2022年河北省中考英语真题

机密★启用前

2022年河北省初中毕业生升学文化课考试

英语试卷

注意事项：1.本试卷共8页，总分120分，考试时间120分钟。

2.答题前，考生务必将姓名、准考证号填写在试卷和答题卡的相应位置。

3.所有答案均在答题卡上作答，在本试卷或草稿纸上作答无效。答题前，请仔细阅读答题卡

上的“注意事项”，按照“注意事项”的规定答题。

4.答选择题时，用2B铅笔将答题卡上对应题目的答案标号涂黑：答非选择题时，请在答题

卡上对应题目的答题区域内答题。

5.考试结束时，请将本试卷和答题卡一并交回。

听力部分

I.听句子，选出句子中所包含的信息（共5小题:每小题1分，满分5分）

1.A.ajobB.atalkC.aplan

2.A.buyfruitB.drinkteaC.cookrice

3.A.June1B.March12C.September10

4.A.They'Dtakeabreak.B.They'llreadatext.C.They'llplayagame.

5.A.Peterwillmeethisuncle,B.Peterwillgotohisuncle'scity.C.Peterwilltakehisuncletothe

airport.

II.听句子，选出该句的最佳答语（共5小题：每小题1分，满分5分）

6.A.Takeiteasy.B.Withpleasure.C.You,too.

7.A.Speaking.B.Ifsforyou.C.Thelineisbusy.

8.A.Ihopeso.B.ThafsOK.C.Gladtohearthat.

9.A.SureIdo.B.Youcandoit.C.Tmathome.

10.A.Goodidea!B.Goodnews!C.Goodluck!

III.听对话和问题，选择正确答案（共8小题：每小题1分，满分8分）

13.Whatshouldthegirlwriteonthecard?

A.Hername.B.Heraddress.C.Thedate.

14.Whatbooksdoesshewanttoborrow?

A.Medicinebooks.B.Historybooks.C.Artsbooks.

15.Howmanybooksdoessheborrowthistime?

A.One.B.Two.C.Three.

16.WhereisTom'smotherwalking?

A.Onthestreet.B.Onthegrass.C.Onthebeach.

17.Whoisbuyingbananas?

A.Tom.B.Tom'sfather.C.Tom'ssister.

18.Whatarethefamilydoing?

A.Flyingakite.B.Havingapicnic.C.Takingaphoto.

IV.听鼠文和问题、选择正确答案（共7小题；每小题1分，满分7分）

19.WhatdoesHenryaskAnntodo?

A.Jointhesoccerteam.B.Dosomerunning.C.Buysportsclothes.

20.Whattimewilltheymeettomorrow?

A.At9：00.B.At9：30.C.At10：00.

21.Whyshouldyoulistentotheotherpersoncarefully?

A.Toknowaboutmovies.B.Tounderstandexamples.C.Toaskhimquestions.

22.Whichisthebestanswertoa"no"question?

A.No.B.Never.C.No,but...

23.Howshouldyouspeakifyourpronunciationisalittledifferent?

A.Slowly.B.Loudly.C.Freely.

24.WhatshouldyoudowhenyoutravelinEnglish-speakingcountries?

A.Getamap.B.SpeakinEnglish.C.Askfriendsforhelp.

25.Whatisthespeakertalkingabout?

A.Howtomaketripsexciting.

B.Howtopracticeyourpronunciation.

C.HowtokeepanEnglishconversationgoing.

V.听短文填空（交5小题：每小题1分，满分5分）

InformationSheet

Name:Linda

Age:26._______________________yearsold

Comefrom:27._______________________

Hair:28.longand

Sport:29.oftenplay_______________________

Cometolearn:30._______________________

笔试部分

VI.单项选择（共10小题：每小题1分，满分10分）

选出可以填入空白处的最佳选项。

1.Whereisyourbrother?Iwanttogive_______abook.

A.meB.youC.himD.her

2.Look!Thefishisswimmingfast_______theriver.

A.atB.inC.ofD.by

3.Isawagoodfilm,______Ican'trememberitsname.

A.soB.orC.forD.but

4.-Michael,thisshirt.

一Oh,itlooksniceonme!

