2021年湖南省常德中考数学英语真题

2021年湖南省常德市中考数学试卷

一、选择题（本大题8个小题，每小题3分，满分24分）

1.4的倒数为（）

A.AB.2C.1D.-4

4

2.若a>b,下列不等式不一定成立的是（)

A.a-5>b-5B.-5a<-5bC.A>kD.a+c>b+c

cc

3.一个多边形的内角和为1800°,则这个多边形的边数为（)

A.9B.10C.11D.12

4.下列计算正确的是（）

A.=Bc.a2+a2^=cr4

3

C.(〃3)2=a5D.^—=a(〃W0)

a2

5.舒青是一名观鸟爱好者，他想要用折线统计图来反映中华秋沙鸭每年秋季到当地避寒越

冬的数量变化情况，以下是排乱的统计步骤：①从折线统计图中分析出中华秋沙鸭每年

来当地避寒越冬的变化趋势：②从当地自然保护区管理部门收集中华秋沙鸭每年来当地

避寒越冬的数量记录；③按统计表的数据绘制折线统计图；④整理中华秋沙鸭每年来当

地避寒越冬的数量并制作统计表.正确统计步骤的顺序是（）

A.②一③一①一④B.③④-①一②C.①-②-④-③D.②-④-③-①

6.计算：（而+17）•遍+1=（）

22_

A.0B.1C.2D.遥T

2

7.如图，已知尺E分别是正方形4BC。的边48与BC的中点，AE与DF交于P.则下列

结论成立的是（）

A.BE=LAEB.PC=PD

2

C.ZEAF+ZAFD=90aD.PE=EC

8.阅读理解：如果一个正整数机能表示为两个正整数小匕的平方和，即,"=/+廿，那么

称"为广义勾股数，则下面的四个结论：①7不是广义勾股数；②13是广义勾股数；③

两个广义勾股数的和是广义勾股数；④两个广义勾股数的积是广义勾股数.依次正确的

是（）

A.②④B.①②④C.①②D.①④

二、填空题（本大题8个小题，每小题3分，满分24分）

9.不等式2x-3>x的解集是.

10.今年5月II日，国家统计局公布了第七次全国人口普查的结果，我国现有人口141178

万人.用科学记数法表示此数为.

11.在某次体育测试中，甲、乙两班成绩的平均数、中位数、方差如下表所示，规定学生个

人成绩大于90分为优秀，则甲、乙两班中优秀人数更多的是班.

人数平均数中位数方差

甲班45829119.3

乙班4587895.8

12.分式方程上+」_=x+2的解为_____.

Xx-lx（x-l）

13.如图，已知四边形是圆。的内接四边形，ZBOD=80°,则N8CD=_____.

■

14.如图，在△ABC中，ZC=90°,平分/CAB,DE工AB于E,若C£>=3,BD=5,

则BE的长为

D

15.刘凯有蓝、红、绿、黑四种颜色的弹珠，总数不超过50个，其中工为红珠，工为绿珠,

64

有8个黑珠.问刘凯的蓝珠最多有个.

16.如图中的三个图形都是边长为1的小正方形组成的网格，其中第一个图形有1X1个小

正方形，所有线段的和为4,第二个图形有2X2个小正方形，所有线段的和为12,第三

个图形有3义3个小正方形，所有线段的和为24,按此规律，则第"个网格中所有线段的

和为.（用含〃的代数式表示）

三、（本大题2个小题，每小题5分，满分10分）

17.计算：20210+3-%«-bsin45°.

18.解方程：/-x-2=0.

四、（本大题2个小题，每小题6分，满分12分）

19.化简：（―g—+5a+9.）+史W_.

a-142_]a-l

20.如图，在RtZ\4O8中，AOYBO,A8J_y轴，O为坐标原点，A的坐标为(〃，夷),

反比例函数yi=3•的图象的一支过A点，反比例函数”="的图象的一支过B点，过

xx

A作轴于“，若△A。”的面积为返.

