2021年湖南省株洲市中考數(shù)學(xué)英語(yǔ)真題

2021年湖南省株洲市中考數(shù)學(xué)試卷

一、選擇題（本大題共10小題，每小題有且只有一個(gè)正確答案，每小題4分，共40分）

1.若a的倒數(shù)為2,則〃=（）

A.AB.2c.-AD.-2

22

2.方程三-1=2的解是（）

2

A.x=2B.x=3C.x=5D.x=6

3.如圖所示，四邊形A8C。是平行四邊形，點(diǎn)E在線段BC的延長(zhǎng)線上，若/L>CE=132°,則乙4=（）

4.某月1日-10日，甲、乙兩人的手機(jī)“微信運(yùn)動(dòng)”的步數(shù)統(tǒng)計(jì)圖如圖所示，則下列錯(cuò)誤的結(jié)論是（）

A.1日-10日，甲的步數(shù)逐天增加

B.1日-6日，乙的步數(shù)逐天減少

C.第9日，甲、乙兩人的步數(shù)正好相等

D.第11日，甲的步數(shù)不一定比乙的步數(shù)多

5-計(jì)算：-4X（）

A.-25/2B.-2C.y/2D?2^/2

6.《九章算術(shù)》之“粟米篇”中記載了中國(guó)古代的“粟米之法”：“粟率五十，粉米三十…”（粟指帶殼的谷

子，粉米指糙米），其意為：“50單位的粟，可換得30單位的物米…”.問題：有3斗的粟（1斗=10升）,

若按照此“粟米之法”，則可以換得的粉米為（）

A.1.8升B.16升C.18升D.50升

7.不等式組［0的解集為（）

1-x+l>0

A.x<\B.xW2C.1<XW2D.無(wú)解

8.如圖所示，在正六邊形ABCDE尸內(nèi)，以AB為邊作正五邊形4BG，/,則/以/=（）

C.14°D.15°

9.二次函數(shù)丫=60?+公+。QW0）的圖象如圖所示，點(diǎn)尸在x軸的正半軸上，且OP=1,設(shè)M=ac（a+6+c）,

則M的取值范圍為（）

A.M<-1B.-1<M<OC.A/<0D.M>0

10.某限高曲臂道路閘口如圖所示，AB垂直地面/i于點(diǎn)4,BE與水平線/2的夾角為a（0°WaW9（）°）,

EF//l\//li,若AB=1.4米，BE=2米，車輛的高度為〃（單位：米），不考慮閘口與車輛的寬度：

①當(dāng)a=90°時(shí)，〃小于3.3米的車輛均可以通過該閘口；

②當(dāng)a=45°時(shí)，/?等于2.9米的車輛不可以通過該閘口；

③當(dāng)a=60°時(shí)，人等于3.1米的車輛不可以通過該閘口.

則上述說(shuō)法正確的個(gè)數(shù)為（）

E

h

A.0個(gè)B.1個(gè)C.2個(gè)D.3個(gè)

二、填空題（本大題共8小題，每小題4分，共32分）

11.計(jì)算：（2a）.

12.因式分解：6，-4孫=.

13.據(jù)報(bào)道，2021年全國(guó)高考報(bào)名人數(shù)為1078萬(wàn)，將1078萬(wàn)用科學(xué)記數(shù)法表示為1.078X10",則〃=.

14.拋擲一枚質(zhì)地均勻的硬幣兩次，則兩次都是“正面朝上”的概率是.

15.如圖所示，線段BC為等腰AABC的底邊，矩形ADBE的對(duì)角線AB與DE交于點(diǎn)。，若。。=2,則

AC=.

16.中藥是以我國(guó)傳統(tǒng)醫(yī)藥理論為指導(dǎo)，經(jīng)過采集、炮制、制劑而得到的藥物.在一個(gè)時(shí)間段，某中藥房

的黃黃、焦山楂、當(dāng)歸三種中藥的銷售單價(jià)和銷售額情況如表：

中藥黃芭焦山楂當(dāng)歸

銷售單價(jià)（單位：元/806090

千克）

銷售額（單位：元）120120360

則在這個(gè)時(shí)間段，該中藥房的這三種中藥的平均銷售量為千克.

