2022年黑龙江省齐齐哈尔市中考英语真题

二。二二年齐齐哈尔市初中学业考试

英语试卷

第一部分语言知识运用（共计55分）

I.单项选择（每小题1分，共10分）

从每小题所给的A、B、C三个选项中，选出一个能填入空白处的最佳选项。

1.MybrotherTomcanplayping-pongwell,buthecan'tplayviolin.

A.the;/B.the;theC./;the

2.一CouldyoupleasetellmehowIcanmakemorefriends?

一Sure.Ithinkbeinghonestisthefirst.

A.stepB.scoreC.sense

3.Inourcitymuseum,therearemanyoldthingsfromtwoyearsagoonshow.

A.thousandsB.thousandsofC.thousand

4.—HaveyouheardShenzhouXIVmannedspacecraft（载人飞船）wassentupsuccessfully?

一Wow,thatsounds.Howgreatourcountryis!

A.interestingB.excitingC.relaxing

5.Tilgotoseniorhighschoolsoon.Ican'tbelievehowfastthetime!

A.wentbyB.wentonC.wentoff

6.5Gtechnologyhasenteredeveryone'slife.Itwillbeusedsoon.

A.hardlyB.exactlyC.widely

7.一Father,TmafraidIcan'twintheEnglishcompetition.

—Believeinyourself,mygirl,andtellyourself.

A.don'tgiveupB.nottogiveupC.togiveup

8.一Whydoyouhavetimetolookafterthehomelessdogs?

—the"doublereduction^^policy（双减政策），Ihavemorefreetime.

A.BecauseofB.EventhoughC.Asfor

9.Sofar,redtourism（旅游业）quicklyandit'sbecomingmoreandmorepopular.

A.developedB.willdevelopC.hasdeveloped

10.Learningtowriteislearningtothink.,youwon'tknowthingsclearly.

A.ifyouwritethemdown

B.unlessyouwritethemdown

C.ifyouwon'twritethemdown

n.完形填空（每小题i分，共15分）

阅读短文，从每小题所给的A、B、C三个选项中，选出••个能填入空白处的最佳选项。

Haveyouarguedwithafriendordoneanythingyouregretted?IIit'shardtoputthingsright,

especiallywhenyourfeelingsarehurt.Knowing12toapologize（道歉）canhelpyoubecomefriends

againandunderstandwhyyouargue,13you'llseparatefromeachotherfbreve匚

Whydoyouargue?

Youargueforallkindsofreasons.Yourfriend'sideais14yoursaboutsomethingoryoursister

alwaysdrivesyoucrazy.Whenyouare15,youmaysayordosomethingtohurtothers.Arguingwith

othersisquitenormalbutit'simportantto16itandlearnfromit.

Whatdoesanapologymean?

Everybodymakesmistakesinhislife.Apologizingisagood17ofadmitting（承认）yourmistakes.

Infact,it'sverydifficulttosaysorrytoothers.Mostofthepeoplethinksayingsorrymeansregrettingwhatthey've

18done.Butaslongasyoudecidetocorrectyourmistakes,youshould19.It'sbelievedthata

goodapologyneedstoshowthatyou'retrulysorry,youwanttoberesponsibleforwhatyoudoandgetforgiveness

（原谅）.

Whatif（万一）ifsnotyourmistake?

Sometimesthemistakeshave20todowithyou,butanotherpersonmayforceyoutosaysorry.Be

suretotrytalkingaboutwhyyouargueatfirst.If21ofyoustillcanagreewitheachother,whatshould

youdo?Keep22andaskaparentorateacherforhelp.

Doesapologizingalwayswork?

AsfarasIknow,anapologyitself23beenough,sotrytoasksomeoneelsehowhefeltwhileyou

werearguing.Explainyoursidetoo,andmake24clearthatyou?11trytoavoidmakingthesamemistake

again.Anapologyisn'tamagicstick.Itmay25peopletimetounderstandandforgive.

