第29期A2版Keys及重点解析：单项填空1-5 DBCCB6-10 DBACA 11-15 DBDCA3.C。考查动词短语辨析。句意：与大多数发明家不同，Tim Berners-Lee将他的发明一一万维网，无偿赠送给公众。hand in上交；pass off消失；give away赠送；bring back归还。6.D。考查名词辨析。句意：失明且贫穷意味着Tom不得不面对许多挑战，但他从未失去信心。campaign活动；commitment承诺；consequence结果；challenge挑战。9.C。考查名词性从句。What在句中引导主语从句，且在主语从句中作主语。l3.D。考查时态。根据时间状语over the past twenty years可知，句子应使用现在完成时态。阅读理解1-4AADB第29期A3版Keys及重点解析：阅读理解1-4 DACD导语：本文是一篇新闻报道，属于“人与社会”主题语境。主要介绍了在大都会艺术博物馆进行的一场著名荷兰画作的展览。2.A。推断。根据第二段.Portrait of Gerard de Lairesse.producing a visually attractive effect toshow the tensions between realism and idealism during this period.可知，这两幅作品放在一起展览是为了呈现现实主义和理想主义之间的冲突，故可推知这两幅作品的创作风格是不同的。4.D。理解具体信息。根据最后一段hear from experts in diverse fields about how theseartworks continue to inspire...rearranges the fiction of flower arrangements.,Audio Guide向观众呈现了这些展出的画作是如何对欣赏过它们的人产生影响。完形填空1-5 CBDCD6-10 ABACD11-15 DBCBC 16-20 AADAB导语：本文是一篇记叙文，属于“人与自我”主题语境。讲述了作者学打保龄球的故事。7.B。本题考查同义或近义关联。此时作者说出了让自己惊讶的话，即答应加入(Goin)保龄球队。join the team与前文being a member of my bowling team属于同义关联。第29期A4版Key(One possible version):实战演练Dear foreign friendsWith the greatest regret,I have to inform you that there has been a change in thecross-country race schedule that was originally planned for next Friday.The heavy rainfall in the past few days has made the designated course unsafe for participants.Ensuring the safety of our participants is our main concern.Therefore,we have decided to makealternativearrangements.The new date of the race will beannounced soon.All other arrangements,including the route and participation details,will remainthe same.We apologize for any inconvenience this change may cause.And we believe that thisadjustment will allow us to deliver a more enjoyable experience to all participants.Thank you foryour understanding and support.Yours,Li Hua

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2023-2024学年6考5.解：(1蜥车头到达0点的时间为4=20m25s"8m/s轿车尾到达0点的时间为4=2044.8)m8 m/s3.18助力车到达0点的时间为x 20 m—=-2.9s7 m/s因为助力车到达0点时，轿车恰好通过0点，所以会发生交通事故。(2)若助力车到达0点的时间小于2.5时，就可以避免发生交通事故。设其最小加速度为a,则有=+代入数据解得a=0.8mh2。

11.已知△ABC中，a,b,c为角A,B,C的对边，acos B+bcos A=csin C,若∠BAC与∠ABC的内角分线交于点I,△ABC的外接圆半径为√2，则△IAB面积的最大值为()A.2√2-2B.4√2-4C.√2-1D.2-212.已知a=2,6=2c=8-81n2,则C.a0)上一点P(3,0)到其焦点的距离为8，则=14.若函数)=-2x十3经过点（a0,>0且6>0，则。+名的最小值为15.已知正三棱锥的各顶点都在表面积为64π的球面上，正三棱锥体积最大时该正三棱锥的高16.已知面向量a,b,c满足|a=|b=a-b=1,c·a=c·b=1,则c=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17一21题为必考题，每个试题考生都为必须作答.第22、23题为选考题，考生根据要求作答)17.(12分)某棉纺厂为了解一批棉花的质量，在该批棉花中随机抽取了容量为120的样本，测量每个样本(一)必考题（共60分）棉花的纤维长度（单位：mm,纤维长度是棉花质量的重要指标），所得数据均在区间[20,32]内，将其按组距为2分组，制作成如图所示的频率分布直方图，其中纤维长度不小于28m的棉花为优质棉+频率/组距0.2002a--a叶020222426283032m(2)已知抽取的容量为120的样本棉花产自于A,B两个试验区，部分数据如下2×2列联表：(1)求频率分布直方图中a的值；A试验区B试验区总计优质棉10非优质棉30120总计将2×2列联表补充完整，并判断是否有99.9%的把握认为优质棉与A,B两个试验区有关系，a+)(c十d)(a十c)6+D其中n=a+b十c+d.n(ad-bc)2参考公式及数据：K2=0.0250.0100.0050.001P(K≥k)0.150.100.055.0246.6357.87910.828ko2.0722.7063.841

