Transcription
Chapter 1Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.Study Guide and Intervention WorkbookStudy Guide and Intervention Workbook (Spanish)Skills Practice WorkbookSkills Practice Workbook (Spanish)Practice WorkbookPractice Workbook 07-827749-30-07-827748-50-07-827750-7ANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbookscan be found in the back of this Chapter Resource Masters booklet.Glencoe/McGraw-HillCopyright by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced onlyfor classroom use; be provided to students, teachers, and families without charge;and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction,for use or sale, is prohibited without prior written permission of the publisher.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027ISBN: 0-07-827725-62 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03Algebra 1Chapter 1 Resource Masters
ContentsVocabulary Builder . . . . . . . . . . . . . . . . viiLesson 1-7Study Guide and Intervention . . . . . . . . . 37–38Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 39Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Reading to Learn Mathematics . . . . . . . . . . . 41Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 42Lesson 1-1Study Guide and Intervention . . . . . . . . . . . 1–2Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 3Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Reading to Learn Mathematics . . . . . . . . . . . . 5Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Lesson 1-8Study Guide and Intervention . . . . . . . . . 43–44Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 45Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Reading to Learn Mathematics . . . . . . . . . . . 47Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 48Lesson 1-2Study Guide and Intervention . . . . . . . . . . . 7–8Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 9Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Reading to Learn Mathematics . . . . . . . . . . . 11Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 12Lesson 1-9Study Guide and Intervention . . . . . . . . . 49–50Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 51Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Reading to Learn Mathematics . . . . . . . . . . . 53Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 54Lesson 1-3Study Guide and Intervention . . . . . . . . . 13–14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 15Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Reading to Learn Mathematics . . . . . . . . . . . 17Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 18Chapter 1 rLesson 1-4Study Guide and Intervention . . . . . . . . . 19–20Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 21Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Reading to Learn Mathematics . . . . . . . . . . . 23Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 24Lesson 1-5Study Guide and Intervention . . . . . . . . . 25–26Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 27Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Reading to Learn Mathematics . . . . . . . . . . . 29Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 30Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . A1Lesson 1-6Study Guide and Intervention . . . . . . . . . 31–32Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 33Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Reading to Learn Mathematics . . . . . . . . . . . 35Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Glencoe/McGraw-Hill1 Test, Form 1 . . . . . . . . . . . . . . 55–561 Test, Form 2A . . . . . . . . . . . . . 57–581 Test, Form 2B . . . . . . . . . . . . . 59–601 Test, Form 2C . . . . . . . . . . . . . 61–621 Test, Form 2D . . . . . . . . . . . . . 63–641 Test, Form 3 . . . . . . . . . . . . . . 65–661 Open-Ended Assessment . . . . . . . 671 Vocabulary Test/Review . . . . . . . . 681 Quizzes 1 & 2 . . . . . . . . . . . . . . . . 691 Quizzes 3 & 4 . . . . . . . . . . . . . . . . 701 Mid-Chapter Test . . . . . . . . . . . . . 711 Cumulative Review . . . . . . . . . . . . 721 Standardized Test Practice . . . 73–74ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A38iiiGlencoe Algebra 1
Teacher’s Guide to Using theChapter 1 Resource MastersThe Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 1 Resource Masters includes the core materials neededfor Chapter 1. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.Vocabulary BuilderPracticePages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.WHEN TO USE Give these pages tostudents before beginning Lesson 1-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.WHEN TO USE Use these masters asWHEN TO USE This master can be usedreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.as a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.Skills PracticeThere is one master foreach lesson. These provide computationalpractice at a basic level.EnrichmentThere is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.WHEN TO USE These masters can beused with students who have weakermathematics backgrounds or needadditional reinforcement.WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened. Glencoe/McGraw-HillivGlencoe Algebra 1