11.A.PerhapsB.RecentlyC.Instead

12.A.whatB.whereC.how

13.A.andB.orC.so

14.A.differentfromB.similartoC.aswellas

15.A.happyB.boredC.angry

16A.solveB.refuseC.complain

17.A.hobbyB.wayC.reason

18.A.neverB.nearlyC.ever

19.A.goawayB.tryyourbestC.talkback

20.A.somethingB.anythingC.nothing

21.A.allB.neitherC.either

22.A.coolB.relaxedC.crazy

23.A.mustn'tB.maynotC.needn't

24.A.thatB.thisC.it

25.A.spendB.takeC.cost

nr短文改错（每小题i分，找出错误和改正错误各o.5分，共io分）

阅读短文，从原文的每一行中找出一处错误并改正，不加词，不删词。

(例如：Mymotheroftengoshoppingonweekends.go-goes)

WiththedevelopmentofChina,lotsofforeignermovetoChinabecause26

theyhaveastronglyinterestinitsculture.Aslongasapersonhasinterest,he27

canturnitintolove,William,whoisanAustralia,hasalreadylivedinChina28

for35years.HehasaChinesenamecallingWangAihuaandhisfriendscall29

himAihua.Inthe1980,hecametoChinaandworkedasateacheratacollege.30

HegraduallyfellinloveofChinaafterhetooka2-monthdrivearoundit.31

ThebeautifulplacesattractedAihua.HewassuchinterestedinChinathathe32

wantedtospreadChinesetraditionalculture.Buthewroteabout15books33-

onthedevelopmentofChinaindifferentperiods.Aihuawasprideofwhat34

hedoes.Inthefuture,hisloveforChinawillneverchange.35

W.交际运用(共20分)

(A)(每小题2分，共10分)

根据对话内容，从A到F选项中，选出能填入空白处的最佳选项，每个选项只使用一次，选项中有一项为

多余项。

A:Hello,Mike.Howwasyourvacation?

B:Ireallyhadagoodtime.

A:36

B:Tvebeentoaforestnearmyuncle'sfarm.

A:37

B:Iwenttherewithmyfriends.

A:38

B:For3days.Iexpecttogothereagain.

A:Luckyyou.Ihadtostayathome.ButFmplanningtotraveltoMountChangbai.

B:Oh,that'sagoodplace.Iwenttherethreeyearsago.

A:CanyougivesomeadviceonmytriptoMountChangbai?

B:39

A:OK,Tildoasyoutellme.40

B:Theyarefriendlyandyouwillenjoyyourselfthere.

A.Howlongdidyoustayintheforest?

B.Whatdoyouthinkofthepeoplethere?

C.Whodidyougotherewith?

D.Wheredidyougo?

E.Wherehaveyoubeen?

F.Youneedtotakemorethickclothes.

(B)(每小题2分，共10分)

结合本题所设置的情境，在每个空白处填入适当的内容完成下列对话。

(A:SunLanB:LiYueC:Waiter)

A:Hi!ThisisSunLan.MayIspeaktoLiYue?

B:Hi,SunLan!4].AreyouinQiqiharnow?

A:Yes,Icamebacklastnight.

B:Thafsgreat.Imissyouverymuch.42?

A:Goodidea!TmavailablethiseveningandIcan'twaittoseeyou.

B:Iheardanewrestaurantjustopened.ThenameisHomemadeBBQ.Let'smeettherefbrdinner.

A:SoundslikefunBut43?

B:It'sacrossfromFu-Mart.Youcanfinditeasily.

A:Let'smakeitsixo'clockthisevening

B:Allright,seeyoulater.

(At6:00PMintherestaurant)

C:44?

B:Yes,I'dlikesomebeef,vegetablesandfish.

C:Anythingelse?

A:Oh,abowlofKoreannoodles.

C:45?

A:Large,please.

C.Waitaminute.Yourfoodwillbereadysoon.

第二部分阅读理解(共计50分)

V.阅读理解(A、B、D每小题1分，C、E、F每小题2分)

(A)

阅读下面文字，从A到F选项中为每个段落选出一个最适合的标题。

Chinaisacountrywithalonghistoryandrichculture.Pleasematchthetopicswiththedescriptionsofthe

followingcultures.

