湖南省湘潭县一中、岳阳县一中2015-2016学年高二英语上学期第三次联考试题

岳阳县一中2015级高二期末考试试卷英语时量：120分钟总分：150分命题：岳阳县一中命题人：王飞帆Part I Listening Comprehension (30 marks)Section A (22.5 marks)Directions: In this section, you’ll hear six conversations between two speakers. Listen carefully and then choose the best answer for each question.You will hear each conversation Twice.Conversation 11.What is wrong with the woman ?A. She is wet all over.B. She has taken the wrong medicine.C. She has caught a cold.2. Where does this conversation most probably take place?A. By the river.B. In the man’s office.C. In the woman’s house.Conversation 23. When will the man go to New York?A. In May.B.In April.C. In March.4. How will the man return?A. By plane.B. By train.C. By car.Conversation 35. Where does the woman want to go?A. An office.B. A fruit shop.C. A police station.6. What does the woman have to do now?A. Wait for Mark at the crossroads.B. Walk head and turn right.C. Walk a little way back.Conversation 47. What has made the man upset?A. He has different tastes from his roommate.B. He has to pay for groceries for the other.C. He has been running out of his money.8. What was the woman’s roommate like?A. She was very kind and helpful.B. She often cooked dinners for the woman.C. She used to have meals for free.9. What advice does the woman give?A. Treating him to a meal in a restaurant.B. Forcing him to move out quickly.C. Having a wholehearted talk with him.Conversation 510. What is the woman worried about ?A. The man’s concert.B. The man’s future.C. The man’s health.11. Where does the woman probably work?A. In a school.B. In a travel agency.C. In a bank.12. What does the man value most?A. Being healthy.B. Being wealthy.C.Being happy.Conversation 613.Where does the conversation probably take place?A. In a supermarket.B. In a bank.C. At the airport.14. What does the woman show before exchanging the money?A. Her passport.B. Her credit card.C. Her ID card.15. How much money will the woman get at last?A. About $190.B. About $ 200.C. About $320.Section B (7.5 marks)Directions: In this section, you will hear a short passage. Listen carefully and then fill in the numbered blanks with the information you have heard. Fill in each blank with NO MORE THAN THREE WORDS.You will hear the short passage twice.Self-introductionMy family name A very common Welsh nameMy given name A 16 nameMy grandfather Once 17 and later a worker18 DoctorsItzhak Perlman 19 of IsraelMy career Working as 20Part II Language knowledge (45 marks)Section A. (15 marks)Directions: For each of the following unfinished sentences there are four chioces marked A,B ,C and D.Choose the best one to complet the sentence.21. Why your cousin in Japan?.A. not visitB. not to visitC. don’t visitD. not you visit22. I promise that the matter will _______.A be taken careB be taken care ofC take careD take care of23. The volleyball match will be put off if it ________.A will rainB rainsC rainedD is raining24. ________ their task in such a short time, they asked us to give them a hand.A. FinishingB. FinishedC. To finishD. Finish25. If I you , I would spend my holiday in France.A. amB.wereC. have beenD. are26. The policeman put down the phone, ＿＿＿with a smile on his face.A.satisfiedB.satisfyingC.to be satisfiedD.having satisfied27. —— What do you suppose made him worried?——＿＿＿lots of money.A.LoseB.LostC.LosingD.Because of losing28. ----The light in the office is still on.----Oh, I forget ___.A.turning it offB. to turn it offC. turning off itD. to turn off it29. _______ is no doubt that the Rockets will defeat the Washington Wizards in the nextgame.A. ItB. AsC. ThatD. There30. I could feel the wind＿＿on my face from an open window.A.to blowB.blowingC.to be blowingD.blown31. If it were not for the fact that you _____ ill, I would ask you to do this right now.A. wereB. had beenC. areD. should be32. —Can you help me with the maths homework ,mom?—You can’t always _____ other’s help for your homework. Do it by yourself this time, Dear.A. wait onB. rely onC. insist onD. turn on33. If I ____ where he lived, I ____ a note to him.A. knew, wouldB. had known, would have sentC. know, would sendD. knew, would have sent34.—Is this the bank _____ offered you a job _____ you stayed the first time you arrived? —Yes, it is.A. the one; in whichB. the one that; during whichC. where; thatD. which; where35. ＿＿＿all my letters, I had a drink and went out.A.FinishedB.Having finishedC.FinishingD.To finishSection B. (18 marks)Directions: For each blank in the following passage there are four words or phrases marked A,B,C and D . Fill in each blank with a word or phrase that best fits the context.Once upon a time, there _36__ a very funny story among three people, the King, the Queen and a servant. One day, as 37 as the King entered the palace, he called in a servant and told him he had to have some important papers immediately. Soon came back the servant 38 a stack of official-looking papers, but 39 this, the King threw them away at once and shouted: “No, no, no bring my important papers!” The servant dashed out and in a minute re-entered with a newspaper in his hand.This time, to his 40 , the King tore it into halves and cried: “No, 41 fool! I must have my important papers RIGHT NOW!!!” However, like the first and second time, the servant failedto bring the King 42 he wanted several times. Even the Queen didn’t know what her husband wanted and just tore a page from her book and 43 it to the King. The King moved around in his chair, crossed and uncrossed his legs and seemed very 44 .At last, the servant held out a roll of 45 . He was puzzled and doubted 46 the King needed it or not. On the contrary, upon getting it, the King 47 as fast as possible. So can you guess what happened to the King?36. A. happened B. lived C.is D. goes37. A. many B. much C. soon D. quick38. A. from B. to C. with D. in39. A. saw B. to see C. seeing D.seen40. A. pleased B.joy C. excitement D.surprise41. A. they B. yourselves C. you D. he42. A. what B.that C. who D. how43. A. carried B. offered C.left D.took44. A. happy B. angry C. anxious D. thoughtful45. A. toilet paper B. newspaper C.paper D. money46. A. who B. that C. why D. whether47. A.ran away B. ran out C. flew away D. take awaySection C (12 marks)Directions: Complete the following passage by filling in each blank with one word that best fits the context.Host: Dr Brain, welcome to our Talk Show. You are a very famous psychologist 48 has written several books about happiness and the things people do to keep themselves happy.Dr Brain: Thank you 49 inviting me. Today, I will take Sang Lan, 50 former gymnast in China, for example to talk about how to find happiness.Host: I see. You often use the example to show how people get happiness even in difficult time. Dr Brain: Yes, 51 we all know, she used to be successful in sport but one day got badly injured .As a result, she had to stop her career and sit in armchair all the time. But the wholeworld can see her remain cheerful and 52 .Host: She must have suffered a lot from her severe injuries and must have been sad.Dr Brain: Though it must have been difficult, 53 she was encouraged not only by her parents and friends but also herself. She was always in high spirits 54 her accident. Shetook pride in her past and felt happy to be alive and lucky to learn new things.Host: That must be why her story so special. And how has Sang Lan adapted55 to her new life? Dr Brain: I think it is her strong will and perseverance that work. She says she likes thinking about meaningful things and keeping herself busy to stay optimistic and positive.Part III Reading Comprehension (30 marks)Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements.Choose the one that fits best according to the information given in the passage.ASchoolgirls have been wearing such short skirts at a Staffordshire school that they’ve beenordered to wear pants instead.All skirts will be banned from September at Paget High School in Branston, Burton upon Trent.Tight-fitting trousers will also be forbidden and Muslim head-dresses will have to be “school blue”color.Head teacher Don Smith said: “One of the big issues for us at the school has been the number of girls who have been wearing inappropriately short skirts.This has been an area of particular concern at a time when there has been a lot of material nationally about the sexualization of young people.”Mr Smith said it would’t be practical to check the length of girls’ skirts and said a blanket ban would be easier for staff to enforce.He said: “We did not want to arrive at a situation where we were telling girls their skirts could only be a certain number of centimeters above or below the knee.”The head teacher said they sought opinions from pupils, parents and other teachers before the uniform rules were changed.The new clothing policy has been explained in a letter sent to parents of the school”s 1,000 pupils and will come into force after the summer holiday.The school also wants pupils to wear clip-on ties instead of traditional neckwear.This rule will be phased(分阶段实施) in over the next year and support will be given to parents unable to afford the new tie.The new uniform regime has not been well received by everyone, however.One parent, whose teenage daughter attends the school, said: “I completely agree some girls were wearing skirts that were too short. However, I think girls should be allowed to be feminine(女性气质的).Other schools manage to let girls wear skirts while making sure they are not inappropriately dressed. I don’t see why Paget can’t do the same.”56.What is the main idea of the passage?A.Paget High school bans all skirts.B.Tight-fitting trousers will be forbidden.C.Muslin head-dress will be forbidden.D.School girls are ordered to wear uniforms.57.Which of the following is TRUE according to the passage?A.Girls can wear skirts which are long enough.B.The school will offer uniforms for free.C.Girls are allowed to wear skirts that cover their knees.D.An overall ban of girls will be carried out.58.According to Paragraph 2,the major problem Paget High School is faced with is that ______.A.pupils have to wear clip-on tiesB.many girls are wearing skirts too shortC.many parents are unable to buy school uniformsD.the new uniform system isn’t accepted by all students59.When the new uniform policy is to be put into force,what is the reaction of girls and theirparents?A.They are all not satisfier with it.B.They can’t agree to it more.C.They are supportive to the policy.D.No parents insist on their daughters wearing short skirts.60.What will