Assessment OptionsIntermediate AssessmentThe assessment masters in the Chapter 1Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use. Four free-response quizzes are includedto offer assessment at appropriateintervals in the chapter. A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.Chapter AssessmentCHAPTER TESTSContinuing Assessment Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents. The Cumulative Review providesstudents an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includesfree-response questions. Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations. The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiplechoice, grid-in, and quantitativecomparison questions. Bubble-in andgrid-in answer sections are provided onthe master. Forms 2C and 2D are composed of freeresponse questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills. Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.AnswersAll of the above tests include a freeresponse Bonus question. Page A1 is an answer sheet for theStandardized Test Practice questionsthat appear in the Student Edition onpages 64–65. This improves students’familiarity with the answer formats theymay encounter in test taking. The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment. The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red. A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunction with one of the chapter tests or as areview worksheet. Glencoe/McGraw-Hill Full-size answer keys are provided forthe assessment masters in this booklet.vGlencoe Algebra 1
NAME DATEPERIODReading to Learn Mathematics1This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon PageDefinition/Description/Example al statementcoordinate systemcounterexample deductive reasoningdih·DUHK·tihvdependent variabledomainequationfunction(continued on the next page) Glencoe/McGraw-HillviiGlencoe Algebra 1Vocabulary BuilderVocabulary Builder
NAME DATEPERIODReading to Learn Mathematics1Vocabulary BuilderVocabulary Term(continued)Foundon PageDefinition/Description/Example hypothesishy·PAH·thuh·suhsindependent variableinequalitylike termsorder of operationspowerrangereplacement setsolving an open sentencevariables Glencoe/McGraw-HillviiiGlencoe Algebra 1
NAME DATE1-1PERIODStudy Guide and InterventionVariables and ExpressionsWrite Mathematical Expressions In the algebraic expression, !w, the letters !and w are called variables. In algebra, a variable is used to represent unspecified numbersor values. Any letter can be used as a variable. The letters ! and w are used above becausethey are the first letters of the words length and width. In the expression !w, ! and w arecalled factors, and the result is called the product.Write an algebraic expression for each verbal expression.a. four more than a number nThe words more than imply addition.four more than a number n4!nThe algebraic expression is 4 ! n.b. the difference of a number squared and 8The expression difference of implies subtraction.the difference of a number squared and 8n2 " 8The algebraic expression is n2 " 8.Example 2Evaluate each expression.b. five cubeda.4Cubed means raised to the third power.3 # 3 3 3 3 Use 3 as a factor 4 times.# 81Multiply.53 # 5 5 5Use 5 as a factor 3 times.# 125Multiply.34ExercisesWrite an algebraic expression for each verbal expression.1. a number decreased by 82. a number divided by 83. a number squared4. four times a number5. a number divided by 66. a number multiplied by 377. the sum of 9 and a number8. 3 less than 5 times a number9. twice the sum of 15 and a number10. one-half the square of b11. 7 more than the product of 6 and a number12. 30 increased by 3 times the square of a numberEvaluate each expression.13. 5214. 3315. 10416. 12217. 8318. 28 Glencoe/McGraw-Hill1Glencoe Algebra 1Lesson 1-1Example 1
NAME DATE1-1PERIODStudy Guide and Intervention(continued)Variables and ExpressionsWrite Verbal Expressionsis important in algebra.ExampleTranslating algebraic expressions into verbal expressionsWrite a verbal expression for each algebraic expression.a. 6n2the product of 6 and n squaredb. n3 " 12mthe difference of n cubed and twelve times mExercisesWrite a verbal expression for each algebraic expression.131. w " 12. % a33. 81 ! 2x4. 12c5. 846. 627. 2n2 ! 48. a3 b39. 2x3" 3146k3510. %11. % b212. 7n513. 3x ! 414. % k515. 3b2 ! 2a316. 4(n2 ! 1)17. 32 ! 2318. 6n2 ! 3 Glencoe/McGraw-Hill232Glencoe Algebra 1
NAME DATE1-1PERIODSkills PracticeVariables and Expressions1. the sum of a number and 102. 15 less than k3. the product of 18 and q4. 6 more than twice m5. 8 increased by three times a number6. the difference of 17 and 5 times a number7. the product of 2 and the second power of y8. 9 less than g to the fourth powerEvaluate each expression.9. 8210. 3411. 5312. 3313. 10214. 2415. 7216. 4417. 7318. 113Write a verbal expression for each algebraic expression.19. 9a20. 5221. c ! 2d22. 4 " 5h23. 2b224. 7x3 " 125. p4 ! 6q26. 3n2 " x Glencoe/McGraw-Hill3Glencoe Algebra 1Lesson 1-1Write an algebraic expression for each verbal expression.