46.Thepaper,usuallyrod,isfoldedbeforeitiscutwithscissors.Themostcommonpicturesareflowers,animals,

andthingsaboutChinesehistory.Itsoundseasybutitmaybedifficulttodo.

47.Tai-chi,whichcomesfromChina,ispopularwithmanypeople.Itisaformofphysicalexercisethattrainsour

mindandbodyinbalanceandcontrol.Ifsslowandcalm.

48.“Mayweallbeblessedwithlongevity(长寿).Thoughmilesapart,wearestillabletosharethebeautyofthe

moontogether.9,waswrittentoSuChebySuShi,apoetduringtheSongDynasty.

49.Abing'sErquanYingyueisapiecewhichallthegreaterhumastersplayandpraise.Ithasbecomeoneofour

nation'streasures.Itssadbeautymakespeoplerecalltheirownpainfulexperiences.

50.ChinesepeoplehavebeencelebratingtheDragonBoatFestivalforcenturies.Itfallsonthe5thdayofthe5th

lunarmonth.Onthisday,peoplewatchtheboatracesandeatzongzi.

A.PaperCutting

B.TraditionalFestival

C.AncientPoem

D.Saying

E.FolkMusic

F.MartialArt（武术）

（B）

June5isWorldEnvironmentDay.Nowadaysmoreandmorepeoplearetryingdifferentkindsofwaystoface

environmentalproblemsaroundtheworld.Whatarepeopledoingtoprotectourhome-theearth?

Mostpeoplearechangingtheirshoppinghabits.Ontheonehand,secondhandclothesmaybeasmartchoice.

Peoplearewillingtobuythesecondhandonestowearinspecialsituationsbecausetheyonlywearthemonceor

twice.Ontheotherhand,therearesomecompaniesforrenting（租）clothesandrentingclothesischeaperthan

buyingthem.Sopeopleareabletosavemoneyandprotecttheenvironment.

Severallargecompanieshavebegundevelopingpaperbottlestotaketheplaceofglassandplasticones

becausetherearelotsofcustomersworryingabouttheenvironment.Theythinkpaperbottleshavemany

advantages.Themostimportantisthatpaperbottlesareeasytorecycleandweighlessthanglassorplasticonesas

well.

Azero-wastelifeisthatpeoplehardlycreateanyrubbish.Azero-wastethemestoreprovidesanumberof

everyday,practicalandpleasantzero-wasteproducts.Thestorehelpspeoplestartonaone-stop,zero-wastelife

journey.Azero-wastelifefollowsthe6Rprinciple（原则）-Refuse,Reduce,Reuse,Repair,RecycleandRot.

Allinall,theearthisourhomeandit'sourdutytoprotectit.

根据文章内容，判断句子正（T）、误（F）。

51.Fewpeoplearoundtheworldarctryingdifferentkindsofwaystofacetheenvironmentalproblems.

52.Inordertosavemoneyandprotecttheenvironment,peoplecannotonlybuysecondhandclothesbutalsorent

clothes.

53.Largecompanieshavedevelopedpaperbottlessuccessfullyandputthemintouse.

54.Peoplecanbuymanyeveryday,practicalandpleasantzero-wastethingsineverystore.

55.Youareplayingapartinprotectingourearthwhilefollowingthe6Rprinciple.

（C）

EnglishStudyAssessment（评价）

Grade:8Name:Amy

Self-assessment

Listeningskill:1234

☆Icanunderstandtheteacher'sinstructionsandfinishthelisteningtasksinclass.□□□□

Speakingskill:

☆Icananswerthequestionsloudlyandclearly.□

☆IcandiscussquestionsandexpressmyselfinsimpleEnglish.□

Readingskill:

☆Icanfindoutthemainideasofpassagesquickly.□□□□

☆IcanreadEnglishnewspapersandmagazineswhicharefitforteenagers.□□□□

Writingskill:

☆IcanwritesomethinginEnglishcorrectly.

