UPCH Maths Test(UCL本预入学数学考试样题)

1)Amansoldtwocamerasfor£240each.Onewassoldforaprofitof20%,andoneforalossof20%.Whatwashisoverallprofitorloss?A.Lossof£20B.Lossof£10C.MadenoprofitorlossD.Profitof£10E.Profitof£202)If1/a=1/b+1/candaandcarebothdoubled,thevalueofbwillbeA.dividedby4B.dividedby2C.unchangedD.multipliedby2E.multipliedby43)WhichofthefollowingexpressionshasthelargestvaluewhenT=-0.25?A.41/TB.−4/TC.4TD.4/T2E.4/(−T)1/24)Theareaofasmallcirclewithdiameterxishalftheareaofalargercirclewhosediameterisy.Whatisthevalueofy/x?A.1B.21/2C.21/2−1D.21/2+1E.(21/2+1)/25)Ifx=2log39+log275then3x=A.81(5)1/3B.81+(5)1/3C.405/3D.135E.NoneofAtoDiscorrect6)Findtheperimeterofthefigurebelow,ifpossible.A.CannotbecalculatedB.34cmC.36cmD.42cmE.46cm7)Aboxcontainingthreebagsofsugarweighs6.0kg.Whenthesameboxcontainsfivebagsofsugaritweighs9.2kg.Howheavyistheemptybox?A.1.2kgB.1.6kgC.2.0kgD.3.2kgE.Can'tbesure8)Ify=cos2xsinxthederivativefunction,dy/dxisA.cosx(2sin2x−cos2x)B.cosx(sin2x−cos2x)C.−2cos2xsinxD.2cos2xsinxE.cosx(1−3sin2x)9)Thesymbol25!denotestheproductofallthewholenumbersfrom1upto25.Iftheactualvalueof25!iscalculated,howmanyzeroswillbeattheend?A.1B.3C.4D.5E.610)Aproductinashopisreducedinpriceby20%.Atthisreducedpricetheshopkeepermakesonly4%profit.Whatpercentageprofit(tothenearestwholepercent)doestheshopkeepermakeatitsnormalsellingprice?A.16B.24C.25D.30E.8411)Asolidspherewithradiusrfitsexactlyinsideacylinder,touchingthesides,thetopandthebottom.Whatfractionofthecylinderisempty?A.2/3B.1/3C.1/2D.3/4E.Itdependsonthevalueofr.12)Wecanwritethenumber384as424wherethebardenotesanegativedigit,sothat424means4×100−2×10+4.Howcouldwewrite1988inthisway?A.2102B.2002C.2122D.2112E.201213)1+22+333+4444+55555+666666+7777777+88888888+999999999equals:A.1097393685B.1097393645C.1097389685D.1097093685E.107739368514)Twosquaresofside2xoverlaptoformaregularoctagon.Howlongiseachsideoftheoctagon?A.2x/3B.x(2−21/2)C.xD.(21/2/2)xE.2x(21/2−1)15)Theareaofthesmallsquareisonethirdoftheareaofthelargesquare.Whatisthevalueofx/y?A.(31/2+1)/2B.1/(3)1/2C.1/9D.31/2E.31/2−116)Whatisthevalueofcot(π/4)+cot(π/6)+cot(π/8)?A.2+21/2+31/2B.21/2−1C.1+31/2+21/2D.31/2+21/2E.1+31/2+2(2)1/217)If4x−5(2x)=−6,thenthevalueofxis:A.1orlog23B.1orlog32C.1or−3/2D.1orlog42E.NoneofAtoDiscorrect18)Ifx⊗y=(xy)1/2thenwhatisthevalueof(3⊗48)⊗9?A.6(3)1/2B.6(3)1/4C.6D.36E.10819)Therealnumberkliesbetween0and1.Theareaofthequadrilateralformedbythelinesy=kx,y=kx+1,x=kyandx=ky+1isA.1/(1−k)B.k/(1−k)C.1/(1−k2)D.k/(1−k2)E.k2/(1−k2)20)Asquarehascentre(2,1).Onevertexisat(5,6).PointsP,Q,RhavecoordinatesP:=(−3,4),Q:=(−1,−4)andR:=(5,−4).Whichofthefollowingareverticesofthesquare?A.P,QandRB.PonlyC.PandRonlyD.QonlyE.PandQonly21)Inthediagrambelow,AB,EFandDCareperpendiculartoBC.AECandBEDarestraightlines.AB=x,EF=handDC=y.Thenhis:A.xy/(x+y)B.(x2+y2)/(2x+2y)C.(x3+y3)/4xyD.(x+y)/xyE.Notenoughinformationisprovidedtosolvetheproblem22)Thenumberofprimevaluesofthepolynomialn3−10n2−84n+840wherenisanintegeris:A.0B.1C.2D.4E.infinite23)Amanhasasquarepieceofpaperwhereeachsidehaslength1m.Twoequalcirclesaretobecutfromthispaper.Whatistheradius,inmetres,ofthelargestpossiblecircles?A.1/(2+21/2)B.[4+2(2)1/2)/16C.[2(2)1/2−1]/7D.21/2/4E.(1+21/2)/824)If2x−2x−2=192,thenwhatisthevalueofx?A.5B.6C.7D.8E.925)Lete(x)=cos4x−sin4xf(x)=1−2sin2xg(x)=(cosx+sinx)(cosx−sinx)h(x)=(1−sinx)(1+tanx)(1+sinx)(1−tanx)Ifthevaluese(π/7),f(π/7),g(π/7)andh(π/7)arecalculated,howmanydifferentanswerswilltherebe?A.1(i.e.allthevaluesarethesame)B.2C.3D.4E.Can'tbedonewithoutacalculator.26)AregularhexagonABCDEFhassidesoflength2cm.MisthemidpointofAB.Whichofthefollowinglinesegmentshavelength131/2cm?A.BDB.BEC.EMD.FME.Noneofthese27)Ifthenumbernisaperfectsquare,whatisthenextperfectsquareaboveit?A.n+n1/2B.n+2(n)1/2+1C.n2+1D.n2+nE.n2+2n+128)Whatistheareaofthelargestequilateraltrianglewhichfitsinsideasquareofsidea?A.(3a4)1/2/4B.[2(3)1/2−3]a2C.(3a4)1/2/2D.(3a4)1/2E.[3(3)1/2−3]a229)TriangleABCissuchthatitsthreeangles∠A,∠B,∠Careintheration3:4:5.WhatistheratioofitsthreesidesBC:CA:AB?A.31/2:41/2:51/2B.(1+21/2):61/2:(1+31/2)C.2:61/2:(1+31/2)D.3:4:5E.61/2:(1+31/2):(21/2+31/2)30)Adrivertravelsanaverageofkmilesadayforthefirstddaysofajourneyandthenmmilesadayforthenextbdays.Thecarusesxlitresofpetrolper100miles.Howmanylitresofpetroldoesthecaruseforthewholejourney?A.x(kd+mb)/100B.(k+m)x/100C.100(k+m)/xD.100(kd+mb)/xE.bdkmx/100