Transcription
Chapter 12Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.Study Guide and Intervention WorkbookSkills Practice WorkbookPractice WERS FOR WORKBOOKS The answers for Chapter 12 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, teacher, and families without charge;and be used solely in conjunction with Glencoe’s Algebra 2. 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: 0-07-828015-XAlgebra 2Chapter 12 Resource Masters1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02
ContentsVocabulary Builder . . . . . . . . . . . . . . . . viiLesson 12-7Study Guide and Intervention . . . . . . . . 735–736Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 737Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 738Reading to Learn Mathematics . . . . . . . . . . 739Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 740Lesson 12-1Study Guide and Intervention . . . . . . . . 699–700Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 701Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 702Reading to Learn Mathematics . . . . . . . . . . 703Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 704Lesson 12-8Study Guide and Intervention . . . . . . . . 741–742Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 743Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 744Reading to Learn Mathematics . . . . . . . . . . 745Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 746Lesson 12-2Study Guide and Intervention . . . . . . . . 705–706Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 707Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 708Reading to Learn Mathematics . . . . . . . . . . 709Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 710Lesson 12-9Study Guide and Intervention . . . . . . . . 747–748Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 749Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 750Reading to Learn Mathematics . . . . . . . . . . 751Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 752Lesson 12-3Study Guide and Intervention . . . . . . . . 711–712Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 713Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 714Reading to Learn Mathematics . . . . . . . . . . 715Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 716Chapter 12 AssessmentChapter 12 Test, Form 1 . . . . . . . . . . . 753–754Chapter 12 Test, Form 2A . . . . . . . . . . 755–756Chapter 12 Test, Form 2B . . . . . . . . . . 757–758Chapter 12 Test, Form 2C . . . . . . . . . . 759–760Chapter 12 Test, Form 2D . . . . . . . . . . 761–762Chapter 12 Test, Form 3 . . . . . . . . . . . 763–764Chapter 12 Open-Ended Assessment . . . . . 765Chapter 12 Vocabulary Test/Review . . . . . . 766Chapter 12 Quizzes 1 & 2 . . . . . . . . . . . . . . 767Chapter 12 Quizzes 3 & 4 . . . . . . . . . . . . . . 768Chapter 12 Mid-Chapter Test . . . . . . . . . . . . 769Chapter 12 Cumulative Review . . . . . . . . . . 770Chapter 12 Standardized Test Practice . 771–772Unit 4 Test/Review (Ch. 11–12) . . . . . . 773–774Lesson 12-4Study Guide and Intervention . . . . . . . . 717–718Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 719Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 720Reading to Learn Mathematics . . . . . . . . . . 721Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 722Lesson 12-5Study Guide and Intervention . . . . . . . . 723–724Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 725Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 726Reading to Learn Mathematics . . . . . . . . . . 727Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 728Lesson 12-6Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . A1Study Guide and Intervention . . . . . . . . 729–730Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 731Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 732Reading to Learn Mathematics . . . . . . . . . . 733Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 734 Glencoe/McGraw-HillANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A39iiiGlencoe Algebra 2
Teacher’s Guide to Using theChapter 12 Resource MastersThe Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 12 Resource Masters includes the core materialsneeded for Chapter 12. These materials include worksheets, extensions, andassessment 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 2 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 12-1.Encourage them to add these pages to theirAlgebra 2 Study Notebook. Remind themto add 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 2 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 2