the new clothing policy include?A.Girls can wear short skirts to look sexy.B.New ties will be given to some girls for free.C.The uniform rules will be changed if necessary.D.Girls’ wearing will be checked regularly.BThere is an exercise method,it was made to stretch muscles and improve strength and balance,soon it is becoming popular in the United States. Here’s more about Gyrotonics and the man who invented this special form of exercise.Gyrotonics is a kind of exercise that combines the movements of dancing and swimming with the mental and physical practice called yoga .It helps lengthen muscles, improve balance, and exercise the joints, the parts of the body where bones join each other.A Hungarian dancer named Juliu Horvath developed this special form of exercise .After he was injured in a dancing accident, Mr. Horvath studied yoga intensely. In the 1980s, he developed a new exercise method and combined it with yoga to stre ngthen dancers’muscles.According to Mr Horvath, his method is based on the octopus, the monkey and the cat. He says these animals have few restrictions. They can move in any direction with control and strength. He designed Gyrotonic movements to help the human body move more freely.A special machine made of wood and weights helps guide the body through the many Gyrotonics exercises. You sit or lie on a flat board. You put your legs or hands through special cloth handles attached to a line with weights. With the tension created by the weights, you must try to move through the exercise.Seven kinds of backbone movements form the base of Gyrotonics. For example, you can stretch your back to the left and right or forwards and backwards. While moving your back, you can also work on arm or leg motions. These movements must be done in a smooth way. Often the motions are circular.When Juliu Horvath first developed Gyrotonics, he was the only teacher. Since then , he has taught almost 70 master trainers. Now, there are more than 800 official schools in the world where you can learn Gyrotonics.61. This passage mainly focuses on .A. Horvath’s successful lifeB. a special kind of exerciseC. some advice on health careD. some uses of a special machine62. According to the passage, what made it possible for Horvath to develop Gyrotonics?A. His dancing-related injury.B. His failure in practicing yoga.C. His good skills of dancing.D. His wish to be a Gyrotonics trainer.63. What do you think inspired Horvath in developing Gyrotonics?A. His experience in dancing.B. His use of a special machine.C. The movements of some animals.D. The ideas from many trainers.64. lf you intend to strengthen your body through Gyrotonics, you have to .A. have a strong bodyB. turn to HorvathC. watch how animals moveD. buy the machine mentioned65. What do we learn from the passage?A. Many Americans have improved their health through Gyrotonics.B. In a way, Gyrotonics is an exercise that improves yoga.C. You only have to move your backbone when doing the exercises.D. Gyrotonics courses can be found in most countries worldwide.CIt was On December 18th, 1908 that three men went up in a balloon. They started early in London. The headman was Auguste Gaudron, and the other two men were Tannar and Maitland. They had a big balloon, and they were ready for a long way.Soon they heard the sea below them. They were carrying the usual rope , and it was hanging down from the basket of the balloon. At the end of the rope they had tied a metal box. This could hold water. Or it could be empty. So they were able to cha nge its weight. They were also carrying some bags of sand.After the sun rose, the balloon went higher. It went up to 3,000 meters, and the air was very cold. The water in the balloon became ice. Snow fell past the men’s basket, and they could see more snow on the ground. There was also some snow on the balloon, and that made it very heavy. It began to go down towards the ground. The men tried to throw out some more sand; but it was hard. They tried to break the icy sand with their knives, but it was not easy. The work was slow and they were still falling; so they had to drop some whole bags of sand. One of them fell on an icy lake below and made a black hole in the ice.At last they pulled the box into the basket. It was still snowing; so they climbed to get away from the snow. They rose to 5,100 meters! Everything became icy. They were so cold that they decided to land. They came down in Poland heavily but safely. They had t raveled 1,797 kilometers from London!66.Three men flew in a balloon _________.A. more than a century agoB. to visit PolandC. for nearly 1,800 kilometersD. to another city67.The metal box was used for _______.A. changing weightB. carrying ropes of the basketC. keeping drinking waterD. carrying the bags of sand68.When the balloon went up h igher, ________.A.they saw the sun go downB. the temperature of the balloon began to fallC. they could see a black hole on the groundD. they made a hole in the basket with their knives69.The balloon landed __________.A. in a foreign countryB. on a lakeC. in LondonD. on the sea70.The three men had to land be cause _______.A.they were very hungryB. they had not enough sandC. they pulled the box into the basketD. they felt too coldPart IV Writing (45 marks)Section A (10 marks)Directions: Read the following passage. Fill in the numbered blanks by using the information from the passage. Write NO MORE THAN THREE WORDS for each answer.By teaching your children fire safety you can make sure they know what to do when a house fire occurs. Making sure that your children know exactly what is required of them cuts down on the chaos of the emergency situation and helps keep your family safe and secure.All children should know about important fire safety procedures such as the need to stay low to the ground in a smoky room, which keeps them from inhaling smoke, as smoke always rises towards the ceiling. Also tell them that they can put a damp towel or a piece of clothing over their faces and breathe in through it in order to cut down on the effects of smoke inhalation even more. In addition, make sure your children know how to correctly stop, drop, and roll when their clothes catch fire. Because it results in lack of oxygen, which puts out the flames. Also your children should know to touch door handles before opening the door to see if they are hot. If they are, it means that there's a fire in the next room, and they should leave the door closed and find another route out of the house.Make sure your children understand that they should never play with lighters or matches. Many children are fascinated by lighters and matches and want to experiment with lighting things on fire to see what happe ns. Hide lighters and matches in some places your children can’t reach.Do regular fire drills to practice your evacuation plan. Make sure everyone knows all the possible exits of the house and that all members of your family know your evacuation plan well enough so that they don't have to waste time thinking if a fire starts. Quick, determined response to a fire will save your family members' lives.Teaching Fire Safety to Children71. for teachingchildren fire safetyChildren should know what to do in case of a house fireIt can help children to 72 of the emergency situation.To teach children 73 Stay low to the ground and 74 with damp towels or clothing.Correctly stop ,drop and roll to put out the fire on the 75 .Don’t open the door s with 76To forbid children from playing with lighters and matches It’s dangerous to77 with lighting things on fire. Keep lighters and matches out of 78 .To do fire drills 79 Make all exits and the evacuation plan 80 .Ensure everyone can respond to a fire quickly and determinedly.Section B (10 marks)Directions: Read the following passage. Answer the questions according to the information given in the passage.As a young man, Al was a skilled artist, a potter. He had a wife and two fine sons. One night, his older son developed a severe stomachache. Thinking it was only some common intestinal（肠的）disorder, neither Al nor his wife took the condition very seriously. But the disease was actually acute appendicitis (阑尾炎), and the boy died suddenly that night.Knowing the death could have been prevented if he had only realized the seriousness of the situation, Al's emotional health declined under the enormous burden of his guilt. To make matters worse his wife left him a short time later, leaving him alone with his six-year-old younger son. The hurt and pain of the two situations were more than Al could handle, and he became an alcoholic.As the alcoholism progressed, Al began to lose everything he possessed — his home, his land, his art objects, everything. Eventually Al died alone in a San Francisco motel room.When I heard of Al's death, I thought, “What a complete failure!” “What a totally wasted life”.As time went by, I began to re-evaluate my earlier harsh judgment. You see, I knew Al's now adult son, Ernie. He is one of the kindest, most caring, most loving men I have ever known. I watched Ernie with his children and saw the free flow of love between them. I knew that kindness and caring had to come from somewhere.I hadn't heard Ernie talk much about his father. One day I worked up my courage to ask him. "I'm really puzzled by something," I said. "I know your father was basically the only one to raise you. What on earth did he do so that you became such a special person?"Ernie sat quietly and reflected for a few moments. Then he said, "From my earliest memories as a child until I left home at 18, Al came into my room every night, gave me a kiss and said, 'I love you, son.'"Tears came to my eyes as I realized what a fool I had been to judge Al as a failure. He had not left any material possessions behind, but he had been a kind loving father, and he left behind one of the finest, most giving man I have ever known.1. Why was Al in guilt? (no more than 12 words)_____________________________________________________________________2. Where did Al die? (no more than 5words)_____________________________________________________________________3. What made Al addicted to alcohol? (no more than 10 words)_____________________________________________________________________4. What did Al’s son Ernie learn from his father? (no more than 11 words)_____________________________________________________________________Section C (25 marks)Directions: Write an English composition according to the instructions given below.请以A friend in need is a friend in deed（患难朋友才是真正的朋友）为题写一篇英语短文。

