2021年北京卷英语高考真题

2021年普通高等学校招生全国统一考试

北京卷・英语

本试卷共11页，共100分.考试时长90分钟.考生务必在答题卡指定区域作答,

在试卷上作答无效.考试结束后，将本试卷和答题卡一并交回.

第一部分知识运用（共两节，30分）

第一节（共10小题；每小题1.5分，共15分）

阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选

出最佳选项，并在答题卡上将该项涂黑.

Recently,Itookatriphomebytrain.Igotaseatoppositeamiddle-agedmanwithsharp

eyes,whokept1ayoungwomaninawindowseatwithalittleboyonherlap.Thewoman's

eyefellontheman'sface,andsheimmediatelylookeddownand2herscarf.

Asthenightworeon,peoplebegantoclosetheireyes,buttheseatsweresouncomfortable

thatonlyaveryheavysleepercouldmanagetogetany3.Thewomanlookedoveratthe

man.Hewasstillstaringather.Shelookedbackathimwithfireinhereyes.Iwasbeginningto

get4,too.

Thetrainmovedon.Thelittleboywas5awakeonhismother'slap,butthewoman

droppedofftosleep.Amomentlater,hebeganto6thehalf-openwindow-onelegwentover

it.Themanjumpedupand7thechildjustbeforehefellout.

The8wokeupthewoman.Sheseemedtobein9,andthenrealitydawned（显

现）・"Yourchildhasbeenlookingforanopportunitytoclimboutofthewindow,9,themansaidas

hegavethechildbacktoher..”SoIhavebeenwatchingthewholetime.nThewomanwas

10?andsowasI.

1.A.guidingB.botheringC.watchingD.monitoring

2.A.adjustedB.changedC.packedD.waved

3.A.airB-joyC.spaceD.rest

4.A.nervousB.embarrassedC.angryD.disappointed

5.A.almostB.stillC.hardlyD.even

6.A.dragB.climbC.knockD.push

7.A.grabbedB.rockedC.touchedD.picked

8.A.alamB.quarrelC.riskD.noise

9.A.sorrowB.reliefC.panicD.pain

10.A.astonishedB.confusedC.concernedD.inspired

第二节（共10小题；每小题1.5分,共15分）

阅读下列短文，根据短文内容填空.在未给提示词的空白处仅填写1个恰当

的单词，在给出提示词的空白处用括号内所给词的正确形式填空.请在答题卡指

定区域作答.

A

Whydowedream?Scientistsaren'tcompletelysure,andtheyhavediverse11

（idea）.Dreamsmightbeasideeffectofmemorymaking.Whenyousleep,yourbrainsorts

througheverything12happenedduringtheday,tryingtolinknewexperiencestoold

memories.Asit13（connect）things,yourbrainturnsthemintoastory,andyougeta

dream.

B

Samisanin-real-lifestreamer（播主），andhelivestreamshimselfjustgoingabouthis

day.Whileridinghisbikehome14acoldnight,hecameacrossasad-lookingelderly

womanwanderingthestreetsbyherself.Thepoorwomanwasn'tabletogivehimanyinformation

about15shelived.Samwalkedhertoanearbyconveniencestoresothatshecould16

（safe）waitforthepolicetotakeherhome.

C

There17（be）adramaticriseinthenumberofextremeweathereventsoverthepast20

years,18（cause）largelybyrisingglobaltemperatures,accordingtoanewreportfromthe

UnitedNations.From2000to2019,therewere7,348majornaturaldisastersaroundtheworld,

19（result）inUSD2,970billionineconomicloss.Muchofthisincreasecanbeduetoclimate

change.Thefindingsshowacriticalneed20（invest）indisasterprevention.

第二部分阅读理解（共两节，38分）

第一节（共14小题；每小题2分，共28分）

阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项，

并在答题卡上将该项涂黑.

A

Ifyouareplanningtostartacareerinthefieldofeducation,science,orculture,thenan

internship（实习）atUNESCOwillbeidealforyou.

Whocanapply?

•Youhavecompletedyourfull-timeuniversitystudies；or

•Youarestudyinginagraduateprogramforamaster'sdegree.

•Applicantsintechnicalassignmentsmusthavereachedthelastyearoftheirstudiesina

technicalinstitution.