A.tryonB.putdownC.takeoffD.throwaway

5.________youcanuseyourdictionary,youwilllearnEnglishbetter.

A.IfB.UnlessC.ThoughD.Before

6.一DoIhavetohandinmyreportnow?

一Ofcourse,you________.We'regoingtodiscussit.

A.canB.can'tC.mustD.mustn't

7.Johniswaitingforme.We________tothebookstoretogether.

A.wentB.havegoneC.willgoD.weregoing

8.Atthistimeyesterday,I________ascienceexamhere.

A.takeB.wastakingC.amtakingD.willtake

9.Sorry,I________amistake.Letmecorrectit.

AwillmakeB.ammakingC.wasmakingD.havemade

10.一Mmm...Delicious.Whatisit?

——Itzongzi,Tony.It'satraditionalfoodinChina.

A.callsB.iscalledC.calledD.wascalled

VIL完形填空（共10小题；每小题1分，满分10分）

阅读下面短文，从各小题所给的四个选项中选出最佳选项。

Kevinisaspecialswimmer.Hetookrisksto11inverycoldplacesbecausehewantedpeopletopay

attentiontoenvironmentalproblems.

Asaboy,KevinvisitednationalparksandhelearnedtheEarthisin12condition.Hefeltworried,and

hewantedto13theEarth.In2009,hewenttoswiminwaternearNorthPoleG匕极）todrawpeople's

attentiontothemeltingglaciers（融化的冰川）.Kevinsaidthattheswimwassopainfulthatitwouldbehis

14timeswimmingincoldwater.In2016,heheardaboutalakeintheHimalayas（喜马拉雅山脉）.It

wasformedbymeltingglaciers.He15toswimincoldwateragain.Itwasdifficulttoswiminthelake.The

airwasso16thatitwashardtobreathe.HetoldpeopleabouthisexperiencesonTV.Hewantedpeopleto

knowthatglaciersintheHimalayasaredisappearing17global（全球的）warmingandthatthere'sless

waterforpeopleinnearby18likeChina,India,andPakistan.

FromKevin'sstory,welearntwo19.WelearnthatpeoplecandoalotofharmtotheEarthwithout

realizingit.Also,welearnthatifwe20thewaywethink,wecandosomethingtoprotectourenvironment.

Withthenewwayofthinkinginourminds,wecanenjoyabrightfuture.

11.A.flyB.swimC.runD.skate

12.A.rightB.safeC.poorD.natural

13.A.protectB.leaveC.findD.share

14.A.lastB.greatC.freeD.long

15.A.hatedB.agreedC.learnedD.decided

16.A.freshB.thinC.clearD.cool

17.A.becauseofB.oppositetoC.accordingtoD.insteadof

18.A.citiesB.countriesC.townsD.villages

19.A.choicesB.reportsC.reasonsD.lessons

20.A.askB.showC.changeD.record

W阅读理解（共15小题：每小题2分，满分30分）

阅读A、B、C、D四篇材料，然后从各小题所给的四个选项中选出最佳选项。

A

WelcometotheCityYouthClub.Findoutwhafsgoingon!

Areyou10-18yearsold?OpenMondaytoFriday.5pm-8pm.

Tellushere：

I'mEmily.Ilikedoingarts.Weoftenpaintpicturesandmakethingsattheclub.Wehaveahelperinthearts

room.He，sreallynice.Peopletalktohimabouttheirproblems.

I'mSam.There'saskateboardparkattheclubandIloveskateboarding.1don'thaveaskateboard,

butthat'sOK.Ithasskateboardsforpeopletouse.

I'mRose.Ilikerockclimbingandthere'sabigclimbingwallattheclub.Youcandorockclimbingon

MondaysandWednesdays.

I'mBob.There'sacoffeeshopandyoucanbuyfoodanddrinkthere.Ihelpinthecoffeeshopon

Fridays.

I'mMark.IworkattheclubonTuesdaysandThursdays.Tmavolunteer-Idon'tgetmoneyformywork.I

likehelpingpeople.

21.Whopaintspicturesandmakesthingsattheclub?

A.Sam.B.Bob.C.Rose.D.Emily.

22.Whencanyoudorockclimbingattheclub?

A.FromMondaytoFriday.B.FromTuesdaytoThursday.

