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四川省遂宁市射洪中学2020届高三数学三诊模拟考试试题文

注意事项:

1.答卷前,考生务必将自己的姓名和准考证号填写在答题卡上。

2.回答选择题时,选出每小题答案后,用铅笔把答题卡对应题目的答案标号涂黑。如需

改动,用橡皮擦干净后,再选涂其它答案标号。回答非选择题时,将答案写在答题卡上。写

在本试卷上无效。

3.考试结束后,将本试卷和答题卡一并交回。

第I卷选择题(60分)

一、选择题:本题共12小题,每小题5分,共60分。在每小题给的四个选项中,只有一项

是符合题目要求的。

1.已知集合A={x|x-1<O},B=[X\X12-2X<0则AB=

A.x|x<0}B.{x\x<l]C.{x|O<x<l)D.x|l<x<2}

2.zwC,若|z|-彳=1+2i,则z=

3

A.--21B.—F2/C.2+2iD.2-2z

22

3.若sin78=m,则sin6=

m+\yjin+iyj\-m

A.C.D.

22

x2—1

4.函数/(x)丁丁的图象大致为

kl

A.

1,1,

5.已知等差数列{4}的前〃项和为S“,%=742+6,。,=4,则数列{不}的前10项和为

23〃

98

民-

A.11lnoc.D.9-

1210

6.将函数/(x)=sin2x的图象向左平移。个单位长度,得到的函数为偶函数,则

。的值为

A冗71

A.—B.-c.-D.—

12634

,1,c

7.已知。=log45,^=-log^3,c-e'n2,则a,b,c满足

A.a<b<cB.b<a<cC.c<a<bD.c<b<a

8.已知双曲线G:二+^^=1与双曲线一二=i有相同的渐近线,则双曲线G的

m/n-10~4

离心率为

A.-B.5C.75D.—

42

71

9.设ABC的内角A,乩。所对的边分别为。,b,c,且。=丁,。+〃=12,则ABC

6

面积的最大值为

A.8B.9C.16D.21

10.《九章算术》是我国古代第一部数学专著,它有如下问题:“今有圆堡我卜融g),周四

丈八尺,高一丈一尺.问积几何?”意思是“今有圆柱体形的土筑小城堡,底面周长为4丈8

尺,高1丈1尺,问它的体积是多少?”(注:1丈=10尺,取力=3)

A.704立方尺B.2112立方尺C.2115立方尺1).2118立方尺

11.正三棱锥底面边长为3,侧棱与底面成60°角,则正三棱锥的外接球的体积为

-16万32万

A.4zrB.167rC.D.

33

1jr

12.若函数〃x)=—cos2x+3Q(siii¥-cosx)+(4a-l)x在一彳上单调递增,则实数。

的取值范围为

」J'-1,;C.1D.

A.-,1B._

_7J_

第II卷非选择题(90分)

二、填空题:本题共4小题,每小题5分,共20分。

13.sin75"+cos75"=

14.设a,b是两个向量,则“卜+可>,一。|”是%力>0”的条件.

15.已知函数J.(x)=alnx—法2图象上一点(21(2)处的切线方程为y=—3x+21n2+2,

贝ija+b=.

16.已知函数/(x)=a?—3/+i,若f(x)存在唯一的零点七,且x0<0,则。的取值范围

是.

三.解答题:共70分。解答应写出文字说明、证明过程或演算步骤。第17〜21题为必考题,

每个试题考生都必须作答。第22、23题为选考题,考生根据要求作答。

(-)必考题:共60分。

17.(12分)已知正项等比数列也}的前〃项和为S“,&=4,S3=7,数列{叫满足

4+1=〃+1(〃GN*),且

(I)求数列{«,}的通项公式;(II)求数列<(>的前〃项和.