Assessment OptionsIntermediate AssessmentThe assessment masters in the Chapter 12Resource 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 2. 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 694–695. 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 2
NAME DATE12PERIODReading to Learn MathematicsThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 12.As you study the chapter, complete each term’s definition or description. Rememberto add the page number where you found the term. Add these pages to your AlgebraStudy Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon PageDefinition/Description/Examplebinomial experimentcombinationcompound eventdependent andindependent events inclusive eventsihn·KLOO·sihvmargin of sampling errormeasure of central tendencymeasure of variation mutually exclusive eventsMYOO·chuh·leenormal distribution(continued on the next page) Glencoe/McGraw-HillviiGlencoe Algebra 2Vocabulary BuilderVocabulary Builder
NAME DATE12PERIODReading to Learn MathematicsVocabulary BuilderVocabulary Term(continued)Foundon PageDefinition/Description/Exampleodds ility distributionrandom variablerelative-frequency histogramsample space skewed distributionSKYOODstandard deviation varianceVEHR·ee·uhn(t)s Glencoe/McGraw-HillviiiGlencoe Algebra 2
NAME DATEPERIOD12-1 Study Guide and InterventionThe Counting PrincipleIndependent EventsIf the outcome of one event does not affect the outcome ofanother event and vice versa, the events are called independent events.FundamentalCounting PrincipleIf event M can occur in m ways and is followed by event N that can occur in n ways,then the event M followed by the event N can occur in m n ways.FOOD For the Breakfast Special at the Country Pantry, customerscan choose their eggs scrambled, fried, or poached, whole wheat or white toast,and either orange, apple, tomato, or grapefruit juice. How many differentBreakfast Specials can a customer order?A customer’s choice of eggs does not affect his or her choice of toast or juice, so the eventsare independent. There are 3 ways to choose eggs, 2 ways to choose toast, and 4 ways tochoose juice. By the Fundamental Counting Principle, there are 3 2 4 or 24 ways tochoose the Breakfast Special.ExercisesSolve each problem.1. The Palace of Pizza offers small, medium, or large pizzas with 14 different toppingsavailable. How many different one-topping pizzas do they serve? 422. The letters A, B, C, and D are used to form four-letter passwords for entering a computerfile. How many passwords are possible if letters can be repeated? 2563. A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different mealscould be ordered if each has a main dish, a salad, and a dessert? 604. Marissa brought 8 T-shirts and 6 pairs of shorts to summer camp. How many differentoutfits consisting of a T-shirt and a pair of shorts does she have? 485. There are 6 different packages available for school pictures. The studio offers 5 differentbackgrounds and 2 different finishes. How many different options are available? 606. How many 5-digit even numbers can be formed using the digits 4, 6, 7, 2, 8 if digits canbe repeated? 25007. How many license plate numbers consisting of three letters followed by three numbersare possible when repetition is allowed? 17,576,0008. How many 4-digit positive even integers are there? 4500 Glencoe/McGraw-Hill699Glencoe Algebra 2Lesson 12-1Example
NAME DATEPERIOD12-1 Study Guide and Intervention(continued)The Counting PrincipleDependent EventsIf the outcome of an event does affect the outcome of another event,the two events are said to be dependent. The Fundamental Counting Principle still applies.ExampleENTERTAINMENT The guests at a sleepover brought 8 videos. Theydecided they would only watch 3 videos. How many orders of 3 different videosare possible?After the group chooses to watch a video, they will not choose to watch it again, so thechoices of videos are dependent events.There are 8 choices for the first video. That leaves 7 choices for the second. After they choosethe first 2 videos, there are 6 remaining choices. Thus by the Fundamental CountingPrinciple, there are 8 7 6 or 336 orders of 3 different videos.ExercisesSolve each problem.1. Three students are scheduled to give oral reports on Monday. In how many ways cantheir presentations be ordered? 62. In how many ways can the first five letters of the alphabet be arranged if each letter isused only once? 1203. In how many different ways can 4 different books be arranged on the shelf? 244. How many license plates consisting of three letters followed by three numbers arepossible when no repetition is allowed? 11,232,0005. Sixteen teams are competing in a soccer match. Gold, silver, and bronze medals will beawarded to the top three finishers. In how many ways can the medals be awarded? 33606. In a word-building game each player picks 7 letter tiles. If Julio’s letters are all different,how many 3-letter combinations can he make out of his 7 letters? 2107. The editor has accepted 6 articles for the news letter. In how many ways can the 6 articlesbe ordered? 7208. There are 10 one-hour workshops scheduled for the open house at the greenhouse.There is only one conference room available. In how many ways can the workshops beordered? 3,628,8009. The top 5 runners at the cross-country meet will receive trophies. If there are 22 runnersin the race, in how many ways can the trophies be awarded? 3,160,080 Glencoe/McGraw-Hill700Glencoe Algebra 2
