Alg 2 Trig Text - Manhasset Secondary School

1 AMSCO School PUBLICATIONS, HUDSON STREET, NEW YORK, 10013 ALGEBRA 2andTRIGONOMETRYAMSCO SAnn Xavier 8/12/08 1:46 PM Page iDedicationTo Jessica Alexander and Uriel Avalos in gratitude for their invaluable work in preparing this text Xavier GantertThe 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 Mathematics series , which accompanied thatcourse of :Richard AuclairMathematics TeacherLa Salle SchoolAlbany, NYDomenic D OrazioMathematics TeacherMidwood High SchoolBrooklyn, NYSteven J.

2 BalasianoAssistant Principal,Supervision MathematicsCanarsie High SchoolBrooklyn, NYGeorge DrakatosMathematics TeacherBaldwin Senior High SchoolBaldwin, NYDebbie CalvinoMathematics Supervisor,Grades 7 12 Valley Central High SchoolMontgomery, NYRonald HattarMathematics ChairpersonEastchester High SchoolEastchester, NYRaymond Scacalossi CoordinatorManhasset High SchoolManhasset, NYText Designer: Nesbitt Graphics, : ICC MacmillanCover Design by Meghan J. ShupeCover Art by Radius Images (RM)Please visit our Web site at: ordering this book, please specify:R 159 PorALGEBRA 2 AND TRIGONOMETRY,Paperback orR 159 HorALGEBRA 2 AND TRIGONOMETRY,HardboundISBN 978-1-56765-703-6 (Paperback edition)ISBN 978-1-56765-702-9 (Hardbound edition)NYC Item 56765-703-5 (Paperback edition)NYC Item 56765-702-8 (Hardbound edition)Copyright 2009 by Amsco School Publications, part of this book may be reproduced in any form without written permission from the in the United States of America1 2 3 4 5 6 7 8 9 1014 13 12 11 10 09 8/12/08 1.

3 46 PM Page iiAlgebra 2 and Trigonometryis a new text for a course in intermediate algebra andtrigonometry that continues the approach that has made Amsco a leader in pre-senting mathematics in a modern, integrated manner. Over the last decade, thisapproach has undergone numerous changes and refinements to keep pace withever-changing textbook is the final book in the three-part series in which Amsco parallelsthe integrated approach to the teaching of high School mathematics promoted bythe National Council of Teachers of Mathematics in its Principles and Standards forSchool Mathematicsand mandated by the New York State Board of Regents in theMathematics Core Curriculum. The text presents a range of materials and explana-tions that are guidelines for achieving a high level of excellence in their under-standing of this book:The real numbersare reviewed and the understanding of operations with irra-tional numbers, particularly radicals, is graphing calculatorcontinues to be used as a routine tool in the study ofmathematics.

4 Its use enables the student to solve problems that require computationthat more realistically reflects the real world. The use of the calculator replaces theneed for tables in the study of trigonometry and geometrycontinues to be an integral part of the visualization ofalgebraic and trigonometric a unifying concept throughout. The algebraic functionsintroduced in Integrated Algebra 1are reviewed, and exponential, logarithmic, andtrigonometric functions are skillsfrom Integrated Algebra 1 are maintained, strengthened, andexpanded as both a holistic approach to mathematics and as a bridge to the use of the graphing calculator to reexamine range, quar-tiles, and interquartile range, to introduce measures of dispersion such as varianceand standard deviation, and to determine the curve that best represents a set ofbivariate 8/12/08 1.

5 46 PM Page iiiIntegrationof geometry, algebra, trigonometry, statistics, and other branches ofmathematics begun in Integrated Algebra 1and Geometryis continued and divided into three About Mathematicsencour-ages the student to reflect on and justify mathematical conjectures, to discovercounterexamples, and to express mathematical ideas in his or her own Skillsprovides routine practice exercises that enable the student andteacher to evaluate the student s ability to both manipulate mathematical symbolsand understand mathematical Skillsprovides exercises inwhich the new ideas of each section, together with previously learned skills, are usedto solve problems that reflect real-life solving, a primary goal of all learning standards, is emphasizedthroughout the text.