17.點(diǎn)A（xi,戶）、B（xi+1,”）是反比例函數(shù)丫=上圖象上的兩點(diǎn)，滿足：當(dāng)xi>0時(shí)，，均有yiV”，則

x

k的取值范圍是.

18.《蝶幾圖》是明朝人戈汕所作的一部組合家具的設(shè)計(jì)圖（“純”為“噓”，同"蝶”），它的基本組件為

斜角形，包括長(zhǎng)斜兩只、右半斜兩只、左半斜兩只、閨一只、小三斜四只、大三斜兩只，共十三只（圖

①中的“粽’和”宴’為“樣”和“只”）.圖②為某蝶幾設(shè)計(jì)圖，其中△ABO和△CBQ為“大三斜”組

件（“一檬二:ft”的大三斜組件為兩個(gè)全等的等腰直角三角形），已知某人位于點(diǎn)P處，點(diǎn)產(chǎn)與點(diǎn)A關(guān)于

直線力。對(duì)稱，連接CP、DP.若/4。。=24°,則NOCP=度.

&

魏?.

?\

?

fwA

9

?

加$/

+

?

?.

???

?

周-

*M/.

*一

4

*

”1

,*18

寶

?

圖①圖②

三、解答題（本大題共8小題，共78分）

19.（6分）計(jì)算:|-2|+V3sin60°-2

20.（8分）先化簡(jiǎn)，再求值：——.（1_2）一1_”其中x=&-2.

?2_4"xJx+2

21.（8分）如圖所示，在矩形ABC。中，點(diǎn)E在線段C。上，點(diǎn)/在線段A8的延長(zhǎng)線上，連接E尸交線

段8c于點(diǎn)G,連接B。，若DE=BF=2.

（1）求證：四邊形8FEZ）是平行四邊形;

22.（10分）將一物體（視為邊長(zhǎng)為2米的正方形A8CD）從地面PQ上挪到貨車車廂內(nèi).如圖所示，剛

K

開始點(diǎn)B與斜面Er上的點(diǎn)E重合，先將該物體繞點(diǎn)8（E）按逆時(shí)針方向旋轉(zhuǎn)至正方形的位置,

再將其沿E尸方向平移至正方形A282c2。2的位置（此時(shí)點(diǎn)為與點(diǎn)G重合），最后將物體移到車廂平臺(tái)面

MG上.已知MG〃PQ,NFBP=30°,過點(diǎn)尸作F”_LMG于點(diǎn)”，工米，EF=4米.

3

（1）求線段FG的長(zhǎng)度；

（2）求在此過程中點(diǎn)A運(yùn)動(dòng)至點(diǎn)42所經(jīng)過的路程.

23.（10分）目前，國(guó)際上常用身體質(zhì)量指數(shù)“BM/”作為衡量人體健康狀況的一個(gè)指標(biāo)，其計(jì)算公式：BMI

=f_（G表示體重，單位：千克；人表示身高，單位：米）.已知某區(qū)域成人的數(shù)值標(biāo)準(zhǔn)為：BMI

h2

<16為瘦弱（不健康）；16WBM/C18.5為偏瘦；18.5WBM/V24為正常；24W8M/V28為偏胖；BMI，

28為肥胖（不健康）.（女性身體屬性與人數(shù)統(tǒng)計(jì)圖）

某研究人員從該區(qū)域的一體檢中心隨機(jī)抽取55名成人的體重、身高數(shù)據(jù)組成一個(gè)樣本，計(jì)算每名成人的

9W數(shù)值后統(tǒng)計(jì)：

（男性身體屬性與人數(shù)統(tǒng)計(jì)表）

（1）求這個(gè)樣本中身體屬性為“正?！钡娜藬?shù)；

（2）某女性的體重為51.2千克，身高為1.6米，求該女性的數(shù)值；

（3）當(dāng)〃，23且"22（〃?、〃為正整數(shù)）時(shí)，求這個(gè)樣本中身體屬性為“不健康”的男性人數(shù)與身體屬

性為“不健康”的女性人數(shù)的比值.