2

(1)求〃的值;

(2)求反比例函数”的解析式.

五、(本大题2个小题，每小题7分，满分14分)

21.某汽车贸易公司销售4、B两种型号的新能源汽车，4型车进货价格为每台12万元，B

型车进货价格为每台15万元，该公司销售2台A型车和5台B型车，可获利3.1万元，

销售1台A型车和2台B型车，可获利1.3万元.

(1)求销售一台A型、一台8型新能源汽车的利润各是多少万元？

(2)该公司准备用不超过300万元资金，采购A、8两种新能源汽车共22台，问最少需

要采购4型新能源汽车多少台？

22.今年是建党100周年，学校新装了国旗旗杆（如图所示），星期一该校全体学生在国旗

前举行了升旗仪式.仪式结束后，站在国旗正前方的小明在A处测得国旗。处的仰角为

45°,站在同一队列B处的小刚测得国旗C处的仰角为23°,已知小明目高AE=1.4米，

距旗杆CG的距离为15.8米，小刚目高B尸=1.8米，距小明24.2米，求国旗的宽度CD

是多少米？（最后结果保留一位小数）

（参考数据：sin23°20.3907,cos23°七0.9205,tan23°弋0.4245）

六、（本大题2个小题，每小题8分，满分16分）

23.我市华恒小区居民在“一针疫苗一份心，预防接种尽责任”的号召下，积极联系社区医

院进行新冠疫苗接种.为了解接种进度，该小区管理人员对小区居民进行了抽样调查，

按接种情况可分如下四类：4类-接种了只需要注射一针的疫苗；B类一种了需要注射二

针，且二针之间要间隔一定时间的疫苗：C类-接接种了要注射三针，且每二针之间要

间隔一定时间的疫苗；。类-还没有接种.图1与图2是根据此次调查得到的统计图（不

完整）.

(1)此次抽样调查的人数是多少人？

(2)接种B类疫苗的人数的百分比是多少？接种C类疫苗的人数是多少人？

(3)请估计该小区所居住的18000名居民中有多少人进行了新冠疫苗接种.

(4)为了继续宣传新冠疫苗接种的重要性，小区管理部门准备在已经接种疫苗的居民中

征集2名志愿宣传者，现有3男2女共5名居民报名，要从这5人中随机挑选2人，求

恰好抽到一男和一女的概率是多少.

24.如图，在RtZVIBC中，NABC=90°,以AB的中点O为圆心，AB为直径的圆交AC

于。，E是BC的中点，OE交BA的延长线于F.

(1)求证：尸。是圆。的切线:

(2)若8C=4,FB=8,求AB的长.

B

DC

七、(本大题2个小题，每小题10分，满分20分)

25.如图，在平面直角坐标系xOy中，平行四边形A8CQ的AB边与y轴交于E点，F是

AO的中点，B、C、。的坐标分别为(-2,0),(8,0),(13,10).

(1)求过B、E、C三点的抛物线的解析式；

(2)试判断抛物线的顶点是否在直线EF上；

(3)设过尸与A8平行的直线交y轴于Q,M是线段EQ之间的动点，射线与抛物

线交于另一点尸，当△PBQ的面积最大时，求产的坐标.

26.如图1,在△ABC中，AB=AC,N是8c边上的一点，力为4V的中点，过点A作BC

的平行线交CO的延长线于T,且AT=BN,连接BT.

(1)求证：BN—CN；

(2)在图1中AN上取一点0,使40=0C,作N关于边AC的对称点连接MT、

MO、0C、。7、CM得图2.

①求证：△TOWS/^AOC；

②设松与AC相交于点P,求证：PD//CM,PD^l-CM.

