(2) Howmanypositiveintegershavecuberootslessthan1+ 2?
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1 (1) Adime,2nickels,and3penniesareinacontainer.Assumethatitisequally likelytoshakeoutanyonecoin.whatistheprobabilityofshakingoutapennyeachof4 timesifthecoinisreturnedaftereachshake?expressyouranswerasacommonfraction. (2) Howmanypositiveintegershavecuberootslessthan1+ 2? (3) What is the probability that the first three cards drawn from a standard deck ofplayingcardswillallbetwo s?expressyouranswerasacommonfraction. (4) A coin machine returns 5 pennies for every nickel inserted and 5 nickels for everypennyinserted.ifashleystartswithonenickelandnopennies,howmanycoinswill shehaveafterusingthemachine7times?doestheanswerdependonwhichcoinsare used? (5) Arectangularfieldis50feetwideand80feetlong.Fencepostsareplaced every10feetaroundthefield.howmanypostsareneeded? (6) Usingthedigits1,2,3,4,and5,howmanyfive-digitpositiveintegerscan beformedifnodigitcanberepeated? (7) Howmanywayscanacommitteeoffourmembersbeselectedfromaclub consisting of 6 members? (8) Inhislocker,Andrewhas2historybooksand3mathbooks.Inhisrushto gettoclass,hegrabs1book,thenasecondbook,withoutstoppingtolook.whatisthe probabilitythathepullsamathbookoutfirstandahistorybookoutsecond?expressyour answer as a common fraction. (9) Ifallmultiplesof4andallmultiplesof5areremovedfromthesetof integers from 1 through 100, how many integers remain?
2 (10) What is the maximum number of points of intersection when 5 lines intersect each other? (11) HazelandBasilareplayingagameinwhicheitherisequallylikelytowinany givenpoint.basilhas4pointstohazel s3points.ifthefirstpersontoget5pointsisthe winner, what is the probability that Basil will win? (12) Inaclassroomthereare6rowsof5deskseach.Whatpercentoftheseats doesastudenthavetochoosefromifhedoesnotwanttositinthefirstorlastseatof anyroworineitherofthetwosiderows? (13) What is the probability of drawing a card from those pictured where the letteristhefirstletterofamonthoftheyear?expressyouranswerasacommonfraction. A B C D E (14) Massaruhas3pencilsinhisbookbag.Twopencilsareblueandoneisred.If he randomly selects two pencils, what is the probability that they are the same color? Express your answer as a common fraction. (15) Everymemberofamathclubistakingalgebraorgeometryand8aretaking both.ifthereare17takingalgebraand13takinggeometry,howmanymembersareinthe club. (16) Compute: 7! 3!2! 6! (8 1)!.Expressyouranswerasacommonfraction. (17) Agameisplayedwithfivecardsnumbered3,6,2,5,and1.Facedown,the cardsareshuffledandthenthreeareturnedfaceup.yourscoreisthesumofthethree numbers showing. What is the probability that your score will be 9? (18) How many three-digit numbers do not contain a zero?
3 (19) Ifamarbleischosenfromabagthatcontains10redmarbles,5blue marblesand15whitemarbles,whatistheprobabilitythatthemarblechosenisblueor red? Express your answer as a common fraction. (20) Whatistheleastnumberofcoinsyoucanhaveandstillpayexactlythecost of any purchase less than one dollar? (21) Thedigits2,3,4,7,and8formafive-digitnumber.Thetensdigitisodd andthenumberisdivisibleby4.howmanynumbersarepossible? (22) Whatfractionofthemultiplesof5between1and99arealsomultiplesof 2? (23) If two numbers are selected randomly without replacement from the set {1,2,3,4,5,6},whatistheprobabilitythattheirproductwillbegreaterthan15?Express your answer as a common fraction. (24) Usingonekindofcheese,onekindofmeat,andonekindofbread,how many different sandwiches can be made from the following: Bread: rye, white, wheat, oatmeal Cheese: Cheddar, swiss Meat: bologna, turkey, ham (25) John saverageformakingfreethrowsinabasketballgameis.80.ina one-and-one free throw situation(he shoots a second basket only if he makes the first), what is the probability that he makes both baskets? Express your answer as a decimal. (26) Supposeyoutossacoinandgetheadsfivetimesinarow.Whatisthe probability, expressed as a common fraction, that you will get heads on the sixth toss? (27) Simplify: 8! 3!4!