NAME DATE1-1PERIODPracticeVariables and ExpressionsWrite an algebraic expression for each verbal expression.1. the difference of 10 and u2. the sum of 18 and a number3. the product of 33 and j4. 74 increased by 3 times y5. 15 decreased by twice a number6. 91 more than the square of a number7. three fourths the square of b8. two fifths the cube of a numberEvaluate each expression.9. 11210. 8311. 5412. 4513. 9314. 6415. 10516. 12317. 1004Write a verbal expression for each algebraic expression.18. 23f19. 7320. 5m2 ! 221. 4d3 " 1022. x3 y423. b2 " 3c3k5624. %4n2725. %26. BOOKS A used bookstore sells paperback fiction books in excellent condition for 2.50 and in fair condition for 0.50. Write an expression for the cost of buying eexcellent-condition paperbacks and f fair-condition paperbacks.27. GEOMETRY The surface area of the side of a right cylinder can be found by multiplyingtwice the number ! by the radius times the height. If a circular cylinder has radius rand height h, write an expression that represents the surface area of its side. Glencoe/McGraw-Hill4Glencoe Algebra 1
NAME DATE1-1PERIODReading to Learn MathematicsVariables and ExpressionsPre-ActivityWhat expression can be used to find the perimeter of a baseballdiamond?Read the introduction to Lesson 1-1 at the top of page 6 in your textbook.Then complete the description of the expression 4s.In the expression 4s, 4 represents theof each side.Lesson 1-1represents theof sides and sReading the Lesson1. Why is the symbol & avoided in algebra?2. What are the factors in the algebraic expression 3xy?3. In the expression xn, what is the base? What is the exponent?4. Write the Roman numeral of the algebraic expression that best matches each phrase.a. three more than a number nI. 5(x " 4)II. x4b. five times the difference of x and 412c. one half the number rIII. % rd. the product of x and y divided by 2IV. n ! 3xy2e. x to the fourth powerV. %Helping You Remember5. Multiplying 5 times 3 is not the same as raising 5 to the third power. How does the wayyou write “5 times 3” and “5 to the third power” in symbols help you remember that theygive different results? Glencoe/McGraw-Hill5Glencoe Algebra 1
NAME DATE1-1PERIODEnrichmentThe Tower of HanoiThe diagram at the right shows the Tower of Hanoipuzzle. Notice that there are three pegs, with a stack ofdisks on peg a. The object is to move all of the disks toanother peg. You may move only one disk at a time anda larger disk may never be put on top of a smaller disk.As you solve the puzzle, record each move in the tableshown. The first two moves are recorded.Peg aPeg b123Peg aSolve.1. Complete the table to solve the Tower of Hanoi puzzle forthree disks.2. Another way to record each move is to use letters. Forexample, the first two moves in the table can be recordedas 1c, 2b. This shows that disk 1 is moved to peg c, andthen disk 2 is moved to peg b. Record your solutionusing letters.3. On a separate sheet of paper, solve the puzzle for fourdisks. Record your solution.Peg cPeg bPeg c1232331214. Solve the puzzle for five disks. Record your solution.5. Suppose you start with an odd number of disks and youwant to end with the stack on peg c. What should be yourfirst move?6. Suppose you start with an even number of disks and youwant to end with the stack on peg b. What should be yourfirst move? Glencoe/McGraw-Hill6Glencoe Algebra 1
