国际学校入学数学测试

TheHaberdashers’Aske’sBoys'School

Elstree,Herts11+EntranceExamination2011MATHEMATICSTime:OneHourFullNameCandidateNumberPleasefollowtheseinstructionsDonotopenthispaperuntilyouaretoldtodoso.Thereare30questionsonthispaper.Donotforgettoturnover.Workquicklybutaccurately.Youarerecommendedtousepencil,butyoucanusepenorbiroifyouwish.SPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGWRITEYOURANSWERSTOTHEQUESTIONSINTHESPACESPROVIDED.YOUMAYUSETHESPACEATTHEBOTTOMOFEACHPAGEFORWORKING.AnswerTOC\o"1-5"\h\zAdd:48+27Subtract:91-25Multiply:62x7Divide:92+4Ihave£8.17creditonmymobilephone.Attheendofaphonecallthisfallsto£7.65.Howmuchdidthecallcost?Thedrink“RaspberryHeaven”is1partraspberryjuice,2partsorangejuiceand3partsapplejuice.Howmuchraspberryjuicedoesa300mlglassofRaspberryHeavencontain?Workouttheproductof528and99.Barbieearns£23,450ayearandherpartnerKenearns£700lessthanBarbie.Howmuchdothecoupleearnaltogether?Convert7.4kilogramsintograms.Arrangethefollowingnumbersinorderofsizestartingwiththesmallest:32.043,0.099,1.072,0.491,0.5Theopeninghoursofmylocalsupermarketare7amto9pmMondaystoSaturdaysand10:30amto4:30pmonSundays.Forhowmanyhoursdoesthissupermarketopeneachweek?Arrangethenumbers,5,3,7and2tomakethelargestpossiblefour-digitnumberwhichisamultipleof5.___Workout0.08multipliedby5.___AnswerAnswerAnswerAnswerAnswerAnswerSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGThenewTVchannel,LazyLiving,broadcastsfor98hoursaweek.Iftwo-seventhsofitsoutputisdevotedtomake-overprogrammesandtheresttocelebritygossip,forhowmanyhourseachweekdoesthechannelbroadcastprogrammesoncelebritygossip?ForbreakfastIeatasliceofbutteredtoastandacupofcoffee.Thetimetakentocompletetheseactivitiesisasfollows:3minutes3minutes1minute2minutesButterthetoastMakecoffeeinmachineJonathanthinksthattheshortesttimetakenformetopreparemybreakfastis6minutes.ExplainbrieflywhyJonathaniswrong.Whatisthecorrectshortesttime?ThechartbelowshowsthemileagebetweenfiveplacesinNorthLondon.ForexampleitgivesthedistancebetweenKentonandHampsteadas4miles.DaisylivesinHampsteadanddriveshersontoschoolatHaberdashers’inthemorningbeforecontinuingontotheofficeinSouthgate.ShethenvisitshersisterinHarpendenbeforedrivinghomeviaHabs.Howfardoesshetravelaltogether?TherateofVAT(value-addedtax)inthiscountryis20%.IntheshopCoCost,thepriceofaTVexcludingVATis£550.WorkoutthecostoftheTVaftertheVATisaddedon.Thepriceofadiamondring,includingVATis£1200.WorkoutthecostoftheringbeforetheVATwasaddedon.TrainAleavesBirminghamNewStreetstationat1747travellingdueNorthontheslowlineat90km/hour.Howmanykilometreshasthistraintravelledwhenthetimeis1817?TrainBleavesBirminghamNewStreetstationat1817alsotravellingdueNorthbutonthefastline.ThespeedoftrainBis135km/hour.AtwhattimedoestrainBovertaketrainA?ThediagrambelowshowsapieceofabstractarthanginguponAndrew’sbedroomwall.Tomakethislookevenmoreinterestinghedecidestorotatethispaintingthrough90degreesclockwise.Inthespaceprovidedshowwhatthepaintingwilllooklikeinitsnewposition.AnswerAnswerAnswerAnswerSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGEveryeveningDianahasabath.Sheturnsonthetapsandwaitspatientlyforthebathtofillbeforesheturnsthemoffandstepsin.Attheendofherbathshestepsoutofthewaterbeforepullingouttheplugtoemptythebath.Agraphofthevolumeofwater(measuredinlitres)plottedagainsttime(measuredinminutes)isshownbelow.Howlongdoesshespendinthebath?Workoutthenumberoflitresofwaterthatflowintothebathperminuteasthebathfillsup.Doesthebathemptyatafaster,slowerorthesamerateasitfills?Faster,slowerorsame?