岳阳县一中2015-2016高二上期期末考试英语试题时量：120分钟分值：150 分第Ⅰ卷第一部分听力（共两节，满分30分）第一节听下面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.What’s the woman going to do this evening?A. Go to a movie.B. Go to a concert.C. Study in the library.（）2.How will the man go to the office?A. By train.B. By taxi.C. By bus.（）3.What’s the probable relationship between the two speakers?A. Classmates.B. Workmates.C. Friends.（）4.What’s the woman doing?A. Ordering some food.B. Selling some food.C. Cooking some food.（）5.Where does the conversation probably take place?A. In a store.B. In an office.C. In a bank.第二节听下面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。

听下面一段对话,回答第6至第7两个小题。

（）6.Where does the man work?A. In a factory.B. In a hotel.C. In a school.（）7.What does the man do?A. A manager.B. A cleaner.C. An electrician.听下面一段对话，回答第8至9两个小题。

湘潭县一中岳阳县一中2015年高二第二次联考历史试卷时量：90分钟分值：150分第一部分基础知识部分（100分）一、单项选择题：（本小题共25小题，每小题2分，共50分）1．《尚书·酒诰》云：“人无于水监（照镜子），当于民监。

”这句话体现的思想是( ) A．兼爱尚贤 B．主权在民C．以民为本 D．道法自然2．据《史记》载：一日，魏太子下车，向一位新贵——宫廷文士田子方致意，竟未得到回礼。

太子问：“究竟富贵者还是贫贱者应当骄傲？”田子方答：“贫贱者。

”并解释，他随时都能在别国宫廷被派上用场。

这反映了( )A．士人为诸侯国所重用B．士人轻视功名利禄C．诸侯国内部等级森严D．忠君思想已经形成3．战国中后期，思想领域出现融合倾向。

下列选项最能反映这一倾向的是( ) A．克已复礼 B．礼法兼用C．民贵君轻 D．选贤举能4. 《汉书·元帝纪》载：宣帝曾训斥太子与儒生关系过于密切：“汉家自有制度，本以霸王道杂之，奈何纯任德教，用周政乎？”宣帝的“自有制度”实质是A. 仁政爱民B.无为而治C.严刑峻法D.儒表法里5．明朝中后期，王阳明学说在中国士大夫中流行。

朝鲜来华使者对此不理解，认为“阳明肆己意，谤辱朱子，实斯文之罪人也”。

结合所学判断，下列选项正确的有( )①朝鲜使者以程朱理学为正宗②王阳明心学超越了理学范畴③王阳明与朱熹观点明显不同④王阳明心学是对儒学的叛逆A．①②B．②③C．①③ D．②④6．《唐律疏议》规定“一准乎礼”，通过引经决狱、引礼入律的方式，将儒家思想贯彻到立法、司法、守法的整个过程中。

这一规定反映的本质是( )A．儒家思想是古代法制的基本原则 B．儒家思想等同于古代的法律制度C．中国古代已建成法制社会 D．其促进了中国近代法制和民主政治的发展7．顾炎武在《日知录》中说：“今将静百姓之心，而改其行，必在制民之产，使之甘其食美其服，而后教化可行，风俗可善也”。

在此，顾炎武强调( )A．培养人才，经世致用B．弘扬道德，规范言行C．富足百姓，移风易俗D．教化民众，静心明志8. 1521年，德国维登堡一家作坊印制了很多幅对帧木板画。

湖南省湘潭县一中、岳阳市一中2015-2016学年高一上学期联考语文试题时量：120分钟分值：120分一、现代文阅读（9分，每小题3分）阅读下面的文字，完成后面各题。

从几内亚开始的新一轮埃博拉疫情正呈加速蔓延之势，目前已报告1323个确诊或疑似病例，其中729人丧生。

有国际医疗组织指出，此轮疫情正面临进一步“失控”的境地。

在历史上，此次埃博拉暴发是最严重的一次，但一直没有引起关注。

可能的原因之一是，埃博拉一直没有走出非洲。

尽管一些专家认为，埃博拉只会在非洲局部暴发流行，像SARS一样产生全球性感染的可能性几乎没有，但是，埃博拉走出非洲也许只是早晚的事。

认为埃博拉不会在全世界流行的理由是，埃博拉感染的渠道是直接接触感染者的血液、精液、分泌物及其他体液，或者接触被感染对象的尸体。

迄今尚未有确认通过空气传播的病例，因此，即使搭乘飞机或火车等公共交通工具时遇到埃博拉感染者，感染的概率也十分低。

只有非洲当地人才会“谈埃色变”，因为埃博拉是迄今死亡率最高的疾病之一，死亡率在50%-90%之间。

由于埃博拉的死亡率极高，世界卫生组织将其划归为病毒第四级，即在实验室里进行分离、实验微生物组织结构时安全隔离分级的最高等级。

第四级病毒会造成致命疾病，并且在绝大多数的情况下是不可救治的，死亡率最高。

除了埃博拉，第四级病毒还有艾滋病病毒（HIV）和拉沙（lassa）病毒等。

然而，在病毒和疫情的凶险上，埃博拉可能是首屈一指的。

由于埃博拉病毒在体内侵蚀和毁坏各种器官，就像绞肉机一样绞碎各种组织器官，使得病人不断把坏死的组织从口中吐出，当无数病人都因体内广泛性内出血而口吐鲜血和坏死的组织，并且七窍流血、脑部受损而挣扎着死亡时，连空气中都散发着血腥味和浓烈的臭味。

同为第四级病毒的HIV只是潜伏在人体的免疫T细胞中慢慢发作，并毁坏T细胞的免疫功能，虽然不能治愈，但HIV感染者和艾滋病病人可以生存较长时间，不会马上死亡，而且如果终生服药，艾滋病病人还可以达到常人一样的寿命（可活到70岁），这是艾滋病与埃博拉的天壤之别。