2

2021年常德市初中学业水平考试英语试题卷

第I卷

第一部分阅读技能（共20小题;每小题2分,满分40分）

阅读下面的材料，从每题所给的A、B、C三个选项中，选出最佳选项回答问题或完成句子。

A

Thecityofmusic

ViennaisabeautifuloldcityontheRiverDanubeinthecenterofEurope.It*sthecapitalcity

ofAustriaandthecenterofEuropeanclassicalmusic.Intheeighteenthcenturyalotofmusicians

cametostudyandworkinVienna.

IntheStraussfamily,thereweretwocomposers（作曲家）calledJohannStrauss:thefather

andtheson.Thefather,JohannStraussheelder,wroteandplayedmusicfortraditionaldances,

calledthewaltz.HisdancemusicmadehimfamousalloverEurope.Theson,JohannStraussthe

younger,wasalsoverysuccessfulandpopular*.Hewroteover150waltzes.In1867hewroteThe

BlueDanubewaltz.

Mozartwasanotherveryimportantcomposer.HewasborninAustriain1756.Beforehewas

six,heplayednotonlythepianobutalsotheviolin.HisfamilytookhimaroundEuropeandhe

gaveconcertsinmanycities.Hewrotehundredsofpiecesofmusic.Buthebecameverypoorand

diedin1791whenhewasonlythirty-five.LikeJohannStrauss,fatherandsonhewasagreat

Europeanmusician,andmanypeoplestillthinkhismusicisperfect.

1.WhereisVienna?

A.InAustralia.B.InAustria.C.InAmerica.

2.WhowroteTheBlueDanubewaltz?

A.JohannStrausstheyounger.B.JohannStrausstheelder.C.Mozart

3.Whatkindofmusicdoesthewaltzbelongto?

A.Bluesmusic.B.Countrymusic.C.Classicalmusic.

4.WhenwasMozartborn?

A.In1867.B.In1791.C.in1756.

Moderation（自我调节）

Payattentiontohowyouleadyourlifemostofthetime.Ahealthylifestyleisonethat

doesn'ttakeextremes（极端）asawayoflife.Bemoderateinwhatyoudo.

Eatwell

Itisimportanttopayattentiontobothwhatyoueatandhowyoueat.AsSocratessaid:"You

shouldeattolive;notlivetoeat.1'Adifferentdiet（饮食）withvegetablesandresfreshfruitsis

goodforthebrain.Alsotaketimeofffbrmeals.

Exercise

Studentsmustknowthevalueofexercisebecauseitplaysanecessarypartin

counterbalancing（抵消）thestress（压力）responsesproducedinourbodiesbyhavingtomeet

exams.

Sleep

Studentsaregettinglessandlessofsleepwhichmightleadtomorestress.Thehoursofsleep

beforemidnightarethoughttobethemosthelpful.Forthisreasonstudentsmustre-regulatetheir

bodyclockandgotobedandgetupatregulartime.

Expressyourself

Thewaystudentsfeelabouttheirworkandotherissuesintheirlifeplaysahugepartinhow

theydealwithstress.Itisadvisablethatstudentsshouldberealisticwhateverhappensintheir

lives.

Tosumup,studiesarereallyveryimportant,butneverattheexpense（代价）ofstudents1

physicalandmentalwellbeing.Besides,ifstudentsfeelwelltheywillbereadytofacethe

challenges（挑战）ofexamsaliveandkicking.

5.Whatfoodisgoodfbrthebrainaccordingtoparagraphtwo?

A.Vegetablesandfruits.B.Hamburgersandmeat.C.Riceandnoodles.

6.Whenisthebesttimeforastudenttogotosleep?

A.At7:00pm.B.At10:00pm.C.At1:0am.

7.Wherecanwemostprobablyreadthisarticle?

A.Inatourguide.B.Onawebpagefortips.C.Inadailynewspaper.

8.What'sthebesttitleofthereading?

A.Stressinpartofstudents'lives

B.Ahealthymindinahealthybody

C.Prepareforyourexamswithahealthybodyandmind

C

UsuallyIwouldn'tcrosstheparkatthistimeofnight.Butwalkingaroundtheparkwould

takemoretime,anditwasrainingsohardthatIcouldn'tevenseeclearlywhatwasrightbefore

me.SoIenteredthepark.AndthatwasthefirststupidthingIdidtonight.