参考答案：1.B2.C3.A4.C5.D6.A7.D8.D9.C10.A11.B12.B由ae8=0.8e,be12=1.2e，ce6=1.6e,用28.合是台总令点则r)专当x<1时，f叫)>0，当x>1时，()<0，所以f(x)在(-0,1)上是增函数，在(1，+∞)上是减函数，于是f(1.2)>f(1.6),即f(b)>f(c),又b,c∈(0,1)，所以b>c;4c0.81.60.80.8×20.8e8-2ee°e0se6ese8xeo8=eo8×e08因为54=625>29=512，所以54>24×25，2,>2因此e8-2>〔)-20，于是f回9，又ce0),所以se,令8因-后。则go-长兰-0-6e6so,所以a在e42()上是指两藏，8880，器98c0,即号<0，二号f(0.8)a>c.故选：B.13.y=2x14.-215.√2-1/-1+V216.0.104设N(x,)，由题意可得：d(M,)=2-+1-=1,即x-2+y-=1,可知x-2+y-1=1表示正方形ABCD,其中A(2,0),B(3,1),C(2,2),D(1,1),即点N在正方形ABCD的边上运动，因为OM=(2,),ON=(x,),由图可知：当cos(M,N)=cos(OM,OW）)取到最小值，即(OM,OW）最大，点N有如下两种可能：①点N为点4，则0成=2.0，可得eos(M,NM）=OM,0N=52=25UruI②点N在线段CD上运动时，此时ON与DC=(1,)同向，不妨取ON-(1,1),答案第1页，共6页

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x=2令z=2y-×,即y支X+号表示斜率为立，数裁距为号的行直线系。11画直线6：y=2X,移直线6到直线，当直线（过点A时，直线（的纵截距最小，Z最小，即Zmn=2×(-1)-2=4,所以2y-x的最小值为-4.故答案为：-415.某玩具厂计划设计一款玩具，准备将一个棱长为4c的正四面体（所有棱长都相等的三棱锥)密封在一个圆柱形容器内，并且这个正四面体在该圆柱形容器内可以任意转动，则该圆柱形容器内壁高的最小值为cm.【答案】26【解析】【分析】依题意该正四面体内接于该圆柱的内切球时，圆柱形容器内壁高的最小，则正四面体外接球的直径即为圆柱形容器内壁的高，求出正四面体外接球的半径，即可得解。【详解】依题意该圆柱内放置一个棱长为4c的正四面体，并且正四面体在该圆柱内可以任意转动，则该正四面体内接于该圆柱的内切球时，圆柱形容器内壁高最小，则正四面体外接球的直径即为圆柱形容器内壁的高，如图正四面体P-ABC,设点P在面ABC内的射影为H,即PH⊥面ABC,43则武心O在PH上，AHAB,cos303所以PH=VPA2-AH2=,/42434W63设外接同的半径为R,OP=OA=R,所以OH=PH-OP-45-R.3在Rt△OAH中，OAP=OH2+AH,即R2=42-R433+3

日1、本试圈满分150分，考试时间120分钟，2、答卷前务必将自已的姓名、学校、班级、准考证号填写在答题卡和答题纸上3、将选邦恩答案填涂在答题卡上，非选择愿按照图号完成在各肠纸上的指定区域内。89誉d第I卷（选择题共60分）114一、选择题：本大题共12小题，每小题5分，共60分在每小题给出的四个选项中，只有一项是符合题目要求的1、若复数z满足(1-2i)z=2+i,则|z=A号B.1.小本)1转数D.√J4152.已知集合A={0l,2,3},B={xx(x-4)<0},则AUB=A.{12,3}B.{x0

(2)若fx+a)-回a>0,则y=fx)是R=2.设六棱锥P-ABCDEF以T=2a为周期的周期函数，(3)若函数y=f(x)的图象关于直线x=a与的高为h,则VPARCDEF=3x=b(a

