东城区2019-2020第二学期高三综合练习(一)英语含答案
..................北京市东城区2019—2020学年度第二学期高三综合练习（一）英语2020.5本试卷共10页，共120分。
考试时长100分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AThe goshawk,a rare bird,once close to extinction,has doubled1(it)number in a national park in the south of England.Around100years ago,there were thought to be no goshawks2 (leave),due to farmers hunting them and their woodland habitats being cut down.However,thanks to conservationists,goshawks are back.By monitoring their nesting sites over time,the teams have been able to protect them from further forestry work.As a result,their number3(grow)from just20pairs to40pairs in the past two years.BOne morning,I told my husband jokingly that he’d dropped the ball because he hadn’t made me coffee and I was having trouble getting motivated4(start)the day.My five-year-old son overheard me and asked what“drop the ball”meant.I told him it was just something like making a mistake.A few minutes later,he came into our bedroom5(hold)an overflowing coffee cup with a dishcloth underneath it to catch the drops.He said to my husband,“You dropped the ball,but I picked the ball up,”and he handed me the worst-tasting,most watered-down but6(sweet) cup of coffee ever.CIn half a century,the Internet has transformed society.Billions of us can connect at the touch of a button.Access7information,banks and shops has never been easier.The world has changed8(dramatic)and continues to do so in ways we couldn’t have imagined.However,the Internet isn’t without disadvantages.By design,it has no central authority,9makes protecting people online or dealing with misinformation a near-impossible task.10the Internet develops will shape our future.If the past50years has been dominated by free and open exchanges,the next50will be about whether rules and restrictions can actually make the Internet,and the world,a better place.第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
At six feet,seven inches tall and weighing253pounds,Father was a quiet giant（巨人）who only roared when he was angry.He would work long days,often11when I was already in bed.My two younger sisters and I both loved and feared him.Hearing the words,“Just wait until your father comes home,”would guarantee the three of us would start12immediately.I was seven years old the night the“giant”became a person,and my13.All it took was the14of a tiny,dirty kitten.I15to the sounds of my father coming home from work.I slipped out of bed and moved quietly towards the living room in hopes of spending a few precious minutes16with my parents without my annoying sisters around.I heard mum say,“We cannot17it.”What was the“it”?The giant saw me and18 I should sit down near him.I was at a loss,although19might be a better word,for I had never seen or heard of a giant crying before.Unshed（满眶）tears20up in his eyes.His cheeks were21from the ones he had cried earlier.The giant reached into a cardboard box and brought out a dirty young cat and22it on my lap.I was soon23,as the giant shared a story with mum.As he spoke,with shakingshoulders caused by24and at times sorrow,he transformed from a giant to a man who became my hero.He25that he was on his way home when he heard two men laughing and talking.As he rounded the corner,he heard the most terrible scream of pain.He couldn’t26what he saw.The men had thrown a kitten into a furnace（火炉）.He yelled and ran up to them but it was too27.He couldn’t save the kitten.The men had run away and he was about to run after them when he saw another kitten at his feet.