湘潭县一中岳阳县一中12月高二联考文科数学时量：120分钟 分值：150分本试卷分为第Ⅰ卷（基础部分100分）和第Ⅱ卷（能力部分50分）两部分，共150分，考试用时120分钟第Ⅰ卷（基础部分100分）一．选择题：本大题共8小题，每小题5分，共40分．请将答案填涂在答题卡上 1.若a ∈R,则“a =1”是“|a |=1”的 （ ）A ．充要条件B ．必要而不充分条件C ．充分而不必要条件D ．既不充分又不必要条件 2.下列通项公式表示的数列为等差数列的是 ( )A 、1+=n n a n B 、12-=n a n C 、n n n a )1(5-+= D 、13-=n a n 3.若函数f (x )＝x 2＋ax ＋1的定义域为实数集R ，则实数a 的取值范围为( )A ．(－2,2)B ．(－∞，－2)∪(2，＋∞)C ．(－∞，－2]∪[2，＋∞)D ．[－2,2]4.直线l ：x －2y ＋2＝0过椭圆左焦点F 1和一个顶点B ，则该椭圆的离心率为 ( )A . 15 B. 255 C. 55 D. 255. 函数f (x )的定义域为开区间(a ，b )，导函数f ′(x )在(a ，b )内的图象如图所示，则函数f (x )在开区间(a ，b )内有极小值点的个数为( ) A ．1 B ．2C ．3D ．46. 命题“所有能被2整除的数都是偶数”的否定．．是 A 所有不能被2整除的数都是偶数 B 所有能被2整除的数都不是偶数 C 存在一个不能被2整除的数是偶数 D 存在一个能被2整除的数不是偶数7. 已知双曲线12222=-by ax 的一个焦点与抛物线2y x =的焦点重合，且双曲线的离心率等于310，则该双曲线的方程为（ ） A ．1922=-y x B ．1922=-y x C ．122=-y x D ．19922=-y x8．若)(x f 的定义域为R ，2)(>'x f 恒成立，2)1(=-f ，则42)(+>x x f 解集为（ ）A ．(1,1)-B ．(1)-+∞，C ．(,1)-∞-D ．(,)-∞+∞二．填空题：本大题共5小题，每小题5分，共25分． 请将答案填在答卷相应位置上9. 已知x >12，则函数y ＝2x ＋12x －1的最小值是10. 在△ABC 中,若4,5,a b c ==则C ∠的大小为11. 已知命题:p 函数(1)1y c x =-+在R 上单调递增;命题:q 不等式20x x c -+≤的解集是∅.若p 且q 为真命题,则实数c 的取值范围是_ ____.12.已知x ,y 满足,1,1,y x x y y ≤⎧⎪+≤⎨⎪≥-⎩则2z x y =+的最大值为13．.设S n 是等差数列{a n }的前n 项和，若a 1>0，S 8＝S 13，S k ＝0，则k 的值为三．解答题：本大题共3小题，共35分．解答应写出文字说明、证明过程或演算步骤． 14. （本小题满分11分）已知点 D 为ΔABC 的边 BC 上一点.且 BD =2DC,,75 =∠ADB ∠ACD=30°,AD =2.求：(I)求CD 的长; (II)求ΔABC 的面积15. （本小题满分12分）已知n S 为等差数列{}n a 的前n 项和,且51630,14S a a =+=.(Ⅰ)求数列{}n a 的通项公式; (Ⅱ)求数列{}2na 的前n 项和公式.16. （本小题满分12分）已知函数3221()(1)(,)3f x x ax a x b a b =-+-+∈R⑴若1x =为()f x 的极值点，求a 的值；⑵若()y f x =的图象在点(1,(1))f 处的切线方程为30x y +-=，求()f x 在区间[2,4]-上的最大值；Ⅱ卷（能力部分50分）一．选择题：（5分）17如图，双曲线12222=-by a x 的左焦点为F 1，顶点为A 1，A 2，P 是双曲线上任意一点，则分别以线段PF 1、A 1A 2为直径的两圆位置关系为A .相交B .相切C .相离D .以上情况都有可能二．填空题：（5分） 18.设曲线1*()n y x n N +=∈在点（1，1）处的切线与x 轴的交点的横坐标为n x ,令lg n n a x =，则1299a a a +++的值为 .三．解答题：本大题共3小题，共40分．解答应写出文字说明、证明过程或演算步骤． 19（本小题满分13分）海事救援船对一艘失事船进行定位：以失事船的当前位置为原点，以正北方向为y 轴正方向建立平面直角坐标系（以1海里为单位长度），则救援船恰好在失事船正南方向12海里A 处，如图．现假设：①失事船的移动路径可视为抛物线24912x y =；②定位后救援船即刻沿直线匀速前往救援；③救援船出发t 小时后，失事船所在位置的横坐标为t 7．（1）当5.0=t 时，写出失事船所在位置P 的纵坐标．若此时两船恰好会合，求救援船速度的大小；（2）问救援船的时速至少是多少海里才能追上失事船？20（本小题满分13分）.已知数列{}n a 的首项14a =，前n 项和为n S ，且)(04231*+∈=---N n n S S n n（Ⅰ）求数列{}n a 的通项公式；（Ⅱ）设函数23121()n n n n f x a x a x a x a x --=++++，/()f x 是函数()f x 的导函数，令/(1)n b f =，求数列{}n b 的通项公式，并研究其单调性21（本小题满分14分）.已知椭圆22221(0,0)x y a b a b+=>>的离心率为12，两焦点之间的距离为4。

湘潭县一中岳阳县一中2015年高二联考数学（理科）时量：120分钟 分值：150分第Ⅰ卷 （选择题 共６0分）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{2,3,4}A =，(){| ,,}B x x n m m n A m n ==⋅∈≠，则集合B 的元素个数为（ ）A ．2B ．3C ．4D ．5 2、设2()log f x x =，则a b >“”是()()f a f b >“” 的（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件3、已知实数m 是2,8的等比中项,则双曲线221y x m-=的离心率为（ ）A ．5B ．2C ．3D ．24、()cos sin f x x x =-在下列哪个区间上是单调递减的（ ）A ．5,44ππ⎡⎤⎢⎥⎣⎦B ．[],0π-C ．[]0,πD ．0,4π⎡⎤⎢⎥⎣⎦5、已知函数()()(),ln ,ln 1x f x x e g x x x h x x =+=+=-的零点依次为,,a b c ，则,,a b c 从大到小的顺序为 （ ）A ．c b a >>B ．c a b >>C ．b c a >>D ．a c b >> 6、三棱锥S ­ABC 及其三视图中的正视图和侧视图如图所示, 则棱S B 的长为（ ）A ． 42B ．27C ．25D ．437、对任意的实数,a b ，记{},max ,,a a ba b b a b ≥⎧=⎨<⎩，若(){}max (),(),R F x f x g x x =∈，第6题图第7题图其中奇函数()y f x =在1x =时有极小值-2，()y g x =是正比例函数，函数()()0y f x x =≥与函数()y g x =的图象如图所示．则下列关于函数()y F x =的说法中，正确的是（ ）A ．()y F x =为奇函数B ．()y F x =在()3,0-为增函数C ． ()y F x =有极大值(1)F -,极小值()0FD ．()y F x =最小值为-2，最大值为2 ８、直线2y x m =+和圆221x y +=交于点,A B ，以x 轴的正方向为始边，OA 为终边（O 是坐标原点）的角为α，OB 为终边的角为β，若AB =，那么()sin αβ-的值是（ ）A ．12 B．2C ． 12±D．2±９、已知数列{}n a 的前n 项和为n S ，11a =.当2n ≥时，12n n a S n -+=，则2015S =（ ）A ．1006B ．1007C ．1008D ．100910、若,x y 满足约束条件1133x y x y x y +≥⎧⎪-≥-⎨⎪-≤⎩，目标函数2z ax y =+仅在点()1,0处取得最小值，则a的取值范围是（ ）A ．[]6,2-B ．()6,2-C ．[]3,1-D ．()3,1-11、设P 是椭圆221259x y +=上一点，M N ，分别是两圆：22(4)1x y ++=和22(4)1x y -+=上的点，则||||PM PN +的最小值、最大值的分别为（ ）A ．9，12B ．8，11C ．8，12D ．10，1212、己知定义在R 上的可导函数()f x 错误!未找到引用源。

