2023年單招考試數(shù)學(xué)、英語(yǔ)試卷+答案 (四)

2023年單獨(dú)招生考試招生文化考試

數(shù)學(xué)試題卷

（滿分120分，考試時(shí)間120分鐘）

一、選擇題：（本題共25小題，共45分.在每小題給出的四個(gè)選項(xiàng)中，只有一

項(xiàng)是符合題目要求的）

1、有四個(gè)關(guān)于三角函數(shù)的命題:

XX1

22

Pi：3R,sin2+cos2=2p2?Rsin(x-y)=sinx-siny

/I-cos2x_.7T

P3-Vx/a%],寸—2"psinx=cosy=>x-Fy=—

其中假命題的是()

(A)P\,P4(B)P],P4(3)P\,03(4)2,Pi

2、已知圓G：（x+iA+e-ip」，圓G與圓G關(guān)于直線x-y-i=°對(duì)稱，則圓G的

方程為（）

（A）（x+2）?+（2）2=]（B）（x-2）2+（y+2）2=]

（C）（x+2）2+（y+2）2=]（D）（x-2）2+（7—2』

2x+y>4,

<x-y>l,

3、設(shè)元丁滿足【A2"2』|JZ=X+*）

（A）有最小值2,最大值3（B）有最小值2,無(wú)最大值

（O有最大值3,無(wú)最小值（D）既無(wú)最小值，也無(wú)最大值

4、已知°=（-3,2）,6=（-1,0）,向量h+6與”26垂直，則實(shí)數(shù)義的值為（）

」1_11

（A）~7（B）7（C）~6（D）6

5、等比數(shù)列｛叫的前n項(xiàng)和為S，,已知$2"1=38,則加=（）

(A)38(B)20(C)10(D)9

EF=—

6、如圖,正方體48cA的棱線長(zhǎng)為1,線段BQ上有兩個(gè)動(dòng)點(diǎn)E,F,且一2,

則下列結(jié)論中錯(cuò)誤的是()

(A)ACLBE

⑻EF〃平面4BCD

(C)三棱錐4-8ER的體積為定值

(D)A4EF的面積與ABEF的面積相等

7、如果執(zhí)行右邊的程序框圖，輸入》=-3力=0.5,那么輸出的各個(gè)數(shù)的和等于()

(A)3(B)3.5(C)4(D)4.5

8、一個(gè)棱錐的三視圖如圖，則該棱錐的全面積(單位：C-)為()

（A）48+12^2^（B）48+24V^

（C）36+12近（D）36+24亞

9、用min{a,b,c}表示a,b,c三個(gè)數(shù)中的最小值。設(shè)/（x）=min{2',x+2,10T}a次）,

則的最大值為（）

(A)4(B)5(C)6(D)7

10.已知三棱錐P-ABC的四個(gè)頂點(diǎn)在球。的球面上，PA=PB=PC,ZXABC是邊長(zhǎng)為

2的正三角形，E,F分別是PA,AB的中點(diǎn)，ZCEF=90°,則球。的體積為()

A.86nB.4&兀c.27671D.aR

11.已知平行四邊形ABCD,則向量通+玩=()

A.BDB.DBC.ACD.CA

12.下列函數(shù)以弘為周期的是()

A.y=sin(x—B.y=2cosxC.y=sinxD.y=sin2x

13.本學(xué)期學(xué)校共開設(shè)了20門不同的選修課，學(xué)生從中任選2門，則不同選法

的總數(shù)是()

A.400B.380C.190D.40

14.已知直線的傾斜角為60°,則此直線的斜率為()

A.-B.-V3C.V3D.亨

15.若sina>0且tanaVO,則角a終邊所在象限是（）

A.第一象限B.第二象限C.第三象限D(zhuǎn).第四象限

---->0

16、不等式4-x的解集是（D）

A、RB、（1,4）C、（-8,l）U（4,+8）D、（一8，）

17、不等式（7+斕5-x）?0的解集是（。）

A、(一7,5)B、(F，-7)U(5,4W)c、(一8,-7]U[5,e)D、[-7,5]

18、若ab<0,則(C)

A、a>0,b>0B、a<0,b>0C、a>0,b<0或a<0,b>0D、a>0,b>0或a<0,b<0

19、下列命題中，正確的是（D）

b

—<aC如果時(shí)>網(wǎng)，那么a>6如果a>b,cxO,則彳

A、a>-aB、2D、

20、在等差數(shù)列應(yīng)｝中,%=-2,4=3,貝產(chǎn)=(A)

A、16B、17C、18D、19

21、在等差數(shù)列｛%｝中,-3,%=2,則(B)