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5.What is the man's pet's name?5AA.Willie.学美花报社B.Mike.C.Harry.EARNING ENGLISH听力材料Text5W:What a cute pet!What's his name,Mike?新课程M:I named him Willie,after my favorite singer,第40期Willie Nelson.(5)高一(B)必修3TEST YOURSELFW:Great name!Still,I'm surprised you didn't(期中质检卷)name him Harry,after your favorite bookgcharacter.第第一节1B第二节1.What are the speakers talking about?听第6段材料，回答第6、7题。④6-7BCA.A pair of jeans.B.A pair of shoes6.What will the man do this afternoon?分C.A pair of gloves.A.See a movie.听力材料Text1B.Take some photos.听M:Wow!They're so pretty and you do look tallerC.Do some shopping.in them!(1)7.When will the speakers meet today?W:Now I need to take them off.They're killing myA.At 2 pm.feet.(1)Ouch,what a pain!B.At 6 pm.度C.At 7 pm.2.Where does the conversation probably take 2 C听力材料Text6place?④W:What are your plans for the afternoon,Mark?NickA.At a bakery store.and I are going to the movies.Do you want to join us?B.At a restaurant.M:I'd love to,but I have to meet Linda.She has an onlineshop selling men's clothes and she wants me to takeC.At the man's home.some photographs for it.(6)I'm meeting her in her听力材料Text2apartment at two.W:Then let's meet for dinner,shall we?How about theW:This bread tastes so good!Did you make itThai Food House we went to last Friday?I'll see youyourself?there at about six o'clock.M:No.My wife got it from the supermarket thisM:I'm afraid it won't be finished then.How about seven?gmorning.(2)g(7)W:Sure,see you.3.What does the man think of the weather inXi'an?④3A听第7段材料，回答第8、9题。8-9ACA.It's too cold.8.Which floor does the woman want to go to?B.It's too warm.A.The 23rd floor.C.It's too wet.B.The 15th floor.听力材料Text3C.The 5th floor.9.Who does the woman think caused the problem?W:Do you like the weather in Xi'an?A.The man.M:Er...too cold for me.(3)I must say I'm used tothe warm winter in Hong Kong.B.The apple seller.W:But I think it's much better than some southernC.The woman with the bags.cities where it is not only cold but also wet原听力材料Text74.What will Mary do first?A.Visit a college.M:What happened?All I did was push the button for theB.Attend a course.15th floor.W:And I just pushed the one for the 23rd floor.(8)C.Go on a vacationM:Did you push the red HELP button?They need to听力材料Text4know we are stuck here.W:No,I'm doing it right now.The lady who got off on theM:Has Mary decided what to do before she goes to5th floor surely took her time getting off.I bet that'scollege?what caused the problem.(9)She was holding the doorW:Oh,yes.She has got everything planned out.She'sfor about five minutes while she was getting out.going to have a holiday for a few weeks and thenM:She was carrying a lot of bags.(9)Look!She droppedshe will attend an English course.(4)an apple on the floor here.Do you want it?W:No,I don't want a snack.I just want to be rescued.

b故b=csnB.4sin(C+)弦定理，c=sinC sin BsinC2imc+25oC-2+25sin CsinCnCe(2),故选A2+2510、【答案】C【解析】依题意，号号-（的.则7≥，故o1,国为-+1问=0，货0为11π5π_3rTx2+p=T+2kπkeD,5π2函数闪图象的一个对称中心，则8-名=年-4，故T=3玩，故0=死=子：而g×行+p3π32解得p吾则四=2号+0：放80=20治，合号+2r≤2+经42mke0,解有2经≤：北e0.双案可知越C2411.【答案)}【解折】由题知，80-2m-名+合=2mar答+急,g(x)是偶函数，,0>0,02.kZ,0=-6k-6122+14912.【答案】【解折】依愿意，5血2a+6os2a-2 i+coe2a=m2c.2ama+1-am2g_士cos2a+sin2a1+tan2a1912+9-4179+413【解折析】依题意，f)=cosx+os=osx(0sx≥0)313.【答案】故函数f(x)在[0，]上单调递2cosx(cosx<0)减.在怀2闲上单调超指，故[V闪l=0=了2)[V]-问专故所球值域为[引递地，故：一的最大值为号（受誓sin(B+C)1115.【答案】√0【解析】依题意，记A,B,C对应的边分别是a,b,c,故sinAsin B2cos(4+B)sin B-2cosC即血B=2如4asC，故b=Va，由BC4C=22,所以b=22,即0=5,由余弦定理知，b=2C=d+-2 ab=2+4+452-10,所以c=0=B.16.【解折】D-2o83=2os8m3=1-45-3=2-45,4分(2)f(x)=2cos2x-8sinx-3=-2sin2x-8sinx-1=-2(sinx+2)2+7.(6因为-1≤sinx≤1，故1≤sinx+2≤3，故-11≤-2(sinx+2)}+7≤5，故f)的值域为[-11,5，(12分)17.【解析】(1)若选①：由正弦定理得，sin AcosC+sinCeos4-in,故n(+C-inBos，2分）4而在△MBC中，5n(4+9=加6r-)=nB,故mB=9 in o,则asB=行5,(3分)则血B=os2B=2,则amB=如82，故am2B1-am2B1-92X77:(6分)2tan B23.16245cosB 416专题07数学答案与解析第2页