24.（10分）如圖所示，在平面直角坐標(biāo)系X。），中，一次函數(shù)y=2x的圖象/與函數(shù)產(chǎn)區(qū)（k>0,x>0）

的圖象（記為「）交于點(diǎn)A,過點(diǎn)A作AB_Ly軸于點(diǎn)8,且AB=1,點(diǎn)C在線段。8上（不含端點(diǎn)），且

oc=t,過點(diǎn)c作直線A〃x軸，交/于點(diǎn)》交圖象r于點(diǎn)區(qū)

（1）求人的值，并且用含/的式子表示點(diǎn)力的橫坐標(biāo)；

（2）連接OE、BE、AE,記△OBE、△AOE的面積分別為Si、S2,設(shè)U=Si-S2,求U的最大值.

25.（13分）如圖所示，AB是00的直徑，點(diǎn)C、。是。。上不同的兩點(diǎn)，直線8。交線段OC于點(diǎn)E、交

過點(diǎn)C的直線CF于點(diǎn)F,若OC=3CE,且9（EF2-C產(chǎn)）=OC2.

（1）求證：直線CF是。。的切線；

（2）連接0￡>、A。、AC.DC,若NCOD=2NBOC.

①求證：XNCDsXOBE：

②過點(diǎn)E作EG〃AB,交線段AC于點(diǎn)G,點(diǎn)M為線段AC的中點(diǎn)，若AO=4,求線段MG的長(zhǎng)度.

26.(13分)已知二次函數(shù)(a>0).

(1)若“=」，b=c--2,求方程以2+9+,=0的根的判別式的值；

2

(2)如圖所示，該二次函數(shù)的圖象與x軸交于點(diǎn)A(xi,0)、B(地，0),且xi<0<x2,與y軸的負(fù)半

軸交于點(diǎn)C,點(diǎn)。在線段。C上，連接AC、BD,滿足NACO=N4B。，-A+C=xi.

a

①求證：△AOC絲△。。&

②連接8C,過點(diǎn)。作。E_LBC于點(diǎn)E,點(diǎn)F(0,xi-X2)在y軸的負(fù)半軸上，連接AF,且NACO=N

株洲市2021年初中學(xué)業(yè)水平考試

英語(yǔ)試題卷

第二部分知識(shí)運(yùn)用（共兩節(jié)，計(jì)25分）

第一節(jié)語(yǔ)法填空（共10個(gè)小題，每小題1分，滿分10分）

從A、B、C三個(gè)選項(xiàng)中選擇正確的答案填空。

21.OnJuly1st,we'llcelebratethebirthdayoftheCPC.

A.hundredthB.hundredC.hundreds

22.Wecarryforwardthespiritofservingthepeoplewhole-heartedly.

A.mightB.shouldC.could

23.TheMonkeyKingcanmake72changeshisshapeandsize.

A.onB.inC.to

24.cuteandlovelythebabiesare!Iwilltakecareofthemlikethey'remyownbabies.

A.WhatB.WhataC.How

25.ThisTVprogramdiscusseswherethebesttealeaves.

A.wereproducedB.haveproducedC.produced

26.Don'tplaywiththeknife,oryou'llcut.

A.itselfB.yourselfC.himself

27.Theactiveladieslikemusictheycandanceto.

A.thatB.whereC.who

28.XiaoYun,thechildwasjustborn.Histwoeldersistersareatschool.

A.youngerB.youngestC.older

29.Look!AllthestudentsEnglishpoems.Pleasetakeaphotofortheparents.

A.arereadingB.havereadC.read

30.AllthestudentsinGradeThreearegoingtothebanksoftheXiangjiangRiver.

A.turnupB.giveupC.cleanup

第二節(jié)完形填空（共10個(gè)小題，每小題2分，滿分20分）

Alisonismybestfriend.Herfamilywona5-daystayinamountainhouse.HermomanddadsaidIcouldjoin.