Amar(formcaptain),Brian(vicecaptain),CharlesandDanielarebestfriendsinthesameclassatschool.Theyalwaysliketostandnexttoeachotherinthelunchqueue.OnMondaysitisaschoolrulethattheformcaptainisatthefrontofthequeuefollowedbythevicecaptain.TherearetwowaysinwhichtheseboyscanqueueuponaMonday:ABCDandABDC.OnTuesdays,theformcaptainmustagainqueueupfirstbuttheremainingthreeboyscanfollowinanyorder.TherearesixwaysinwhichtheseboyscanqueueuponaTuesday.Fourofthesewaysarelistedbelow.Writedowntheremainingtwo:ABCD,ABDC,ACBD,ACDB,,OnWednesdaystherearenorestrictionsandallfourboyscanqueueuptogetherinanyorder.Inhowmanywayscanthisbedone?Isoldeenjoysmakingcubes.Shefirstdrawsoutshapesonpiecesofcardboardandthenfoldsthemalongthelinestoformacube.Thediagramsbelowshowsixattempts.Unfortunatelyonlyfiveoftheseactuallywork.Crossouttheshapewhichisimpossible.Aspartofamathematicsprojectaclassisaskedtolookupthelengthsofobjectsontheinternet.Theseobjectsarelistedintherectanglesbelowandthemeasurementsaregiveninthetriangles.Unfortunatelytheseobjectsandmeasurementshavebeenmuddledup.Drawlinesonthediagramtomatcheachobjectwithitscorrectlength.WidthofWembleyStadiumpitch300mmHeightofanaverageman5600kmDistancefromLondontoNewYork135mLengthofapieceofstandardA4paper1750mmHeightoftheLondonEye8800mHeightofMountEverest6900cmInthisquestionyoumayassumethefollowingexchangerates:1Britishpound(£)=1.5Americandollars(US$)1Britishpound(£)=2NewZealanddollars(NZ$)ThepriceofahoodieintheLondonbranchofAbergavennyandFiltchis£80.InNewYorkthepriceisUS$90.HowmuchdoIsavebybuyingthehoodieinNewYork?GiveyouranswerbothinUSdollarsandpounds.Saving=US$and£MyfriendSheilalivesinAuckland,NewZealand.ShesavesUS$60ifshebuysthishoodieinNewYork.HowmuchdoesitcostinNewZealand?GiveyouranswerinNewZealanddollars.NZ$WorkouttheexchangerateforconvertingNewZealanddollarsintoAmericandollars:NewZealanddollar(NZ$)=Americandollars(US$)Sevenchildren,A,B,C,D,E,F,Gtakepartinacompetition.Usetheinformationbelowtofillinthetable:TherearenotiedpositionsDbeatACwasthewinnerIfyoumultiplythepositionsofAandDyougetthepositionofFAandEareinnexttoeachotherinthetable.BbeatGAnswerAnswerAnswerAnswerAnswerAnswerSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGSPACEFORWORKINGTheaverageofasetofnumbersisworkedoutbyaddingthenumberstogetherandthendividingbythenumberofnumbers.Workouttheaverageof:1,11,44,74,7,13Describe,inwords,asimplepatternthatyounoticeabouttheseanswers:Class6AgoonaGeographytriptoEastbourneandinvestigatethesizeofpebblesonthebeach.Jonniepicksupsevensmallpebblesandmeasurestheirlengthsinmillimetres.Thelengthsofthefirstsixpebblesare:1,1,1,4,7,13Assumingthatthepatternthatyouobservedabovecontinuestohold,workoutthelengthofJonnie’sseventhpebble.Tristanisgivensixbagsoffruit.BagAcontains2apples,4orangesand3pears.BagBcontains3apples,1orangeand2pears.BagCcontains4apples,5orangesand3pears.BagDcontains4apples,6orangesand4pears.BagEcontains6apples,4orangesand3pearsBagFcontains7apples,7orangesand7pears.Heisallowedtochooseoneofthesebagsandthenpickjustonepieceoffruitfromthatbagatrandom.Whichbagshouldhechooseifheistomaximisehischanceofpickinganapple?Whichbagshouldhechooseifheistominimisehischanceofpickingapear?Thediagrambelowshowsasequenceofsquaresdrawnonagrid.Thecoordinatesofthecentreofsquarenumber1are(1,1).Thecoordinatesofthecentreofsquarenumber2are(2,3).Thefirstnumberinthepairisthex-coordinateandthesecondnumberisthey-coordinate.Writedownthecoordinatesofthecentreofsquarenumber3squarenumber4squarenumber10squarenumber234They-coordinateofthecentreofoneofthesquaresinthissequenceis2177.Workoutthex-coordinateofthissquare.123456xSPACEFORWORKINGSPA