C.OnMondaysandWednesdays.D.OnTuesdaysandThursdays.

23.WhatdoesMarkliketodoattheclub?

A.Helppeople.B.Sellfood.C.Makemoney.D.Goskateboarding.

B

LastyearIhadatripwithmyfriend,Nancy.Theweatherwascloudyexceptforonenight.NancyandIsalin

thefieldandwefeltrelaxed.Wetalkedaboutthefantastictrip,lookingatthestars."It'sapitywedon'tknow

whichstarswe'relookingat,Jenny,"saidNancy."IknowsomeofthemJIanswered.NancyfeltsurprisedwhenI

finallyfinishedtellingherallthenamesIknew.

MyinterestinstarsbeganwhenIwaseight.Myaunttookmetoaplanetarium（天文馆）.Aguideshowed

usthegroupsofstarsandtoldusstoriesabouthowtheygottheirnames.Thestorieswerewonderful.

Everyoneknowswecanseethestarsbetterwhenit'snotcloudy,butlotsofpeopledon'trealizethatabright

moonalsostopsusseeingverymuch.IalwayslookforthePlough（北斗星）,becauseonceIseethat,Icanfind

theNorthStarandotherstars.

Iwantedtolearnmoreaboutthestars,soItookacourseattheclub.Therearesomanylightsinthecitythat

wehavetogointothecountrysidetoseeanystars.Tmplanningtomakevideosaboutstarsinthecountryside.Til

postthemonlineforeveryonetowatch.Mygreatestdreamistobeanastronaut（宇航员）andIwishIcouldhave

aspacetravel.

24.HowdidNancyfeelafterJennytoldherthenamesofstars?

A.Relaxed.B.Surprised.C.Angry.D.Wonderful.

25.WhatisJennyplanningtodo?

A.Haveaspacetravel.B.Takecoursesonline.

C.Makevideosaboutstars.D.Giveatalkaboutnames.

26.WhichofthefollowingwouldJennyprobablyagreewith?

A.Studentsshouldmovetothecountryside.

B.Children'sfavoritehobbyistowritestories.

C.Thebestplacetowatchstarsisthecitycenter.

D.Abrightmoonmaystoppeopleseeingverymuch.

C

Presentation（展示）skillsareimportantatschoolandinotherareasoflifeSomepeopledon'tlikegiving

presentationsbecausetheydon'tknowwhattosayorbecausetheygetnervousaboutpublicspeaking.Here'ssome

advicetohelpyoumakepresentationseasierandmoreenjoyable.

1.Getorganised

Thebestpresentationsarewellplannedandclearlyorganized.Thinkabouttopics（话题）andchoosea

properone.Inonetopic,threeorfourmainideaswillbefine.Thebeginningofyourpresentationshouldbe

interesting.Forexample,youcantellashort,funnystorytomakepeoplelaugh.

2.Usephotosorvideos

Trytousephotosorvideos.Thesethingsmakeyourperformancemoreexcitingandhelpyourememberwhat

you'regoingtosay.However,youshouldn'tusetoomany.The"star"ofyourpresentationshouldbeyou,notyour

photosorvideos.

3.Practicebeforeyourperformance

Youneedtopracticemanytimesbeforethe“bigday”.Practicesayinganyunusualwords.Thenwritethemain

ideasonsmallcardstohelpyouremember.Practiceinfrontofamirrorandtimeyourpresentation.Finally,you

canrecordyourperformanceoraskafriendtowatchyouandthenmakesuggestionsforimprovements.

4.Connectwithyouraudience（观众）

Alwayslookattheaudiencewhenyouspeak.Standupstraight,butdon'tstandstillormovearoundmuch.

Finally,besuretothankyouraudiencewhenyoufinishspeaking.It?sasimplebutgoodwaytoendany

presentation.

27.Howcanyouinterestyourlistenersatthebeginning?

A.Bylistingyourideas.B.Bytellingafunnystory.

C.Bystandingupstraight.D.Bysayingsimplewords.

28.Whichisthe"bigday"accordingtothetext?

A.Thedayyoupreparevideos.B.Thedayyougetsomeadvice.

C.Thedayyouvisityourfriends.D.Thedayyoumakeapresentation.