SoonafterIwalkedintothepark.Isawamanunderatreeupahead.Myheartfell.The

storiesI'dheardabouttheparkwereallcomingintomyheadatthismoment.Anyonewithaclear

mindwouldjustturnback.Butme?No.Ididanotherstupidthing:Idecidedtohurrypasthim.

JustwhenIwaspassingtheman,heraisedhisheadandgavemethestrangestsmileeverI

gotscaredandstartedrunning.""Hey"themanshoutedfrombehind."Wait"Hewasrunningafter

me!

Iranlikecrazy.Ihadhopedthetreeswouldkeepsomerainoff.Andtheydid.Buttheyalso

madetheparklookevendarker.Icouldn'tseewhatwasaheadofme.Then,Iranintosomething.

Itwastheman!

"Don'tkillme!"Icried.

"What?Iwastryingtogivebackyourbag!Youdroppedit*'ThemangavememybagNow,

IfeltsayingthattothemanwasthestupidestthingIdidtonight.

9.Whydidhewriterenterthepark?

A.Itwassafertogoacrossthepark.

B.Togoacrosstheparkwouldsavetime.

C.Thetreesintheparkcouldkeeptherainoff.

10.Whatdidthewritermeanby"thefirststupidthing0"anotherstupidthing""thestupidest

thing'1?

A.Hefeltproudofhimself.

B.Heregrettedwhathehaddone.

C.Hefeltashamedofmakingsomanymistakes.

11.The"drop"inhasthesamemeaningastheunderlinedoneinthelastbuttwo

paragraph.

A.Hedroppedofffromhisbike.

B.Oh,theyhavehadtodroptheirprices.

C.Excuseme,Miss,you'vedroppedyourumbrella.

12.Whafsthebettitleforthepassage?

A.AStrangeManB.AScaryParkC.ABraveCross

D

InDarayya,acityinSyria,there*salibraryandithas15,000

booksonalmosteverysubjectyoucanthinkof.However,itisdifferent

fromanylibrariesyouknow:Iisasecretundergroundlibrary,andonly

peopleinDarayyaknowwhereitis.

Overtheyears,warhasshakenDarayyabadly.△Storesareclosedoneafter

another,andsoareschools.TohelpthekidsinDarayyawiththeirlearning,AnasAhmad,a19

year-oldstudent,andhisfriendsdecidedtobuildalibrary.Theybuiltthelibraryundertheground

tokeepitsafefrombombing.Butitisdangeroustocollectbooksforthelibrary.Often,Ahmad

andhisfriendsloforbooksinhousesthatwerebombed.Theyneedtobecarefulbecausethey

maybekilledinanotherbombing.

Youmayask,"InaplacelikeDarayya,wouldpeoplebeinterestedinbooks?""Justlikethe

bodyneedsfood,themindneedsbooks,'saysonelibraryuser.Inthelibrary,peopleenjoy

theirtimeofreadingandforgetabouttheterribleworldabove,sotheirlifedoesn'tseemsohard.

Throughreading,theyareabletodreamofabetterlifeafterwar.

13.WhatdoweknowaboutDarayya'slibrary?

A.Itwasbuiltduringthewar.

B.Ithasbeenbombedmanytimes.

C.MostofitsbooksarefromoutsideofDarayya.

14.Whichcanbestreplace"______△__________"inthepassage?

A.Everyday,housesarebombedandpeoplearekilled.

B.Everynight,peoplecometohelptobuildthelibrary.

C.EveryMonday,kidscometothelibrarytoreaddifferentbooks.

15.WhydopeopleinDarayyagotothelibraryevenduringthewar?

A.Theycangetfreefood.

B.Theyfindjoyandhopeinreading.

C.Theywanttolearnhowtowinthewar.

