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设函数
,.若函数的图象与轴恰有两个公共点,则实数的取值范围是().
A. B.
C. D.
二、填空题:
本大题共4个小题,每小题5分,共20分.把答案填写在题中横线上.
13.函数的最大值是.
14.展开式中,常数项是__________.
15.若平面向量α,β满足|α|≤1,|β|≤1,且以向量α,β为邻边的平行四边形的面积为,则α与β的夹角的取值范围是。
16在斜三棱柱中,底面是以∠ABC为直角的等腰三角形,点在平面ABC上的射影为AC的中点D,AC=2,=3,则与底面ABC所成角的正切值为.
三、解答题:
本大题共6个小题,共70分.解答应写出文字说明、证明过程或演算步骤.
17.(本小题满分10分)
在⊿中,角的对边分别为,且
(Ⅰ)求的值;
(Ⅱ)若,且,求的值.
18.为了比较注射两种药物后产生的皮肤疱疹的面积,选200只老鼠做试验,将这200只老鼠随机地分成两组,每组100只,其中一组注射药物(称为组),另一组注射药物(称为组),则两组老鼠皮肤疱疹面积(单位:
)的频率分布表、频率分布直方图分别如下.
(Ⅰ)为方便两组试验对比,现都用分层抽样方法从两组中各挑出20只老鼠,求两组皮肤疱疹面积同为的这一区间应分别挑出几只?
(Ⅱ)在(Ⅰ)的条件下,将两组挑出的皮肤疱疹面积同为这一区间上的老鼠放在一起观察,几天后,从中抽取两只抽血化验,求组中至少有1只被抽中的概率.
19.(本题满分12分)如图,在平行四边形ABCD中,AB=2BC,∠ABC=120°
。
E为线段AB的中点,将△ADE沿直线DE翻折成△A’DE,使平面A’DE⊥平面BCD,F为线段A’C的中点。
(Ⅰ)求证:
BF∥平面A’DE;
(Ⅱ)设M为线段DE的中点,求直线FM与平面A’DE所成角的余弦值。
20.(本小题满分12分)
已知数列的前n项和为,且(),
(1)求证:
数列是等比数列;
(2)设数列的前n项和为,
,试比较与的大小.
21.椭圆C的中心为坐标原点O,焦点在y轴上,离心率e=
,椭圆上的点到焦点的最短距离为1-
直线与y轴交于点P(0,m),与椭圆C交于相异两点A、B,且.
(1)求椭圆方程;
(2)若求m的取值范围.
22.(本题满分12分)
已知函数,其中为实数.
(Ⅰ)当时,求曲线在点处的切线方程;
(Ⅱ)是否存在实数,使得对任意,恒成立?
若不存在,请说明理由,若存在,求出的值并加以证明.
2019-2020年高三压轴信息卷数学理
题号
1
2
3
4
5
6
7
8
9
10
11
12
答案
C
D
A
B
∵
=3
∴-x1=3x2∴
消去x2,得3(x1+x2)2+4x1x2=0,∴3(
)2+4
=0
整理得4k2m2+2m2-k2-2=0 13′
m2=
时,上式不成立;
m2≠
时,k2=
,
因λ=3∴k≠0∴k2=
>
0,∴-1<
m<
-
或
<
容易验证k2>
2m2-2成立,所以(*)成立.即所求m的取值范围为(-1,-
)∪(
,1)∪{0}
22.解:
(Ⅰ)时,,,,
又所以切线方程为………6分
(Ⅱ)1°
当时,,则
令,,
再令,
当时,∴在上递减,
∴当时,,
∴,所以在上递增,,所以
2°
时,,则
由1°
知当时,在上递增
当时,,
所以在上递增,∴
∴;
及2°
得:
………12分
2019-2020年高三周末练习(第11周)英语试卷
第一部分:
听力(共两节,满分20分)
该部分分为第一、第二两节。
注意:
回答听力部分时,请将答案标在试卷上。
听力部分结束前,你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节(共5小题;
每小题1分,满分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,并标在试卷的相应位置。
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。
每段对话仅读一遍。
1.HowdoesJanefeel?
A.Satisfied.B.Happy.C.Depressed.
2.Whyaretherenoroomsavailable?
A.Becauseofaconference.
B.Becauseofamarathon.
C.Becauseofanoutdoormusicfestival.