18.(12分)鱼卷是泉州十大名小吃之一,不但本地人喜欢,而且深受外来游客的赞赏.小张从

事鱼卷生产和批发多年,有着不少来自零售商和酒店的客户当地的习俗是农历正月不生产鱼

卷,客户正月所需要的鱼卷都会在上一年农历十二月底进行一次性采购小张把去年年底采购

鱼卷的数量x(单位:箱)在[100,200)的客户称为“熟客”,并把他们去年采购的数量制成下

表:

采购数X[100,120)[120,140)[14(),160)[160,180)[180,200)

客户数10105205

(I)根据表中的数据作出频率分布直方图,并估计采购数在168箱以上(含168箱)的“熟客”

人数;

(H)若去年年底“熟客”们采购的鱼卷数量占小张去年年底总的销售量的|,估算小张去年

年底总的销售量(同一组中的数据用该组区间的中点值为代表);

(III)由于鱼卷受到游客们的青睐,小张做了一份市场调查,决定今年年底是否在网上出售鱼

卷,若不在网上出售鱼卷,则按去年的价格出售,每箱利润为20元,预计销售量与去年持平;若

在网上出售鱼卷,则需把每箱售价下调2至5元,且每下调0元(2«加W5)销售量可增加1000®

箱,求小张今年年底收入H单位:元)的最大值.

19.(12分)如图,在多面体EfABCD中,AB//CD,AB1BC,£8,平面ABCD,

BEUDF,CD=2BC=4AB=4,BE=2DF=4.

(I)求证:ACLEF-,

(II)求三棱锥A-CD尸的体积.

20.(12分)中心在原点的椭圆£的一个焦点与抛物线=4y的焦点关于直线对

称,且椭圆£与坐标轴的一个交点坐标为(2,0).

(I)求椭圆£的标准方程;

(II)过点(0,-2)的直线/(直线的斜率4存在且不为0)交£于46两点,交x轴于点。

点1关于x轴的对称点为〃,直线做交x轴于点Q.试探究IOPWOQI是否为定值?请说明

理由.

21.(12分)已知函数/(x)=/-ax+21nx.

(I)当。=50寸,求/(幻的单调区间;

(H)若八幻有两个极值点看,々,且!<玉<!<工2,求。取值范围.(其中e为自然对数的

3e

底数).

(-)选考题:共10分。请考生在第22、23题中任选一题作答。如果多做,则按所做的第

一题计分。

22.[选修4-4:坐标系与参数方程](10分)

x=i+L

2x=cos6

已知直线/:〈«为参数),曲线G:(6为参数).

V3.y=sin8

⑴设/与G相交于A5两点,求用;

1C

(II)若把曲线G上各点的横坐标压缩为原来的]倍,纵坐标压缩为原来的冷倍,得到曲线

c2,设点户是曲线G上的一个动点,求它到直线/的距离的最大值.

23.[选修4-5:不等式选讲](10分)

已知:x〉0,y>0,且x+y=6

(I)若|x-5|+|y-4饪6求x的取值范围;

(II)|%—5|+|y一4闺m—2卜恒成立,求应的取值范围.

高三三诊模拟考试

文科数学参考答案

1.C2.B3.B4.D5.B6.D7.A8.C9.B10.B

11.D12.D

14.充分必要15.316.(2,+oo)

丽*=4,by=1,

17.(I)根据题意,设他}的公比为4,所以{解得{。

bi+b、q+瓦/7,q=2.

又4用―/=〃+1,

所以4=(4一6I)+(4-一/-2)+…+(%—W)+(七-4)+4

,八c,+n2+n

〃+(〃+1)+・・.+2+1==

v722

121

山)因为刀=心

n+\

所以

18.解:(1)作出频率分布直方图,如图

•厥率图距,

0.020

,...

f

0.010.,、二、,二

0005;……■J…三/'

oV一而[拓[航如前珈■荣购量(箱)

根据上图,可知采购量在168箱以上(含168箱)的“熟客”人数为

50x20x|0.005+0.020x阿一侬|

I20J=17

(2)去年年底“熟客”所采购的鱼卷总数大约为

110x10+130x10+150x5+170x20+190x5=75()00

小张去年年底总的销售量为7500+。=12000(箱)

8

⑶若不在网上出售鱼卷,则今年年底小张的收入为丫=1200x20=240000(元);

若在网上出售鱼卷,则今年年底的销售量为(12000+100/〃)箱,每箱的利润为(20。,

则今年年底小张的收入为

y=(20—⑼•(12000+1000m)=1000(-m2+8m+240)=100()[—(加-4/+256],

当加=4时,F取得最大值256000

256000>2物)00,

.•.小张今年年底收入y的最大值为256000元.