NAME DATEPERIOD12-1 Skills PracticeThe Counting PrincipleState whether the events are independent or dependent.1. finishing in first, second, or third place in a ten-person race dependent2. choosing a pizza size and a topping for the pizza independent4. The 232 members of the freshman class all vote by secret ballot for the classrepresentative to the Student Senate. independentSolve each problem.5. A surveying firm plans to buy a color printer for printing its maps. It has narrowed itschoice to one of three models. Each of the models is available with either 32 megabytesof random access memory (RAM), 64 megabytes of RAM, or 128 megabytes of RAM.From how many combinations of models and RAM does the firm have to choose? 96. How many arrangements of three letters can be formed from the letters of the wordMATH if any letter will not be used more than once? 247. Allan is playing the role of Oliver in his school’s production of Oliver Twist. Thewardrobe crew has presented Allan with 5 pairs of pants and 4 shirts that he can wear.How many possible costumes consisting of a pair of pants and a shirt does Allan have tochoose from? 208. The 10-member steering committee that is preparing a study of the public transportationneeds of its town will select a chairperson, vice-chairperson, and secretary from thecommittee. No person can serve in more than one position. In how many ways can thethree positions be filled? 7209. Jeanine has decided to buy a pickup truck. Her choices include either a V-6 engine or aV-8 engine, a standard cab or an extended cab, and 2-wheel drive or 4-wheel drive. Howmany possible models does she have to choose from? 810. A mail-order company that sells gardening tools offers rakes in two different lengths.Customers can also choose either a wooden, plastic, or fiberglass handle for the rake.How many different kinds of rakes can a customer buy? 611. A Mexican restaurant offers chicken, beef, or vegetarian fajitas wrapped with either cornor flour tortillas, and topped with either mild, medium, or hot salsa. How many differentchoices of fajitas does a customer have? 18 Glencoe/McGraw-Hill701Glencoe Algebra 2Lesson 12-13. Seventy-five raffle tickets are placed in a jar. Three tickets are then selected, one afterthe other, without replacing a ticket after it is chosen. dependent
NAME DATE12-1 PracticePERIOD(Average)The Counting PrincipleState whether the events are independent or dependent.1. choosing an ice cream flavor and choosing a topping for the ice cream independent2. choosing an offensive player of the game and a defensive player of the game in aprofessional football game independent3. From 15 entries in an art contest, a camp counselor chooses first, second, and third placewinners. dependent4. Jillian is selecting two more courses for her block schedule next semester. She mustselect one of three morning history classes and one of two afternoon math classes.independentSolve each problem.5. A briefcase lock has 3 rotating cylinders, each containing 10 digits. How many numericalcodes are possible? 10006. A golf club manufacturer makes irons with 7 different shaft lengths, 3 different grips, 5different lies, and 2 different club head materials. How many different combinations areoffered? 2107. There are five different routes that a commuter can take from her home to the office. Inhow many ways can she make a round trip if she uses a different route coming thangoing? 208. In how many ways can the four call letters of a radio station be arranged if the firstletter must be W or K and no letters repeat? 27,6009. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, andany digit can be repeated? 8,000,00010. How many 7-digit phone numbers can be formed if the first digit cannot be 0, and anydigit can be repeated? 9,000,00011. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, and ifno digit can be repeated? 483,84012. How many 7-digit phone numbers can be formed if the first digit cannot be 0, and if nodigit can be repeated? 544,32013. How many 6-character passwords can be formed if the first character is a digit and theremaining 5 characters are letters that can be repeated? 118,813,76014. How many 6-character passwords can be formed if the first and last characters aredigits and the remaining characters are letters? Assume that any character can berepeated. 45,697,600 Glencoe/McGraw-Hill702Glencoe Algebra 2