6 Students are challenged to apply what has been learned to thesolution of both routine and non-routine stressed both in the text and in the Teacher s Manual wheremany suggestion are given for teaching strategies and alternative assessment. TheManual provides opportunities for extended tasks and hands-on Enrichment Activitiesthat challenge students to explore topics ingreater depth are provided in each chapter of the this text, the real number system is expanded to include the complex num-bers, and algebraic, exponential, logarithmic, and trigonometric functions are inves-tigated. The student is helped to understand the many branches of mathematics, toappreciate the common threads that link these branches, and to recognize intent of the author is to make this book of greatest service to the averagestudent through detailed explanations and multiple examples.

7 Each section providescareful step-by-step procedures for solving routine exercises as well as the non-routine applications of the material. Sufficient enrichment material is included tochallenge students of all :Concepts are carefully developed using appropriate language and mathemati-cal symbolism. General principles are stated clearly and examples serve as models for students with detailed explanations ofthe mathematical concepts that underlie the solution. Alternative approaches aresuggested where and carefully graded exercises are given in abundance to develop skillsand to encourage the application of those skills. Additional enrichment materialschallenge the most capable text is offered so that teachers may effectively continue to help students tocomprehend, master, and enjoy mathematics as they progress in their 8/12/08 1.

8 46 PM Page ivvCONTENTSC hapter 1 THE INTEGERS11-1 Whole Numbers, Integers, and the Number Line21-2 Writing and Solving Number Sentences51-3 Adding Polynomials91-4 Solving Absolute Value Equations and Inequalities131-5 Multiplying Polynomials171-6 Factoring Polynomials221-7 Quadratic Equations with Integral Roots271-8 Quadratic Inequalities30 chapter Summary35 Vocabulary36 Review Exercises37 chapter 2 THE RATIONAL NUMBERS392-1 Rational Numbers402-2 Simplifying Rational Expressions442-3 Multiplying and Dividing Rational Expressions 482-4 Adding and Subtracting Rational Expressions532-5 Ratio and Proportion572-6 Complex Rational Expressions612-7 Solving Rational Equations642-8 Solving Rational Inequalities70 chapter Summary74 Vocabulary74 Review Exercises75 Cumulative Review77 chapter 3 REAL

9 NUMBERS AND RADICALS793-1 The Real Numbers and Absolute Value803-2 Roots and Radicals843-3 Simplifying 8/12/08 1:46 PM Page vviCONTENTS3-4 Adding and Subtracting Radicals943-5 Multiplying Radicals983-6 Dividing Radicals1023-7 Rationalizing a Denominator1043-8 Solving Radical Equations108 chapter Summary113 Vocabulary114 Review Exercises114 Cumulative Review117 chapter 4 RELATIONS AND FUNCTIONS1194-1 Relations and Functions1204-2 Function Notation1274-3 Linear Functions and Direct Variation1304-4 Absolute Value Functions1364-5 Polynomial Functions1404-6 The Algebra of Functions 1494-7 Composition of Functions1554-8 Inverse Functions1604-9 Circles1674-10 Inverse Variation174 chapter Summary178 Vocabulary180 Review Exercises180 Cumulative Review184 chapter 5 QUADRATIC FUNCTIONS AND COMPLEX NUMBERS1865-1 Real Roots of a Quadratic Equation1875-2 The Quadratic

10 Formula1935-3 The Discriminant1985-4 The Complex Numbers2035-5 Operations with Complex Numbers2095-6 Complex Roots of a Quadratic Equation2175-7 Sum and Product of the Roots of a Quadratic Equation2195-8 Solving Higher Degree Polynomial Equations2245-9 Solutions of Systems of Equations and Inequalities229 chapter Summary239 Vocabulary240 Review Exercises241 Cumulative 8/12/08 1:46 PM Page viCONTENTSviiChapter 6 SEQUENCES AND SERIES2476-1 Sequences 2486-2 Arithmetic Sequences2526-3 Sigma Notation2576-4 Arithmetic Series2626-5 Geometric Sequences2666-6 Geometric Series2706-7 Infinite Series273 chapter Summary279 Vocabulary280 Review Exercises280 Cumulative Review283 chapter 7 EXPONENTIAL FUNCTIONS2867-1 Laws of Exponents2877-2 Zero and Negative Exponents2897-3 Fractional Exponents2937-4 Exponential Functions and Their Graphs2987-5 Solving Equations Involving Exponents3047-6 Solving Exponential Equations3067-7 Applications of Exponential Functions308 chapter Summary314 Vocabulary315 Review Exercises315