19.(I)平面ABC。,ACu平面ABC。:.EB±AC

AB±BC,AB//CDZABC=ZBCD=90

又CO=28C=4A6=4—=—=-.-.AABC-A5CD

BCCD2

则NC43=NO3C

ZABD+ZDBC=90/.NABD+NCAB=90/.AC1.BD

又EBcBD=B..AC,平面DBEF

又EVu平面DBEF:.AC±EF

(II)三棱锥A—COE的体积:

匕-CDF=%.Db=;SM0c.DE=;Xg.BC.CO.Of=1

20.(1)因为椭圆£的一个焦点与抛物线C:/=4y的焦点关于直线y=x对称,

所以椭圆£的右焦点为(1,0),所以c=l.

又椭圆《与坐标轴的一个交点坐标为(2,0),所以。=2,又匕2=/_。2=3,

22

所以椭圆£的标准方程为土+匕=1.

43

(2)设直线/的方程为丁=丘-2,b0,则点尸伍,0),设A(x”yJ,6(冷当)

2,

工+J

则点。(知-乂),联立直线/与椭圆£的方程有,43

y=kx-2

1

得(3+4女2卜2-16"+4=0,所以有A=48(4炉一1)>0,即%?>-

4

16k

X.4-X2=r

3+4左y+yx-x,L

且《:,即直线劭的方程为上上二——

4%+XW-%

玉”互市

X,2+WX2版|工2—2(%+*2)

令\y=0,得点0的横坐标为北

y+%%(玉+々)—4

8Z—324-24kc,

代入得:%=T^^=F=2Z,

所以10Pl•|。。1=|4・々|=32k=4,所以IOPIJOQI为定值4.

K

21.⑴/(X)的定义域为(0,+8),r(X)=2x—5+2=2、5x+2=(2匚乂1上2)

XXX

“X)的单调递增区间为(0,)和(2,+8),单调递减区间为2).

(2Vf'(x\=2x-a+-=2广9+2,/(力有两个极值点

XX

.,.令g(x)=2x2-izx+2,则g(尤)的零点为,且;<%<,<%.

1・△=a2_]6>0,・,.aV-4或a>4<%+9=耳>0,%/=1'a>4.

根据根的分布,则g(3>0且g(-)<0即2x1—!-62+2>0,2---+2<0.

3e93e-e

,a的取值范围是2e+2<a<型

e3

22.(1)/的普通方程为y=G(x-l),G的普通方程为炉+>21,

y=>/3(x-l)

联立方程组<解得交点为A(l,0),6

无2+/=1

所以|A@==1:

1八

X--cos6

2(16)

(2)曲线。2:<(。为参数).设所求的点为尸二cosd—sin。,

垂>.122J

y=—sin”a

.2

cos0--sin8一6

则P到直线/的距离2

V3+T

当cos(q=-1时,d取得最大值更+逅.

24

23.(1)把y=6-x代入原不等式得|x-5|+|x—2区6,

x<22<x<5\x>5

此不等式等价于<或V或<

5—x+2—6“[5-x+x-2<6x—5+x-246

113113

分别解得:耳“<2或2。<5货5<X«5,故原不等式解集为匕方

(2)|x—5|+|y—4因x+y—9|=3,当且仅当0<xW5,()<yW4时取等号,

A|w-2|<3,故一lWmW5.

赠送:高二英语下学期第二次月考(期中)试题

注意事项:

三、本试卷共10页全卷满分150分,答题时间为120分钟;

四、答卷前,考生须准确填写自己的姓名、准考证号,并认真核准条形码上的姓名、准

考证号;

五、选择题必须使用2B铅笔填涂,非选择题必须使用0.5毫米黑色墨水签字笔书写,

涂写要工整,清晰;

六、考试结束后,监考员将答题卡按顺序收回,装袋整理;试卷不回收。

第一部分:听力(共两节,满分30分)

第一节(共5小题;每小题L5分,满分7.5分)

听下面5段对话。每段对话后有一个小题,从题中所给的A,B,C三个选项中选出最佳选

项,听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话只读

一遍。

1.Whatarethetwospeakerstalkingabout?

A.Examination.B.Travel.C.Health.