NAME DATEPERIOD12-1 Reading to Learn MathematicsThe Counting PrinciplePre-ActivityHow can you count the maximum number of license plates a statecan issue?Read the introduction to Lesson 12-1 at the top of page 632 in your textbook.Assume that all Florida license plates have three letters followed by threedigits, and that there are no rules against using the same letter or numbermore than once. How many choices are there for each letter? for each digit?Reading the Lesson1. Shamim is signing up for her classes. Most of her classes are required, but she has twoelectives. For her arts class, she can chose between Art, Band, Chorus, or Drama. For herlanguage class, she can choose between French, German, and Spanish.a. To organize her choices, Shamim decides to make a tree diagram. Let A, B, C, and Drepresent Art, Band, Chorus, and Drama, and F, G, and S represent French, German,and Spanish. Complete the following diagram.b. How could Shamim have found the number of possible combinations without making atree diagram? Sample answer: Multiply the number of choices for herarts class by the number of choices for her language class: 3 4 12.2. A jar contains 6 red marbles, 4 blue marbles, and 3 yellow marbles. Indicate whether theevents described are dependent or independent.a. A marble is drawn out of the jar and is not replaced. A second marble is drawn.dependentb. A marble is drawn out of the jar and is put back in. The jar is shaken. A secondmarble is drawn. independentHelping You Remember3. One definition of independent is “not determined or influenced by someone or somethingelse.” How can this definition help you remember the difference between independentand dependent events? Sample answer: If the outcome of one event does notaffect or influence the outcome of another, the events are independent. Ifthe outcome of one event does affect or influence the outcome ofanother, the events are dependent. Glencoe/McGraw-Hill703Glencoe Algebra 2Lesson 12-126; 10
NAME DATEPERIOD12-1 EnrichmentTree Diagrams and the Power RuleIf you flip a coin once, there are two possibleoutcomes: heads showing (H) or tails showing (T).The tree diagram to the right shows the four (22)possible outcomes if you flip a coin twice.Example 1Flip 2HHTstartHTTFlip ip 2OutcomesHTHTHHHTTHTTExample 2Draw a tree diagram toshow all the possible outcomes for flippinga coin three times. List the outcomes.Flip 1Flip 1In a cup there are ared, a blue, and a yellow marble. Howmany possible outcomes are there ifyou draw one marble at random,replace it, and then draw another?Draw 1RstartThere are eight (23) possible outcomes. Witheach extra flip, the number of outcomesdoubles. With 4 flips, there would be sixteen(24) outcomes.BYDraw 2OutcomesRBYRBYRBYRRRBRYBRBBBYYRYBYYThere are nine (32) possible outcomes.The Power Rule for the number of outcomes states that if an experiment isrepeated n times, and if there are b possible outcomes each time, there arebn total possible outcomes.Find the total number of possible outcomes for each experiment. Usetree diagrams to help you. 1. flipping a coin 5 times2. doing the marble experiment 6 times3. flipping a coin 8 times4. rolling a 6-sided die 2 times5. rolling a 6-sided die 3 times6. rolling a 4-sided die 2 times7. rolling a 4-sided die 3 times8. rolling a 12-sided die 2 timesGlencoe/McGraw-Hill704Glencoe Algebra 2
NAME DATEPERIOD12-2 Study Guide and InterventionPermutations and CombinationsPermutationsWhen a group of objects or people are arranged in a certain order, thearrangement is called a permutation.n!(n r )!PermutationsThe number of permutations of n distinct objects taken r at a time is given by P(n, r ) .Permutationswith Repetitionsn!The number of permutations of n objects of which p are alike and q are alike is .p!q!The rule for permutations with repetitions can be extended to any number of objects thatare repeated.From a list of 20 books, each student must choose 4 books for bookreports. The first report is a traditional book report, the second a poster, the thirda newspaper interview with one of the characters, and the fourth a timeline of theplot. How many different orderings of books can be chosen?Since each book report has a different format, order is important. You must find the numberof permutations of 20 objects taken 4 at a time.n!(n r)!20!P(20, 4) (20 4)!20! 16!11120 19 18 17 16 15 1 16 15 1P(n, r) Permutation formulan 20, r 4Simplify.Divide by common factors.1 116,280 1 1Books for the book reports can be chosen 116,280 ways.ExercisesEvaluate each expression.1. P(6, 3) 1202. P(8, 5) 67203. P(9, 4) 30244. P(11, 6) 332,640How many different ways can the letters of each word be arranged?5. MOM 36. MONDAY 7207. STEREO 3608. SCHOOL The high school chorus has been practicing 12 songs, but there is time for only5 of them at the spring concert. How may different orderings of 5 songs are possible?95,040 Glencoe/McGraw-Hill705Glencoe Algebra 2Lesson 12-2Example