29.Whatisthegoodwaytoendyourpresentation?

A.Torepeattopics.B.Toshowthanks.

C.Tomakesuggestions.D.Tosharemainideas.

30.Whichquestioncouldbesthelpusfindoutthewriter'spurpose?

ADidthewritertrytoteachusskills?

B.Didthewriterhelpusunderstandideas?

C.Didthewriterinviteustoattendacourse?

D.Didthewriteraskustobepoliteinpublic?

D

Nobodywantstolose,butwemustacceptthatlosingisapartoflife.Afterall,wecan'twinallthetime.

However,wecanlearnsomethingvaluablefromeveryfailure（失败）.Thismayhelpussucceedinthefuture.So

wemustknowhowtobeagoodloser.

Wemustnotbeafraidoflosing.Whenwelose,justtakeitwithasmileandlookonthebrightsideofit.

Failurecan'tbeavoidedinourlife.Edisonfailed10,000timesbeforeheinventedthelightbulb（灯泡）.When

hewasaskedhowhefelt,hesaidthathehadn'tfailed10,000timesbuthadlearned10,000thingswhichdidn't

work.Wemustknowthathistoryisfullofexamplesofmenandwomenwhoachievedsuccessalthoughtheyfailed

manytimes.

Losingisnotverydisgraceful.Wemustacceptourfailureandlearntotakeadvantageofit.Rememberthatit

canbehelpful.Takeactiontowalkoutofit.Whenwelose,thinkaboutwhatwedidandhowwecanimprove.If

someoneelsecanhelp,we'Hbeluckyenough.Maybeheorshehasbeenthroughthesameexperiencebefore.

Manypeopleenjoyhelpingotherssolveproblems.Thiscansaveusalotoftimeinlearninghowtoavoidthesame

mistakesinthefuture.

Weshouldfaceourfailurewhenwelose.Thereisonlyonewinnerineverycompetition.Somewin,while

somelose.Thatisausualwayoflife.Ifweofferourcongratulations（祝贺）tothewinnersandshareintheir

happiness,wewon'tfeelsorryforourfailure.

Inaword,beingagoodloserwillhelpustosucceedinlife.Itmightbepainfulatthebeginning,butthereare

manyadvantages.Goodloserssetexamplestous,andmostimportantly,theyfinallywin.

31.Whatcanwelearnfromeveryfailureaccordingtothetext?

A.Awayoflife.B.Avaluablething.C.Ageneralrule.D.Asecretofsuccess.

32.Inthewriter'seyes,whydidEdisonachievesuccess?

A.Hegothelpfromothers.B.Hehappenedtomakeit.

C.Heavoidedpossiblemistakes.D.Hesawthebrightsideoflosing.

33.Whatdoestheunderlinedword“disgraceftil”probablymean?

A.Bad.B.Personal.C.Dangerous.D.Interesting.

34.Whatdoesthewriteradvisetheloserstodoinacompetition?

A.Expresstheregrets.B.Forgetthefailure.

C.Shareinthewinners'enjoyment.D.Joininanothercompetition.

35.Whatisthebesttitleforthetext?

A.IdeasaboutHowtoAvoidMistakesB.ExperienceinDealingwithProblems

C.AdviceonHowtoBeaGoodLoserD.AdvantagesofbothSuccessandFailure

IX.任务型阅读（共5小题；每小题2分，满分10分）

阅读下面短文，按要求完成各题。

“Icouldtellitwashimbythewayhewalked."Ifyou'veeversaidthat,youunderstandbiometrics（生物识

另ll技术）.Biometrictechnologyisanimportanttopicinourworkandprivatelives.Itincludestheuseoffinger

printsorknowingaperson'svoice.Itisthescienceaboutwhatapersonlookslikeandhowapersondoesthings.

Liketreeleaves,notwohumanbeingsareexactlythesame.They'vegotdifferenteyesanddifferenthair.And

everyonehasadifferentwayofwalkingormoving.