A、%二°B、4=0C、%=oD、各項(xiàng)都不為0

22、在等比數(shù)列也，｝中,q=3,q=—2,則―(c)

A、96B、48C、-96D、192

23、在等差數(shù)列中,已矢口%=1，出+%=50,貝”《+%=（c)

A、0B、-20C、50D、500

24、在等差數(shù)列｛%｝中，已知6=5,%+%=18，貝y3+%=（B)

A、0B、18C、-34D、96

在等比數(shù)列中，已知%一元，%=4,則該數(shù)列前五項(xiàng)的積為（C

25、)

A、4B、3C、1D、2

二、填空題：(共30分)

1廿lim(Jx?-x+1+x-%)=1?.

1.右,貝?。輐=.

2.有30個(gè)頂點(diǎn)的凸多面體，它的各面多邊形內(nèi)角總和是.

3.長(zhǎng)為的線段AB的兩個(gè)端點(diǎn)在拋物線y=Y上滑動(dòng)，則線段AB中點(diǎn)

M到x軸距離的最小值是.

iz2

4.已知復(fù)數(shù)4=37,Z2=2"l,則復(fù)數(shù)44的虛部等于.

5.從某社區(qū)150戶高收入家庭，360戶中等收入家庭，90戶低收入家庭中，用

分層抽樣法選出100戶調(diào)查社會(huì)購(gòu)買力的某項(xiàng)指標(biāo)，則三種家庭應(yīng)分別抽取的

戶數(shù)依次為.

三、解答題：(本題共4小題，每小題10分，共40分.解答應(yīng)寫出文字說(shuō)明、

證明過(guò)程或演算步驟.)

1、由這些數(shù)據(jù)，科學(xué)家推測(cè)出植物每天高度增長(zhǎng)量V是溫度x的函數(shù)，且這種函

數(shù)是反比例函數(shù)、一次函數(shù)和二次函數(shù)中的一種.

(1)請(qǐng)你選擇一種適當(dāng)?shù)暮瘮?shù)，求出它的函數(shù)關(guān)系式，并簡(jiǎn)要說(shuō)明不選擇另外

兩種函數(shù)的理由；

(2)溫度為多少時(shí)，這種植物每天高度的增長(zhǎng)量最大？

(3)如果實(shí)驗(yàn)室溫度保持不變，在10天內(nèi)要使該植物高度增長(zhǎng)量的總和超過(guò)

250mm,那么實(shí)驗(yàn)室的溫度x應(yīng)該在哪個(gè)范圍內(nèi)選擇？請(qǐng)直接寫出結(jié)果.

求過(guò)點(diǎn)(4，-2),且與直線》-3歹+3=0平行的直線方程。

求經(jīng)過(guò)點(diǎn)C(2,-3),且平行于過(guò)M(1,2)和N(-1,-5)兩點(diǎn)的直線的

直線方程。

求過(guò)直線%+2八1=0與2x-3y+5=0的交點(diǎn)，且與直線/：6x-2y+5=°垂直的直

線方程.

參考答案：

一、選擇題：

1-5:ABBAC

6-10:DBACD

11-15:CDCCB

16-20:DDCDA;

21-25:BCCBC.

二、填空題：

1

1.2

2.10080°

I2

3,1

4

4.5

5.25,60,15

三、問(wèn)答題：

1、解析:

c=49

4?！?6+c=49

(1)選擇二次函數(shù)，設(shè)戶—+"+c,得［4a+2b+c=41,解得匕=49

關(guān)于x的函數(shù)關(guān)系式是V=-x2—2'+49.

不選另外兩個(gè)函數(shù)的理由：

注意到點(diǎn)(0,49)不可能在任何反比例函數(shù)圖象上，所以V不是x的反比例函數(shù);

點(diǎn)(-4,41)，(-2,49),(2,41)不在同一直線上，所以》不是》的一次

函數(shù).

(2)由⑴，得y=-Y-2X+49,.-.7=-(X+1)2+50

,.,〃=T<0,.,.當(dāng)x=T時(shí)，歹有最大值為50.

即當(dāng)溫度為一1℃時(shí)，這種植物每天高度增長(zhǎng)量最大.