湖南湘潭岳阳2015-2016高二上学期数学期中联考试卷（理带答案）岳阳县一中、湘潭县一中201年高二联考理科数学试卷时量：120分钟分值：10分命题：彭小霞（岳阳县一中）审题：王冲（湘潭县一中）一、选择题：本大题共12个小题，每小题分，共60分，在每小题给出的四个选项中有且只有一项是符合题目要求的1、已知集合，则集合中的元素个数（）A．1 B．2 ．3 D．42、已知双曲线的一条渐近线方程为，则该双曲线的离心率为( ) A．B．．D．23、已知为钝角，，则（的中点，则异面直线EF与GH所成的角为（）A．B．．D．8、给出如下四个命题：①若“ ”为真命题，则均为真命题；②“若”的否命题为“若，则”；③“ ”的否定是“ ”；④“ ”是“ ”的充分不必要条．其中不正确的命题是( )A．①②B．②③．①③D．③④9、已知，，其中，则、的大小关系是（）A．B．．D．10、一个多面体的三视图如图2所示，则该多面体的表面积为（）A．B．．D．11、设函数的定义域为,若函数满足条：存在,使在上的值域是则称为“倍缩函数”，若函数为“倍缩函数”，则的范围是( ) A．B．．D．12、从双曲线的左焦点引圆的切线，切点为，延长交双曲线右支于点，若为线段的中点，为坐标原点，则与的大小关系为（）A．B．．D．不确定二、填空题：本大题共4个小题，共20分，将答案填写在题中的横线上13、在直角坐标系中，设集合，在区域内任取一点P ，则满足的概率是．14、设抛物线焦点F,经过点P(4，1)的直线与抛物线相交于A、B 两点，且点P恰好为线段AB的中点，则|AF|+|BF|=1、如图3，已知点在线段上，，用和表示向量，则等于16、若函数( )满足且时, ,函数,则函数在区间内零点有个．三、解答题：解答应写出字说明，证明过程或演算步骤17、（本小题满分10分）如图, 已知四边形ABD和BEG均为直角梯形，AD∥B、E∥BG，且，平面ABD⊥平面BEG，B=D=E=2AD=2BG=2．(Ⅰ)求证：AG∥平面BDE；(Ⅱ)求几何体EG-ABD的体积．18、（本小题满分12分）函数是定义在上的奇函数,且(Ⅰ)求的解析式,(Ⅱ)用函数单调性的定义证明在上是增函数．19、（本小题满分12分）已知直线与双曲线x2－2＝1的左支相交于不同的两点A、B，线段AB的中点为点，定点(－2，0)．(Ⅰ)求实数的取值范围；(Ⅱ)求直线在轴上的截距的取值范围．20、（本小题满分12分）如图，在三棱锥中，，，侧面为等边三角形，侧棱．（Ⅰ）求证：；（Ⅱ）求证：平面平面；（Ⅲ）求二面角的余弦值．21、（本小题满分12分）已知数列中，，，其前项和满足（，）（Ⅰ）求数列的通项公式；（Ⅱ）设为非零整数，），试确定的值，使得对任意，都有成立．22、（本小题满分12分）已知椭圆，过焦点垂直于长轴的弦长为1，且焦点与短轴两端点构成等边三角形．（Ⅰ）求椭圆的方程；（Ⅱ）过点的直线l交椭圆于A，B两点，交直线于点E，，，判断是否为定值，若是，计算出该定值；若不是，说明理由．高二理数答案一、B A D A B B A D A B二、填空题：13、14、10 1、16、_ 8 _个．三、解答题：17、证明：（1）在平面BDG中，过G作GN⊥E交BE于，连D，则由已知知；G=N，N∥B∥DA,且G∥AD,G=AD，故四边形ADG为平行四边形，AG∥D……4分∵D 平面BDE，AG 平面BDE，AG∥平面BDE………………分（Ⅱ）………………10分18、【解】(Ⅰ)由题知, 是上的奇函数,所以,即……3分所以又因为,所以, …6分(Ⅱ) 则有……………………9分由,所以,又由所以即,又因,所以,即所以函数在区间上为增函数……………………………………………12分19、解：(Ⅰ)．把直线＝x＋1代入x2－2＝1整理有(1－2)x2－2x－2＝0，…2分∵设A(x1，1)，B(x2，2)，由韦达定理可知x1＋x2＝＜0，①x1&#8226;x2＝＞0．②………………4分且&#8710;＝(－2)2－4(1－2)&#8226;(－2)＝42－8 2＋8＞0得－＜＜③………………分∴1＜＜………………6分(Ⅱ)．∵，，即∴：＝x＋………………9分在轴线截距为＝，………………10分当∈(1，)，有＞2或＜－2－………………12分20、解：（Ⅰ）设中点为，连结，，………… 1分因为，所以又，所以………………… 2分因为，所以平面因为平面，所以……… 3分（Ⅱ）由已知，，所以，又为正三角形，且，所以…………………… 分因为，所以所以由（Ⅰ）知是二面角的平面角所以平面平面…………………………………………… 7分（Ⅲ）方法1：由（Ⅱ）知平面过作于，连结，则所以是二面角的平面角………………………………… 10分在中，易求得因为，所以………………………… 11分所以即二面角的余弦值为……12分方法2：由（Ⅰ）（Ⅱ）知，，两两垂直以为原点建立如图所示的空间直角坐标系易知，，，所以，设平面的法向量为，则即令，则，所以平面的一个法向量为……………………… 10分易知平面的一个法向量为所以由图可知，二面角为锐角所以二面角的余弦值为…………………………………… 12分21、解：（Ⅰ）．由已知，（，），……2分∴数列是以为首项，公差为1的等差数列．∴………4分（Ⅱ）．∵，∴，要使恒成立，∴恒成立，∴恒成立，∴恒成立．………6分（ⅰ）当为奇数时，即恒成立，当且仅当时，有最小值为1，∴……………8分（ⅱ）当为偶数时，即恒成立，当且仅当时，有最大值，∴即，又为非零整数，则．…………10分综上所述，存在，使得对任意，都有．…12分22、解：（Ⅰ）由条得，所以方程……4分（Ⅱ）易知直线l斜率存在，令由……分………………6分由得…………………7分由得……………8分将代入有…………12分。

