奥数六年级初赛.doc
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奥数六年级初赛.doc

奥数六年级初赛.doc

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各位同学:你们除了提高数学题难度,也应该开始多接触英语试题。不要求每个单词都会,但要了解条件、明确解题要求,缩短审题时间。尽力去理解多做,万事开头难,读多了也就这么多词汇。还是那句话,做题讲究“实效”,不会做的空着,后面我留了答案。许老师PartⅠ:Questions1to10,10markseach1234Attherightisshowna4×4grid.Wewishtofillinthegridsuchthateachrow,eachcolumn,andeach2×2squareoutlinedbythethicklinescontainsthedigits1through4.Somegridshavealreadybeenfilledin.Findthenumberofwayswecancompletetherestofthegrid.Answer:Theareasofthefacesofacuboidare84cm2,70cm2and30cm2.Findthevolumeofthecuboidincm3.Answer:Thefractioncanbewrrittenintheformwherethegreatestcommondivisorofmandnis1,Findm+n.Answer:FindthesumofalltheintegersN>1withthepropertiesthattheeachprimefactorofNiseither2,3,5or7,andNisnotdivisiblebyanyperfectcubegreaterthan1.Answer:Alargefreshwaterreservoirhastwotypesofdrainagesystem,smallpipesandlargepipes.6largepipes,ontheirown,candrainthereservoirin12hours.3largepipesand9smallpipes,atthesametime,candrainthereservoirin8hours.Howlongwill5smallpipes,ontheirown,taketodrainthereservoir?Answer:minutesATMMERECLOUEPETAAAAAPM+Atalocalvillagegala,theentirepopulationturnedup,500people.Theeventraised£3,000.Ticketswerepricedasfollows:£7.48perman,£7.12perwomanand£0.45perchild.Howmanychildrenwerethere?Answer:Eachofthedistinctlettersinthefollowingadditionproblemrepresentsadifferentdigit.IfA=4,findthenumberrepresentedbytheword“MEET”.Answer:1212878Lettwo8×12rectanglesshareacommoncornerandoverlap.Thedistancefromthebottomrightcornerofonerectangletotheintersectionpointalongtherightedgeofthatrectangleis7.Whatistheareaoftheshadedregion?Answer:Aspyhadtosendthe4-digitcodetoheadquarters.Forsecurityreasons,hesentinsteadthe9separate4-digitcodesshown.Ineachofthe9codes,atleastoneofthedigitsa,b,c,anddoccursinitscorrectposition.Whatisthevalueof?Answer:Inhowmanywayscanonearrangethenumbers21,31,41,51,61,71and81suchthatthesumofeveryfourconsecutivenumbersisdivisibleby3?Answer:PartⅡ:Questions11to14,20markseachTownAandtownBareconnectedbyahighway,withaservicestationatthemidpo