-6cx<4

2、解：設(shè)兩直線斜率分別為加且勺=&

一3’，所求直線方程為13夕-10=0

3、解：設(shè)兩直線斜率分別為左、且占=總

k2-(-5)7

由已知'1一(T)

、7,、

—3)=廣2)

7x-2y-20=0

4、解：設(shè)所求直線4的斜率為左，解方程組

3x+2y+1=0(9x+6y+3=0

2x-3歹+5=04x-6^4-10=0

.??兩直線交點(diǎn)為（T」）

由已知直線,6x-2y+5=0,得斜率無(wú)=3

/,11

,11

:.k、=--=—

1k3

7y—1=—（x+1）

二直線人的方程為：,3’

即x+3y_2=0

2023年單獨(dú)招生統(tǒng)一考試

英語(yǔ)試卷

（滿分120分,考試時(shí)間90分鐘）

一、選擇題：（本題共20小題，每小題3分，共60分）

1.Inmyopinion,mattersisnotone'slooks,butone'sinner

thoughts.

A.that

B.it

C.what

D.this

2.Itishardtosaywhatkindofpersonheis.Sometimesheisveryfriendly;

atothertimeshebeverycold..

A.can

B.must

C.will

D.shall

3.Manyatimeheranswersinthetestpaperbecausesheisnot

confidentenoughofherselfespeciallywhenitcomestoacriticalmoment.

A.thegirlhaschanged

B.haschangedthegirl

C.didthegirlchange

D.hasthegirlchanged

4.alittleearlier,Iwouldhavecaughtthetrain.

A.DidIleaveB.WouldIleave

C.HadIleftD.HaveIleft

5.Thisistheonlyshirtwehavenow.Ifyoudon'twanttotake()

youmaycomeandhavealookroundtomorrow.

A、another

B、anyand

C、it

D、oneis

6.Asteachersandstudents,weneedtoouroldideasand

prejudicesandlearntobemoreinbothourteachingandstudy.

A.putaway;flexible

B.putout;clever

C.putdown;clever

D.putaside;flexible

7.Youmeanthepositionisstillnotoccupied?

---Yes,butyoumustknowthatourjobisverydemanding.

A.WithpleasureC.Don,tmentionit

B.Idon,tmindD.That'sallright

8.一I'd1iketoinviteyoutoaconcertthisevening.

---Thankyou,butI'11befreeI'mnotsureatthemoment.

A^whileifC、whenD、whether

9.Payattentiontoroadsignwhiledrivingin____foreigncountryo

A^a;aB、the;theC、the；aD>a;the

10.Ialwayspreferstartingearlyleavingeverythingtothelast

minuteo

A、ratherthanB、incaseC、orelseD、forfear

11.WethinknousewithSelmaLet'stellhisfather.()

A、this,toquarrelB、it,toquarrelC、this,quarrelingD、

it,quarreling

12.Themaninbluemustbeyourbrother,?()

A、mustn'theB、needn'theC、isheD、isn,the

13.Theyhavedoneagoodjob()

A、Sohavethey.AndsoyouhaveB、Sotheyhave.Andsohaveyou

C、Sotheyhave.AndsoyouhaveD、Sohavethey.Andsohaveyou

14.Charleswasaloneathome,withlookingafterhim.

A.someone

B.anyone

C.notone

D.noone

15.Progresssofarverygoodandwearesurethattheworkwillbe

finishedontime.

A.was

B.hadbeen

C.hasbeen

D.willbe

16.Thefarm___wevisitedlastweekistheone___LiLei'sfatheronce

worked()

A、where,thatB、that,whereC、onwhich,whereD、that,that

17.Leavehereatonce,oryouwill___thepolice.()

A^callinB、callonC、callforD、callup

18.Once,theshowcanneverbeforgotten.()

A、seeB、seeingC、toseeD、seen

19.Thereasonhisbeinglateishedidn'tcatchtheearly

bus.（）

A、for,becauseB、of,thatC、for,thatD>of,because

20.Itisrequiredthatthemoneypaidimmediately.（）

A、willbeB、mustbeC、beD、itis

二、填空題：（共30分）

Sometimesitisbetternottoknowthe_1ofacountrythatyouare

visiting___2_itistoknowjustalittleofit.The___3___isthis:

thenativesofyourhostcountrywilloftenrushto_4_ifyouseem

completelylostandhelpless.Buttheywillusuallymisunderstandyour

smallattemptstospeaktheirlanguage.Theywillthinkthatyouknow_5_

morethanyoudo.Forexample,Ionceaskedthreepeopleincarefully

memorizedphrasebookSpanishhowtogettoabusstationinMexicoCity.

Inreplyeachofthempouredoutafloodof（大量）complicatedSpanish.

Theresultwas___6_Ididn'tunderstandawordandwandered（徘徊）around

foranhourbeforeIfoundthestation.—7—Ihadmissedthebus.The

nexttimeImetasituation1ikethisinanothercity,Iwasalotsmarter,

soIacteddumbly（啞）.Tryingtolookverypitiful,I—8_astrangerand

askedsimply,“Busstation?”Henotonlytoldmehowtogetthere.He

showedmethe_9—,walkingthreeblocksoutofhiswaytohelpapoor,

dumbandhelpless___10_.