Afewweekslater,we31.

“Whatagreatplace!wAlison'sdadsaid.

"It'slookinglikealittlecloudy/saidAlison'smom,lookingatthesky.

Asyoumighthaveguessed,thecloudsdidmean32.LOTSofrain.

“Iguesswellhavetofindsomethingelsetodo/saidAlison.

We33acoupleofboardgamesandapackofcards.Atfirstitwasfun,34weendedup

playingthosegamesforabout30hours,stoppingonlytoeatandsleep!

“Icannotplayanymore/Isaidonthethirdday."Howaboutwejustreadbyourselvesforawhile?"

“Ihaveabetteridea/saidAlison.Z/Howaboutwe35instead?"

“Ithinkalittlequiettimewouldbenice/Isaid,openingabookIhadbrought.

“Oh,comeon!Don'tbe36.I'llpickthefirstsong/Alisonstartedsinging.

“Couldyoupleaseleavemealone?”Isnapped（怒氣沖沖地說(shuō)）.

“Wow!Happily!”shesappedhack.Z/Howaboutwebothleaveeachotheraloneforever?

Thismakesmethinkoftheexpression"toomuchofagoodthing”.Alison'sdadsaid,“Youknowhowone

pieceofcaketastes37,but10piecesofcakeistoomuch?Spendingeverysecondwithanyone一evenyour

favoriteperson-islike38toomuchcake.”

“Iguessthatmakessense/Alisonsaid.Shelookedat39.'Tmsorryfornotunderstanding?

'Tmsorryforsnappingatyou/Isaid.

Theweathergotwaybetteronthefourthday,soweactuallygottogooutside.Thehikingwasreallyfun!The

happiestpartofallisthatAlisonandIarestillgreat40.Wejustmakesuretogiveeachothersomepeace

whenweneedit.

31.A.arrivedB.leftC.ran

32.A.snowB.rainC.wind

33.A.stoleB.drewC.found

34.A.soB.butC.and

35.A.singB.readC.write

36.A.surprisingB.excitingC.boring

37.A.smellyB.deliciousC.bitter

38.A.eatingB.buyingC.making

39.A.herB.himC.me

40.A.friendsB.studentsC.players

第三部分閱讀技能（共20個(gè)小題：每小題2分，滿分40分）

閱讀下面的材料，從每題所給的A、B、C三個(gè)選項(xiàng)中，選出最佳選項(xiàng)回答問題或完成句子。

A

ENGLISHDAY

June22(Allday)

YangzhouMiddleSchool

DifferentEnglishactivitiesindifferentplaces

Alltheteachersarevolunteers.

Sam(Foreignteacher)MissLi,MissChenandMr.Zhang

Topic:EnglishsongsTopic:ReadingMissLiu

Place:PlaygroundPlace:ClassroomsTopic:Englishpoems

Place:Inthepavilion

MissYa,MissPengandMissHe

Topic:SpokenEnglish

Place:Underthetrees

41.Howmanyteacherswillteach?

A.FourB.Seven.C.Eight.

42.Thispicturemainlyintroducesan.

A.EnglishdayB.EnglishclassC.Englishcorner

B

Timespentonrcsding

Rrt4ie（beeii■■■>>

Rfttflat?，匕1?“?fiF??

■?“??，pr，MMBe?...Km■Rii

HrM”Hber補(bǔ)MZMtlrrUh??

RrHlatMlaMeitCi

Rra4iac>?iari^bMe?

~??拿”??KiI

?St2SM

niaetnperda

43.Whatdopeoplespendthemosttimeon?

A.PCs.B.Printedbooks.C.Smartphones.

44.Howmanypartsdoesthetablecover?

A.6.B.7.C.ll.

45.Thetablemainlytellsuspeople'sreading.

A.habitsB.levelsC.methods

C

Foodisakindofculture.It'sanation'smemoryandpride.ThefamousFrenchbaguette（長(zhǎng)棍面包）isoneof

theirmemoriesandprides.Frenchpeoplethinkitshouldbeprotected.z/ltismuchmorethanjustakindofbread.