2.HowdoesthewomanwanttogotoShanghai?

A.Bycar.B.Bytrain.C.By

plane.

3.Whatdoesthewomanlike?

A.Singing.B.ReadingC.Dancing.

4.WhyhasNinasadthesedays?

A.Shedidn'tpasstheexam.

B.Sheispoorinhealth.

C.Herfatherdied.

5.Howmanychairsdothespeakersneedacccordingtothewoman?

A.ThreeB.Thirty.C.Thirty-three.

第二节(共15小题;每小题L5分,满分22.5分)

请听下面5段对话或独白,每段对话或独白后有几个小题,从题中所给的A,B,C三个选

项中选出最佳选项,并标在试卷的相应位置,听每段对话或独白前,你将有时间阅读各个小

题,每小题5秒钟,听完后,各小题将给出5秒钟的作答时间。每段对话或独白读两遍。

请听第6段材料,回答第6、7小题。

6.Whatistheprobablerelaationshipbetweenthespeakers?

A.Brotherandsister.B.Workmates.C.Classmates.

7.Whatisthemanprobablylookingfor?

A.HiscarB.IlisbookC.Ilispet

请听第7段材料,回答第8、9小题。

8.Whichlanguagedoesthemanwanttolearn?

A.FrenchB.German.C.Japaness

9.Wheredoesthemanlive?

A.InLodon.B.InPairsCInTokyo

请听第8段材料,回答第10至12小题。

10.Wherehasthewomanbeen?

A.ThemeetingroomB.Thelibrary.C.Theoffice.

11.Whatdoesthemanaskthewomantohelpwith?

A.Gettinganewjob.

B.Makingadecision.

C.Gettingmoremoney.

12.What?sthewomanysadvice?

A.Tokeephisparentsjob.

B.Tomakeacomprision.

C.Toacceptthenewjob.

请听第9段材料,回答第13至16小题。

13.Whatdoesthemando?

A.Alawyer.B.Apoliceman.CAjournalist.

14.Whatdidtherobberdo?

A.liemadethewomangetontheground.

B.Hetalkedtothewomandirectly.

C.Heaskedthewomanformoney.

15.Whatwastherobberlike?

A.Veryyoung.B.Verystrong.C.Verytall.

16.Whydoesthewomanwanttogonow?

A.Sheisfrightened.

B.Shehastogotoclass.

C.Shedoesn,tknowwhatelsetosay.

请听第10段材料,回答第17至20小题。

17.WhenwasKatharineborn?

A.In1907.B.In1917.C.In1927

18.WhatkindofjobdidKatharinetakeaftergraduatingfromuniversity?

A.AreporterB.AlawyerC.Anofficial

19.WhoisPhilipGraham?

A.Katharine?sassistantB.KatharineJshusbandC.

Katharineyslawyer

20.WhatcanweknowaboutKatharine?

A.Sheboughtafailingnewspaper.

B.Shewasborninaverypoorfamily.

C.ShemadeTheWashingtonPostfamousalloverthecountry.

第二部分阅读理解(共两节,满分40分)

第一节(共15小题;每小题2分,满分30分)

阅读下列四篇短文,从每小题所给的A、B、C和D四个选项中,选出最佳选项,并在答题卡

上将该选项涂黑。

A

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21.Whatdoesthehospitalspeciallyoffertopets?

A.Petlicensesandtimely

care.B.Clinicroomsand

petplaymates.

C.Goodpetdoctorsandfullservices.D.The

bestmedicineandtreatment.

22.Whatisthemostimportantforpethealth?

A.Foodand

exercise.

B.Nutritionandprevention.

C.Technologyand

equipment.D.Experience

andpatience.

23.Whatistheauthor,spurposeinwritingthepassage?

A.Tomakeanadvertisementforapethospital.

B.Toinformpetownershowtotreattheirpets.

C.Tointroduceatrustedveterinariantopetowners.

D.Totellpeopletotreattheirpetsbetter.

B

AteamofengineersatHarvardUniversityhasbeeninspiredbyNaturetocreate

thefirstroboticfly.Themechanicalflyhasbecomeaplatformforaseriesofnew

high-techintegratedsystems.Designedtodowhataflydoesnaturally,thetiny

machineisthesizeofafathousefly.Itsminiwingsallowittostayintheair

andperforincontrolledflighttasks.

