PAT-2010
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OXFORDCOLLEGESPHYSICSAPTITUDETEST(PAT)Pleasefillinyourname,thenameofyourschoolorcollege,andifyouknowthemyourUCASnumberandOxfordCollegeofpreference,intheboxesbelow.
Name
School/CollegeIfyouareanindividualcandidate,takingthistestawayfromaschoolorcollege,pleasewritethenameofyourexaminationcentreinthisbox.
UCASNumber(ifknown)
OxfordCollegeofPreferenceSpecialProvisionFortheuseofteachers/invigilatorsonly.Pleaseindicateanyspecialprovisionmadeforthecandidate(e.g.extratime,useofwordprocessor,etc.)addinganoteofthereasonforit.
SignatureofInvigilator:........................................................................ForOxforduseonlybelow:
Maths1234567891011TotalPhysics1213141516171819202122232425TotalTHECOLLEGESOFOXFORDUNIVERSITYPHYSICSWednesday3November2010Timeallowed:2hoursForcandidatesapplyingforPhysics,andPhysicsandPhilosophy
Therearetwoparts(AandB)tothistest,carryingequalweight.Answersshouldbewrittenonthequestionsheetinthespacesprovidedandyoushouldattemptallthequestions.Spaceforroughworkinghasbeenleftattheendofthepaper.
Marksforeachquestionareindicatedintherighthandmargin.Thereareatotalof100marksavailableandthetotalmarksforeachsectionareindicatedatthestartofasection.Youareadvisedtodivideyourtimeaccordingtothemarksavailable,tospendequaleffortonpartsAandB,andtoattemptallthequestionsonthepaper.
Nocalculators,tablesorformulasheetsmaybeused.AnswersinPartAshouldbegivenexactlyunlessindicatedotherwise.NumericanswersinPartBshouldbecalculatedto2significantfiguresunlessotherwisedirected.
Useg=10ms−2.
DoNOTturnoveruntiltoldthatyoumaydoso.PartA:MathematicsforPhysics[50Marks]1.(i)Solvesin3x=√3cos3xforxintherange0≤x≤π[3]
(ii)Solvecos2x−sinx+1=0forxalsointherange0≤x≤π[3]
2.Theequationofthelargercircleinthefigurebelowis(x−1)2+(y−1)2=1.Findtheequationofthesmallercircle.[4]
y
x3.Showthatx=−1isarootofthepolynomialequationx3+2x2−5x−6=0,andfindtheothertworoots.[5]
4.FindtheequationofthelinepassingthroughthepointsA(2,3)andB(1,5)inthex−yplane.[4]5.Findtheareaoftheshadedregionofthecircleinthefigurebelow,asafunctionoftheradiusR.R
½R[5]
6.ArectangleisformedbybendingalengthofwireoflengthLaroundfourpegs.Calculatetheareaofthelargestrectanglewhichcanbeformedthisway(asafunctionofL).[4]7.(i)Calculatelog39[2](ii)Simplifylog4+log16−log2[2]
8.(i)Calculate(16.1)2[2]
(ii)Calculate10.11×3.2[2]9.Thefirst,fourth,andseventhtermsofanarithmeticprogressionaregivenbyx3,x,andx2respectively(wherex=0andx=1).Findx,andthecommondifferenceoftheprogression.[5]
10.Inagameofdice,aplayerinitiallythrowsasingledie,andreceivesthenumberofpointsshown.Ifthedieshowsa6,theplayerthenthrowsthedieagainandaddsthenumbershowntohis/herscore.Theplayerdoesnotthrowthediemorethantwice.Calculatetheprobabilitythattheplayerwillgainanevennumberofpoints.[4]11.Sketchthecurves:y=x2andx=y2,labelthepointsofintersectionandcalculatetheareabetweenthetwocurves.[5]PartB:Physics[50Marks]
Multiplechoice(10marks)Pleasecircleoneanswertoeachquestiononly.12.ArocksamplecontainstworadioactiveelementsAandB,withhalflivesof8000and16000yearsrespectively.IftherelativeproportionofA:Bisinitially1:1,whatistheirrelativeproportionafter16000years?
A2:1B1:2C3:1D1:3[1]
13.TworesistorsR1andR2areconnectedinserieswithapotentialdifferenceVacrossthem.ThepowerdissipatedbytheresistorR1is:
AV2R1/(R1+R2)2BV2R22/(R1(R1+R2)2)CV2R1×(R1+R2)2DV2R22×(R1(R1+R2)2)[1]
14.Ablockofconcrete,ofmass100kg,liesona2m-longplankofwoodatadistance0.5mfromoneend.Ifabuilderliftsuptheotherendoftheplank,howmuchforcemustheapplytolifttheblock?
A125NB12.5NC250ND25N[1]
15.AplanefliesinadirectionNW(accordingtotheplane’sinternalcompass)atanairspeedof141km/hr.Ifthewindattheplane’scruisealtitudeisblowingwithaspeedof100km/hrdirectlyfromthenorth,whatistheplane’sactualspeedanddirectionrelativetotheground?
A141km/hr,SWB100km/hr,WC141km/hr,SD223km/hr,NNW[1]
16.Ateacherwantstolistentoaprogrammeonhisfavouriteradiostation,broadcastingatafrequencyof1000kHz,buthisradioonlyindicatesthewavelengthofthestation.Towhatwavelengthmusttheteachertunehisradiotoheartheprogramme?
A300mB300000mC0.0033mD50m[1]