ItisasymbolofFrance——it'sliketheEiffelTower/saidDominigueAnract,presidentoftheConfederationof

FrenchBakers.

Soit'snowonderthatagroupofFrenchcookswantthebaguettetobecomeaformofintangiblecultural

heritage（非物質(zhì)文化遺產(chǎn)）listedbyUNESCO.Frenchcultureleadershavegivenasuggestiontothecountry's

president.

UNESCO'sintangibleheritagelistaimstoprotectculturefromtheinfluenceoftheworld.CooksinFrance

believethatifthebaguetteisonthelist,itwillbebetterprotected.ThelistalreadyincludesBelgianbeerand

Neapolitanpizza.

Thebaguettehasbeenprotectedbylawsince1993.Thelawsaysthebreadmustbemadewithonlythe

followingthings:water;wheatflour,yeastandsalt.Theflourshouldbefermented（發(fā)酵）for15to20hoursata

certaintemperature.Thisstrictrulemakesthefoodspecialanddelicious.

SixmillionbaguettesaresoldeverydayinFrance.However;assupermarketscontinuetotakeover,tensof

thousandsofshopshaveclosedsincethe1950s."Thefirstthingweaskofachildistogobuyabaguette/Anract

said."Wethinkitimportanttoprotectthesehabits/7

46.WhoisAnract?

A.PresidentoftheConfederationofFrenchBakers.

B.PresidentofUNESCO.

C.Managerofasupermarket.

47.Thecookswantthebaguettetobeonthelistbecauseitwill.

A.bebettercooked

B.becomeasymbolofFrance

C.bebetterprotected

48.Thebaguettehasbeenprotectedbylawsince.

A.1950B.1993C.2020

49.HowmanybaguettesaresoldeverydayinFrance?

A.Sixmillion.B.Tenthousand.C.Sixthousand.

50.Thepassagemainlytellsus.

A.whatthesymbolofFranceis

B.howtomakeFrance'sfamousbread

C.France'sfamousbreadshouldbeprotected

D

Ifyou'veeverwalkedthroughfog（霧），youmighthavenoticedthatyourskinandhairgetwet.Thisis

becausefogismadeoftinywaterdrops.Scientistsarehelpingpeoplecollectthesedropstomakedrinkingwater.

Insometowns,thereisnofreshwater.Peopletherehavetousetruckstocarryfreshwater.Itisexpensive.

Sincerainfallstotheground,itcaneasilybecollectedintotanks（水箱）.Butthewaterdropsthatmakeup

fogdon'thittheground.Instead,theyfloat（漂浮）intheair.Toturnfogintowater,youhavetocatchthewater

drops.

Afogcatcherismadeofnetswithtwoposts.Thenetsareusuallysetuponahilltop.Asfogpassesby,the

netscatchthewaterdrops.Thedropsrundownthenetsandintochannels.Thechannelsleadthewaterintolarge

tankswhereitcanbestored.Afogcatchercancollect10,000litersofwateraday.Scientistshavehelpedsetup

fogcatchersfortownsinChile,NepalandMexico.

Fogcatchersareagreatwayforpeopleinsmallandlonelytownstohavetheirownfreshwater.Centuries

beforescientistscreatedfog-catchingnets,naturewasmakingfogintowateronitsown.Asfogpassedthrough

themountains,largeleavesgotthedropsjustlikethenetsdo.Peoplelearnedtodrinkthewatercollectedonthe

leaves.Thankstomodernfogcatchers,enoughwatercanbemadeforawholetown!

51.Whatdoestheword"It"inParagraph2mean?

A.Trucks'carrying.B.Raincollecting.C.Fogcatching

52.Whatisafogcatchermadeof?

A.Tanks.B.Leaves.C.Nets.

53.Afogcatchercancollectofwateraday.

A.1,000litersB.10,000litersC.11,000liters

54.Centuriesagopeoplelearnedtodrinkthewatercollected.

A.inchannelsB.onthenetsC.ontheleaves

55.Whatcanbethebesttitleofthepassage?