16.Thesentence—"Justlikethebodyneedsfood,themindneedsbooks,"saysoeelibrary

user,-isused.

A.toanswerthequestionabove

B.toofferasolutiontoaproblem

C.togiveasupportingexamplefbratopic

E

MynameisAliceBlack.Iamthirteenyearsold,andIcomefrom

MountElmSheepStationinSouthAustralia.Ihavegottwo

sisters-JeniferiselevenandLisaisseven.Weareallpupilsatthe

SchooloftheAir

TheSchooloftheAirisaschoolforchildrenwholivefarfromthecities,andwhoareina

placewhichdoesnothavealocalschool.Sowehave"air"lessonsovertheradiooronthe

computer.OurteachersareatPortAugusta,acitywhichisabout160kilometersaway.

Inthemorning,wegotoourschoolat8:45._△Whenwegetthere,weturnonthe

radioorcomputerandlistentowhatweshoulddo.Fromthenuntiltwelve,wejustdoourusual

lessons.Intheafternoon,ourmummakesusdosomehomework-well,nothomework,butmore

workaroundthehouse.

Wesendourexercise"books"toourteachersbyemailonFridaynight.Theymarkthemon

MondayandTuesday,andthensendthemback.WegetthemonWednesday.

TheInternetandthetelephonehelpusgetintouchwithourteachersquicklyandeasilyWe

talktoourteachersonceaweekforabouttenminutes.Theytellusifwearemakingprogress

NextyearIwillstartatanewschoolinPortAugusta.Iwillspendtheweekdaysthereandcome

homeatweekends.Itwillbegoodtobewithteenagersofmyage,butIwillmissmyfamily.I

hopeIwillbehappythere.

17.Fromthepassageweknowthat.

A.theBlackfamilyisverypoor

B.theBlackslivesfarfromPortAugusta

CthereisasmalllocalschoolneartheBlackfamily

18.Whichsentencecanbestreplace"____△__________"inthepassage?

A.Itisreallyjustasmallbuilding.

B.Whatfunitistogotoschool

C.Itisreallyanearlytime.

19.Inthe4thparagraph,theunderlinedword“them"meansinChinese.

A.课本B.作业C.课程

20.Whatdotheteachersprobablysaytotheirpupilsonthephone?

A.Doyouhaveanysuggestionsaboutourlessons?

B.WillyoucometoourschoolinPortAugusta?

C.Howareyoudoingwithyourlessons?

第二部分知识运用（共两节，满分30分）

第一节完形填空（共15小题;每小题1分，满分15分）

阅读下面的短文，掌握其大意，然后从短文后各题所给的A、B、C三个选项中，选出可以

填入空白处的最佳选项。

Johnwasapoorbutverysmartkidandhealwaysgottopgradesatschool.Hewas_21_so

hedidn'thaveanyfriends.Hisclassmate,Kevin,wasameankid,whobullied（欺负）almost

everyoneincludingJohn.Hedidwellinmostsubjects,but_22_failedmath.

Thetwokidscouldn'tbemoredifferent,butanactof_23_connectedthem.Oneday,John

sawaladydropapurseonhiswaytoschool.Theladydidn*t_24_that.Johncaughtupwithher

andhandedthepursetoher.

TheladyhappenedtobeKevin's_25_.Thatevening,shetoldKevinaboutthekindlittleboy

who_26_thepursetoher.Shesaid,"Hisname'sJohn.Iguesshegoestoyourschool."What?"

Kevinsaid_27_,"DidyoumeanpoorJohn,myclassmate?"

TothankJohn,Kevinandhismomdecidedtoinvitehimoverforsome_28_.Thenextday,

whenJohnsawbigKevinrunningtowardshim,hegotreallyscared.HethoughtKevinwasgoing

to_29_him,Unexpectedly,Kevingavehimabighug,"Thankyou__30_returningmymom's

purseyesterday!"