Whataretherequirements?

•Youmustbeatleast20yearsold.

•Youshouldhaveagoodcommand（掌握）ofeitherEnglishorFrench.

•Youmusthaveanexcellentknowledgeofoffice-relatedsoftware.

•Youshouldbeabletoworkwellinateamandadapttoaninternationalworking

environment.

•Youshouldpossessstronginterpersonalandcommunicationskills.

Whatdoyouneedtoprepare?

・Visa：Youshouldobtainthenecessaryvisas.

•Travel：Youmustarrangeandfinanceyourtraveltoandfromthelocationwhereyouwilldo

yourinternship.

•Medicalinsurance：Youmustshowproofofacomprehensivehealthinsurancevalid（有效

的）inthetargetcountryfortheentireperiodoftheinternship.UNESCOwillprovidelimited

insurancecoverageuptoUSD30,000fortheinternshipperiod.

•Medicalcertificate：Youmustprovideamedicalcertificateindicatingyouarefittowork.

•Motivationletter：Youshouldhaveyourmotivationletterreadybeforefillingoutthe

applicationform.

YourapplicationwillbeaccessedbyUNESCOmanagersandwillstayinourdatabaseforsix

months.Wedonotrespondtoeverycandidate.Ifselected,youwillbecontactedbyamanager.If

youdonotreceiveanyupdatewithinsixmonths,itmeansthatyourapplicationhasnotbeen

successful.

21.Accordingtothispassage,applicantsarerequiredto.

A.holdamaster'sdegreeinscience

B.haveinternationalworkexperience

C.befluentineitherEnglishorFrench

D.presentaletterfromatechnicalinstitution

22.WhatwillUNESCOprovidefortheinternshipperiod?

A.Limitedmedicalinsurancecoverage.

B.Trainingincommunicationskills.

C.Amedicalcertificateforwork.

D.Financialsupportfortravel.

23.Whatshouldapplicantsdobeforefillingouttheapplicationform?

A.ContactUNESCOmanagers.B.Getaccesstothedatabase.

C.Keepamotivationletterathand.D.Workinateamforsixmonths.

B

Irememberthedayduringourfirstweekofclasswhenwewereinformedaboutoursemester

（学期）projectofvolunteeringatanon-profitorganization.Whentheteacherintroducedusto

thedifferentorganizationsthatneededourhelp,mylastchoicewasOperationIraqiChildren

（OIC）.Myfirstimpressionoftheorganizationwasthatitwasnotgoingtomakeenoughofa

differencewiththeplansIhadinmind.

Then,anOICrepresentativegaveussomedetails,whichsomewhatinterestedme.After

doingsomeresearch,Ibelievedthatwecouldreallydosomethingforthosekids.WhenIwent

onlinetotheOICwebsite,IsawpicturesoftheIraqichildren.Theirfacesweresopowerfulin

sendingamessageoftheirdespair（绝望）andneedthatIjoinedthisprojectwithout

hesitation.Wedecidedtocollectasmanyschoolsuppliesaspossible,andmakethemintokits——

——onekit,onechild.

Themostrewardingdayforourgroupwasprojectday,whenalltheeffortsweputinto

collectingtheitemsfinallycametogether.WhenIsawthevarioussupplieswehadcollected,ithit

methateverykitweweretobuildthatdaywouldeventuallybeinthehandsofanIraqi

child.Overthepastfourmonths,IhadneverimaginedhowIwouldfeelonceourprojectwas

completed.Whilemakingthekits,IrealizedthatIhadlostsightofthetruemeaningbehindit.I

hadonlyfocusedonthefactthatitwasanotherschoolprojectandoneIwantedtogetagood

gradeon.Whenthekitswerecompleted,andreadytobesentoverseas,thewarmfeelingIhad

wasoneIwouldneverforget.

Inthebeginning,Idaredmyselftomakeadifferenceinthelifeofanotherperson.Nowthat

ourprojectisover,IrealizethatIhaveaffectednotonlyonelife,butten.Withourefforts,ten

youngboysandgirlswillnowbeabletofurthertheireducation.

24.HowdidtheauthorfeelaboutjoiningtheOICprojectinthebeginning?

A.Itwouldaffecthis/herinitialplans.

B.Itwouldinvolvetravelingoverseas.