Thistechnologycantellyoufromothers.Atthemomentifyoutravelthroughanairport,youneedyourID

cardorpassport.Ifyougotoyourbanktogetsomemoney,youneedacardandaspecialnumber.Butwhatshould

youdoifyouloseyourpassportorforgetyournumber?Biometrictechnologycansolvethisproblem.The

technologyisbecomingmoreandmorepopularwitholdpeoplebecausetheynolongerneedtoremembertheir

passwords（密码）.

Thistechnologyisallaroundusinourlife.Weusethemtounlockasmartphone,getintoourhomes,startour

carswithoutakeyorevenpayforourshopping.

Nothingisperfect.Peopleareworriedaboutthesafetyoftheirprivateinformation.However,thetechnology

willbecomemuchbetterinthefuture,anditwillbecomemoreandmoreimportantinourdailylife.

1题完成句子；2、3题简略回答问题；4题找出并写下第二段的主题句；5题将画线句子译成汉语。

36.Biometrictechnologyincludesorknowingaperson'svoice.

37.Whatarepeopleworriedabout?

38.Wherecanthetechnologybeusedaccordingtothetext?（至少写出文中提到的两个地方）

39.

40.

X.词语运用（共10小题；每小题1分，满分10分）

阅读下面短文，在空白处填入一个适当的单词(有提示词的，填入所给单词的正确形式)。

Mrs.Zhangismyneighbor.Herhouseisnextto41(my).Sheisawarmand42(friend)

person.Sheispopularamongus.Shealways43(like)tohelpothers.Andsheoftenaskspeople

44shecandoforthem.Sheoftensayshello45mefromherfrontgardenwhenIcomebackhome.

Sheplantsdifferent46(kind)ofbeautifulflowersinhergarden.ItwasMrs.Zhang'sbirthdaylast

Saturday.Sheheldapartyand47(invite)alltheneighbors.Shemade48verybigcakewithfresh

flowersonit.Itwasmy49(one)timetoseesuchacake.Ithoughtitwasthe50(nice)cakeI

hadevereaten.Wesang,dancedandtalkedanditwasreallyagreattime.

XL基础写作(包括A、B两部分，A部分5分，B部分15分，共20分)

A)连词成句(共5小题；每小题1分，满分5分)

将所给词语连成句子，要求符合语法，语句通顺，大小写正确，词语不得重复使用。句末标

点已给出。

51.beautiful,thepark,how,is

_____________________________________!

52.green,I,trees,like,the

53.at,overthere,look,thesign

54.what,it,say,does

9

55.can't,we,it,climbtrees,says

B)书面表达(满分15分)

56.假如你是学校英文网站的主编，准备在网站设立DialoguewithTeachers专栏(column).

请根据下面的提示写一篇短文，谈一谈设立此专栏的目的。

提示：(1)Developagoodrelationship(understand,becomefriends).

(2)Givesomesuggestions(onhomework,after-schoolactivities,...).

注意：(1)短文须包括提示中的两个要点，可适当发挥。

(2)文中不得出现真实的地名、校名和人名。

(3)词数80个左右(开头已给出，不计入总词数)。

Weplantohaveanewcolumn——DialoguewithTeachersontheschoolEnglishwebsite.

机密★启用前

2022年河北省初中毕业生升学文化课考试

英语试卷

注意事项：1.本试卷共8页，总分120分，考试时间120分钟。

2.答题前，考生务必将姓名、准考证号填写在试卷和答题卡的相应位置。

3.所有答案均在答题卡上作答，在本试卷或草稿纸上作答无效。答题前，请仔细阅读答题卡

上的“注意事项”，按照“注意事项”的规定答题。

4.答选择题时，用2B铅笔将答题卡上对应题目的答案标号涂黑：答非选择题时，请在答题

卡上对应题目的答题区域内答题。

5.考试结束时，请将本试卷和答题卡一并交回。

听力部分

I.听句子，选出句子中所包含的信息（共5小题:每小题1分，满分5分）

1.A.ajobB.atalkC.aplan

2.A.buyfruitB.drinkteaC.cookrice

3.A.June1B.March12C.September10

4.A.They'Dtakeabreak.B.They'llreadatext.C.They'llplayagame.

5.A.Peterwillmeethisuncle,B.Peterwillgotohisuncle'scity.C.Peterwilltakehisuncletothe

airport.