湘潭县一中岳阳县一中2015年高二联考数学（理科）时量：120分钟 分值：150分第Ⅰ卷 （选择题 共６0分）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{2,3,4}A =，(){| ,,}B x x n m m n A m n ==⋅∈≠，则集合B 的元素个数为（ ）A ．2B ．3C ．4D ．5 2、设2()log f x x =，则a b >“”是()()f a f b >“” 的（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件3、已知实数m 是2,8的等比中项,则双曲线221y x m-=的离心率为（ ）AB ．2CD4、()cos sin f x x x =-在下列哪个区间上是单调递减的（ ）A ．5,44ππ⎡⎤⎢⎥⎣⎦B ．[],0π-C ．[]0,πD ．0,4π⎡⎤⎢⎥⎣⎦5、已知函数()()(),ln ,ln 1x f x x e g x x x h x x =+=+=-的零点依次为,,a b c ，则,,a b c 从大到小的顺序为 （ ）A ．c b a >>B ．c a b >>C ．b c a >>D ．a c b >> 6、三棱锥S ­ABC 及其三视图中的正视图和侧视图如图所示, 则棱S B 的长为（ ）A ．B．C． D．7、对任意的实数,a b ，记{},max ,,a a ba b b a b≥⎧=⎨<⎩，若(){}max (),(),R F x f x g x x =∈，第6题图第7题图其中奇函数()y f x =在1x =时有极小值-2，()y g x =是正比例函数，函数()()0y f x x =≥与函数()y g x =的图象如图所示．则下列关于函数()y F x =的说法中，正确的是（ ）A ．()y F x =为奇函数B ．()y F x =在()3,0-为增函数C ． ()y F x =有极大值(1)F -,极小值()0FD ．()y F x =最小值为-2，最大值为2 ８、直线2y x m =+和圆221x y +=交于点,A B ，以x 轴的正方向为始边，OA 为终边（O 是坐标原点）的角为α，OB 为终边的角为β，若AB =，那么()sin αβ-的值是（ ）A ．12 BC ． 12±D．±９、已知数列{}n a 的前n 项和为n S ，11a =.当2n ≥时，12n n a S n -+=，则2015S =（ ）A ．1006B ．1007C ．1008D ．100910、若,x y 满足约束条件1133x y x y x y +≥⎧⎪-≥-⎨⎪-≤⎩，目标函数2z ax y =+仅在点()1,0处取得最小值，则a的取值范围是（ ）A ．[]6,2-B ．()6,2-C ．[]3,1-D ．()3,1-11、设P 是椭圆221259x y +=上一点，M N ，分别是两圆：22(4)1x y ++=和22(4)1x y -+=上的点，则||||PM PN +的最小值、最大值的分别为（ ）A ．9，12B ．8，11C ．8，12D ．10，1212、己知定义在R 上的可导函数()f x 的导函数为()f x '，满足()()f x f x '<，且(2)f x +为偶函数，(4)1f =，则不等式()e xf x <的解集为（ ）A ．()2,-+∞B ．()4,+∞C ．()1,+∞D ．()0,+∞第Ⅱ卷（非选择题 共90分）二、填空题：本大题共４小题，每小题5分，共2０分. 把答案填在答题卡的相应位置. 13、椭圆2255x ky +=的一个焦点是(0,2)，那么实数k 的值为 .14、以下茎叶图记录了甲，乙两组各四名同学的植树棵数，分别从甲，乙两组中随机选取一名同学，则这两名同学的植树总棵数为19的概率是 .15、曲线)0(sin π≤≤=x x y 与直线21=y 围成的封闭图形的面积是 . 16、已知三棱柱111C B A ABC -的侧棱垂直于底面，各顶点都在同一球面上，若该棱柱的体积为3，2AB =， 60,1=∠=BAC AC ，则此球的表面积等于 .三、解答题：本大题共6小题，共7０分.解答应写出文字说明，演算步骤或证明过程. 解答写在答题卡上的指定区域内. 17、（本小题满分10分）已知函数2()1,()65f x x g x x x =-=-+-. （1）若()()g x f x ≥，求实数x 的取值范围； （2）求()()g x f x -的最大值. 18、（本小题满分12分）设锐角△ABC 的三内角,,A B C 的对边分别为 ,,a b c 向量m(1,sin )A A = ，n 3(sin ,)2A = ，已知m 与n 共线.（1）求角A 的大小；（2）若2a =，c B =，且△ABC B 的取值范围.19、（本小题满分12分）已知四棱锥P ABCD -中PA ⊥平面ABCD ，点Q 在棱PA 上，且44PA PQ ==，底面为直角梯形，090,CDA BAD ∠=∠=2,1,AB CD AD ===,M N 分别是,PD PB 的中点．（1）求证：MQ // 平面PCB ；（2）求截面MCN 与底面ABCD 所成二面角的大小. 20、（本小题满分12分）已知正项等比数列{}n a ()*N n ∈，首项13a =，前n 项和为n S ，且33S a +，55S a +，44S a +成等差数列．⑴ 求数列{}n a 的通项公式； ⑵ 求数列{}n nS 的前n 项和n T ．NMQP DCBA21、（本小题满分12分）已知函数32(),f x x ax =-其中R,x a ∈为参数 （1）记函数1()()ln 6g x f x x '=+，讨论函数()g x 的单调性； （2）若曲线()y f x =与x 轴正半轴有交点且交点为P ，曲线在点P 处的切线方程为()y g x =,求证：对于任意的正实数x ，都有()()f x g x ≥.22、（本小题满分12分）如图，已知直线与抛物线()220y px p =>交于,M N 两点，点D 的坐标为(，OD MN ⊥交MN 于点D ，,OM ON ⊥抛物线的焦点为F .(1) 求p 的值；(2) 记条件（1）所求抛物线为曲线C ，过点F 作两条斜率存在且互相垂直的直线12,l l ，设1l 与曲线C 相交于点,A B ，2l 与曲线C 相交于点,D E ，求→AD ·→EB 的最小值．湘潭县一中岳阳县一中2015年高二联考数学（理科）时量：120分钟 分值：150分第Ⅰ卷 （选择题 共６0分）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{2,3,4}A =，(){| ,,}B x x n m m n A m n ==⋅∈≠，则集合B 的元素个数为（ B ）A ．2B ．3C ．4D ．52、设2()log f x x =，则a b >“”是()()f a f b >“” 的( B )A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件3、已知实数m 是2,8的等比中项,则双曲线221y x m-=的离心率为 （ A ） AB ．2CD4、()cos sin f x x x =-在下列哪个区间上是单调递减的（ D ）A ．5,44ππ⎡⎤⎢⎥⎣⎦B ．[],0π-C ．[]0,πD ．0,4π⎡⎤⎢⎥⎣⎦5、已知函数()()(),ln ,ln 1x f x x e g x x x h x x =+=+=-的零点依次为,,a b c ，则,,a b c 从大到小的顺序为 ( A )A ．c b a >>B ．c a b >>C ．b c a >>D ．a c b >>6、三棱锥S ­ABC 及其三视图中的正视图和 侧视图如图所示, 则棱S B 的长为（A ） A ．B． C．D．7、对任意的实数,a b ，记{},max ,,a a ba b b a b≥⎧=⎨<⎩，若(){}max (),(),R F x f x g x x =∈，其中奇函数()y f x =在1x =时有极小值-2，()y g x =是正比例函数，函数()()0y f x x =≥与函数()y g x =的图象如图所示．则下列关于函数()y F x =的说法中，正确的是（ Ｃ ）第6题图A ．()y F x =为奇函数B ．()y F x =在()3,0-为增函数C ． ()y F x =有极大值(1)F -,极小值()0FD ．()y F x =最小值为-2，最大值为2８、直线2y x m =+和圆221x y +=交于点,A B ，以x 轴的正方向为始边，OA 为终边（O 是坐标原点）的角为α，OB 为终边的角为β，若AB =，那么()sin αβ-的值是 _________（ D ） A ．12B．2 C ． 12± D．2± ９、已知数列{}n a 的前n 项和为n S ，11a =.当2n ≥时，12n n a S n -+=，则2015S = ( Ｃ )A ．1006B ．1007C ．1008D ．1009解：当2n ≥时，由12n n a S n -+=得112n n n S S S n ---+=即1n n S S n -+= ① 所以11n n S S n ++=+ ②②－①得111n n S S +--=，又11a =即11S =数列{}21n S -构成等差数列，()201511008111008S =+-⨯=10、若,x y 满足约束条件1133x y x y x y +≥⎧⎪-≥-⎨⎪-≤⎩，目标函数2z ax y =+仅在点()1,0处取得最小值，则a的取值范围是（ B ） A ．[]6,2- B ．()6,2-C ．[]3,1-D ．()3,1-11、设P 是椭圆221259x y +=上一点，M N ，分别是两圆：22(4)1x y ++=和22(4)1x y -+=上的点，则||||PM PN +的最小值、最大值的分别为（ C ）A ．9，12B ．8，11C ．8，12D ．10，1212、己知定义在R 上的可导函数()f x 的导函数为()f x '，满足()()f x f x '<，且(2)f x+为偶函数，(4)1f =，则不等式()e x f x <的解集为 （ D ）A ．()2,-+∞B ．()4,+∞C ．()1,+∞D ．()0,+∞解：构造函数()(),x f x F x e =则()()2()()()()x x x x f x e f x e f x f x F x e e ''--'== 因为()()f x f x '<，及0xe >所以()0F x '<，函数()F x 在R 上单调递减 由(2)f x +为偶函数，(4)1f =，得(0)1f =()()1x f x F x e=<得0x >，即不等式()e x f x <的解集为()0,+∞ 第Ⅱ卷（非选择题 共90分）二、填空题：本大题共４小题，每小题5分，共2０分. 把答案填在答题卡的相应位置. 13、椭圆2255x ky +=的一个焦点是(0,2)，那么实数k 的值为 . 答案：114、以下茎叶图记录了甲，乙两组各四名同学的植树棵数，分别从甲，乙两组中随机选取一名同学，则这两名同学的植树总棵数为19的概率是 .