C.Itwouldnotbringhim/heragoodgrade.

D.Itwouldnotliveuptohis/herexpectations.

25.Whatmainlyhelpedtheauthorchangehis/herattitudetowardtheproject?

A.ImagesofIraqichildren.B.Researchbyhis/herclassmates.

C.Ateacher'sintroduction.D.Arepresentative^comments.

26.Theauthor'sOICprojectgroupwouldhelptenIraqichildrento..

A.becomeOICvolunteersB.furthertheireducation

C.studyinforeigncountriesD.influenceotherchildren

27.Whatcanweconcludefromthispassage?

A.One'spotentialcannotalwaysbeunderrated.

B.Firstimpressioncannotalwaysbetrusted.

C.Actionsspeaklouderthanwords.

D.Hewhohesitatesislost.

C

Hundredsofscientists,writersandacademicssoundedawarningtohumanityinanopen

letterpublishedlastDecember：Policymakersandtherestofusmustengageopenlywiththerisk

ofglobalcollapse.Researchersinmanyareashaveprojectedthewidespreadcollapseas”a

crediblescenario（情景）thiscentury

Asurveyofscientistsfoundthatextremeweatherevents,foodinsecurity,andfreshwater

shortagesmightcreateglobalcollapse.Ofcourse,ifyouareanon-humanspecies,collapseiswell

underway.

Thecallforpublicengagementwiththeunthinkableisespeciallygermaneinthismomentof

still-uncontrolledpandemicandeconomiccrisesintheworld'smosttechnologicallyadvanced

nations.Notverylongago,itwasalsounthinkablethataviruswouldshutdownnationsandthat

safetynetswouldbeprovensodisastrouslylackinginflexibility.

Theinternationalscholars'warningletterdoesn'tsayexactlywhatcollapsewilllooklikeor

whenitmighthappen.Collapseology,thestudyofcollapse,ismoreconcernedwithidentifying

trendsandwiththemthedangersofeverydaycivilization.Amongthesignatories（签署者）ofthe

warningwasBobJohnson,theoriginatoroftheuecologicalfootprintconcept,whichmeasures

thetotalamountofenvironmentalinputneededtomaintainagivenlifestyle.Withthecurrent

footprintofhumanity,“itseemsthatglobalcollapseiscertaintohappeninsomeform,possibly

withinadecade,certainlywithinthiscentury,“Johnsonsaidinanemail.

Onlyifwediscusstheconsequencesofourbiophysicallimits,theDecemberwarningletter

says,canwehavethehopetoreducetheiraspeed,severityandharm.Andyetmessengersof

thecomingdisturbancearelikelytobeignored.Weallwanttohopethingswillturnoutfine.As

apoetwrote,

Manisavictimofdope（麻醉品）

Intheincurableformofhope.

Thehundredsofscholarswhosignedtheletterareintent（执着）onquietinghopethat

ignorespreparedness."Let'slookdirectlyintotheissueofcollapse,heysay,“anddealwiththe

terriblepossibilitiesofwhatweseetheretomakethebestofatroublingfuture.”

28.Whatdoestheunderlinedword"germane”inParagraph3probablymean?

A.Scientific.B.Credible.

C.Original.D.Relevant.

29.Asforthepublicawarenessofglobalcollapse,theauthoris.

A.worriedB.puzzled

C.surprisedD.scared

30.Whatcanwelearnfromthispassage?

A.Thesignatoriesmaychangethebiophysicallimits.

B.Theauthoragreeswiththemessageofthepoem.

C.Theissueofcollapseisbeingprioritized.

D.Theglobalcollapseiswellunderway.

D

Earlyfifth-centuryphilosopherSt.Augustinefamouslywrotethatheknewwhattimewas

unlesssomeoneaskedhim.AlbertEinsteinaddedanotherwrinklewhenhetheorizedthattime

variesdependingonwhereyoumeasureit.Today'sstate-of-the-artatomic（原子的）clockshave

provenEinsteinright.Evenadvancedphysicscan'tdecisivelytelluswhattimeis,becausethe

answerdependsonthequestionyou'reasking.