II.听句子，选出该句的最佳答语（共5小题：每小题1分，满分5分）

6.A.Takeiteasy.B.Withpleasure.C.You,too.

7.A.Speaking.B.Ifsforyou.C.Thelineisbusy.

8.A.Ihopeso.B.ThafsOK.C.Gladtohearthat.

9.A.SureIdo.B.Youcandoit.C.Tmathome.

10.A.Goodidea!B.Goodnews!C.Goodluck!

IIL听对话和问题，选择正确答案（共8小题：每小题1分，满分8分）

11.WhatisLilydoing?

12.Wherewilltheygo?

13.Whatshouldthegirlwriteonthecard?

A.Hername.B.Heraddress.C.Thedate.

14.Whatbooksdoesshewanttoborrow?

A.Medicinebooks.B.Historybooks.C.Artsbooks.

15.Howmanybooksdoessheborrowthistime?

A.One.B.Two.C.Three.

16.WhereisTom'smotherwalking?

A.Onthestreet.B.Onthegrass.C.Onthebeach.

17.Whoisbuyingbananas?

ATom.B.Tom'sfather.C.Tom'ssister.

18.Whatarethefamilydoing?

A.Flyingakite.B.Havingapicnic.C.Takingaphoto.

IV.听施文和问题、选择正确答案（共7小题；每小题1分，满分7分）

19.WhatdoesHenryaskAnntodo?

A.Jointhesoccerteam.B.Dosomerunning.C.Buysportsclothes.

20.Whattimewilltheymeettomorrow?

A.At9：00.B.At9：30.C.At10：00.

21.Whyshouldyoulistentotheotherpersoncarefully?

A.Toknowaboutmovies.B.Tounderstandexamples.C.Toaskhimquestions.

22.Whichisthebestanswertoa"no"question?

A.No.B.Never.C.No,but...

23.Howshouldyouspeakifyourpronunciationisalittledifferent?

A.Slowly.B.Loudly.C.Freely.

24.WhatshouldyoudowhenyoutravelinEnglish-speakingcountries?

A.Getamap.B.SpeakinEnglish.C.Askfriendsforhelp.

25.Whatisthespeakertalkingabout?

A.Howtomaketripsexciting.

B.Howtopracticeyourpronunciation.

C.HowtokeepanEnglishconversationgoing.

V.听短文填空（共5小题：每小题；分，满分5分）

InformationSheet

Name:Linda

Age:26._______________________yearsold

Comefrom:27._______________________

Hair:28.longand_______________________

Sport:29.oftenplay_______________________

Cometolearn:30._______________________

笔试部分

VI.单项选择（共10小题：每小题1分，满分10分）

选出可以填入空白处的最佳选项。

【1题答案】

【答案】c

【2题答案】

【答案】B

【3题答案】

【答案】D

【4题答案】

【答案】A

【5题答案】

【答案】A

【6题答案】

【答案】C

【7题答案】

【答案】C

【8题答案】

【答案】B

【9题答案】

【答案】D

【10题答案】

【答案】B

VIL完形填空（共10小题；每小题1分,满分10分）

题答案】

【答案】ILB12.C13.A14.A15.D16.B17.A18.B19.D20.C

W阅读理解（共15小题：每小题2分，满分30分）

阅读A、B、C、D四篇材料,然后从各小题所给的四个选项中选出最佳选项。

A

[21-23题答案】

【答案】21.D22.C23.A

【24~26题答案】

【答案】24.B25.C26.D

【27~30题答案】

【答案】27.B28.D29.B30.A

D

【31~35题答案】

【答案】31.B32.D33.A34.C35.C

IX.任务型阅读（共5小题；每小题2分，满分10分）

【36~40题答案】

【答案】36.theuseoffingerprints

37.Peopleareworriedaboutthesafetyoftheirprivateinformation.

38.Weusethemtounlockasmartphone,getintoourhomes.（至少写出文中提到的两个地方）

39.Thistechnologycantellyoufromothers.