解：记甲组四名同学为1A ，2A ，3A ，4A ，他们植树的棵树依次为9，9，11，11：乙组四名同学为1B ，2B ，3B ，4B ，他们植树的棵树依次为9，8，9，10，分别从甲，乙两组中随机选取一名同学，所有可能的结果有16个，它们是（1A ，1B ）（1A ，2B ）（1A ，3B ）（1A ，4B ）（2A ，1B ）（2A ，2B ）（2A ，3B ）（2A ，4B ）（3A ，1B ）（3A ，2B ）（3A ，3B ）（3A ，4B ）（4A ，1B ）（4A ，2B ）（4A ，3B ）（4A ，4B ）.设选出的两名同学的植树总棵数为19为事件C ，则C 中的结果有4个，它们是（1A ，4B ）（2A ，4B ）（3A ，2B ）（4A ，2B ），故所求概率为41)(=C P15、曲线)0(sin π≤≤=x x y 与直线21=y 围成的封闭图形的面积是 .3π16、已知三棱柱111C B A ABC -的侧棱垂直于底面，各顶点都在同一球面上，若该棱柱的体积为3，2AB =， 60,1=∠=BAC AC ，则此球的表面积等于__π8_____________.三、解答题：本大题共6小题，共7０分.解答应写出文字说明，演算步骤或证明过程. 解答写在答题卡上的指定区域内. 17、（本小题满分10分） 已知函数2()1,()65f x x g x x x =-=-+-. （1）若()()g x f x ≥，求实数x 的取值范围； （2）求()()g x f x -的最大值. 解：（1）当1x ≥时，()1f x x =-由()()g x f x ≥得2651x x x -+-≥-整理得()()140x x --≤所以[]1,4x ∈当1x <时，()1f x x =-+由()()g x f x ≥得2651x x x -+-≥-+整理得()()160x x --≤所以[]1,6x ∈又1x <，得x ∈∅综上，实数x 的取值范围[]1,4x ∈（2）由（1）知()()g x f x -的最大值必在[]1,4x ∈上取到()22599()()651244g x f x x x x x ⎛⎫-=-+---=--+≤ ⎪⎝⎭当94x =时()()g x f x -取到最大值9418、（本小题满分12分）设锐角△ABC 的三内角,,A B C 的对边分别为 ,,a b c 向量m (1,sin )A A = ，n 3(sin ,)2A = ，已知m 与n 共线.（1）求角A 的大小；（2）若2a =，c B =，且△ABC B 的取值范围.解：（1）因为m 与n 共线，则3sin (sin )2A A A +=即23sin cos 2A A A +=…………… 2分所以1cos 232222A A -+=即sin 216A π⎛⎫-= ⎪⎝⎭………………5分 A 为锐角，则262A ππ-=，所以3A π=……………6分（2）因为2a =，c B =，则1sin 2ABCSac B =2122B =⨯⨯2B = 1cos 22B-=B =. ……………………（9分）由已知，B <，即1cos 22B >. …………………… （10分）因为B 是锐角，所以023B π<<，即06B π<<，故角B 的取值范围是0,6π⎛⎫⎪⎝⎭…………（12分） 19、（本小题满分12分）已知四棱锥P ABCD -中PA ⊥平面ABCD ，点Q 在棱PA 上，且44PA PQ ==，底面为直角梯形，090,CDA BAD ∠=∠=2,1,AB CD AD ===,M N 分别是,PD PB 的中点．（1）求证：MQ // 平面PCB ；（2）求截面MCN 与底面ABCD 所成二面角的大小.NMQP DCBA解析（一）：以A 为原点，以,,AD AB AP 分别为,,x y z 建立空间直角坐标系O xyz -，由2,1,AB CD AD ===44PA PQ ==，,M N分别是,PD PB 的中点，可得：()()))()()0,0,0,0,2,0,,,0,0,4,0,0,3,2,A B CDP Q M ⎫⎪⎪⎝⎭()0,1,2N∴()()2,1,0,0,2,4BC PB =-=-，MQ ⎛⎫=⎪ ⎪⎝⎭………2分 设平面的PBC 的法向量为()0,,n x y z =，则有：())()()00,,1,000,,0,2,40240n BC x y z y n PB x y z yz ⎧⊥⇒⋅-=⇒-=⎪⎨⎪⊥⇒⋅-=⇒-=⎩令1z =，则()022,2,1x y n ==⇒=， ……………4分∴)02,102MQ n ⎛⎫⋅=-⋅= ⎪ ⎪⎝⎭，又MQ ⊄平面PCB∴MQ //平面PCB ……………6分（2）设平面的MCN 的法向量为(),,n x y z =， 又()2,1,2,2,0,22CM CN ⎛⎫=--=- ⎪ ⎪⎝⎭则有：()()(),,1,202022,,2020n CM x y z x y z n CN x y z z ⎧⎛⎫⊥⇒⋅--=⇒--+=⎪ ⎪ ⎪⎪⎝⎭⎨⎪⊥⇒⋅=⇒+=⎪⎩令1z =，则()12,1,1x y n ==⇒=， …………9分又()0,0,4AP =为平面ABCD 的法向量，∴41cos ,242n AP n AP n AP⋅===⨯⋅，又截面MCN 与底面ABCD 所成二面角为锐二面角，∴截面MCN 与底面ABCD 所成二面角的大小为3π………12分 解析（二）：（1）AP E ED ED 取的中点，连结，则//CN ， …………1分////Q EP MQ ED MQ CN 依题有为的中点，所以，所以， ………3分又MQ ⊄平面PCB ，CN平面PCB , ∴MQ //平面PCB …………6分（2）易证：平面//MEN 底面ABCD ，所以截面MCN 与平面MEN 所成的二面角即为平面MCN 与底面ABCD 所成的二面角因为PA ⊥平面ABCD ，所以PA ⊥平面MENE EF MN F QF QF MN ⊥⊥过做，垂足为，连结，则由三垂线定理可知，由（1）可知,,,M C N Q 四点共面所以QFE ∠为截面MCN 与平面MEN 所成的二面角的平面 角………9分R =1t MEN ME NE MN EF ∆在中，，所以：tan QFE ∠ 所以：3QFE π∠=………………12分20、（本小题满分12分）已知正项等比数列{}n a ()*N n ∈，首项13a =，前n 项和为n S ，且335544,,S a S a S a +++成等差数列．⑴ 求数列{}n a 的通项公式； ⑵ 求数列{}n nS 的前n 项和n T ． 解：⑴依题意，设13-=n n q a ……1分，33a S +、55a S +、44a S +成等差数列，所以)()()(2443355a S a S a S +++=+……2分，即)2()2()2(2432132154321a a a a a a a a a a a a ++++++=++++，化简得354a a =……4分，从而142=q ，解得21±=q ……4分，因为{}n a （*∈N n ）是正项数列，所以21=q ，n n a 26=……5分⑵由⑴知)211(6n n S -=……6分，)2(6)233(6)222(6)211(632n n nn T -++-+-+-=)2232221(6)1(332n n nn n T ++++-+= ……8分，设n n n R 223222132++++= ，则122232212-++++=n n nR ……10分，两式相减得nn n n n n R 2222212121211132+-=-+++++=- ……11分， 所以12)2(312)1(36)1(3-++-+=-+=n n n n n n R n n T ……12分21、（本小题满分12分）已知函数32(),f x x ax =-其中R,x a ∈为参数 （1）记函数1()()ln 6g x f x x '=+，讨论函数()g x 的单调性； （2）若曲线()y f x =与x 轴正半轴有交点且交点为P ，曲线在点P 处的切线方程为()y g x =,求证：对于任意的正实数x ，都有()()f x g x ≥.解：（1）证明：函数()g x 的定义域是()0,+∞()232,f x x ax '=-()21()32ln 6g x x ax x =-+()111()622633a a g x x a x x x '=-+=+-≥- 当6a ≤时，则203a-≥，所以()0g x '≥，所以函数()g x 在定义域()0,+∞上单调递增.当6a >时，令233()03x ax g x x -+'==，则12x x ==可知函数()g x 在⎛ ⎝⎭上单调递增，在⎝⎭单调递减，在⎫+∞⎪⎪⎝⎭上单调递增. （2）令()0,f x =则0x =或x a =若曲线()y f x =与x 轴正半轴有交点，则0a >且交点坐标为(),0P a又()232,f x x ax '=-则()2f a a '=所以曲线在点P 处的切线方程为()2y ax a =-，即23()g x a x a =-令3223()()()h x f x g x x ax a x a =-=--+()()()22323h x x ax a x a x a '=--=+-函数()h x 在区间()0,a 上单调递增，在区间(),a +∞上单调递减，所以当x a =时，()h x 有最小值，所以()0h x ≥，则()()f x g x ≥ 22、（本小题满分12分）如图，已知直线与抛物线()220y px p =>交于,M N 两点，点D 的坐标为(，OD MN ⊥交MN 于点D ，,OM ON ⊥抛物线的焦点为F .(3) 求p 的值；(4) 记条件（1）所求抛物线为曲线C ，过点F 作两条斜率存在且互相垂直的直线12,l l ，设1l 与曲线C 相交于点,A B ，2l 与曲线C 相交于点,D E ，求→AD ·→EB 的最小值．解：（1）设()()1122,,,M x y N x y ，由,OM ON ⊥得12120x x y y+= 由已知得直线MN的方程是)1yx =-即40x-=，则有()()1212440y y+=即)121240y y y y ++= ①由40x -=与22ypx =消去x ，得280y p +-= ② 所以1212,8y y y y p +=-=- ③ 把③代入①得()82340p p ---+=解得2p =当2p =时方程②成为2160y +-=，显然此方程有实数根 所以2p =（2）由（1）知抛物线方程为24y x =由题意知，直线l 1的斜率存在且不为0，设为k ，则l 1的方程为y ＝k (x －1)．由⎩⎪⎨⎪⎧y ＝k (x －1)，y 2＝4x ．得k 2x 2－(2k 2＋4)x ＋k 2＝0．设A (x 1，y 1)，B (x 2，y 2)，则x 1，x 2是上述方程的两个实根，于是x 1＋x 2＝2＋4k2，x 1x 2＝1．∵l 1⊥l 2，∴l 2的斜率为－1k．设D (x 3，y 3)，E (x 4，y 4)，则同理可得x 3＋x 4＝2＋4k 2，x 3x 4＝1． 故→AD ·→EB ＝(→AF ＋→FD )·(→EF ＋→FB )＝→AF ·→EF ＋→AF ·→FB ＋→FD ·→EF ＋→FD ·→FB＝|→AF ||→FB |＋|→FD ||→EF |＝(x 1＋1)(x 2＋1)＋(x 3＋1)(x 4＋1)＝x 1x 2＋(x 1＋x 2)＋1＋x 3x 4＋(x 3＋x 4)＋1 ＝1＋(2＋4k2)＋1＋1＋(2＋4k 2)＋1＝8＋4(k 2＋1k2)≥8＋4×2k 2·1k2＝16．当且仅当k 2＝1k2，即k ＝±1时，→AD ·→EB 取最小值16．。