“部+船≥”的,当角位当=形的锐等乡龙影物线的对路作可知，=脚=警我中=的一学，五=梦一号复16【答案列【g狮1a1-3=a,-2.+1)4=号1一3=一出一24一=(0，一1>与4>，到列乡每男克弹，女0+1=话-，+1,441-1=4，（a,-1)>0,,mw4>a>w>>2,1,0Sw,的整劲福分是11,(答案11)路(2号【解新1(1)证明：连丝BD,E,F分别是核AC,BC的中点，EP∥AB:EFC面CEF,AB吐面CEF,,AB∥面CEFD,F分别是烧B,C,BC的中点，BF∥CD,BF=CD.,四边形BDCF是行四边形，则BD∥CF,CGFC面CEF,BDt面CEF,,BD∥面CEF,,AB,BDC面ABD,且AB门BD=B,源ABD∥面CEF:ADC面ABD,,AD∥面GEF;分(2)取A1C的中点O,连批OB,OE,易证OB,OC,OE两两垂直，则以O为原点，分别以0B,OC,O龙的方向为工，y,2轴的正方向，建立如图所示的空同直角坐标系，设AB=4,则(0，-2,3，(0,2,0)，D(B,1,0),E(0,0,3),F(B,1,3),头而i=(B,3,-3),A2=(0,2,0),C2-(0,-2,3,E乎=，1,0，……8分设面ADE的法向量为n=(x,头，名)，则n,Ai=gx+3外-3z=0,n·A2=2y=0:9令1-3，得n=B,0,1,难料数学答案第3页（共5页）

·文数·参考答案及解析心+心-合因为防=(a-0+6,所以ac一19.解：(1)若选①2ac因为2cosA(ccos B+bcos C)=a,6,所以SA=号PA,PBsin要+号PB·PC所以2cosA(sin Ccos B+sin Bcos C)=sinA,所以2 cos Asin A=sinA,因为sinA≠0，所以sin+号PA·PCsin-=s血音=，所以PA,PB+PB·PC+PA.6a1分又0°

榆林市2022~2023年度高三第四次模拟检测数学试题参考答案（理科）1.B因为P={-2,2},Q={-1,0,2,3},所以PUQ={-2,-1,0,2,3}2.D因为x=(1一i)(3十i)=4一2i,所以复数之在复面内对应的点位于第四象限3.D因为a=2√2，b=√6，所以渐近线的方程为2√2x士√6y=0,即2x士√3y=0.A因为tan a=tan (a十买)-，所以an2。一21+5×135.D因为f(x)=2.x十aem,所以∫(0)=a.因为f(0)=-1,所以f(x)的图象在x=0处的切线方程为y=ax一1.由题意易知a≠0，令x=0,得y=-1,令y=0,得x=,所以2·-1·1日1-1，所以a=士26.C将函数y=cos2x的图象向右移0个单位长度，所得函数图象的解析式为y=cos[2(x无)]-os(2x一无)，再把所得图象各点的横坐标缩小到原来的2（纵坐标不变），所得图象的函数解析式是y=c0s(4r一无).令42=π，∈乙，则x=+年，k∈乙.当=0时，2π4017.C因为=0.3>0.5，所以6=0.3∈(2,1).因为a=logV2-号logs2<号1og3=号c=0.52>1,所以a