“We have to28it;we have to keep it!”said the giant.“It needs a29,”said mum.“I can help,Mommy!”Reminded of my presence,mum and my hero sent me off to bed.As I fell asleep,I heard mum running some water.We named the kitten Cinder and it joined our family.I never saw“the giant”again;I only saw my hero and a man whose heart was30than he was.11.A.greeting B.chatting C.returning D.wandering12.A.waiting B.escaping C.preparing D.behaving13.A.model B.hero C.tutor D.friend14.A.visit B.story C.arrival D.life15.A.awoke B.listened C.rushed D.dreamed16.A.straight B.alone C.indoors D.gradually17.A.keep B.leave C.train D.clean18.A.appealed B.urged C.indicated D.proposed19.A.regretful B.hopeless C.unwilling D.terrified20.A.built B.rolled C.blocked D.welled21.A.wet B.red C.bright D.fresh22.A.spread B.placed C.led D.dropped23.A.discovered B.forgotten C.convinced D.relieved24.A.fear B.surprise C.anxiety D.anger25.A.argued B.emphasized C.explained D.summarized26.A.believe B.prove C.guess D.judge27.A.bad te C.fast D.far28.A.help B.cure C.feed D.buy29.A.meal B.rest C.bath D.lift30.A.lighter B.purer C.warmer rger第二部分：阅读理解（共两节，40分）第一节（共15小题；每小题2分，共30分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
2019届北京市东城区高三高考二模英语试题解析
2019北京市东城区高三二模英语试题第一部分：知识运用（共两节，45分）第一节语法填空（共10小题：每小题1.5分，共15分）AWorld Environment Day is a UN Environment-led global event, ___1___ takes place on June 5 every year and is celebrated by thousands of communities worldwide. Since it began in 1972, it has grown to become the ___2___ (large) of all the celebrations of environment each year. China owns half the world’s electric vehicles and 99% of the world’s electric buses. By ___3___ (host) World Environment Day 2019, the Chinese government will be able to showcase its innovation and progress toward a cleaner environment.答案：1. which2. largest3. hosting这是一篇说明文。
文章介绍世界环境日。
【1题详解】考查非限制性定语从句。
句意：世界环境日是一项由联合国环境规划署发起的全球性活动，每年6月5日举行，全世界成千上万的社区都在庆祝。
此处event是先行词，指物，在后面的非限制性定语从句中作主语，that不能引导非限制性定语从句，故填which。
【2题详解】考查形容词最高级。
句意：自1972年开始举办以来，它已成为每年举办的所有环境庆祝活动中规模最大的一个。
根据空格前的the和句意可知此处用形容词最高级，故填largest。
北京市东城区2019届高三第二学期综合练习(一)英语试题
北京市东城区2019学年度第二学期高三综合练习（一）英语试题本试卷共1 2页，共1 50分。
考试时间l 20分钟。
注意事项：1．考生务必将答案答在答题卡上，在试卷上作答无效。
2．答题前考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写。
3．答题卡上选择题必须用2 B铅笔作答，将选中项涂满涂黑，黑度以盖住框内字母为准，修改时用橡皮擦除干净。
非选择题必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答，未在列应的答题区域内作答或超出答题区域作答的均不得分。
第一部分：听力理解（共三节，30分）第一节（共5小题；每小题1．5分，共7．5分）听下面5段对话。
每段对话后有一道小题，从每题所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你将有l0秒钟的时间来回答有关小题和阅读下一小题。
每段对话你将听一遍。
1．What does the man want to drink?A．Tea．B．Coffee．C．Hot water．2．Which cake does the man order?3．Where are the speakers?A．In the hotel．B．In the cinema．C．At the airport．4．What’s the man probably doing?A．Driving a car．B．Reading a map．C．Looking for a gas station．5．How does the man feel after retirement?A．Lonely．B．Depressed．C．Relaxed．第二节（共15小题；每题1．5分，满分22．5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。
北京市东城区2019届高三下学期综合练习(一)英语试卷含详解
2019年4月北京市东城区2018—2019学年度第二学期高三综合练习（一）英语试题本试卷共10页，共120分。
考试时长100分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分, 共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写一个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