"Youmeanthatnicelady?”Johnasked

"Yes.She_31_inviteyouoverforsomehome-bakedcookies.""Well,Ihavetogetmy

mother'spermission（允许）first.n

Afterschool,theywalkedtogethertoJohn'shome.John*smomwasmorethanhappytosee

hissonwithafriendfora_32_.SheagreedatonceafteraskingKevinifhisparentswereOKwith

that.

Thetwokids_33_thefreshlybakedcookiesKevin'smomserved.Then,theydidthe

homeworktogether.Kevinwasamazed_34_Johnexplainedtheusuallyverydifficultmath

homeworkandmadeitlooksoeasy.

WithJohn'shelp,Kevinpassedmathtests_35_,andheseldombulliedanyone.They

becamebestfriendsaswell.

21.A.friendlyB.braveC.shy

22.A.alwaysB.sometimesC.never

23.A.braveryB.kindnessC.friendship

24.A.noticeB.seeC.care

25.A.auntB.motherC.grandma

26.A.leftB.showedC.returned

27.A.angrilyB.worriedlyC.surprisedly

28.A.snacksB.mealsC.fruits

29.A.thankB.beatC.wake

30.A.forB.toC.of

31.A.askstoB.comestoC.wantsto

32.A.prizeB.challengeC.change

33.A.sentB.enjoyedC.got

34.A.howB.whyC.when

35.A.hopefullyB.successfullyC.luckily

注意事项：用o.5毫米黑色笔迹的签字笔将答案写在答题卡上，写在本试卷上无效。

第二部分知识运用（共两节，满分30分）

第二节语法填空（共15小题;每小题1分，满分15分）

阅读下面的材料，在空白处填入适当内容（1个单词）或括号内单词的正确形式（1个或几

个单词），使句子通顺正确。

36.WhenIwentpastthebankyesterday,Isawoldmanlyingonthestreet.

37.-IsthisLinda'swatch?

-No,itisn't.（she）isred.Redisherfavoritecolor.

38.Lucyishard-workingandshehardlyever（hang）outonschoolnights.

39.-I'mhungry,mum.

-Theresomebreadonthetable.Remembertowashyourhands.

40.Look,the(child)arehavingagoodtimeflyingkitesinthepark.

41.Weused(have)apartytowelcomeournewfriendonweekends.

42.paymuchattentiontoyourhandwriting.Youneedtowrite(careful).

43.clevertheboyis!HejustwonthefirstprizeinSuperBrain.

44.TofightagainstCovid-19,thenursedidn'tstopworking,shewastired.

45.-ThedragonBoatFestivaliscoming,whatareyougoingtodothatday?

-I(visit)mygrandparentsinmyhomevillage.

46.OneofthemostfamousMarvelheroiccharacter-Spiderman,(create)in1962.

47.-Whydidn'tyouanswermyWechatphoneateighto'clocklastnight?

-Sorry,I(take)awalkwithmyfriendalongtheriver.

48.SomedayChangdewillbecomeas(busy)asShenzhen.

49.-Oh,mygod!isWangFengnow?Thefootballmatchisstartingsoon.

-Hemaybeinthelibrary.Heoftenreadsatthistime.

50.ChinesescientistYanLongping,renownedordevelopingthefirsthybirdricestrain,diedof

organfailureat91May22th,2021.

第三部分写作技能(共三节，满分30分)

第一节英汉互译(共5小题;每小题1分，满分5分)

阅读短文，将文中划线部分译成汉语或英语。

Fridayishereandmostofusenjoywhattheweekendbrings.51.Maybeyouwillspend

sometimeonyourhobby.52.没有爱好就没有真正的快乐。Hobbieshelpourhappiness.They

giveuspurpose,meaning,acreativeoutlet,andtheycanevenrelievestress.

Oneofmyblogentries,fromMayof2016,tellsushowhobbiescanhelpusidentifysomeof

ourpassionsandthatinturncangiveusinterestingcontenttoincludeinalifestoryormemoir.

53.Certainly