☆Icanimitate（模仿）theexamplestowritearticles.

Watchingskill:

☆IcanknowmoreaboutforeignculturefromEnglishvideosorfilms.□□□□

Groupassessment

☆AmycanhelpthegroupmembersalotwithEnglish.□□□□

Englishteacherassessment□□□□

☆AmycantakeanactivepartintheEnglishclassandgetgoodgrades.Totalpoints:35

Comments（评语）：

02）己［30-40Welldone!:②,:工21-29Keepitup!㊂Below20Tryharder!

阅读以上信息，从每小题所给的A、B、C三个选项中选出一个最佳选项。

56.Thisterm,AmycanimprovekindsofskillsinEnglishclass.

A.fiveB.sixC.seven

57.haveassed（评价）Amy.

A.Amy,herEnglishteacherandherparents

B.Amy,groupmembersandherEnglishteacher

C.HerEnglishteacher,herparentsandgroupmembers

58.Amyistheweakestinandsheshouldworkharderatitnextterm.

A.speakingB.writingC.watching

59.ThecommentforAmyshouldbe“

A.Welldone!B.Keepitup!C.Tryharder!

60.Whydothestudentsuse"EnglishStudyAssessment^^?

AToexplainwhytheyhavepassedtheexam.

B.Tocheckhowmuchprogresstheyhavemade.

C.Totelltheirparentswhatthey'vedoneatschool.

（D）

阅读短文，根据首字母或所给词的适当形式填空，使文章语义通顺。

Haveyoueverseenpop-ups(弹出窗口)whenyougoonline?

Thesedaysit'scommonforyoutogetapop-upwhichletsyou61(put)theAppin"teenmode(模

式)“everytimeyoubegintouseAppslikeQQorTiktok.AlotofApps,especiallyvideoApps,haveaddedthis

feature(功能)toprotectteenagers.It9ssaidthatitwillbringteenagers62(good)experiencesthanbefore

andmakesurethey9reusingtheAppsinahealthierway.Forexample,AppslikeTiktokhavethefeaturetoprevent

teenagersfromwatchingvideosforlongandwiththefeature,theymightonlybeallowed63(watch)for40

minutes.Thevideosthatteenagerscanwatcharemadesuretobesafeandeveneducational.Thereareno

advertisementsandteenagerscannotpayanym64fbrthevideos.InQQ'steenmode,teenagerscanonly

talktopeopleontheircontactlists.65(they)chatrecordsshowpinyin,whichisusefulforprimaryschool

students.

However,theteenmodedoesnotworkforallApps,a66toarecentreportbytheNationalConsumer

Council.Therearen'tany67(different)betweentheteenmodeandthenormalmodeinsomeApps.Andin

somevideoApps,theteenmodewon'tstart68userswatchvideosfor40minutes.Butuserscangetpastit

b69clicking(点击)“Iknow“andcontinuewatching.

Thoughyoucanlearnalotfromshortvideos,it'sn70tocontrolthetime.

(E)

Oncetherewerefourbeggars(乞丐).Oneday,theymetatanoldtempleatnight.Theywereveryupset

becausenoneofthemhadmuchtoeat.

“Ionlygotthispieceofmeattoday.^^thefirstsaid."Ialmostgotnothing,thesecondsaid,“Ijustpickedupa

potatooutsidethevegetablestoreduringtheday."Thethirdsaidthatallhehadwasasmallbottleofsalt.The

fourthbeggarhadnotdonemuchbetter,onlygotsomeoldbeans,buttheyaren'tverymice!^^

Astheysataroundthefire,thebeggarwithonlyabottleofsalthadagreatidea"Let'sputallourthings

togetherandboilthem.Inthisway,wecanmakeatastydishandshareit."Theyallagreed.However,thefirst

beggarthought,4idon'twanttoshare.Tiljustpretendtothrowmymeatintothepot.They511neverknowandI'll

eatmymeatalonelater?5Sohepretendedtoputthemeatintothepot.Andatthesametimetheotherbeggarshad

similarideastohim.Atthattime,thetemplewastoodarkforthebeggarstoseewhattheothersweredoing.

