国际学校入学数学测试.docx

国际学校入学数学测试.docx

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国际学校入学数学测试

TheHaberdashers’Aske’sBoys’School

Elstree,Herts

11+EntranceExamination2011

MATHEMATICS

Time:

OneHour

FullName...........................................................

CandidateNumber......................................

Pleasefollowtheseinstructions

∙Donotopenthispaperuntilyouaretoldtodoso.

∙Thereare30questionsonthispaper.Donotforgettoturnover.

∙Workquicklybutaccurately.Youarerecommendedtousepencil,butyoucanusepenorbiroifyouwish.

WRITEYOURANSWERSTOTHEQUESTIONSINTHESPACESPROVIDED.

YOUMAYUSETHESPACEATTHEBOTTOMOFEACHPAGEFORWORKING.

Answer

1.Add:

_______

2.Subtract:

_______

3.Multiply:

_______

4.Divide:

_______

5.Ihave£8.17creditonmymobilephone.Attheendofaphone

callthisfallsto£7.65.Howmuchdidthecallcost?

_______

6.Thedrink“RaspberryHeaven”is1partraspberryjuice,2parts

orangejuiceand3partsapplejuice.Howmuchraspberryjuice

doesa300mlglassofRaspberryHeavencontain?

_______

7.Workouttheproductof528and99._______________

8.Barbieearns£23,450ayearandherpartnerKenearns£700

lessthanBarbie.Howmuchdothecoupleearnaltogether?

__________

9.Convert7.4kilogramsintograms._________

10.Arrangethefollowingnumbersinorderofsizestartingwith

thesmallest:

32.043,0.099,1.072,0.491,0.5

_______________________________________________________________

11.Theopeninghoursofmylocalsupermarketare7amto9pmMondays

toSaturdaysand10:

30amto4:

30pmonSundays.Forhowmanyhours

doesthissupermarketopeneachweek?

__________

12.Arrangethenumbers,5,3,7and2tomakethelargestpossible

four-digitnumberwhichisamultipleof5._________

13.Workout0.08multipliedby5._________

SPACEFORWORKING

Answer

14.ThenewTVchannel,LazyLiving,broadcastsfor98hoursaweek.

Iftwo-seventhsofitsoutputisdevotedtomake-overprogrammes

andtheresttocelebritygossip,forhowmanyhourseachweek

doesthechannelbroadcastprogrammesoncelebritygossip?

_________

15.ForbreakfastIeatasliceofbutteredtoastandacupofcoffee.Thetime

takentocompletetheseactivitiesisasfollows:

Browntoastintoaster3minutes

Butterthetoast1minute

Makecoffeeinmachine2minutes

Jonathanthinksthattheshortesttimetakenformetopreparemy

breakfastis6minutes.ExplainbrieflywhyJonathaniswrong.

________________________________________________________________

Whatisthecorrectshortesttime?

________

16.ThechartbelowshowsthemileagebetweenfiveplacesinNorthLondon.

ForexampleitgivesthedistancebetweenKentonandHampsteadas

4miles.

DaisylivesinHampsteadanddriveshersontoschoolatHaberdashers’inthemorningbeforecontinuingontotheofficeinSouthgate.ShethenvisitshersisterinHarpendenbeforedrivinghomeviaHabs.Howfardoesshetravelaltogether?

_________

SPACEFORWORKING

Answer

17.TherateofVAT（value-addedtax）inthiscountryis20%.

IntheshopCoCost,thepriceofaTVexcludingVATis£550.

WorkoutthecostoftheTVaftertheVATisaddedon.________

Thepriceofadiamondring,includingVATis£1200.

WorkoutthecostoftheringbeforetheVATwasaddedon.________

18.TrainAleavesBirminghamNewStreetstationat1747travelling

dueNorthontheslowlineat90km/hour.

Howmanykilometreshasthistraintravelledwhenthetime

is1817?

____________

TrainBleavesBirminghamNewStreetstationat1817alsotravelling

dueNorthbutonthefastline.ThespeedoftrainBis135km/hour.

AtwhattimedoestrainBovertaketrainA?

_____________

19.ThediagrambelowshowsapieceofabstractarthanginguponAndrew’s

bedroomwall.Tomakethislookevenmoreinterestinghedecidesto

rotatethispaintingthrough90degreesclockwise.Inthespaceprovided

showwhatthepaintingwilllooklikeinitsnewposition.

SPACEFORWORKING

Answer

20.EveryeveningDianahasabath.Sheturnsonthetapsandwaits

patientlyforthebathtofillbeforesheturnsthemoffandstepsin.

Attheendofherbathshestepsoutofthewaterbeforepullingout

theplugtoemptythebath.

Agraphofthevolumeofwater（measuredinlitres）plottedagainsttime

（measuredinminutes）isshownbelow.

Howlongdoesshespendinthebath?

__________

Workoutthenumberoflitresofwaterthatflowintothebath

perminuteasthebathfillsup.__________

Doesthebathemptyatafaster,slowerorthesamerateasitfills?

Faster,slowerorsame?

