACTIONS53914-1 The Meaning of an Algebraic Fraction54014-2 Reducing Fractions to Lowest Terms54114-3 Multiplying Fractions54514-4 Dividing Fractions54814-5 Adding or Subtracting Algebraic Fractions55014-6 Solving Equations with Fractional Coefficients55614-7 Solving Inequalities with Fractional Coefficients56214-8 Solving Fractional Equations565 Chapter Summary569 Vocabulary570 Review Exercises570 Cumulative Review573 Chapter 15 PROBABILITY57515-1 Empirical Probability57615-2 Theoretical Probability58415-3 Evaluating Simple Probabilities59015-4 The Probability of (A and B)59615-5 The Probability of (A or B)59915-6 The Probability of (Not A)60515-7 The Counting Principle, Sample Spaces, and Probability60915-8 Probabilities with Two or More Activities61715-9 Permutations62715-10 Permutations with Repetition63615-11 Combinations63915-12 Permutations, Combinations, and Probability646 Chapter Summary651 Vocabulary653 Review Exercises653 Cumulative Review657 Chapter 16 STATISTICS66016-1 Collecting Data66116-2 Organizing Data66716-3 The Histogram67516-4 The Mean, the Median, and the Mode680 CONTENTSxi16-5 Measures of Central Tendency and Grouped Data69016-6 Quartiles, Percentiles, and Cumulative Frequency69816-7 Bivariate Statistics710 Chapter Summary724 Vocabulary725 Review Exercises725 Cumulative Review729 INDEX731 CHAPTER11 CHAPTERTABLE OFCONTENTS1-1 The Integers1-2 The Rational Numbers1-3 The Irrational Numbers1-4 The Real Numbers1-5 Numbers as MeasurementsChapter SummaryVocabularyReview ExercisesNUMBERSYSTEMS The athletic department needs to transport 125students.