"It'sextremelyimportantforustothinkaboutthisasawholesystemand

notjustthesumofabunchofindividualcomponents(元件),“saidRobertWood,the

Harvardengineeringprofessorwhohasbeenworkingontheroboticflyprojectfor

overadecade.Afewyearsago,histeamgotthego-aheadtostartpiecingtogether

thecomponents."Theaddeddifficultywithaproject1ikethisisthatactuallynone

ofthosecomponentsareofftheshelfandsowehavetodevelopthemallonourown,〃

hesaid.

Theyengineeredaseriesofsystemstostartanddrivetheroboticfly."The

seeminglysimplesystemwhichjustmovesthewingshasanumberofinterdependencies

ontheindividualcomponents,eachofwhichindividuallyhastoperformwell,but

thenhastobematchedwelltoeverythingit,sconnectedto,〃saidWood.Theflight

devicewasbuiltintoasetofpower,computation,sensingandcontrolsystems.Wood

saysthesuccessoftheprojectprovesthattheflyingrobotwiththesetinycomponents

canbebuiltandmanufactured.

Whilethisfirstroboticflyerislinkedtoasmall,off-boardpowersource,

thegoaliseventuallytoequipitwithabuilt-inpowersource,sothatitmight

somedayperformdata-gatheringworkatrescuesites,infarmers*fieldsoronthe

battlefield."Basicallyitshouldbeabletotakeoff,landandflyaround,〃hesaid.

Woodsaysthedesignoffersanewwaytostudyflightmechanicsandcontrol

atinsect-scale.Yet,thepower,sensingandcomputationtechnologiesonboardcould

havemuchbroaderapplications."Youcanstartthinkingaboutusingthemtoanswer

openscientificquestions,youknow,tostudybiologyinwaysthatwouldbedifficult

withtheanimals,butusingtheserobotsinstead,〃hesaid.〃Sotherearealotof

technologiesandopeninterestingscientificquestionsthatarereallywhatdrives

usonadaytodaybasis.〃

24oThedifficultytheteamofengineersmetwithwhilemakingtheroboticflywas

that.

A.theyhadnomodelintheir

mindB.theydidnothavesufficienttime

C.theyhadnoready-madecomponentsD.theycouldnot

assemblethecomponents

25.Itcanbeinferredfromparagraphs3and4thattheroboticfly.

A.consistsofaflightdeviceandacontrolsystem

B.canjustflyinlimitedareasatthepresenttime

C.cancollectinformationfrommanysources

D.hasbeenputintowideapplication

26.Whichofthefollowingcanbelearnedfromthepassage?

A.Theroboticflyerisdesignedtolearnaboutinsects.

B.Animalsarenotallowedinbiologicalexperiments.

C.Thereusedtobefewwaystostudyhowinsectsfly.

D.Wood'sdesigncanreplaceanimalsinsomeexperiments.

27.Whichofthefollowingmightbethebesttitleofthepassage?

A.FatherofRobotic

Fly

B.InspirationfromEngineeringScience

C.RoboticFlyImitatesRealLife

InsectD.HarvardBreaksThroughinInsectStudy

C

Whenitcomestomedicalcare,manypatientsanddoctorsbelieve"moreis

better.Butwhattheydonotrealizeisthatovertreatment—toomanyscans,toomany

bloodtests,toomanyprocedures-maybringharm.Sometimesatestleadsyoudown

apathtomoreandmoretesting,someofwhichmaybeinvasive,ortotreatmentfor

thingsthatshouldbeleftalone.

TerrencePower,forexample,complainedthatafterhiswifelearnedshehad

Wegener*sdisease,anuncommondisorderoftheimmunesystem,theyfounditdifficult

torefusetestingrecommendedbyherdoctor.Thedoctorinsistedonofficevisits

everythreeweeks,evenwhenshewasfeelingwell.Hefrequentlyorderedbloodtests

andX—rays,andrepeatedlyreferredhertospecialistsforevenminorcomplaints.

Evenwhentestscamebacknegative,morewereordered,andshewashospitalizedas

preventionwhenshedevelopedacold.Shehadasmanyas25doctorvisitsduringone

six-monthperiod.Thecouplewasspendingabout$30,000ayearforhercare.