ATons of waste is being left on Mount Qomolangma by a ___1___ (grow) number of visitors, which bothers many people. A team will deal with the task ___2___ the climbing season ends this May, by which time there will be fewer visitors. Garbage ___3___ (collect) on Qomolangma requires two to three years of training, according to Cering Dandar, a mountaineer and guide.【答案】1. growing2. when/after3. collection这是一篇说明文。
讲述了珠穆拉玛峰上随着游客增多而带来的成吨的垃圾困扰了许多人。
【1题详解】考查形容词。
句意：越来越多的游客在珠穆朗玛峰上留下了大量的垃圾，这让很多人感到困扰。
number为名词，需要形容词修饰，故填growing。
【2题详解】考查连词。
句意：一个团队将在今年5月登山季节结束后处理这项任务。
表示“在五月登山季节结束之后”应用after；也可以填when，表示“当五月登山季节结束时”，引导时间状语从句。
【区级联考】北京市东城区2019届高三第二学期综合练习(一)英语试题(原卷版)
北京市东城区2018—2019学年度第二学期高三综合练习（一）英语试题本试卷共10页，共120分。
考试时长100分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分, 共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写一个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
ATons of waste is being left on Mount Qomolangma by a ___1___ (grow) number of visitors, which bothers many people. A team will deal with the task ___2___ the climbing season ends this May, by which time there will be fewer visitors. Garbage ___3___ (collect) on Qomolangma requires two to three years of training, according to Cering Dandar, a mountaineer and guide.BFood is one of the most basic and important daily needs. It gives us the strength and energy we need ___4___ (work) and play. Food also plays a role in our social interactions. Whether we ___5___ (celebrate) important occasions or just relaxing with friends, eating is an important social pastime. It is also an important part of our culture. ___6___ a particular people like to eat can tell us a lot ___7___ a country’s geography, histo ry and traditions.CGoing to museums has become a trendy thing to do during the holidays in China. A popular choice this Spring Festival was the Palace Museum, ___8___ a special exhibition was staged to provide a virtual royal experience for visitors. The entire museum ___9___ (decorate) with newly-restored ancient royal lanterns and spring couplets, including a set of the Chinese character “Fu” ___10___ (write) by five Qing Dynasty emperors.第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
2020年东城高三一模英语试题及答案(2020.05)
北京市东城区2019—2020学年度第二学期高三综合练习（一）英语2020.5本试卷共10页，共120分。
考试时长100分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AThe goshawk,a rare bird,once close to extinction,has doubled1(it)number in a national park in the south of England.Around100years ago,there were thought to be no goshawks2 (leave),due to farmers hunting them and their woodland habitats being cut down.However,thanks to conservationists,goshawks are back.By monitoring their nesting sites over time,the teams have been able to protect them from further forestry work.As a result,their number3(grow)from just20pairs to40pairs in the past two years.BOne morning,I told my husband jokingly that he’d dropped the ball because he hadn’t made me coffee and I was having trouble getting motivated4(start)the day.My five-year-old son overheard me and asked what“drop the ball”meant.I told him it was just something like making a mistake.A few minutes later,he came into our bedroom5(hold)an overflowing coffee cup with a dishcloth underneath it to catch the drops.He said to my husband,“You dropped the ball,but I picked the ball up,”and he handed me the worst-tasting,most watered-down