1.A、habitB、customsC、peopleD、language

2.A、ifB、unlessC、thanD、when

3.A、causeB、reasonC、explanationD、memory

4.A、helpB、showC、tellD>direct

5.A、alittleB、noC>alotD>many

6.A、thenB、whatC、soD、that

7.A、BeforelongB、SoonafterC、BythenD>Justthen

8.AmetB、stoppedC、caughtD、it

9.A、routeB、andC、streetD、place

10.A、isB、strangerC、workerD、comer

三、，閱讀理解:（共20分）

A

“Iwouldalmostratherseeyoudead,“RobertS.Cassatt,aleadingbanker

（專艮行家）ofPhiladelphia,shoutedwhenhistwenty-year-oldeldest

daughterannouncedthatshewantedtobecomeanartist.Inthe19thcentury,

playingatdrawingorpaintingondisheswasallrightforayounglady,

butseriousworkinartwasnot.Andwhentheyounglady'sfamilyranked

among（躋身于）thebestofPhiladelphia'ssocial（社交界的）families,

suchanideacouldnotevenbeconsidered.

ThatwashowMaryCassatt,born1844,beganherstruggleasan

artist.ShedidnottremblebeforeherfatherJsanger.Instead,sheopposed

（抗拒）himwithcourageandatlastmadehimchangehismind.MaryCassatt

gaveuphersocialposition（社會(huì)地位）andallthoughtofahusbandand

afamily,whichinthosetimeswasunthinkableforayounglady.Inthe

end,afterlongyearsofhardworkandperseverance（堅(jiān)持），shebecame

America'smostimportantwomanartistandtheinternationallyrecognized

leadingwomanpainterofthetime.

1.HowdidMr.Cassattreact（反應(yīng)）whenhisdaughtermadeherannouncement?

A.Hefearedforherlife.B.Hewasveryangry.

C.Henearlykilledher.D.Hewarnedher.

2.WhatinfactwasMr.Cassatt'smainreasoninopposinghisdaughterJ

swish?

A.Drawingandpaintingwassimplyunthinkableamongladiesinthose

days.

B.Hedidnotbelievehisdaughterwantedtoworkseriouslyinart.

C.HebelievedanartistJslifewouldbetoohardforhisdaughter.

D.Ladiesofgoodfamiliessimplydidnotbecomeartistsinthose

times.

3.WhatmadeMaryCassatt's"struggle“tobecomearecognizedartist

especiallyhard?

A.Shewasawoman.B.Herfatheropposedher.

C.Shehadnosocialposition.D.ShedidnotcomefromanartistJ

sfamily.

4.WhatdoweknowaboutMaryCassatt'smarriage（婚姻）？

A.Hermarriagefailedbecauseshenevergaveathoughttoherhusband

andfamily.

B.Shenevermarriedbecauseshedidnotwanttobejustawifeand

mother.

C.Aftermarriageshedecidetogiveupherhusbandratherthanher

career（事業(yè)）.

D.Shedidnotmarrybecauseforaladyofhersocialpositionto

marrybelowherwasunthinkable.

5.WhatdoweknowaboutRobertCassatt,scharacterfromthetext?

A.HewasacruelmanB.Hewasastubborn（固執(zhí)的）man

C.HeknewnothingaboutartD.Heknewlittleabouthisdaughter

6.WhatdoweknowaboutMaryCassatt'scharacter?

A.Shewasbraveingoingagainstoldideas

B.Shegottiredofalwaysobeyingherfather

C.Shehatedplayingatdrawingandpainting

D.Shedidnotmindbeingpooratall

7.Aswelearnfromthetext,whichofthefollowingwasgenerally

consideredthemostimportantinthelifeofawomanintheU.S.inMary

Cassatt'stimes?

A.MoneyB.CareerC.MarriageD.Courage

B

Theclockstruckelevenatnight.Thewholehousewasquiet.Everyonewas

inbedexceptme.Underthestronglight,Ilookedsadlybeforemeata

hugepileofthattroublesomestuff（東西）theycall"books”

Iwasgoingtohavemyexaminationthenextday."WhencanIgotobed?”

Iasked

myself.Ididn'tanswer,InfactIdarednot.

Theclockstrucktwelve."Oh,dear!”Icried."Tenmorebookstoreadbefore

leango

tobed!”Wepupilsarethemostwretchedcreaturesin