3.Wheredoestheconversationprobablytakeplace?
A.Inahouseagent.B.Onthecampus.C.Inachurch.
4.Whatdoesthewomanmean?
A.Shedoesn’tthinkmuchoftheroom.
B.Theroomisfixedattheman’srequest.
C.Sheagreeswiththeman.
5.WhywasJanenervous?
A.Becauseshehadtotypeapaper.
B.Becauseshethoughtherpapermightbelate.
C.Becauseshewasafraidoffailingtheexam.
第二节(共15小题;
每题1分,满分15分)
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,每小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料,回答第6至8题。
6.What’sBob’sson’shobby?
A.Workinginthegarden.B.Collectingcoins.C.Collectingstamps.
7.Wheredoesthewomanwanttogosomeday?
A.Japan.B.China.C.Canada.
8.Whydoesn’tBobhavearealhobby?
A.Becausehe’stoobusy.B.Becausehe’slazy.C.Becausehe’scrazyaboutwork.
听第7段材料,回答第9至11题。
9.Howmuchisthetrainfare?
A.12Yuan.B.20Yuan.C.40Yuan.
10.Whereshouldthemangetonthetrain?
A.Onplatformnumber3.B.Onplatformnumber4.C.Onplatformnumber5.
11.Howoftendothetrainsearound?
A.Abouteverythirtyminutes.
B.Abouteverytwentyminutes.
C.Abouteverytenminutes.
听第8段材料,回答第12至14题。
12.Whereisthemanliving?
A.Inahotel.B.Inanewapartment.C.Athome.
13.WhenwillthewomanleaveforBerkeley?
A.Nextweek.B.Nextmonth.C.Theweekafternext.
14.Whatwillthetwospeakersdoat7:
00p.m.onSaturday?
A.Seeamovie.B.Haveadinner.C.Attendaparty.
听第9段材料,回答第15至17题。
15.Whatisprobablythe“Cops”?
A.ATVshow.B.Abook.C.Afilm.
16.Whatdoweknowabouttheboyatthefastfoodrestaurant?
A.Hesmokedheavily.B.Hehadalotofcandy.C.Hedrankalotofalcohol.
17.Whatarethetwospeakersinmon?
A.Theybothsmokecigarettes.
B.Theybothdrinkalcohol.
C.Theybothhavedrugs.
听第10段材料,回答第18至20题。
18.WhatdoRussianperformersdowhentheyreceivetheapplause?
A.Theydon’tclapuntiltheyleavethestage.
B.Theyusuallyclaptogetherwiththeirfans.
C.Theyusuallyrisefromtheseats.
19.Whydidpeopleclaphandsaverylongtimeago?
A.Toshowthattheylikedoragreedtosomething.
B.Toexpresstheirgreatadmirationforaperformer.
C.Toattempttodrivetheperformersoutofthestage.
20.Whatisthespeakermainlytalkingabout?
A.Thedreamofeveryperformer.
B.ThehistoryofclappinginRussia.
C.Thedifferentmeaningsofclapping.
第二部分:
英语知识运用(共两节,满分35分)
第一节:
单项填空(共15小题,每小题1分,满分15分)
21.Theworkerscouldhardlytheboss’sbadtemperbutunderhissupervisiontheyhadto
themselvestoworkingharder.
A.tolerate;
contributeB.bear;
dedicate
C.stand;
resignD.putupwith;
invest
22.Deeplyhisunhappychildhood,theboy’sseemedquiteoddandstrange.
A.relatingto;
charactersB.associatedwith;
personality
C.linkedby;
virtuesD.connectingto;
morality
23.Itisimpossibletoliveinsocietyandindependentofsociety;
andthereforeitisdifficultto
societyofinequalityaswellascorruption.
A.remove;
fromB.rid;
ofC.substitute;
withD.simplify;
by
24.Havingbeentrainedforoneandahalfyears,shemanagedtogetaprofessionalqualification
afirst–degreenurse.
A.consistingwithB.agreedwithC.correspondingtoD.correspondedwith
25.Crusoeisn’tgoodenoughfigure,buthisoutstandingskillpensatesforit.
A.inresponsetoB.intermsofC.infavourofD.inhonourof
26.Ifyoucan’twinfromthepublic,thegoldmedalwillmeannothingtoyou.