but6(sweet) cup of coffee ever.CIn half a century,the Internet has transformed society.Billions of us can connect at the touch of a button.Access7information,banks and shops has never been easier.The world has changed8(dramatic)and continues to do so in ways we couldn’t have imagined.However,the Internet isn’t without disadvantages.By design,it has no central authority,9makes protecting people online or dealing with misinformation a near-impossible task.10the Internet develops will shape our future.If the past50years has been dominated by free and open exchanges,the next50will be about whether rules and restrictions can actually make the Internet,and the world,a better place.第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
东城区2019-2020第二学期高三综合练习(一)语文含答案
..................北京市东城区2019—2020学年度第二学期高三综合练习（一）语文2020.5本试卷共8页，150分。
考试时长150分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
一、本大题共5小题，共18分。
阅读下面的材料，完成1-5题。
材料一网络直播并非由我国产生，早在1995年，美国苹果公司就已经进行了目前看来最早的一场网络直播，直播的内容是一场音乐会。
但由于当时技术所限，这一直播只是音频直播，并未实现画面的同步。
如果从专业角度来对网络直播进行定义，它其实就是一种借用互联网技术实现的媒体演示，不过是能够从一个内容源分发到多个用户端，实现内容的共享而已。
网络直播行为涉及的各参与方包括直播平台、主播以及直播的用户。
其中，直播平台作为信息发布的承载者，为行业提供实时网络服务及技术支持；主播则负责直播节目的具体内容的发布，例如策划、编辑、制作、与直播间观众进行互动等，作为节目的把控需要具有较强的综合能力，是信息发布的实施者；网络直播的用户，具体指网络直播的观众，作为直播信息辐射的主体，是网络直播内容的主要受众。
中国演出行业协会与腾讯研究院联合发布的《网络表演（直播）社会价值报告》深刻分析了网络直播的重要社会价值：一方面，网络直播满足了青年人丰富娱乐生活的精神文化需求，代表了互联网业务的未来方向。
直播为好奇心强的青年人打开了一扇窗，有机会了解日常生活环境外的多元体验。
主播与观众通过问答、点播、打赏等方式全方位互动，实现密集化的社交互动，观众之间基于共同的兴趣爱好达到情感共鸣。
另一方面，直播用户数量迅速增加，占网民近半，高学历高收入高职级群体成为主流用户，直播用户人群素质快速提升，也将带来内容生产和消费的主流化，成为直播内容去低俗、精品化、专业化的优良土壤。
实质上，直播有着非常广泛的群众基础，好的直播产品对增强社会归属感和凝聚力有着独特的优势。
东城2020高三一模英语试卷及答案版可编辑
北京市东城区2019—2020 学年度第二学期高三综合练习（一）英语本试卷共10 页，共120 分。
考试时长100 分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AThe goshawk, a rare bird, once close to extinction, has doubled 1 (it) number in anational park in the south of England. Around 100 years ago, there were thought to be no goshawks2 (leave), due to farmers hunting them and their woodland habitats being cut down. However,thanks to conservationists, goshawks are back. By monitoring their nesting sites over time, theteams have been able to protect them from further forestry work. As a result, their number 3(grow) from just 20 pairs to 40 pairs in the past two years.BOne morning, I told my husband jokingly that he’d dropped the ball because he hadn’t m me coffee and I was having trouble getting motivated 4 (start) the day. My five-year-old sonI told him it was just something like making aoverheard me and asked what “drop the ball” meant.mistake. A few minutes later, he came into our bedroom 5 (hold) an overflowing coffee cupdropped the ball,with a dishcloth underneath it to catch the drops. He said to my husband, “Youand he handed me the worst-tasting, most watered-down but 6but I picked the ball up,” (sweet) cup of coffee ever.CIn half a century, the Internet has transformed society. Billions of us can connect at the touchof a button. Access 7 information, banks and shops has never been easier. The world haschangedInternet8 (dramatic) and continues to do so in ways we couldn’t have imagined. However, the isn’t without disadvantages. By design, it has no central authority, 9 makes protecting peopleonline or dealing with misinformation a near-impossible task.10 the Internet develops will shape our future. If the past 50 years has been dominatedby free and open exchanges, the next 50 will be about whether rules and restrictions can actuallymake the Internet, and the world, a better place.第二节完形填空（共20小题；每小题分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