Forgetabouttimeasanabsolute.Whatif,insteadofconsideringtimeintermsofastronomy,

werelatedtimetoecology?Whatifweallowedenvironmentalconditionstosetthetempo（节奏）

ofhumanlife?We'reincreasinglyawareofthefactthatwecan'tcontrolEarthsystemswith

engineeringalone,andrealizingthatweneedtomoderate（调节）ouractionsifwehopetolivein

balance.Whatifourdefinitionoftimereflectedthat?

Recently,Iconceptualizedanewapproachtotimekeepingthat'sconnectedtocircumstances

onourplanet,conditionsthatmightchangeasaresultofglobalwarming.We'renowbuildinga

clockattheAnchorageMuseumthatreflectsthetotalflowofseveralmajorAlaskanrivers»which

aresensitivetolocalandglobalenvironmentalchanges.We'veprogrammedittomatchanatomic

clockifthewaterwayscontinuetoflowattheirpresentrate.Iftheriversrunfasterinthefutureon

average,theclockwillgetaheadofstandardtime.Iftheyrunslower,you'llseetheopposite

effect.

Theclockregistersbothshort-termirregularitiesandlong-termtrendsinriverdynamics.It*s

asortofobservatorythatrevealshowtheriversarebehavingfromtheirowntemporalframe（时

间框架），andallowsustowitnessthosechangesonoursmartwatchesorphones.Anyonewho

optstogoonAlaskaMeanRiverTimewillliveinharmonywiththeplanet.Anyonewho

considersrivertimeinrelationtoatomictimewillencounteramajorimbalanceandmaybe

motivatedtocounteractitbyconsuminglessfuelorsupportinggreenerpolicies.

Evenifthismethodoftimekeepingisnovelinitsparticulars,earlyagriculturalsocietiesalso

connectedtimetonaturalphenomena.Inpre-ClassicalGreece,forinstance,peopleucorrected

officialcalendarsbyshiftingdatesforwardorbackwardtoreflectthechangeofseason.Temporal

connectiontotheenvironmentwasvitaltotheirsurvival.Likewise,rivertimeandother

timekeepingsystemswe'redevelopingmayencourageenvironmentalawareness.

WhenSt.Augustineadmittedhisinabilitytodefinetime,hehighlightedoneoftime*smost

noticeablequalities：Timebecomesmeaningfulonlyinadefinedcontext.Anytimekeepingsystem

isvalid,andeachisaspraiseworthyasitspurpose.

31.WhatisthemainideaofParagraph1?

A.Timekeepingisincreasinglyrelatedtonature.

B.Everyonecandefinetimeontheirownterms.

C.Thequalitiesoftimevarywithhowyoumeasureit.

D.Timeisamajorconcernofphilosophersandscientists.

32.TheauthorraisesthreequestionsinParagraph2mainlyto.

A.presentanassumptionB.evaluateanargument

C.highlightanexperimentD.introduceanapproach

33.Whatcanwelearnfromthispassage?

A.Thosewhodonotgoonrivertimewillliveanimbalancedlife.

B.NewwaysofmeasuringtimecanhelptocontrolEarthsystems..

C.Atomictimewillgetaheadofrivertimeiftheriversrunslower.

D.Modemtechnologymayhelptoshapetherivers9temporalframe.

34.Whatcanweinferfromthispassage?

A.Itiscrucialtoimprovethedefinitionoftime.

B.Afixedframewillmaketimemeaningless.

C.Weshouldliveinharmonywithnature.

D.Historyisamirrorreflectingreality.

第二节（共5小题；每小题2分，共10分）

根据短文内容，从短文后的七个选项中选出能填入空白处的最佳选项，并

在答题卡上将该项涂黑.选项中有两项为多余选项.

Musichaslongbeenconsideredtobeanenjoyablepastimeformanypeople.35

Thementalhealthbenefitsfrommusiccan'tbeargued.Musiccouldalsobehelpingyouwith

manyotherhealthproblemsbehindthescenes.

36However,forthesamereason,musiccanbeverybeneficialifoneisinpain.By

distracting（分心）themindfromthepain,music,peoplesay,canlowerstressandanxiety

levels.This,ofcourse,canleadtolesspain.

Manypeopleenjoyrelaxingmusicintheeveningpriortogoingtobed.37Whilethe

validityoftheideaisstillbeingassessed,theloweredstresscanevenbetiedbacktoblood

pressure.Similarly,accordingtoresearchers,listeningtojust30minutesofsoftmusiceveryday

mayhelpwithhealthybloodsugarlevels,throughtheloweringofstressandanxiety.