Finally,oneofthemsuggestedthatthedishshouldbereadyand,inturn,eachofthemhelpedhimselftoit.

Theydrankthehotwaterinsilence,learningthatselfishness(自私)doesn'ttasteallthatgood.

阅读短文，回答下列问题。

71.Howdidthefourbeggarsfeelwhentheymetoneday?

72.Whatdidthesecondbeggargetduringtheday?

73.Whowantedtosharewithothersintheend?

74.Didtheyhaveatastydish?

75.Whatdoyoulearnfromthestory?

(F)

Thenatureisfullofmysteries.WhenautumnarrivesintheUnitedStatesandCanada,youcanseeoneof

nature's,greatestscenes—theyearlymigration(迁徙)ofthemonarchbutterflies(帝王蝶).

NootherbutterflyintheworldmigratesliketheorangeandblackmonarchbutterfliesofNorthAmerica.(A)

Theycannotliveforlongperiodsincoldweather.SoeachautumnaroundOctober,thebutterfliestravelupto3,000

kilometerssouthto(B).SomeevenflytothemountainsofMexico.Plentyofmonarchbutterfliesalmost

blockoutthesky.Andyoucanheartheirwingsbeating.

ThebutterfliesusuallyspendtwomonthsreachingMexico.Afterfivemonthsofstay,theyheadbacknorthin

spring.Butnotonebutterflyfinishesthewholeround-trip.They(C)eggsalongthewayanddie.Three

generationsofbutterflieswillliveanddieduringthespringjourneyalone.Thefourthandfinalgenerationsofthe

yearareborninearlyautumn.ButthebutterflieshardlyrestbeforestartingthelongjourneysouthagaintoMexico.

Themostamazingthingaboutthesemonarchbutterfliesisthattheyalwaysreturntothe(D)treesin

Mexicothattheirgreat-great-grandparentsusedthewinterbefore.

Whatmysteriousmonarchbutterflies!Theyremindusofournation.Millionsofpeople,generationafter

generationusetheirbloodandlivestobuildupourhappylife.Soasteenagers,weshould(E).

阅读短文，根据题目要求完成下列任务。

76.用英文写出文中(A)处£日上所指代的内容。

77.为文中(B)处选择一个适合的短语，使句意完整：

A.seenaturalscenes

B.enjoythewarmsunshine

C.spendwinterinwarmerplaces

78.在文中(C)处和(D)处各填上一个适当的词，使文章的意思完整。

(C)(D)

79.在文中找出一个与所给英文释义相匹配的单词。

:allthemembersofafamilyofaboutthesameage

80.Complete(E)afteryoureadthepassage.

第三部分书面表达(共计15分)

VI.书面表达(本题共15分，其中A题5分，B题10分)

(注意：文中不能出现考生真实姓名、校名和老师名，否则不给分)

A：

81.2022北京冬奥会的成功举办，掀起了全民对冰雪运动的热爱。SOS儿童村为了给孩子们进行冰雪

专项训练，现招聘10名志愿者。请为SOS儿童村写一则招聘广告。

招聘条件：1.擅长冰雪运动(滑冰，滑雪ski)2.善于和孩子们相处3.周六上午工作

联系人:丁老师（电话号

要求：1.字迹工整，表达清楚，语法正确；2.词数：30-50词。

VolunteersWantedforSOSVillage

B：

82.中国共产主义青年团已经走过了百年历程。作为新时代青年中的一员，未来属于我们，希望寄予

我们，奋斗的青春更美丽。请以“HowtoMakeMyselfBetter”为题，谈谈你将如何塑造更好的自己。

要求：1.字迹工整，段落清晰，表达清楚，语法正确，行文连贯；

2.思维导图中的提示词仅供参考，可适当发挥；

3.词数：80-100词。

HowtoMakeMyselfBetter

二。二二年齐齐哈尔市初中学业考试

英语试卷

第一部分语言知识运用（共计55分）

I.单项选择（每小题1分，共10分）

从每小题所给的A、B、C三个选项中，选出一个能填入空白处的最佳选项。

【1题答案】

【答案】C

【2题答案】

【答案】A

【3题答案】

【答案】C

【4题答案】

【答案】B

【5题答案】

【答案】A

【6题答案】

【答案】C

【7题答案】

【答案】B

【8题答案】

【答案】A

【9题答案】

【答案】C

【10题答案】

【答案】B

II.完形填空（每小题1分，共15分）

[11-25题答案】

【答案】1LA12.C13.B14.A15.C16.A17.B18.C19.B20.C21.