A.CatchingFogB.CatchingRainC.CatchingSnow

E

"Mom!Ifoundone!Ifoundarock!”

IheardthosewordsagainandagainlastsummerasIsatbythewindow,whichfacesaparkinthesmalltown

whereIlive.

TheKindnessRocksProject,whichwasstartedafewyearsagobyamominMassachusetts,hasspread

aroundtheworld.Kids,families,andpeopleofallagesaretakingpartinpaintingrocks,hidingrocks,andfinding

paintedrocksallovertheplace.Somepostphotosoftherocksonsocialmedia（傳媒）,andotherssimplymove

therocksforsomeoneelsetofind.Sometaketherockshomeandthenreplacethemwithnewonesthatthey

createdandhid.

Nine-year-oldtwinsHarryandHannahDeVriezehavepaintedhundredsofrockswiththeirparents.Most

evenings,thefamilyandtheirsmalldogwalkaroundwithawagon（運(yùn)貨車）fullofrocksthattheyhideasthey

walk.

"It'safunfamilyactivity/Hannahsays.

〃Wew川doitinthewintertoo/Hannahsays.

BenBurinsky,agenine,andhisbrother,Luke,ageseven,werevisitingrelatives（親戚）whentheyfoundtheir

firstpaintedrockinapark.Theyweresoexcitedthattheywenthomeandpaintedtheirownrocks,thenhidthem

forotherstofind.

〃Myboyslovedfindingtherockinthepark,especiallysinceitwasasuperhero/theirmother,JudyBurinsky,

says./zllovehowsomethingsosmallcanbringasmiletomychildren'sfaces.Inreturn,theylearnthevalueof

givingbacktoothers//

KadynKinney,agenine,andhisseven-year-oldbrother,Jayce,havealsopaintedmanyrocks.Theyloveto

hiderocksandlookforrockswiththeirmomanddad.Whentheirgrandmothervisited,theygaveherpainted

rockstotakehomeandhideintheFloridatownwhereshelives.Whenaskedhowmanyrockshehaspaintedso

far,Jaycesays,“Trustme!I'vepaintedmorethan30.”

56.Theactivitywasstartedin.

A.NewYorkB.FloridaC.Massachusetts

57.HowoldisHarry?

A.7.B.9.C.10.

58.Whatdoestheunderlinedword“value“inParagraph8mean?

A.價(jià)值B.價(jià)格C.代價(jià)

59.Jaycehaspaintedmorethanrocks.

A.14B.18C.30

60.Whatisthemainideaofthepassage?

A.Thekindpeople.B.TheKindnessRocksProject.

C.Thepaintedrocks.

第四部分寫作技能（共三節(jié)，滿分40分）

第一節(jié)雙向翻譯（共5個(gè)小題，每小題3分，滿分15分）

根據(jù)上下文將文中畫線部分譯成漢語(yǔ)或者英語(yǔ)。

TheInternetandyourfriendsinfluenceyourbeautystandards.61.你的朋友總是在網(wǎng)上發(fā)照片。Theywant

toshowofftheirbeautifuldressesorstrongbodies,andyouwillcompareyourselftothem.

Firstofall,nottofollowpopularbeautystandardsblindly.Theyareoutofreachfor99%ofus,soit'sbetter

tojustforgetaboutthem.

62.Anothersuggestionistotsllyourselfthatyouarespecial.Talkaboutyourfeelingswithsomeoneyou

trust.Hearinghowmuchtheyvalueyoucanhelpyoufeelcomfortableinyourownskin.63.每個(gè)人都了不起。

Everyonehastheirowntalents.

Finally,itisagoodideatotrytodirectyourattentionawayfrombadthoughts.Toachievethis,youshoulddo

somethingyouenjoy.Youcanenjoyyourselvesbylearning.64.Thisisalifelongjourneybecauseeven/daybrings

somethingnew.Youcanalsotakepartinsocialactivities,likeplayingsportswithyourfriends.Thesethingscan

helpyoutakeyourmindoffmattersthatworryyouandmakeyoufeelgoodaboutyourself