NAME DATE1-2PERIODStudy Guide and InterventionOrder of OperationsEvaluate Rational Expressions Numerical expressions often contain more than oneoperation. To evaluate them, use the rules for order of operations shown below.StepStepStepStepExample 11234Evaluate expressions inside grouping symbols.Evaluate all powers.Do all multiplication and/or division from left to right.Do all addition and/or subtraction from left to right.Example 2Evaluate each expression.a. 7 ! 2 " 4 # 47!2 4"4#7!8"4# 15 " 4# 11a. 3[2 ! (12 3)2]3[2 ! (12 ' 3)2] # 3(2 ! 42)# 3(2 ! 16)# 3(18)# 54Multiply 2 and 4.Add 7 and 8.Subtract 4 from 15.b. 3(2) ! 4(2 ! 6)3(2) ! 4(2 ! 6) # 3(2) ! 4(8)# 6 ! 32Divide 12 by 3.Find 4 squared.Add 2 and 16.Multiply 3 and 18.3 ! 234 3b. %2Add 2 and 6.Multiply left toright.# 38Evaluate each expression.Add 6 and 32.3 ! 233!8#%%42 342 3Evaluate power in numerator.114 3Add 3 and 8 in the numerator.1116 3Evaluate power in denominator.1148Multiply.#%2#%#%ExercisesEvaluate each expression.1. (8 " 4) 22. (12 ! 4) 63. 10 ! 2 34. 10 ! 8 15. 15 " 12 ' 46. %7. 12(20 " 17) " 3 68. 24 ' 3 2 " 329. 82 ' (2 8) ! 24 ! 3212 ! 112. %%2 42 " 8'2(5 ! 2) 215. %%52 " 320(3) ! 2(3)18. %%8(2) " 48'410. 32 ' 3 ! 22 7 " 20 ' 511. %13. 250 ' [5(3 7 ! 4)]14. %%4(52) " 4 34(4 5 ! 2)16. %% Glencoe/McGraw-Hill15 ! 6030 " 517. %%74 32 " 3 23 582 " 22(2 8) ! 4Glencoe Algebra 1Lesson 1-2Order ofOperations
NAME DATEPERIODStudy Guide and Intervention1-2(continued)Order of OperationsEvaluate Algebraic Expressions Algebraic expressions may contain more than oneoperation. Algebraic expressions can be evaluated if the values of the variables are known.First, replace the variables by their values. Then use the order of operations to calculate thevalue of the resulting numerical expression.ExampleEvaluate x3 ! 5(y # 3) if x & 2 and y & 12.x3 ! 5(y " 3) #####23 ! 5(12 " 3)8 ! 5(12 " 3)8 ! 5(9)8 ! 4553Replace x with 2 and y with 12.Evaluate 23.Subtract 3 from 12.Multiply 5 and 9.Add 8 and 45.The solution is 53.Exercises4535Evaluate each expression if x & 2, y & 3, z & 4, a & % , and b & % .1. x ! 72. 3x " 53. x ! y24. x3 ! y ! z25. 6a ! 8b6. 23 " (a ! b)8. 2xyz ! 59. x(2y ! 3z)y2x7. %210. (10x)2 ! 100a12. a2 ! 2bz2 " y2x14. 6xz ! 5xy15. %25ab ! yxz17. %13. %216. %%2! xz "19. % 3xy " 47x11. %2! yz "! %Glencoe/McGraw-Hill(z " y)2x5a2by18. (z ' x)2 ! axx!zy ! 2z21. % ! %! z 'y x " ! y 'z x "20. %8Glencoe Algebra 1