NAME DATEPERIOD12-2 Study Guide and Intervention(continued)Permutations and CombinationsCombinationsAn arrangement or selection of objects in which order is not important iscalled a combination.Combinationsn!(n r )!r !The number of combinations of n distinct objects taken r at a time is given by C(n, r ) .Example 1SCHOOL How many groups of 4 students can be selected from aclass of 20?Since the order of choosing the students is not important, you must find the number ofcombinations of 20 students taken 4 at a time.n!(n r)!r!20!C(20, 4) (20 4)!4!20! or 484516!4!C(n, r) Combination formulan 20, r 4There are 4845 possible ways to choose 4 students.Example 2In how many ways can you choose 1 vowel and 2 consonants from aset of 26 letter tiles? (Assume there are 5 vowels and 21 consonants.)By the Fundamental Counting Principle, you can multiply the number of ways to select onevowel and the number of ways to select 2 consonants. Only the letters chosen matter, notthe order in which they were chosen, so use combinations.C(5, 1)C(21, 2)One of 5 vowels are drawn.Two of 21 consonants are drawn.5!(5 1)!1!5!21! 4! 19!2!21!(21 2)!2!C(5, 1) C(21, 2) 5 210 or 1050Combination formulaSubtract.Simplify.There are 1050 combinations of 1 vowel and 2 consonants.ExercisesEvaluate each expression.1. C(5, 3) 102. C(7, 4) 353. C(15, 7) 64354. C(10, 5) 2525. PLAYING CARDS From a standard deck of 52 cards, in how many ways can 5 cards bedrawn? 2,598,9606. HOCKEY How many hockey teams of 6 players can be formed from 14 players withoutregard to position played? 30037. COMMITTEES From a group of 10 men and 12 women, how many committees of 5 menand 6 women can be formed? 232,848 Glencoe/McGraw-Hill706Glencoe Algebra 2
NAME DATEPERIOD12-2 Skills PracticePermutations and CombinationsEvaluate each expression.1. P(6, 3) 1202. P(8, 2) 563. P(2, 1) 24. P(3, 2) 65. P(10, 4) 50406. P(5, 5) 1207. C(2, 2) 18. C(5, 3) 109. C(4, 1) 410. C(8, 7) 811. C(3, 2) 312. C(7, 4) 35Determine whether each situation involves a permutation or a combination. Thenfind the number of possibilities.13. seating 8 students in 8 seats in the front row of the school auditorium14. introducing the 5 starting players on the Woodsville High School basketball team at thebeginning of the next basketball gamepermutation; 12015. checking out 3 library books from a list of 8 books for a research papercombination; 5616. choosing 2 movies to rent from 5 moviescombination; 1017. the first-, second-, and third-place finishers in a race with 10 contestantspermutation; 72018. electing 4 candidates to a municipal planning board from a field of 7 candidatescombination; 3519. choosing 2 vegetables from a menu that offers 6 vegetable choicescombination; 1520. an arrangement of the letters in the word rhombuspermutation; 504021. selecting 2 of 8 choices of orange juice at a storecombination; 2822. placing a red rose bush, a yellow rose bush, a white rose bush, and a pink rose bush in arow in a planter permutation; 2423. selecting 2 of 9 kittens at an animal rescue sheltercombination; 3624. an arrangement of the letters in the word isoscelespermutation; 30,240 Glencoe/McGraw-Hill707Glencoe Algebra 2Lesson 12-2permutation; 40,320
NAME DATE12-2 PracticePERIOD(Average)Permutations and CombinationsEvaluate each expression.1. P(8, 6) 20,1602. P(9, 7) 181,4403. P(3, 3) 64. P(4, 3) 245. P(4, 1) 46. P(7, 2) 427. C(8, 2) 288. C(11, 3) 1659. C(20, 18) 19010. C(9, 9) 112. C(9, 3) C(6, 2) 126011. C(3, 1) 3Determine whether each situation involves a permutation or a combination. Thenfind the number of possibilities.13. selecting a 4-person bobsled team from a group of 9 athletescombination; 12614. an arrangement of the letters in the word Canadapermutation; 12015. arranging 4 charms on a bracelet that has a clasp, a front, and a backpermutation; 2416. selecting 3 desserts from 10 desserts that are displayed on a dessert cart in a restaurantcombination
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 12 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. T
