Fermat滑铁卢数学竞赛(Grade 11).docx

Fermat滑铁卢数学竞赛(Grade11)CanadianInstituteofActuariesCharteredAccountantsSybaseiAnywhereSolutionsScoring:Thereisnopenaltyforanincorrectanswer.Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.PartA:Eachcorrectanswerisworth5.1.Ifx=3,thenumericalvalueof522xis(A)1(B)27(C)13(D)31(E)32.332232+isequalto(A)3(B)6(C)2(D)32(E)53.Ifitisnow9:04a.m.,in56hoursthetimewillbe(A)9:04a.m.(B)5:04p.m.(C)5:04a.m.(D)1:04p.m.(E)1:04a.m.4.Whichoneofthefollowingstatementsisnottrue?(A)25isaperfectsquare.(B)31isaprimenumber.(C)3isthesmallestprimenumber.(D)8isaperfectcube.(E)15istheproductoftwoprimenumbers.5.ArectangularpictureofPierredeFermat,measuring20cmby40cm,ispositionedasshownonarectangularpostermeasuring50cmby100cm.Whatpercentageoftheareaoftheposteriscoveredbythepicture?(A)24%(B)16%(C)20%(D)25%(E)40%6.GisaistallerthanHenrybutshorterthanJustina.IvanistallerthanKatiebutshorterthanGisa.Thetallestofthesefivepeopleis(A)Gisa(B)Henry(C)Ivan(D)Justina(E)Katie7.Arectangleisdividedintofoursmallerrectangles.Theareasofthreeoftheserectanglesare6,15and25,asshown.Theareaoftheshadedrectangleis(A)7(B)15(C)12(D)16(E)108.Inthediagram,ABCDandDEFGaresquareswithequalsidelengths,and=°DCE70.Thevalueofyis(A)120(B)160(C)130(D)110(E)1409.Thenumbers1through20arewrittenontwentygolfballs,withonenumberoneachball.Thegolfballsareplacedinabox,andoneballisdrawnatrandom.Ifeachballisequallylikelytobedrawn,whatistheprobabilitythatthenumberonthegolfballdrawnisamultipleof3?(A)320(B)620(C)1020(D)520(E)12020.ABCDisasquarewithABx=+16andBCx=3,asshown.TheperimeterofABCDis(A)16(B)32(C)96(D)48(E)24PartB:Eachcorrectanswerisworth6.11.Alinepassingthroughthepoints02,?()and10,()alsopassesthroughthepoint7,b().Thenumericalvalueofbis(A)12(B)92(C)10(D)5(E)1412.Howmanythree-digitpositiveintegersareperfectsquares?(A)23(B)22(C)21(D)20(E)1913.A“double-singlenumberisathree-digitnumbermadeupoftwoidenticaldigitsfollowedbyadifferentdigit.Forexample,553isadouble-singlenumber.Howmanydouble-singlenumbersaretherebetween100and1000?(A)81(B)18(C)72(D)64(E)9014.Thenaturalnumbersfrom1to2100areenteredsequentiallyin7columns,withthefirst3rowsasshown.Thenumber2002occursincolumnmandrown.Thevalueofmn+isColumn1Column2Column3Column4Column5Column6Column7Row11234567Row2891011121314Row315161718192021MMMMMMMM (A)290(B)291(C)292(D)293(E)294x+163xABDC15.Inasequenceofpositivenumbers,eachtermafterthefirsttwotermsisthesumofallofthepreviousterms.Ifthefirsttermisa,thesecondtermis2,andthesixthtermis56,thenthevalueofais(A)1(B)2(C)3(D)4(E)516.Ifacadbcbd+=68andcd+=4,whatisthevalueofabcd+?(A)17(B)85(C)4(D)21(E)6417.Theaverageageofagroupof140peopleis24.Iftheaverageageofthemalesinthegroupis21andtheaverageageofthefemalesis28,howmanyfemalesareinthegroup?(A)90(B)80(C)70(D)60(E)5018.ArectangularpieceofpaperAECDhasdimensions8cmby11cm.CornerEisfoldedontopointF,whichliesonDC,asshown.TheperimeteroftrapezoidABCDisclosestto(A)33.3cm(B)30.3cm(C)30.0cm(D)41.3cm(E)35.6cm19.If238610ab=(),whereaandbareintegers,thenba?equals(A)0(B)23(C)?13(D)?7(E)?320.Inthediagram,YQZCisarectanglewithYC=8andCZ=15.EquilateraltrianglesABCandPQR,eachwithsidelength9,arepositionedasshownwithRandBonsidesYQandCZ,respectively.ThelengthofAPis(A)10(B)117(C)9(D)8(E)72PartC:Eachcorrectanswerisworth8.21.If31537521219?+?=Lnn,thenthevalueofnis(A)38(B)1(C)40(D)4(E)3922.Thefunctionfx()hasthepropertythatfxyfxfyxy+()=()+()+2,forallpositiveintegersxandy.Iff14()=,thenthenumericalvalueoff8()is(A)72(B)84(C)88(D)64(E)80continued.Figure1Figure223.Theintegersfrom1to9arelistedonablackboard.Ifanadditionalmeightsandkninesareaddedtothelist,theaverageofallofthenumbersinthelistis7.3.Thevalueofkm+is(A)24(B)21(C)11(D)31(E)8924.Astudenthastwoopen-toppedcylindricalcontainers.(Thewallsofthetwocontainersarethinenoughsothattheirwidthcanbeignored.)Thelargercontainerhasaheightof20cm,aradiusof6cmandcontainswatertoadepthof17cm.Thesmallercontainerhasaheightof18cm,aradiusof5cmandisempty.Thestudentslowlylowersthesmallercontainerintothelargercontainer,asshowninthecross-sectionofthecylindersinFigure1.Asthesmallercontainerislowered,thewaterfirstoverflowsoutofthelargercontainer(Figure2)andtheneventuallypoursintothesmallercontainer.Whenthesmallercontainerisrestingonthebottomofthelargercontainer,thedepthofthewaterinthesmallercontainerwillbeclosestto(A)2.82cm(B)2.84cm(C)2.86cm(D)2.88cm(E)2.90cm25.Thelengthsofallsixedgesofatetrahedronareintegers.Thelengthsoffiveoftheedgesare14,20,40,52,and70.Thenumberofpossiblelengthsforthesixthedgeis(A)9(B)3(C)4 (D)5(E)6