Whenitcomestohearthealth,thereisspeculation（推测）thatit'snotthestyleofmusic,

butratherthetempothatmakesitsogoodforyourhearthealth.InoneEuropeanstudy,

participantslistenedtomusicastheresearchersmonitoredtheirheartratesandblood

pressure.38Ontheotherhand,whenthemusicslowed,theparticipants'stressand

anxietylevelsbecamelowerandtheeffectsonheartratesappearedtofollowsuit.

39Butthereisawholerangeofotherhealthissuesthatturninguptheradiocouldbe

beneficialfor,whichiswhatmakesmusicsovaluable.

A.Thisfeelingcanalsoresultinmanyotherhealthproblems.

B.Someexpertssaythatmusiccanbeharmfulifitistooloud.

C.Thisideaisalittleoff-the-wallbutstillhasscientificbacking.

D.Theysayitcanplayabigroleincalmingthebrainenoughtosleep.

E.Theimplicationsofmusiconoverallwell-beingarereallyimpressive.

F.Itisalsohighlypopularduetotheindividualizedeffectsonstressandanxiety.

G.Interestingly,themorecheerfulthemusicwas,thefastertheirheartrateswere.

第三部分书面表达（共两节，32分）

第一节（共4小题；第40、41题各2分，第42题3分，第43题5分，共12

分）

阅读下面短文，根据题目要求用英文回答问题.请在答题卡指定区域作答.

Recentresearchsuggeststhatifanargumentgetsresolved,theemotionalresponsetied

toitissignificantlyreducedoralmostcompletelyerased.Thus,itmaybeworthbringingupissues

withyourfriends,familymembers,orclassmatesratherthanholdingthemback.

Thereisadifferencebetweenarguingandfighting.Arguingisthatyouandyouropponent

presentyourconcernsanddiscussthefeelingsandissuesrelatedtothoseconcerns.Youcan

engageinanargumentrespectfullywithoutstirringup（激起）anger.Fighting,however,usually

involvespersonalattacks,raisingofvoices,andstormingout.Discussingyourissuesand

resolvingtheminsteadofstuffingthemdowncanimproveyouremotionalhealth.Inastudy,

2.000peoplewereaskedtorecordtheirfeelingsandexperiencesforeightdaysinarow.When

peoplehadanargumentthattheyconsideredresolved,theyhadhalfthereactivity（情绪反应）

ofthosewhoavoidedanargument.Reactivityisanincreaseinnegativeemotionsoradecreasein

positiveemotions.Inotherwords,resolvinganargumentcutsyournegativefeelingsbyhalf.One

daylater,peoplewhohadaresolvedargumentreportednoincreaseofnegativeemotions

comparedwiththosewhoavoidedanargument.Thismeansthatresolvinganargumentcanfeel

likeyouhavereachedastateofresolution—andyouarelesslikelytobeannoyed.

Moreover,theolderyouare,themorelikelyyouwillcometoaresolutionafteran

argument.Thismaybebecausemorelifeexperienceusuallyleadstomoredefinedpriorities.You

aremorelikelytodistinguishbetweenwhatmattersandwhatdoesnot.

Itiseasiertoavoidadiscussion,butriskingtalkingaboutitmayeventuallyleadtoabetter

outcome.

40.Accordingtothispassage,whatisarguing?

41.Whyisitthat“theolderyouare,themorelikelyyouwillcometoaresolutionafteran

argument：

42.Pleasedecidewhichpartisfalseinthefollowingstatement,thenunderlineitandexplain

why.

Resolvingargumentscanimproveyouremotionalhealth,becauseitincreasesyourreactivity

andreducesthechanceofyougettingangry.

43.Inadditiontoimprovingemotionalhealth,whatdoyouthinkaresomeotherbenefitsof

resolvinganargument?（Inabout40words）

第二节（20分）

假设你是红星中学高三学生李华.你和英国好友Jim原定本周末一起外出，你因故不能

赴约.请你用英文给他写一封电子邮件，内容包括：

1.表达歉意并说明原因；

2.提出建议并给出理由.