4 (28) On a digital clock showing hours and minutes, how many different readings between noon and midnight contain at least two 3 s? (29) How many different six-digit numbers can be formed using three 5 s, two 4 s,andone6? (30) You are buying 15 doughnuts for your MATHCOUNTS team and coach. If thedoughnutsarepackagedsinglyorinsetsof3or4,inhowmanydifferentwayscanyou select your order? Copyright MATHCOUNTS Inc. All rights reserved
5 Answer Sheet Number Answer Problem ID 1 1/16 1BAA BB41 3 1/5525 B03B 4 29 coins, no D00C 5 26 posts 015B B 7 15 CBCA 8 3/10 323A integers BCD ACB BA3A percent 4C3B 13 2/5 BB0B B members B4D /60 143B 17 1/5 DACB A1 19 1/2 C2C coins 3ACB numbers 45AB 22 9/19 455B 23 4/15 2BCB A CBC /2 5AAB ABB B02B numbers 4A2B ways D15B Copyright MATHCOUNTS Inc. All rights reserved
6 Solutions (1) 1/16 ID:[1BAA1] (2)14 ID:[2BB41] (3) 1/5525 ID:[B03B] (4)29coins,no ID:[D00C] (5)26posts ID:[015B] (6)120 ID:[515B] (7)15 ID:[CBCA] (8) 3/10 ID:[323A1] (9) 60 integers ID:[BCD22] (10) 10 ID:[ACB02] Themaximumoccurswheneverypairoflinesyieldsanewpointofintersection.Thereare ( 5 ) 2 = 10 waystochoosethesepairs.
7 (11) 3 4 ID:[BA3A1] (12) 40 percent ID:[4C3B] (13) 2/5 ID:[BB0B] (14) 1 3 ID:[02B41] Massaruhasthreewaysofchoosingtwopencils.Hecaneitherchoosetwobluepencils,the redpencilandthefirstbluepencil,ortheredpencilandthesecondbluepencil.thus,the probabilitythatthetwopencilshechoosesarethesamecoloris 1 3. (15) 22 members ID:[B4D41] (16) 1/60 ID:[143B] (17) 1/5 ID:[DACB] (18) 729 ID:[225A1] (19) 1/2 ID:[C2C22] (20)9coins ID:[3ACB]
8 (21) 12 numbers ID:[45AB] (22) 9/19 ID:[455B] (23) 4/15 ID:[2BCB] (24) 24 ID:[223A1] (25).64 ID:[CBC51] SinceJohn saverageformakingfreethrowsis.80,theprobabilitythathemakesthefirst shotis.80.ifhemakesthisshot,hewillthengetachancetoshootasecondbasket.the probabilitythathemakesthissecondbasket(giventhathealreadymadethefirstone)is still.80,sotheprobabilitythathemakesbothbasketsis(.80)(.80)=.64. (26) 1/2 ID:[5AAB] (27) 280 ID:[5ABB]
9 (28)26 ID:[B02B] Wecandividethenumberofwaystheclockcancontaintwo3sintothreecases. CaseI:Theclockreadsx:33 Fromnoontomidnight,therearetwelvehours(thatis,xcanrangefrom1to12). Thus, this case gives 12 such readings. CaseII:Theclockreads3:x3 Becausethereare60minutesinahour,xcanrangefrom0to5,giving6suchreadings. However,notethatwehavealreadycountedthe3:33reading.Thus,thiscaseyields5new readings. CaseII:Theclockreads3:3x Here,xcanrangefrom0to9,giving10readings.However,again,the3:33readinghas been counted. So, this case gives 9 new readings. Thus,thereare12+5+9= 26 differentreadings. (29) 60 numbers ID:[4A2B] (30)15ways ID:[D15B] Copyright MATHCOUNTS Inc. All rights reserved
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Use the following games to help students practice the following [and many other] grade-level appropriate math skills.
![Use the following games to help students practice the following [and many other] grade-level appropriate math skills.](/thumbs/85/92403514.jpg "Use the following games to help students practice the following [and many other] grade-level appropriate math skills.")
ON Target! Math Games with Impact Students will: Practice grade-level appropriate math skills. Develop mathematical reasoning. Move flexibly between concrete and abstract representations of mathematical
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Here s a game I like plying with students I ll write a positive integer on the board that comes from a set S You can propose other numbers, and I tell you if your proposed number comes from the set Eventually
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Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.
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1. The tree diagrams below show the sample space of choosing a cushion cover or a bedspread in silk or in cotton in red, orange, or green. Write the number of possible outcomes. A 6 B 10 C 12 D 4 Find
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