40.这种技术在我们的生活中无处不在。

X.词语运用（共10小题；每小题1分，满分10分）

【41〜50题答案】

【答案】41.mine

42.friendly

43.likes44.what

45.to46.kinds

47.invited

48.a49.first

50.nicest

XL基础写作（包括A、B两部分，A部分5分，B部分15分，共20分）

A）连词成句（共5小题；每小题1分，满分5分）

将所给词语连成句子，要求符合语法，语句通顺，大小写正确，词语不得重复使用。句末标

点已给出。

[51题答案】

【答案】Howbeautifultheparkis

【52题答案】

【答案】Ilikethegreentrees

【53题答案】

【答案】Lookatthesignoverthere

【54题答案】

【答案】Whatdoesitsay

[55题答案】

【答案】Itsayswecan'tclimbtrees

B）书面表达（满分15分）

[56题答案】

【答案】例文

Weplantohaveanewcolumn—DialoguewithTeachersontheschoolEnglishwebsite.Wehopetohelp

studentsandteachersunderstandeachotherandeventuallybecomegoodfriendsthroughthiscolumn.Ifyouhave

anyquestions,youcanasktheteacherdirectlythroughthecolumn,andtheteacherwillreplyontime.

Atthesametime,someteacherswillputforwardsomesuggestionsonhowtoworkefficientlyandsolve

problems.Ofcourse,wewillalsomakesuggestionsforafter-schoolactivities.Whentheexamcomes,some

teacherswillgivesomesuggestionsonhomeworkandhowtoreview.赠送：

初中数学必考定理公式汇编

一、数与代数

1.数与式

(1)实数

实数的性质：

①实数a的相反数是一a,实数a的倒数是[(aWO)；

a

②实数a的绝对值：

a(a>0)

\a\=<0(〃=0)

-a(a<0)

③正数大于0,负数小于0,两个负实数，绝对值大的反而小。

二次根式：

①积与商的方根的运算性质：

4ab-4a-4b(a20,bNO);

口=巧(a20,b>0)；

\by[b

②二次根式的性质：

而用二,(心。)

11[-a(a<0)

(2)整式与分式

①同底数塞的乘法法则：同底数幕相乘，底数不变，指数相加，即

(m、n为正整数)；

②同底数塞的除法法则：同底数基相除，底数不变，指数相减，即/+优

(aNO,m、n为正整数，m>n)；

③累的乘方法则：塞的乘方，底数不变，指数相乘，即(仍)"=优优(n为正整

数)；

④零指数：a°=1(aWO)；

⑤负整数指数：a-n=—（ar0,n为正整数）；

an

⑥平方差公式：两个数的和与这两个数的差的积等于这两个数的平方，即

（〃+/?）（〃一/?）=a2-b2；

⑦完全平方公式：两数和（或差）的平方，等于它们的平方和，加上（或减

去）它们的积的2倍，BP（a+b）2=a2+2ab+h2

分式

①分式的基本性质：分式的分子和分母都乘以（或除以）同一个不等于零的

整式，分式的值不变，即q=伫%；0=生士，其中m是不等于零的代数式；

bbxmbb-i-m

②分式的乘法法则：

bdbd

③分式的除法法则：（C^O）；

bdbcbe

④分式的乘方法则：（*"=《（n为正整数）；

⑤同分母分式加减法则：-±-=—;

CCC

⑥异分母分式加减法则：-±-=^^;

cbbe

2.方程与不等式

①一元二次方程ax2+hx+c^O（aW0）的求根公式：

—b+yb~-4czc,2A、m

x=-------------------（b-4ac>0）

la

②一元二次方程根的判别式：A=^_4ac叫做一元二次方程以2+以+°=0（a

r0）的根的判别式：

△>00方程有两个不相等的实数根;

△=0。方程有两个相等的实数根；

A<0=方程没有实数根；

③一元二次方程根与系数的关系：设修、*2是方程加+陵+。=0（aWO）的

两个根，那么匹+W=/，再/二£；

aa

不等式的基本性质：

①不等式两边都加上（或减去）同一个数或同一个整式，不等号的方向不

变；

②不等式两边都乘以（或除以）同一个正数，不等号的方向不变；

③不等式两边都乘以（或除以）同一个负数,不等号的方向改变；

3.函数

一次函数的图象：函数y=kx+b（k、b是常数，kWO）的图象是过点（0,b）且

与直线y=kx平行的一条直线；

一次函数的性质：设y=kx+b（kWO）,则当k>0时、y