东城区2020-2021学年第二学期高三综合练习(一)英语试题及答案
北京市东城区2021年高三年级一模考试英语试卷2021.4本试卷共10页，共100 分。
考试时长90 分钟。
考生务必将答案答在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，30分）第一节完形填空（共10小题；每小题1.5分，共15分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
A Labrador has been doing an important job to help people stay safe during the COVID-19 pandemic.Eight-year-old Roby runs through the streets of the hilly city of Medellin several times a day with a 1 in his jaws, taking vegetables, fruit and packaged foods to customers of the Fresh4U mini-market.“He helps us to maintain social distancing,” said Roby’ owner, Sherry Botero. “And people 2 it when we send the dog.” Roby enjoys eating carrots 3 to him by customers, a tip for bringing a basket of food.Roby wasn’t always a star. He was accepted into the family 4 by Ms Botero after repeated requests by her son to 5 a dog.But Ms Botero quickly 6 with the dog. And when she opened a mini-market four years ago, he started to accompany her to make deliveries.Roby can’t read 7 . But he remembers the names of customers who have previously rewarded him with treats. And with some practice, he has learned to go to their houses on his own.“He knows the names of five or six of our customers,” Ms Botero said, “So I send the goods with a receipt in the basket, and my customers 8 me through a bank transfer(转账；转移).”Roby might not know that he’s become an 9 worker. But he is happy to help his owner and 10 his daily pay.1. A. bag B. chain C. basket D. stick2. A. respect B. love C. follow D. notice3. A. gifted B. returned C. lent D. donated4. A. intentionally B. regretfully C. immediately D. unwillingly5. A. adopt B. train C. adore D. walk6. A. got away B. kept in touch C. caught up D. fell in love7. A. minds B. addresses C. numbers D. receipts8. A. treat B. help C. pay D. impress9. A. essential B. honest C. optimistic D. adventurous10. A. spend B. calculate C. collect D. increase第二节语法填空（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
北京市东城区2019-2020学年第二学期高三综合练习(二)英语试卷及评分标准
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北京市东城区2019-2020学年度第二学期高三综合练习(一)参考答案
北京市东城区2019-2020学年度第二学期高三综合练习（一）数学参考答案及评分标准 2020.5一、选择题（共10小题，每小题4分，共40分）（1）D （2）B （3）A （4）D （5）A （6）D （7）C （8）B （9）C （10）C 二、填空题（共5小题，每小题5分，共25分）（11）3 （12）160 （13）221(1)2x y -+= （14）321214，（15）③④三、解答题共6小题，共85分。
解答应写出文字说明，演算步骤或证明过程。
(16)（本小题14分）解：（Ⅰ）如图，因为 四边形ABCD 为平行四边形，所以 //AD BC ，因为 BC ⊂平面PBC ，AD ⊄平面PBC ，所以 //AD 平面PBC ． …………6分 （Ⅱ）取C 为坐标原点，过点C 的PD 平行线为z 轴，依题意建立如图所示的空间直角坐标系-C xyz ． 由题意得，(0,1,1)P -，(1,0,0)A ，(0,0,0)C ，(1,1,0)B ． 所以(0,1,1)PC −−→=-，(1,1,0)CB −−→=，(1,0,0)−−→=-AC ． 设平面PBC 的法向量为(,,)n =x y z ，则 0,0,n n −−→−−→⎧⋅=⎪⎨⎪⋅=⎩PC CB即0,0.-=⎧⎨+=⎩y z x y令1=-y ，则1=x ，1=-z ． 所以 (1,1,1)n =--．因为ABCD 为平行四边形，且AB AC ⊥， 所以 ⊥CD AC ． 因为PD ⊥面ABCD ， 所以 ⊥PD AC ． 又因为=I CD PD D ， 所以⊥AC 面PDC ．所以 平面PDC 的法向量为=(1,0,0)-uuu rAC ，所以cos ,||||n n n ⋅〈〉==AC AC AC uuu ruuu r uuu r由题意可知二面角--D PC B 的平面角为钝角，所以二面角--D PC B余弦值的大小为3-………………………………14分 (17)（本小题14分）解：（Ⅰ）因为ππ()sin()cos ()66f x a x x =--+-221ππsin()cos()3πππsin()cos[()+]662π()sin()6a x x a x x a x =--+-=----=+--2216221121所以 函数()f x 的最小正周期πT =.因为 a >0，所以函数()f x 的最大值和最小值分别为,a a --2. 