NAME DATE1-2PERIODSkills PracticeOrder of OperationsEvaluate each expression.1. (5 ! 4) 72. (9 " 2) 33. 4 ! 6 34. 28 " 5 45. 12 ! 2 26. (3 ! 5) 5 ! 17. 9 ! 4(3 ! 1)8. 2 ! 3 5 ! 410. 10 ! 2 6 ! 411. 14 ' 7 5 " 3212. 6 ' 3 7 ! 2313. 4[30 " (10 " 2) 3]14. 5 ! [30 " (6 " 1)2]15. 2[12 ! (5 " 2)2]16. [8 2 " (3 ! 9)] ! [8 " 2 3]Lesson 1-29. 30 " 5 4 ! 2Evaluate each expression if x & 6, y & 8, and z & 3.17. xy ! z18. yz " x19. 2x ! 3y " z20. 2(x ! z) " y21. 5z ! ( y " x)22. 5x " ( y ! 2z)23. x2 ! y2 " 10z24. z3 ! ( y2 " 4x)y ! xz225. % Glencoe/McGraw-Hill3y ! x2z26. %9Glencoe Algebra 1
NAME DATE1-2PERIODPracticeOrder of OperationsEvaluate each expression.1. (15 " 5) 22. 9 (3 ! 4)3. 5 ! 7 44. 12 ! 5 " 6 25. 7 9 " 4(6 ! 7)6. 8 ' (2 ! 2) 77. 4(3 ! 5) " 5 48. 22 ' 11 9 " 329. 62 ! 3 7 " 910. 3[10 " (27 ' 9)]11. 2[52 ! (36 ' 6)]52 4 " 5 425(4)13. %%(2 5)2 ! 43 "512. 162 ' [6(7 " 4)2]7 ! 324 214. %%215. %2Evaluate each expression if a & 12, b & 9, and c & 4.16. a2 ! b " c217. b2 ! 2a " c218. 2c(a ! b)19. 4a ! 2b " c220. (a2 ' 4b) ! c21. c2 (2b " a)bc2 ! ac23. %%2(a " b)25c25. %%22. %24. %%2c3 " ab4b2 " 2c2a!c"bCAR RENTAL For Exercises 26 and 27, use the following information.Ann Carlyle is planning a business trip for which she needs to rent a car. The car rentalcompany charges 36 per day plus 0.50 per mile over 100 miles. Suppose Ms. Carlyle rentsthe car for 5 days and drives 180 miles.26. Write an expression for how much it will cost Ms. Carlyle to rent the car.27. Evaluate the expression to determine how much Ms. Carlyle must pay the car rentalcompany.GEOMETRY For Exercises 28 and 29, use the following information.The length of a rectangle is 3n ! 2 and its width is n " 1. The perimeter of the rectangle istwice the sum of its length and its width.28. Write an expression that represents the perimeter of the rectangle.29. Find the perimeter of the rectangle when n # 4 inches. Glencoe/McGraw-Hill10Glencoe Algebra 1
NAME DATE1-2PERIODReading to Learn MathematicsOrder of OperationsPre-ActivityHow is the monthly cost of internet service determined?Read the introduction to Lesson 1-2 at the top of page 11 in your textbook.In the expression 4.95 ! 0.99(117 " 100),regular monthly cost of internet service,represents therepresents thecost of each additional hour after 100 hours, andrepresents the number of hours over 100 used by Nicole in a given month.Reading the Lesson2. What does evaluate powers mean? Use an example to explain.3. Read the order of operations on page 11 in your textbook. For each of the followingexpressions, write addition, subtraction, multiplication, division, or evaluate powers totell what operation to use first when evaluating the expression.a. 400 " 5[12 ! 9]b. 26 " 8 ! 14c. 17 ! 3 6d. 69 ! 57 ' 3 ! 16 419 ! 3 46'2e. %%51 ' 7299f. %%2Helping You Remember4. The sentence Please Excuse My Dear Aunt Sally (PEMDAS) is often used to rememberthe order of operations. The letter P represents parentheses and other grouping symbols.Write what each of the other letters in PEMDAS means when using the order ofoperations. Glencoe/McGraw-Hill11Glencoe Algebra 1Lesson 1-21. The first step in evaluating an expression is to evaluate inside grouping symbols. Listfour types of grouping symbols found in algebraic expressions.