注意：1.词数100左右;

2.开头和结尾已给出，不计入总词数.

DearJim,

Yours,

LiHua

2021年普通高等学校招生全国统一考试（北京卷）

英语参考答案

第一部分知识运用（共两节，30分）

第一节（共10小题；每小题1.5分，共15分）

l.C2.A3.D4.C5.B

6.B7.A8.D9.C10.A

第二节（共10小题；每小题1.5分，共15分）

11ideasI2.that13.connects14.on15.where

16.safely17.hasbeen18.caused19.resulting20.toinvest

第二部分阅读理解（共两节，38分）

第一节（共14小题；每小题2分，共28分）

21.C22.A23.C24.D25.A

26.B27.B28.D29.A30.B

31.B32.D33.C34,C

第二节（共5小题；每小题2分，共10分）

35.F36.B37.D38.G39.E

第三部分书面表达（共两节，32分）

第一节（共4小题；第40、41题各2分，第42题3分，第43题5分，共12

分）

40.Arguingisdiscussingyourworries,relatedfeelingsandproblemswiththeotherparty.

41.Itisbecausemorelifeexperiencemayhelppeoplebetteridentifyprioritiesinlife.

42.Resolvingargumentscanimproveyouremotionalhealth,becauseitincreasesyourreactivity

andreducesthechanceofyougettingangry.

Resolvingargumentshelpstodecreaseyourreactivity.

43.略.

第二节（20分）

范文：

DearJim,

I'msorrythatIwon'tbeabletogohikingwithyouthisSaturday.

Ibegantocoughyesterdaymorning,soIwenttoseeadoctor.Shetoldmeitwasabadcold,

andIwouldhavetostayathomeforafewdays.

rdreallyliketospendsometimewithyou.IsitOKwithyouifwetakeatriptoZhangjiakou

nextSaturday?It*soneofthehostcitiesforthe2022WinterOlympics.Pleaseletmeknowwhat

youthink.

Again,I'msorryabouttheinconvenience.

Hopetohearfromyousoon.