_______________

SPACEFORWORKING

Answer

21.Amar（formcaptain）,Brian（vicecaptain）,CharlesandDanielare

bestfriendsinthesameclassatschool.Theyalwaysliketostandnexttoeachotherinthelunchqueue.

OnMondaysitisaschoolrulethattheformcaptainisatthefrontofthequeuefollowedbythevicecaptain.TherearetwowaysinwhichtheseboyscanqueueuponaMonday:

ABCDandABDC.

OnTuesdays,theformcaptainmustagainqueueupfirstbuttheremainingthreeboyscanfollowinanyorder.TherearesixwaysinwhichtheseboyscanqueueuponaTuesday.Fourofthesewaysarelistedbelow.Writedowntheremainingtwo:

ABCD,ABDC,ACBD,ACDB,_______,_________

OnWednesdaystherearenorestrictionsandallfourboyscanqueueuptogetherinanyorder.Inhowmanywayscanthisbedone?

____________

22.Isoldeenjoysmakingcubes.Shefirstdrawsoutshapesonpiecesofcardboardandthenfoldsthemalongthelinestoformacube.

Thediagramsbelowshowsixattempts.

Unfortunatelyonlyfiveoftheseactuallywork.

Crossouttheshapewhichisimpossible.

SPACEFORWORKING

23.Aspartofamathematicsprojectaclassisaskedtolookupthelengthsof

objectsontheinternet.

Theseobjectsarelistedintherectanglesbelowandthemeasurementsare

giveninthetriangles.

Unfortunatelytheseobjectsandmeasurementshavebeenmuddledup.

Drawlinesonthediagramtomatcheachobjectwithitscorrectlength.

SPACEFORWORKING

Answer

24.Inthisquestionyoumayassumethefollowingexchangerates:

1Britishpound（£）=1.5Americandollars（US$）

1Britishpound（£）=2NewZealanddollars（NZ$）

ThepriceofahoodieintheLondonbranchofAbergavennyandFiltch

is£80.InNewYorkthepriceisUS$90.HowmuchdoIsavebybuying

thehoodieinNewYork?

GiveyouranswerbothinUSdollarsandpounds.

Saving=US$___________and£___________

MyfriendSheilalivesinAuckland,NewZealand.ShesavesUS$60ifshe

buysthishoodieinNewYork.HowmuchdoesitcostinNewZealand?

GiveyouranswerinNewZealanddollars.

NZ$___________

WorkouttheexchangerateforconvertingNewZealanddollarsintoAmericandollars:

1NewZealanddollar（NZ$）=______Americandollars（US$）

25.Sevenchildren,A,B,C,D,E,F,Gtakepartinacompetition.

Usetheinformationbelowtofillinthetable:

Position

Child

1st

2nd

3rd

4th

5th

6th

7th

▪Therearenotiedpositions

▪DbeatA

▪Cwasthewinner

▪IfyoumultiplythepositionsofAandDyougetthepositionofF

▪AandEareinnexttoeachotherinthetable.

▪BbeatG

SPACEFORWORKING

Answer

26.Theaverageofasetofnumbersisworkedoutbyaddingthenumberstogether

andthendividingbythenumberofnumbers.

Workouttheaverageof:

1,1,1_______

1,1,4_______

1,4,7_______

4,7,13_______

Describe,inwords,asimplepatternthatyounoticeabouttheseanswers:

_______________________________________

Class6AgoonaGeographytriptoEastbourneandinvestigatethesizeofpebblesonthebeach.Jonniepicksupsevensmallpebblesandmeasurestheirlengthsinmillimetres.Thelengthsofthefirstsixpebblesare:

1,1,1,4,7,13

Assumingthatthepatternthatyouobservedabovecontinuestohold,workoutthelengthofJonnie’sseventhpebble.________

27.Tristanisgivensixbagsoffruit.

BagAcontains2apples,4orangesand3pears.

BagBcontains3apples,1orangeand2pears.

BagCcontains4apples,5orangesand3pears.

BagDcontains4apples,6orangesand4pears.

BagEcontains6apples,4orangesand3pears

BagFcontains7apples,7orangesand7pears.

Heisallowedtochooseoneofthesebagsandthenpickjustonepieceof

fruitfromthatbagatrandom.

Whichbagshouldhechooseifheistomaximisehischanceofpickingan

apple?

_________

Whichbagshouldhechooseifheistominimisehischanceofpickinga

pear?

_________

SPACEFORWORKING

Answer

28.Thediagrambelowshowsasequenceofsquaresdrawnonagrid.

Thecoordinatesofthecentreofsquarenumber1are（1,1）.

Thecoordinatesofthecentreofsquarenumber2are（2,3）.

Thefirstnumberinthepairisthex-coordinateandthesecond

numberisthey-coordinate.

Writedownthecoordinatesofthecentreof

squarenumber3___________________

squarenumber4___________________

squarenumber10___________________

squarenumber234___________________

They-coordinateofthecentreofoneofthesquaresinthissequenceis

2177.Workoutthex-coordinateofthissquare.________________

SPACEFORWORKING

29.Inthetrianglesshownbeloweachnumberisthesumofthetwonumbersdirectlyunderneathit.Forexample,26=12+14and5=1+4.