NAME DATE1-2PERIODEnrichmentThe Four Digits ProblemOne well-known mathematic problem is to write expressions forconsecutive numbers beginning with 1. On this page, you will use thedigits 1, 2, 3, and 4. Each digit is used only once. You may use addition,subtraction, multiplication (not division), exponents, and parenthesesin any way you wish. Also, you can use two digits to make one number,such as 12 or 34.Express each number as a combination of the digits 1, 2, 3, and 4.1 # (3 & 1) " (4 " 2)18 #35 # 2(4 1) ! 32#19 # 3(2 ! 4) ! 136 #3#20 #37 #4#21 #38 #5#22 #39 #6#23 # 31 " (4 & 2)40 #7#24 #41 #8#25 #42 #9#26 #43 # 42 ! 1310 #27 #44 #11 #28 #45 #12 #29 #46 #13 #30 #47 #14 #31 #48 #15 #32 #49 #16 #33 #50 #17 #34 #Does a calculator help in solving these types of puzzles? Give reasons for your opinion. Glencoe/McGraw-Hill12Glencoe Algebra 1
NAME DATEPERIODStudy Guide and Intervention1-3Open SentencesSolve Equations A mathematical sentence with one or more variables is called anopen sentence. Open sentences are solved by finding replacements for the variables thatresult in true sentences. The set of numbers from which replacements for a variable may bechosen is called the replacement set. The set of all replacements for the variable thatresult in true statements is called the solution set for the variable. A sentence thatcontains an equal sign, #, is called an equation.Example 1Find the solutionset of 3a ! 12 & 39 if thereplacement set is {6, 7, 8, 9, 10}.Replace a in 3a ! 12 # 39 with eachvalue in the replacement set.3(6)! 12 ! 39 30 ( 393(7)! 12 ! 39 33 ( 393(8)! 12 ! 39 36 ( 393(9)! 12 ! 39 39 # 393(10)! 12 ! 39 42 ( 39Example 22(3 ! 1)3(7 # 4)Solve %% # b.2(3 ! 1)%% # b Original equation3(7 " 4)2(4)% # b Add in the numerator; subtract in the denominator.3(3)false8% # b Simplify.9false89falseThe solution is % .truefalseSince a # 9 makes the equation3a ! 12 # 39 true, the solution is 9.The solution set is {9}.!11Find the solution of each equation if the replacement sets are X # % , % , 1, 2, 34 2and Y # {2, 4, 6, 8}.12521. x ! % # %2. x ! 8 # 113. y " 2 # 64. x2 " 1 # 85. y2 " 2 # 346. x2 ! 5 # 5 %7. 2(x ! 3) # 78. % ( y ! 1)2 # %14"116949. y2 ! y # 20Solve each equation.10. a # 23 " 1145811. n # 62 " 4218 " 32!312. w # 62 3215 " 627 " 2413. % ! % # k14. % # p15. s # %16. 18.4 " 3.2 # m17. k # 9.8 ! 5.718. c # 3 % ! 2 % Glencoe/McGraw-Hill131214Glencoe Algebra 1Lesson 1-3Exercises