若选①，则a =1 ，函数π()2sin(2)16f x x =--；若选②，则-3为函数()f x 的最小值，从而a =1 ，函数π()2sin(2)16f x x =--； 选③，ππ(1)sin(2)1166a +⨯--=，从而a =1 ，函数π()2sin(2)16f x x =-- .……8分（Ⅱ）由（Ⅰ）知函数()f x 的最大值为1；因为 关于x 的方程()f x =1在区间[,]m 0上有两个不同解，当[,]x m ∈0时， πππ[,]666x m -∈--22. 所以5ππ9π262m -<≤2，解得4π7π33m <≤. 所以，实数m 的取值范围是4π7π[,)33. ………………………………14分 (18)（本小题14分）解（Ⅰ）由图知，在北斗二代定位的50个点中，横坐标误差的绝对值大于10米有3个点，所以 从中随机选出一点，此点横坐标误差的绝对值大于10米的概率为30.0650=. …………4分 （Ⅱ）由图知, A B C D ，，，四个点位中纵坐标误差值小于4-的有两个点: C D ，.所以 X 所有可能取值为0,1,2.02241(0)6===C P X C ,1122242(1)3C C P X C ===,22241(2)6C P X C ===.所以 X 的期望1210121636EX =⨯+⨯+⨯=. …………12分 （Ⅲ）北斗二代定位模块纵坐标误差的方差大于北斗三代. …………14分(19) （本小题14分）解：（Ⅰ）因为 2222:1(0)x y E a b a b+=>>，所以 222a b c =+.因为 四边形12AF BF 为正方形，且面积为2, 所以 22b c =，1(2)(2)22b c ⨯=. 所以 1b c ==，2222a b c =+=.所以 椭圆22:12x E y +=. …………4分（Ⅱ）设平行直线1:l y kx m =+，2:l y kx m =-，不妨设直线y kx m =+与2212x y +=交于()()1122,,,C x y D x y ，由2212x y y kx m ⎧+=⎪⎨⎪=+⎩，得()2222x kx m ++=， 化简得：()222214220k x kmx m +++-=，其中 22222(4)4(21)(22)16880km k m k m ∆=-⨯+⨯-=-+>，即2221m k <+.所以 122421kmx x k +=-+，21222221m x x k -=+， 由椭圆的对称性和菱形的中心对称性，可知OC OD ⊥， 所以 12120x x y y +=，11y kx m =+，22y kx m =+，()()()()()2212121212222222222222222222221221421212222422132221x x y y k x x km x x m m k k m m k k k m m k k m k m m k m k k +=++++-+-++=++---++=+--=+，所以 22322m k =+.||CD==≤所以当且仅当k =时，||CD此时 四边形CDMN周长最大值为 …………14分(20)（本小题15分）解：（Ⅰ）当1a =时，()ln 21f x x x '=-+，所以(1)1f '=-. 又因为(1)1f =-，所以 切线方程为()11y x +=--，即0x y +=. …………4分 （Ⅱ）()ln 21f x x ax '=-+，设 ()ln 21g x x ax =-+，当0a ≤时,易证()g x 在()0+∞，单调递增，不合题意.当0a >时 ()12g x a x '=-， 令()0g x '=，得12x a=，当10,2x a ⎛⎫∈ ⎪⎝⎭时，()0g x '>，()g x 在10,2a ⎛⎫⎪⎝⎭上单调递增， 当1,+2x a ⎛⎫∈∞⎪⎝⎭时，()0g x '<，()g x 在1,2a ⎛⎫+∞ ⎪⎝⎭上单调递减， 所以 ()g x 在12x a =处取得极大值11ln 22g a a ⎛⎫= ⎪⎝⎭. 依题意，函数()ln 21g x x ax =-+有两个零点， 则11ln 0,22g a a ⎛⎫=>⎪⎝⎭即112a >， 解得 102a <<.又由于1112e a <<，11=20g a e e ⎛⎫-⋅< ⎪⎝⎭，12212a e a +>，由21(0)x e x x >+>得1122222111()22122(2)111100222aa g ea e a a a a a ++⎡⎤=+-⋅+<+-⋅+++=--<⎢⎥⎣⎦实数a 的取值范围为102a <<时，()f x 有两个极值点. …………13分 （Ⅲ）由（Ⅱ）可知，当1a >时， 111()ln ln 0222g x g a a ⎛⎫<=<<⎪⎝⎭， 所以()f x 在(0+)∞，上单调递减，()f x 在区间(]0,2a 上的最小值为2(2)2(ln 22)f a a a a =-. ………15分(21)（本小题14分）解：（Ⅰ）由于2=n A x n ：，(2)T 为满足不等式+()(N )n t x x t n t n *-≥-∀∈的*t 构成的集合，所以 有：2+4(2)(N ,)*-≥-∀∈≠n t n n n t ， 当 2n >时，上式可化为+2n t *≥， 所以 5t *≥.当 =1n 时，上式可化为3t *≤.所以 (2)T 为[35]，. …………4分（Ⅱ）对于数列123n A x x x x L L ：，，，，，，若()T t +(N 1)t t ，∀∈>中均只有同一个元素，不妨设为a . 下面证明数列A 为等差数列.当 =+1n t 时，有1(1)(1)t t x x a t +-≥∀>L L ； 当 =1n t -时，有1(1)(2)t t x x a t --≤∀>L L ； 由于(1)，(2)两式对任意大于1的整数均成立，所以 有1=(1)t t x x a t +-∀>成立，从而数列12n x x x ，，，，L L 为等差数列. …………8分 （III) 对于数列123n A x x x x L L ：，，，，，，不妨设{}()T i a =，{}()T j b =，1i j a b <<≠，， 由{}()T i a =可知：()j i x x a j i -≥-，由{}()T j b =可知：()i j x x b i j -≥-，即()j i x x b j i -≤-， 从而()()j i a j i x x b j i -≤-≤-， 所以a b ≤.设()T i {}i t =，则 23n t t t ≤≤≤≤L L ， 这说明如果1i j <<，则i j t t ≤.因为对于数列123n A x x x x L L ：，，，，，，()T t +(N 1)t t ，∀∈>中均只有一个元素， 首先考察=2t 时的情况，不妨设21x x >， 因为212x x t -≤，又()T 2为单元素集， 所以212x x t -=.再证332t x x =-，证明如下： 由3t 的定义可知：332t x x ≥-，3132x x t -≥， 所以31332max 2x x t x x ，-⎧⎫=-⎨⎬⎩⎭又由2t 的定义可知32221=x x t x x -≥-， 所以32213133222=x x x x x x t x x -+--≥-≥，所以 323x x t -=.若32t t > ， 即3322t x x t =->，则存在正整数(4)m m ≥，使得22(2)m m t x x -=-(3)L L ， 由于212323431k k k x x t x x t x x x x t --=≤-≤≤-≤≤-≤≤L L 所以 211233()(2)mmm ii i i i x x x xt m t --==-=-≥>-∑∑，这与(3)矛盾.所以 32t t =.同理可证2345t t t t ====L ，即数列123n A x x x x L L ：，，，，，，为等差数列. …………14分。