2026年研究生入學考試英語數(shù)學專業(yè)課筆試試題及答案考試時長：120分鐘滿分：100分班級：__________姓名：__________學號：__________得分：__________試卷名稱：2026年研究生入學考試英語數(shù)學專業(yè)課筆試試卷考核對象：報考研究生入學考試的考生題型分值分布-判斷題（總共10題，每題2分）總分20分-單選題（總共10題，每題2分）總分20分-多選題（總共10題，每題2分）總分20分-案例分析（總共3題，每題6分）總分18分-論述題（總共2題，每題11分）總分22分總分：100分---一、判斷題（每題2分，共20分）1.Thepassivevoiceshouldalwaysbeavoidedinacademicwriting.2.Thederivativeof\(e^x\)is\(e^x\).3.Inanormaldistribution,themean,median,andmodeareequal.4.ThePythagoreantheoremappliesonlytoright-angledtriangles.5.Quantummechanicsdescribesthebehaviorofparticlesatmacroscopicscales.6.TheGreatWallofChinaisvisiblefromspacewiththenakedeye.7.Apolygonwithfivesidesiscalledapentagon.8.Thespeedoflightinavacuumisapproximately299,792kilometerspersecond.9.DNAwasfirstdiscoveredbyGregorMendel.10.TheEarthistheonlyplanetinthesolarsystemwithliquidwateronitssurface.二、單選題（每題2分，共20分）1.Whichofthefollowingisacorrectuseofthepastperfecttense?A.Shewrotealetteryesterday.B.Shehadwrittenaletterbeforesheleft.C.Shewritesalettereveryday.D.Shewillwritealettertomorrow.2.Theintegral\(\int_0^1x^2\,dx\)evaluatesto:A.1B.0.5C.2D.03.Inabinarysearchtree,themaximumheightofatreewith\(n\)nodesis:A.\(\log_2n\)B.\(n\)C.\(n^2\)D.\(2^n\)4.Thechemicalsymbolforgoldis:A.GoB.GdC.AuD.Ag5.Thecentrallimittheoremstatesthatthesamplingdistributionofthesamplemeanapproaches:A.Anormaldistributionassamplesizeincreases.B.Abinomialdistributionassamplesizeincreases.C.APoissondistributionassamplesizeincreases.D.Auniformdistributionassamplesizeincreases.6.Theareaofacirclewithradius\(r\)isgivenby:A.\(2\pir\)B.\(\pir^2\)C.\(4\pir^2\)D.\(\pir\)7.Theprimaryfunctionofthemitochondriainacellis:A.ProteinsynthesisB.EnergyproductionC.DNAreplicationD.Celldivision8.ThecapitalcityofJapanis:A.SeoulB.BeijingC.TokyoD.Shanghai9.Theslopeoftheline\(y=3x-4\)is:A.-4B.3C.4D.010.ThepHofpurewaterat25°Cis:A.7B.6C.8D.5三、多選題（每題2分，共20分）1.Whichofthefollowingareexamplesofrenewableenergysources?A.SolarenergyB.WindenergyC.CoalD.NuclearenergyE.Hydroelectricpower2.TheoremsinEuclideangeometryinclude:A.Pythagoras'theoremB.ThelawofsinesC.ThefundamentaltheoremofalgebraD.TheparallelpostulateE.Thelawofcosines3.Keycomponentsofacomputer'scentralprocessingunit(CPU)include:A.Arithmeticlogicunit(ALU)B.ControlunitC.Randomaccessmemory(RAM)D.Graphicsprocessingunit(GPU)E.Centralprocessingunit(CPU)itself4.Theperiodictableisorganizedby:A.AtomicnumberB.AtomicmassC.ElectronconfigurationD.ChemicalreactivityE.Molecularweight5.Inabalancedbinarysearchtree,theheightdifferencebetweenleftandrightsubtreesofanynodeis:A.0B.1C.2D.3E.46.TheGreatBarrierReefislocatedin:A.TheAtlanticOceanB.ThePacificOceanC.TheIndianOceanD.TheArcticOceanE.TheMediterraneanSea7.Theprocessofphotosynthesisinvolves:A.CarbondioxideabsorptionB.WatersplittingC.OxygenreleaseD.GlucoseproductionE.Nitrogenfixation8.MajorriversinAsiainclude:A.TheNileB.TheYangtzeC.TheAmazonD.TheGangesE.TheYellowRiver9.Theoriesofrelativityinclude:A.SpecialrelativityB.GeneralrelativityC.QuantummechanicsD.StringtheoryE.Platetectonics10.Functionsofthehumanbraininclude:A.MemorystorageB.MovementcontrolC.DigestionregulationD.LanguageprocessingE.Emotionregulation四、案例分析（每題6分，共18分）案例1（數(shù)學）Acompanyproducesaproductwithafixedcostof\$5,000andavariablecostof\$20perunit.Thesellingpriceperunitis\$50.