NAME DATEPERIODStudy Guide and Intervention1-3(continued)Open SentencesSolve InequalitiesAn open sentence that contains the symbol ), *, , or , is calledan inequality. Inequalities can be solved the same way that equations are solved.ExampleFind the solution set for 3a # 8 ' 10 if the replacement set is{4, 5, 6, 7, 8}.Replace a in 3a " 8 10 with each value in the replacement set.3(4)3(5)3(6)3(7)3(8)"""""88888? 10? 10? 10? 10? 10 4 107 1010 1013 1016 10falsefalsefalsetruetrueSince replacing a with 7 or 8 makes the inequality 3a " 8 10 true, the solution set is {7, 8}.ExercisesFind the solution set for each inequality if the replacement set isX & {0, 1, 2, 3, 4, 5, 6, 7}.1. x ! 2 42. x ' 3 ) 6x33. 3x 183x8x54. % 15. % , 26. % * 27. 3x " 4 58. 3(8 " x) ! 1 * 69. 4(x ! 3) , 20Find the solution set for each inequality if the replacement sets are! 1412"X & % , % , 1, 2, 3, 5, 8 and Y & {2, 4, 6, 8, 10}10. x ! 3 5x211. y ' 3 ) 612. 8y ! 3 , 512y5y413. % ) 414. % , 215. % * 216. 4x ! 1 , 417. 3x ! 3 , 1218. 2( y ! 1) , 1820. 3y ! 2 * 821. % (6 " 2x) ! 2 * 31419. 3x " % ) 2 Glencoe/McGraw-Hill1412Glencoe Algebra 1
NAME DATE1-3PERIODSkills PracticeOpen SentencesFind the solution of each equation if the replacement sets are A & {4, 5, 6, 7, 8} andB & {9, 10, 11, 12, 13}.1. 5a " 9 # 262. 4a " 8 # 163. 7a ! 21 # 564. 3b ! 15 # 485. 4b " 12 # 286. % " 3 # 036bFind the solution of each equation using the given replacement set.1254# 1234547. % ! x # % ; % , % , 1, %1456# 23 3 5 44 4 39. % (x ! 2) # % ; % , % , % , %23139# 495 2 79 3 98. x ! % # % ; % , % , % , % 10. 0.8(x ! 5) # 5.2; {1.2, 1.3, 1.4, 1.5}Solve each equation.12. y # 20.1 " 11.96 ! 1831 " 2513. % # a46 " 153 ! 2814. c # %2(4) ! 43(3 " 1)16. %% # n15. %% # bLesson 1-311. 10.4 " 6.8 # x6(7 " 2)3(8) ! 6Find the solution set for each inequality using the given replacement set.17. a ! 7 ) 13; {3, 4, 5, 6, 7}18. 9 ! y ) 17; {7, 8, 9, 10, 11}19. x " 2 * 2; {2, 3, 4, 5, 6, 7}20. 2x 12; {0, 2, 4, 6, 8, 10}21. 4b ! 1 12; {0, 3, 6, 9, 12, 15}22. 2c " 5 * 11; {8, 9, 10, 11, 12, 13}y223. % , 5; {4, 6, 8, 10, 12} Glencoe/McGraw-Hillx324. % 2; {3, 4, 5, 6, 7, 8}15Glencoe Algebra 1
NAME DATEPERIODPractice1-3Open Sentences!13"Find the solution of each equation if the replacement sets are A & 0, % , 1, % , 222and B & {3, 3.5, 4, 4.5, 5}.121. a ! % # 12. 4b " 8 # 63. 6a ! 18 # 274. 7b " 8 # 16.55. 120 " 28a # 786. % ! 9 # 1628bFind the solution of each equation using the given replacement set.781712# 1213 7 5 224 12 8 37. % ! x # % ; % , % , % , % , % 34278# 2112128. % (x ! 2) # % ; % , 1, 1 % , 2, 2 %9. 1.4(x ! 3) # 5.32; {0.4, 0.6, 0.8, 1.0, 1.2} 10. 12(x ! 4) # 76.8 ; {2, 2.4, 2.8, 3.2, 3.6}Solve each equation.11. x # 18.3 " 4.897 " 2541 " 2314. % # k37 " 918 " 1112. w # 20.2 " 8.9513. % # d5(22) ! 4(3)4(2 " 4)4(22 " 4)3(6) ! 615. y # %%16. %%#p3Find the solution set for each inequality using the given replacement set.17. a
3. a number squared 4. four times a number 5. a number divided by 6 6. a number multiplied by 37 7. the sum of 9 and a number 8. 3 less than 5 times a number 9. twice the sum of 15 and a number 10. one-half the square of b 11. 7 more than the product of 6 and a number 12. 30 increased by 3