Yours,

LiHua

2021年普通高等学校招生全国统一考试

数学

本试卷共4页，22小题，满分150分，考试用时120分钟。

注意事项：1.答卷前，考生务必将自己的姓名、考生号、考场号和座位号填写在答题卡上。用

2B铅笔将试卷类型(B)填涂在答题卡相应位置上，将条形码横贴在答题卡右上角“条形码粘贴

处”。

2.作答选择题时，选出每小题答案后，用28铅笔在答题卡上对应题目选项

的答案信息点涂黑：如需改动，用橡皮擦干净后，再选涂其他答案，答案不

能答在试卷上，

3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目

指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新答案：不准使用铅笔和涂

改液。不按以上要求作答无效。

4.考生必须保持答题卡的整洁，考试结束后，将试卷和答题卡一井交回。

一、选择题：本题共8小题，每小题5分，共40分。在每小题给出的四个选项中，只有一项是

符合题目要求的。

1.设集合A={x|-2<x<4}.B={2,3,4,5},!^AnB=

A.{2}B.{2,3}C.{3,4,}D.{2,3,4}

2.已知z=2-i,则(z(g+i)=

A.6-2iB.4-2iC.6+2iD.4+2i

3.已知圆锥的底面半径为近，其侧面展开图为一个半圆，则该圆锥的母线长为

A.2B.2v2C.4D.4及

4.下列区间中，函数f(x)=7sin(x—2单调递增的区间是

A.(0,E)B.(H,2c.(",—)D.(―,2

1111

5.已知RR是椭圆C亘+亡=1的两个焦点，点M在C上，则|MFj•|MFz|的最大值为

94

A.13B.12C.9D.6

6.若tan8=-2,则皿心皿.）=

sin§+COS6

A.一

B.二

C.-

D.-

7.若过点（a,b）可以作曲线y=e”的两条切线，则

A.eb<a

B.ea<b

C.0<a<eb

D.0<b<ea

8.有6个相同的球，分别标有数字1,2,3,4,5,6,从中有放回的随机取两次,每次取1个球，甲表

示事件“第一次取出的球的数字是1"，乙表示事件“第二次取出的球的数字是2”，丙表示事件

“两次取出的球的数字之和是8”，丁表示事件”两次取出的球的数字之和是7"，则

A.甲与丙相互独立

B.甲与丁相互独立

C.乙与丙相互独立

D.丙与丁相互独立

二、选择题：本题共4小题，每小题5分，共20分。在每小题给出的选项中，有多项符合题目

要求。全部选对的得5分，部分选对的得2分，有选错的得0分。

9.有一组样本数据x„xz,…,x„,由这组数据得到新样本数据y“力,…,y”其中

yi=Xi+c(i=l,2,―,n),c为非零常数，则

A.两组样本数据的样本平均数相同

B.两组样本数据的样本中位数相同

C.两组样本数据的样本标准差相同

D.两组样本数据的样本极差相同

10.已知0为坐标原点，点Pi(cosa,sina),P2(cos6,-sing),P3(cos(a+0),sin(a+P)),

A(l,0),则

A.loKrioKi

B.IA^I=IAKI

C.OA^OK=OK^OK

D.OA^OK=OP.­OR,

11.已知点P在圆(x-5)2+(y-S)2=16上，点A(4,0),B(0,2),则

A.点P到直线AB的距离小于10

B.点P到直线AB的距离大于2

C.当NPBA最小时，PB|=3v<2

D.当NPBA最大时，|PB|=3V2

12.在正三棱柱ABC-月iBiQ中，AB=AAI=1,点P满足而=ABC+“BB；，其中入d[0,1],“e

[0,1],则

A.当入=1时，的周长为定值

B.当H=1E1寸，三棱锥P-&BC的体积为定值

C.当入=：时，有且仅有一个点P,使得APJ.BP

D.当匕=驹，有且仅有一个点P,使得AJU平面AB$

三.选择题：本题共4小题，每小题5分，共20分

13.己知函数f(x)=x"a-2X-2-x)是偶函数，则a=

14.已知0为坐标原点，抛物线C：y2=2px(p>0)的焦点为F,P为C上一点，PF与x轴垂直，Q为x

轴上一点，且PQL0P,若|FQ|=6,则C的准线方程为一

15.函数f(x)=|2x-l|-21nx的最小值为

16.某校学生在研究民间剪纸艺术时，发现此纸时经常会沿纸的某条对称轴把纸对折.规格为

20dmX12dm的长方形纸.对折1次共可以得到10dmX2dm.20dmX6dm两种规格的图形，它们的面

积之和又=240dm；对折2次共可以得5dmXl2dHi,10dmX6dm,20dmX3dm三种规格的图形,它们的

面积之和5：=180dm-'.以此类推.则对折4次共可以得到不同规格图形的种数为_____:如果对折

n次，那么Z；s父=______dm2

四、解答题：本题共6小题，共70分，解答应写出文字说明、证明过程或演算步骤。

17.(10分)已知数列｛/｝满足%=1,%+，片—个饕

5+2,n为偶数

⑴记7=1,写出比，b2,并求数列他小的通项公式;

⑵求｛/｝前前20项和

18.(12分)

某学校组织“一带一路"知识竞赛，有A,B两类问题•每位参加比赛的同学先在两类问题

中选择类并从中随机抽I仅一个问题问答，若回答错误则该同学比赛结束；若回答正确则从另一

类问题中再随机抽取一个问题回答，无论回答正确与否，该同学比赛结束.A类问题中的每个问

题回答正确得20分，否则得0分：B类问题中的每个问题回答正确得80分，否则得0分。

己知小明能正确回答A类问题的概率为0.8,能正确回答B类问题的概率为0.6.且能正确

回答问题的概率与回答次序无关。

(1)若小明先回答A类问题，记X为小明的累计得分，求X的分布列：

(2)为使累计得分的期望最大，小明应选择先回答哪类问题？并说明理由。

19.(12分)

记AABC的内角A,B,C的对边分别为a.,b.,c,己知》2=ac,点D在边AC上，BDsin

ZABC=asinC.

(1)证明：BD=b：

(2)若AD=2DC.求cosNABC.

20.(12分)

如图，在三棱锥A-BCD中.平面ABD_L平面BCD,

AB=AD.O为BD的中点.

(1)证明：0A±CD：

(2)若AOCD是边长为1的等边三角形.点E在"

棱AD上.DE=2EA.且二面角E-BC-D的大小