(a)Writethecostfunction\(C(x)\)andrevenuefunction\(R(x)\),where\(x\)isthenumberofunitsproduced.(b)Determinethebreak-evenpoint.(c)Calculatetheprofitfunction\(P(x)\)andfindtheprofitwhen200unitsareproduced.案例2（英語）Astudentwritesthefollowingsentence:"Thecatwaschasedbythedogquickly."(a)Identifythegrammaticalerror.(b)Rewritethesentencecorrectly.(c)Explainwhytheoriginalsentenceisincorrect.案例3（專業(yè)課）Aresearcherconductsanexperimenttotesttheeffectofanewdrugonbloodpressure.Thestudyinvolves50participants,with25receivingthedrugand25receivingaplacebo.Themeanbloodpressurebeforetreatmentis120mmHgforbothgroups.Aftertreatment,themeanbloodpressureforthedruggroupis115mmHg,whileitremains118mmHgfortheplacebogroup.(a)Whattypeofstudydesignisthis?(b)Identifytheindependentanddependentvariables.(c)Suggestastatisticaltesttocomparetheresults.五、論述題（每題11分，共22分）論述1（英語）Discusstheimportanceofcoherenceandcohesioninacademicwriting.Provideexamplestoillustratehowtheseelementscontributetotheclarityandeffectivenessofawrittenargument.論述2（數(shù)學）Explaintheconceptofalimitincalculus.Howdoesthelimitofafunctionrelatetoitscontinuityanddifferentiability?Provideexamplestosupportyourexplanation.---標準答案及解析一、判斷題1.×(Thepassivevoicecanbeusedinacademicwritingwhentheactorisunknownorirrelevant.)2.√3.√4.√5.×(Quantummechanicsdescribesmicroscopicparticles;classicalmechanicsappliestomacroscopicscales.)6.×(TheGreatWallisnotvisiblefromspacewithoutmagnification.)7.√8.√9.×(DNAwasdiscoveredbyFriedrichMiescher;Mendelstudiedinheritance.)10.×(Marsalsohasliquidwater,e.g.,inpolaricecaps.)二、單選題1.B2.B(\(\int_0^1x^2\,dx=\frac{x^3}{3}\Big|_0^1=\frac{1}{3}\))3.B4.C5.A6.B7.B8.C9.B10.A三、多選題1.A,B,E2.A,D,E3.A,B,E4.A,C,D5.A,B6.B,C7.A,B,C,D8.B,D,E9.A,B10.A,B,D,E四、案例分析案例1（數(shù)學）(a)\(C(x)=5000+20x\),\(R(x)=50x\)(b)Break-evenpoint:\(5000+20x=50x\)→\(30x=5000\)→\(x=\frac{5000}{30}\approx166.67\)units.(c)\(P(x)=R(x)-C(x)=50x-(5000+20x)=30x-5000\).Profitfor200units:\(P(200)=30(200)-5000=6000-5000=1000\).案例2（英語）(a)Theerroristheplacementof"quickly."(b)"Thedogquicklychasedthecat."(c)Intheoriginalsentence,"quickly"modifies"chased,"makingtheactionthesubjectoftheadverb.Thecorrectstructureplaces"quickly"aftertheverbtomodifyit.案例3（專業(yè)課）(a)Randomizedcontrolledtrial.(b)Independentvariable:Drug(drugvs.placebo).Dependentvariable:Bloodpressure.(c)Independentsamplest-test.五、論述題論述1（英語）Coherenceandcohesionareessentialinacademicwritingastheyensurethelogicalflowofideasandthesmoothconnectionbetweensentencesandparagraphs.Coherencereferstotheinternallogicofthetext,whilecohesioninvolvestheuseoflinguisticdevicesliketransitionwordsandpronouns.Fore