Afterseveralyearsofphysicalsufferingandnearfinancialruinfromthe

medicalcosts,thecouplebeganquestioningthetreatmentafterdiscussingwithother

patientsinonlinesupportgroups.〃It'sareallyhardthingtodeterminewhenthey,ve

crossedtheline,〃Mr.Powersaid."Youthinkshe'sgettingthebestcareintheworld,

butafterawhileyoustarttowonder:Whatisthepurpose?”Mr.Powerthenspoke

withhisownprimarycaredoctor,whoadvisedhimtofindanewspecialisttooversee

Mrs.Power,scare.Underthenewdoctor*scare,theregulartestingstoppedandMrs.

Power'sconditionstabilized.Nowsheseesthedoctoronlyfourorfivetimesayear.

28.Whatisthemainideaofthispassage?

A.Treatmentsdonotalwayscauseharmfulsideeffects

B.Patientstendtobelievemoretestingisbettertreatment.

C.Toomuchmedicalcaremaynotbebeneficialtopatients.

D.Doctorsgenerallyrecommendofficevisitsthatarenecessary.

29.WhichofthefollowingwasaproblemforMrs.Powerduringhermedicaltreatment?

A.Shehadtobehospitalizedforthreeweekswhenevershehadacold.

B.Whentestresultsshowedshewasfine,herdoctorstillorderedmoretests.

C.Shedidnothaveanyinsurance,soshebecamepennilessbecauseofherillness.

D.Herdoctoraskedhertoconsultotherspecialistsduetoherconstantcomplaints.

30.Whodoes"they"inthethirdparagraphmostlikelyreferto?

A.Doctors.B.Otherpatients.C.Mr.andMrs.

Power.D.Theonlinesupportgroups.

31.WhatledtothePowers'doubtaboutMrsPower,streatment?

A.Mrs.Power'sconditiongettingworse.B.Theresults

ofherbloodtests.

C.Knowingaboutotherpatients'treatment.D.TheadvicefromMr.

Power'sdoctor.

D

Anyonewhoisafraidoffailureandafraidtofacechallengeswi11nevertaste

success,sosaidourprofessorinmarketing.Ilaugheditoffatthattime,butgot

frightenedwhenitactuallyhappenedinmylife.

IlandedinasmallcityintheMiddleEasttosetupafirm,aworld-class

carrentalfirm.Havingdecidedontheproject,Iearnestlysettledinpreparation.

Withapositivemind,Itoldmyselfnothingshouldstopmenow,andwasmorethan

keentomakeitasuccess.

However,theleastexpectedthinghappened.IraqinvadedKuwait.Tensionran

highintheregion.Eventuallythewarbrokeout,andmanypeoplefledthecountry,

leavingmyfirmindeeptrouble.

Asusual,“thingsbecomedifficult,andeveryeffortseemstobring

disappointment,itcanbetemptingtoloweryourexpectationsorevenwaterdownyour

goalsandambitions.Iwasnoexception.Ithoughtofrunningaway.Iremembered

thewordsofThomasEdison,“Manyoflife'sfailuresarepeoplewhodidnotrealize

howclosetheyweretosucceedwhentheygaveup.”

Idecidedtohangon,tellingmyself,“Iamnotafraidofchallengesand

obstacles.〃Istayedonthroughmonthsofuncertaintyandinsecurity.Financesran

low,andbankscouldnotwaittogettheirdues.Toaddtoallthis,thebankseven

threatenedtotakeallmyvehicles.IfeltImadeawrongdecisiontomovethere.

Iwasnowreadytofacefailure.

Iwaslivingagainstallhopes,believingthatsomethinggoodwouldhappen.

After2monthsthewarended.Mypersistencepaidoff:peoplestartedfloodingback

andthecarbookingspickedup,fivetimesover.

Successcomestotheonewhodares,evenafterfailure,tothinkpositively

andlookforwardconfidently.Afterall,itisonlytheexperiencethatmakesaman

tough.Failuredoesnotmeanyouwillnevermakeit.Itmeansthatitwilltakea

littlelonger.Itprovidesuswithalearningexperience.

32.Themainmet

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