绝密★启用前（全国卷）理科数学参考答案1.【答案】A【解析】列举可知，集合A={4},所以CvA={1,2,3}2.【答案】C【解析】因为z=i+,5=ai+2+i5-)、=2+(a-1)i,对应的点为(2，a-),(2+i)(2-i)由题意，a-1=4,所以a=-3.3.【答案】D【解析】常数项为1-2C2C4+(-2)2C4=-594.【答案】B【解析】因为a+2b=a+b,所以a+4b+4ab=a2+lb+2a·b,所以3b+2ab=0,因为a=216,所以36+46Pcos(a,6)=0,所以cos(a,6)=-子5.【答案】B【解析1因为00-200.所以00=告0，=合，所以+(-(2图，所以3r-兮，所以华-36.【答案】D【解析】如图，可行域为△ABC所围成的区域其中4(2).c(售引，满足+0的区城为△400，且OD∥BC,所以x+y<0的概率P=S△4op9S△ABCAc-257.【答案】C【解析】直线与抛物线C,联立，y=4x,消去x,整理得y-4y-4=0,y=x-1理科数学参考答案（全国卷）第1页（共10页）

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Text 7M:Anna,there was a strong earthquake in Japan.W:When did it take place?M:It happened near the northeast coast of Japan on Wednesday night.There was a tsunami warning,but it was liftedthe next morning.No large waves appeared.W:I hope it hasn't caused any deaths.M:Unfortunately,the quake killed four people and left at least 140 people injured.Also,a train carrying about 100people went off the rails because of the quake.And two major highways are being carefully inspected before theycan re-open.W:That's very bad.So I think it's necessary to know how to survive an earthquake.Do you know how to do that?M:Oh,I've read an article about it.Are you interested?W:Yes.I'm all ears.Text 8M:Good morning,madam.Can I help you?W:Yes,please.I bought this small TV set here recently and when I got it home I couldn't get it to function well.Youshould check it.M:When did you buy it?W:I bought it on June 5th.That's two days ago.M:What exactly is wrong with the TV?W:Well,I bought it so I could watch TV while I was cooking for the family.That's why I just bought a small one.Itcould fit on the shelf next to the dining room door.Anyway,when I got it back and turned it on,there was onlysound,with no picture.M:Hmm.I'm so sorry for that.That's very strange.I'll return it to the repair department right now.W:Actually,I have lost faith in the quality.I claim the refund.M:Sorry again for that.We offer a "7-Day No Reason Return".Let me register that for you.Text 9W:Have you noticed that people keep visiting the house next door?M:The empty one,you mean?W:Yes,today is the third time this week that I have seen people there.They were there for ages.M:It's been empty for a long time,hasn't it?It must be in a very poor state.W:It is.I wouldn't be surprised if the floor is broken.M:Maybe the people you've seen have come to fix it.W:They probably come to buy it.I heard people talking about it in the local shop the other day.M:Oh,really?What were they saying?W:They were saying some people from London had looked at the house and they were thinking of turning it into ahotel.M:How would you feel about having a hotel next door to you?W:I can't imagine what it would be to have strangers coming and going every day.I mean,we don't know them.We're not sure if they're good people or bad people.M:Your worry makes sense.W:So I suppose I'd prefer to have an empty house next door to me.Text 10W:Ashleigh Barty,the world's No.1 women's tennis player,shocked the sports world on Wednesday byannouncing that she is retiring from tennis.Barty,who is just 25,says that it's time for her to chase other dreams.Barty made the announcement in a video.In the video,Barty discussed her thoughts about retiring with her good friend Casey Dellacqua.Dellacqua,who isalso a retired tennis player,used to be Barty's doubles partner.Barty made it clear that playing professional tennis atan extremely high level is very demanding and stressful.She said she knew how much work it took to bring the best outof herself.She added she didn't have that in her anymore.Even though she was only 25,Barty has been playing tennis for a long time.She started when she was four andturned professional ten years later.For over two years,Barty has been ranked the world's No.1 women's tennisplayer.She has won 15 important women's singles tournaments in her career.In 2019,Barty won the French Open.In 2021,she won Wimbledon.And in January 2022,she won the Australian Open.Barty said she knew some peoplewouldn't understand her decision,but she's okay with that.英语参考答案（雅礼版）一4

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