湘潭县一中岳阳县一中12月高二联考英语温馨提示：本试卷共分两个部分：水平测试（100分）和能力测试（50分），满分150分，时量90分钟。

第一部分水平测试（共三个部分，满分100分）第一部分听力（30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从试题所给的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. When will the woman probably finish her homework?A.By 10:10B.By 10:20C.By 10:302. What wil the man do tonight?A.Go skatingB.Make cardsC.Go shopping3.What does the woman think of the math problem?A.StrangeB.DifficultC.Simple4.What are the two speakers mainly talking about?A.A hospitalB.Some job informationC.The man’s work5.What’s the weather like now?A.FineB.CloudyC.Rainy第二节（共15小题；每小题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，各小题将给出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、7题。

6.How did the woman probably feel when watching the movie?A.UpsetB.BoredC.Excited7.Whom did the woman watch the movie with?A.Her cousinB.Her uncleC.Her father听第7段材料，回答第8、9题8.How much should the man pay for a night?A.＄80B.＄90C.＄1009.How long will the man stay at the hotel?A.3 daysB.4 daysC.5days听第8段材料，回答第10至12题.10.Why did the man move?A.He changed his work.B.He wanted to live near his office.C.His company offered him an apartment.11.How does the man go to work now?A.On footB.By busC.By subway12.How long does it take the woman to go to work?A.Twenty minutesB.Half an hourC.An hour听第9段材料，回答第13至16题。

湘潭桃源澧县岳阳2015级一年一期联合考试试卷语文时量：150分钟分值：150分一、语言基础知识及运用（18分，每小题3分）1.下列词语字形全都正确．．．．的一组是（）A．峥嵘笙萧袅娜东道主切齿拊心陨身不恤B．作揖桀骜丰姿租赁权慷慨羽声短小精悍C．惺忪恶耗陪衬打瞌睡星辉斑澜叱咤风云D．碟血酝酿啼唱包身契摒息以待挥斥方遒2.依次填入下列各句横线处的成语，最恰当．．．的一组是（）①极端恐怖组织伊斯兰国（IS）将手无寸铁的无辜的中国公民樊京辉和挪威人质杀害，并把血腥的尸体图片刊发在其官方网络月刊《达比克》上，他们的这种做法真是_____________。

②当国家面临灾难时，如果我们都一味地_____________，而不是像烛之武、刘和珍、梁启超、屈原一样勇敢地承担起挽狂澜于既倒、扶大厦之将倾的责任，那我们的国家便失去了希望。

③史玉柱绝对是当今商界最具传奇色彩的人物。

早年，他凭借巨人汉卡和脑黄金迅速腾飞。

然后因“巨人大厦”项目迅速坠落，几年蛰伏后，又凭借脑白金和《征途》_____________。

A．惨无人道洁身自好死灰复燃B．惨绝人寰明哲保身东山再起C．惨无人道明哲保身东山再起D．惨绝人寰洁身自好死灰复燃3.下列选项中，不全包含．．．．通假字的一项是（）A．①蒲苇纫如丝，磐石无转移②行李之往来，共其乏困B．①燕王诚振怖大王之威②忳郁邑余侘傺兮C．①曰归曰归，岁亦莫止②夜缒而出，见秦伯D．①卒起不意，尽失其度②匪我愆期，子无良媒4.下列加点词中，不全是．．．古今异义词的一组是（）A．①微夫人．．乎此时也．．之力不及此②吾独穷困B．①樊於期偏袒．．体无比．．扼腕而进②可怜C．①备他盗之出入与非常．．．．也②长余佩之陆离D．①忧心．．．．孔疚，我行不来②对酒当歌，人生几何5.能与上联“月送花香浮小院”相互对应构成一副完整对联的一项是（）A．风摇竹影到书斋 B．绿叶红花映山前C．梦随春风到海角 D．风送萤火到满苑6．学习古诗文，我们接触到了古代一些可亲可敬之人，也学到了很多文化常识，请你从以下四个选项中选出表述不正确．．．的一项（）A．《左传》是我国第一部叙事详细的编年史著作，相传是春秋末年鲁国史官左丘明所作。