B22.A23.B24.C25.B

ID.短文改错（每小题1分，找出错误和改正错误各0.5分，共10分）

【26~35题答案】

【答案】26.foreigner-foreigners

27.strongly—strong

28.Australia——Australian

29.calling―called

30.1980—1980s/1980's

31.of—with

32.such-so

33.But—And/So

34.pride—proud

35.does—did

W.交际运用(共20分)

(A)(每小题2分，共10分)

【36~40题答案】

【答案】36.E37.C38.A39.F40.B

(B)(每小题2分，共10分)

【41〜45题答案】

【答案】41.ThisisLiYuespeaking/ThisisLiYue/LiYuespeaking/It5sLiYue/IfsLiYuespeaking

42.Whatabout/Howaboutmeeting(thisevening)/WhynotAVhydon'twemeet(thisevening)/Shallwemeet(this

evening)/Lefsmeet(thisevening),shallwe

43.whereistherestaurant/whereisit/can/couldyoutellmewhereit/therestaurantis

44.MayItakeyourorder/CanItakeyourorder/MayIhaveyourorder/CanIhaveyourorder

45.Whatsizewouldyoulike/Whatsizedoyouwant

第二部分阅读理解(共计50分)

V.阅读理解(A、B、D每小题1分，C、E、F每小题2分)

(A)

【46~50题答案】

【答案】46.A47.F

48.C49.E50.B

(B)

【51~55题答案】

【答案】51.F52.T

53.F54.F

55.T

(C)

【56~60题答案】

【答案】56.A57.B58.C59.A60.B

(D)

【61~70题答案】

【答案】61.put

62.better63.towatch

64.(m)oney

65.Their66.(a)ccording

67.differences

68.until69.(b)y

70(n)ecessary

(E)

[71-75题答案】

【答案】71.Theyfelt/were(very)upset./Upset.

72.Apotato./Hegotapotato.

73.Nobody./Noone.

74.No,theydidn't.

75.Selfishnessdoesn'ttasteallthatgood./Weshouldn'tbeselfish.AVeshouldlearntoshare.

(F)

【76~80题答案】

【答案】76.TheorangeandblackmonarchbutterfliesofNorthAmerica/Monarchbutterflies77.C

78.①.lay②.same##very

79.generation

80.pulltogethertomakeourcountrystrongerandstronger/studyhardtomakeacontributiontoourcountry

第三部分书面表达(共计15分)

VI.书面表达(本题共15分，其中A题5分，B题10分)

(注意：文中不能出现考生真实姓名、校名和老师名，否则不给分)

A：

[81题答案】

【答案】范文：

VolunteersWantedforSOSVillage

SOSVillageneeds10volunteersforthechildren.Areyougoodatskatingorskiing?Areyougoodwith

children?AreyoufreeonSaturdaymorning?PleasecallMr.Dinga

B：

【82题答案】

【答案】例文

HowtoMakeMyselfBetter

Asateenager,IthinkIshouldworkhardertomakemyselfbetter.

Firstofall,itisimportanttolivehealthily.Iwilleatmorefruitandvegetables.Iwillalsotakeexerciseevery

dayandgetenoughsleep.Whafsmore,Ishouldworkhardatallmysubjects.Tilnotbeafraidtofacechallenges

anymoreandtrymybesttosolvetheproblems.Besides,itisnecessarytohaveagoodrelationshipwithfamilyand

friends.Lastbutnotleast,it'sourresponsibilitytotakecareofourparents.TilalsodowhatIcantohelpother

people.