A.gamesB.knowledgeC.recognitionD.notice
27.Makesurethegasisturnedoffafterabath,whichwouldcausedanger.
A.somehowB.meanwhileC.otherwiseD.furthermore
28.Herexcellentperformanceinthepetitionprovedthatshewasawinner.
A.valueB.worthyC.worthD.worthwhile
29.thesecretofnature,theyyoungscientisthaslittletimeforentertainment.
A.Devotedtobetray
B.Devotinghimselftobringtolight
C.Devotedtounearthing
D.Devotingtoexploring
30.Thosesuccessfuldeafdancersthinkthatdancingisanactivitysightmattersmorethanhearing.
A.whenB.whoseC.whichD.where
31.___iswell-knowntoallisthatthexxShanghaiWorldExpohasbeenbroughttoanend.
A.AsB.ThatC.WhatD.It
32.Sincethenewdirectortookoffice,wehaveworked___hours,-thatistosay,weworkmorefreely.
A.flexibleB.pulsoryC.strictD.endless
33.___inaheavytrafficjaminataxiwhileyouarehurryingtotheairportisquiteaunpleasantexperience.
A.HavingcaughtB.Beingcaught
C.CaughtD.Havingbeingcaught
34.MyfamilyweremovingtothecountrysideandIhadtomakesome___andlearntoleada
differentlifethere.
A.allowanceB.acmodation
C.adjustmentD.assessment
35.TheChinesecaptainwasreleasedbyJapanfinally,___nearlyamonthofdetention(扣押),whichhasseriouslyharmedtherelationshipbetweenthetwocountries.
A.endedB.endingC.toendD.beingended
第二节:
完形填空(共20题;
每小题1分,满分20分)
Itwasawintermorning,justacoupleofweeksbeforeChristmas.Whilemostpeoplewere36_theircars,Trevor,myhusband,hadto_37_earlytoridehisbikefourkilometersawayfromhometowork.Onarrival,he_38__hisbikeoutsidethebackdoorasheusuallydoes.After_39_
10hoursoflabor,hisreturnedtofindhisbike40.
Thebike,ablackKona18speed,wasouronlytool.Trevorusedittogetto41,puttingin60-hourweeksto__42__hisyoungfamily.Andthebikewasalsousedtogetgroceries,43usfromhavingtowalklongdistancesfromwherewelive.
Iwasso44_thatsomeonewouldstealourbikethatIwrotetothenewspaperandtoldthemourstory.Shortlyafterthat,severalpeopleinourarea45tohelp.Onewonderfulstranger46boughtabike,thencalledmyhusbandtopickitup.47myhusbandhadawaytogettoandfromhisjob.Itreallyisa(an)48thatapletestrangerwouldgooutoftheirwayforsomeonetheyhavenevermetbefore.Peoplesaythatasmilecanbe49fromonepersontoanother,butactsofkindnessfrom50areevenmoreso.Thisexperiencehashadaspreadingeffectinourlivesbecauseit51ourfaithinhumanityasawhole.Andithas_52ustobemoremindfulofwaysthatwe,too,can53withothers.Nomatterhowbigorhowsmall,anactofkindnessshowsthatsomeone54.Andtheresultscanbe55.
36.A.coolingdownB.warmingupC.speedingupD.slowingdown
37.A.getupB.wakeupC.turnupD.riseup
38.A.piledB.pushedC.parkedD.paused
39.A.puttinginB.puttingonC.puttingoffD.puttingaway
40.A.brokenB.robbedC.hiddenD.gone
41.A.studyB.shopC.workD.deliver
42.A.liveB.supportC.serveD.protect
43.A.gettingB.protectingC.savingD.allowing
44.A.surprisedB.thrilledC.puzzledD.sad
45.A.offeredB.supportedC.providedD.agreed
46.A.stillB.finallyC.evenD.yet
47.A.NowandthenB.OnceinawhileC.OnceagainD.Soonerorlater
48.A.honorB.pityC.sympathyD.respect
49.A.thrownB.passedC.sentD.got
50.A.friendsB.strangersC.relativesD.parents
51.A.weakenedB.spreadC.reducedD.strengthened
52.A.movedB.forcedC.urgedD.influenced
53.A.shareB.connectC.dealD.work
54.A.likesB.caresC.worriesD.wonders
55.A.shortB.promising