Bydoingthese,Iwillmakemyselfbetterandbetter.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的倒数是工(aWO)；

a

②实数a的绝对值：

a(a>0)

同=v0(〃=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：

-fab=Va--Jb(a，0,b20)；

[a_4a

(a30,b>0)；

\'b=lb

②二次根式的性质:

a{a>0)

■Ja2=M=«

-a(a<0)

(2)整式与分式

①同底数塞的乘法法则：同底数累相乘，底数不变，指数相加，即心•“"=/+"

（m、n为正整数）；

②同底数塞的除法法则：同底数塞相除，底数不变，指数相减，即/+优=优"-"

（aWO,m、n为正整数，m>n）；

③累的乘方法则：幕的乘方,底数不变,指数相乘，即（"）"="%"（n为正整

数）；

④零指数：«°=1（aWO）；

⑤负整数指数：尸=+（arO,n为正整数）；

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

（a+b）（a-b）-a2-h2;

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+b2；

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0=丝々q=X,其中m是不等于零的代数式；

bhxmbb+m

②分式的乘法法则：巴£=竺；

bdhd

③分式的除法法则：（c^o）；

bdbche

④分式的乘方法则：（."=5（n为正整数）；

⑤同分母分式加减法则：0±2=*；

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+bx+c^O（aW0）的求根公式：

—h+b~—4ac.2.

x=------------4ac>0）

2a

②一元二次方程根的判别式：△=。2_4四叫做一元二次方程办2+法+°=0（a

W0）的根的判别式:

△>0=方程有两个不相等的实数根；

△=0=方程有两个相等的实数根；

△<0。方程没有实数根；

③一元二次方程根与系数的关系：设演、壬是方程/+&+c=0（aWO）的

两个根，那么X|+x,=-2,X,x2=—；

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随x的增大而增大；

当k〈0,y随x的增大而减小；

正比例函数的图象：函数y=心的图象是过原点及点（1,k）的一条直线。

正比例函数的性质：设了=颔4#0）,则：

①当k>0时，，y随x的增大而增大；

②当k<0时，y随x的增大而减小；

反比例函数的图象：函数y=&（kWO）是双曲线；

反比例函数性质：设y=&(kWO),如果k>0,则当x>0时或x<0时，y分别

X

随x的增大而减小；如果k<0,则当x>0时或x<0时，y分别随x的增大而增大；

二次函数的图象：函数>+法+c(a#O)的图象是对称轴平行于y轴的

抛物线；

①开口方向：当a>0时，抛物线开口向上，当a<0时，抛物线开口向下；

②对称轴：直线》=-2；

2a

③顶点坐标(-2,丝匕/)；

2a4。

④增减性：当a〉0时，如果xK—2,则y随x的增大而减小，如果》>—2,

2a2a

则y随x的增大而增大；当a<0时，如果则y随x的增大而增大，如果

2a

X>-—,则y随X的增大而减小；

2a

二、空间与图形

1.图形的认识

⑴角

角平分线的性质：角平分线上的点到角的两边距离相等，角的内部到两边距

离相等的点在角平分线上。

(2)相交线与平行线

同角或等角的补角相等，同角或等角的余角相等；

对顶角的性质：对顶角相等

垂线的性质：

①过一点有且只有一条直线与已知直线垂直；

②直线外一点有与直线上各点连结的所有线段中，垂线段最短；

线段垂直平分线定义：过线段的中点并且垂直于线段的直线叫做线段的垂直

平分线;

线段垂直平分线的性质：线段垂直平分线上的点到线段两端点的距离相等,

到线段两端点的距离相等的点在线段的垂直平分线；

平行线的定义：在同一平面内不相交的两条直线叫做平行线；

平行线的判定：

①同位角相等，两直线平行；

②内错角相等，两直线平行；

③同旁内角互补，两直线平行；

平行线的特征：

①两直线平行，同位角相等；

②两直线平行，内错角相等；

③两直线平行，同旁内角互补；

平行公理：经过直线外一点有且只