2014高考真题

绝密★启用前2014年普通高等学校招生全国统一考试（上海卷）英语试卷（满分150分，考试时间100分钟）考生注意：1.考试时间120分钟, 试卷满分150分。

2.本考试设试卷和答题纸两部分。

试卷分为第I卷（第1－12页）和第II卷（第13页），全卷共13页。

所有答题必须涂（选择题）或写（非选择题）在答题纸上，做在试卷上一律不得分。

答题前,务必在答题纸上填写准考证号和姓名,并将核对后的条形码贴在指定位置上,在答题纸反而清楚地填写姓名。

第I卷（共103分）I. Listening prehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. A policewoman. B. A judge. C. A reporter. D. A waitress.2. A. Confident. B. Puzzled. C. Satisfied. D. Worried.3. A. At a restaurant. B. At a car rental agency.C. In a bank.D. In a driving school.4. A. A disaster. B. A new roof. C. A performance. D. A TV station.5. A. Catch the train. B. Meet Jane.C. Get some stationery.D. Clean the backyard.6. A. Ask for something cheaper. B. Buy the vase she really likes.C. Protect herself from being hurt.D. Bargain with the shop assistant.7. A. Use a puter in the lab. B. Take a chemistry course.C. Help him revise his report.D. Get her puter repaired.8. A. Amused. B. Embarrassed.C. Shocked.D. Sympathetic.9. A. She doesn't plan to continue studying next year.B. She has already told the man about her plan.C. She isn't planning to leave her university.D. She recently visited a different university.10. A. It spoke highly of the mayor.B. It misinterpreted the mayor's speech.C. It made the mayor's view clearer.D. It carried the mayor's speech accurately.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. 70. B. 20. C. 25. D. 75.12. A. The houses there can't be sold. B. It is a place for work and holiday.C. The cabins and facilities are shared.D. It is run by the residents themselves.13. A. A skiing resort. B. A special munity.C. A splendid mountain.D. A successful businesswoman.Questions 14 through 16 are based on the following news.14. A. Those who often sent text messages. B. Those who suffered from heart disease.C. Those who did no physical exercise.D. Those who were unmarried.15. A. They responded more slowly than usual. B. They sent more messages.C. They typed 10 percent faster on average.D. They edited more passages.16. A. Why chemical therapy works.B. Why marriage helps fight cancer.C. How unmarried people survive cancer.D. How cancer is detected after marriage.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.plete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.plete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)My Stay in New YorkAfter graduation from university, I had been unable to secure a permanent job in my small town. So I decided to leave home for New York, （25）______I might have a better chance to finda good job. （26）______ (earn) some money to pay the daily expenses, I started work in a local café as a waiter. I believe that （27）______ ______ ______ I was offered a good position, I would resign at once.Over time, the high cost of living became a little burden on my already （28）______ (exhaust) shoulder. On the other hand, my search for a respectable job had not met with much success. As I had studied literature at university, I found it quite difficult to secure a suitable job in big panies. Mother had just said that （29）______ I want to have a better career ad-vancement, I had to find work in the city. Perhaps （30）______my mother had told me was deeply rooted in my mind. I just did as she had expected.Soon I had lived in the city for over six months but I still did not like it. Apparently, I had difficulty （31）______ (adapt) myself to life in the city, let alone finding a job to my delight. After nine months of frustration, I eventually decided to go back to my small town. Not until I returned （32）______I realize that a quiet town life was the best for me.(B)The giant vending machine (自动售货机) is a new village shop Villagers have long been used to facing a drive when they run out of basic supplies. However, help is now nearer at hand in form of the country’s first automatic pushbutton shop. Now res idents in the Derbyshire Village of Clifton can buy groceries around the clock after the huge vending was installed outside a pub in the village this week.Peter Fox, who is （33）______electrical engineer, spent two and a half years working on the project. The machine （34）______ (equip) with securing cameras and alarms and looks like a mini shop with a brick front, a grey roof and a display window.Mr. Fox said he hoped his invention, （35）_____ is set to be installed in other villages in the area over the ing months, will mark a return to convenience shopping for rural munities.He said:“ I had this idea a few years ago but I couldn’t find a manufacture w ho could deliver what I wanted, so I did it by （36）_____. The result is what amounts to huge outdoor vending machine. Yet I think the term “automatic shop” is far（37）______ (appropriate)In recent years, the mercial pressure from supermarket chains （38）_____ (force) village shops across the country to close. In 2010, it was estimated that about 400 village shops closed, （39）______ (urge) the local government to give financial support to struggling shops orsetup new munities stores.Hundreds of munities have since stepped in and opened up their won volunteerrun shops, but Mr. Fox hopes his new invention will offer a solution （40）______those villages without a local shop.Section BDirections: plete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Let's say you've decided you want to eat more healthfully. However, you don't have time to carefully plan menus for meals or read food 41at the supermarket. Since you really 42 yourself to a healthier lifestyle, a little help would e in handy, wouldn't it? This is where a "choice architect" can help43some of the burden of doing it all yourself. Choice architects are people who organize the contexts in which customers make decisions. For example, the person who de-cides the layout of your local supermarketincluding which shelf the peanut butter goes on, and how the oranges are piled up — is a choice architect.Governments don’t have to44healthier lifestyles through laws for example, smoking bans. Rather, if given an environment created by a choice architectone that encourages us to choose what is bestwe will do the right things. In other words, there will be designs that gently push customers toward making healthier choices, without removing freedom of choice. This idea bines freedom to choose with 45hints from choice architects, who aim to help people live longer, healthier, and happier lives.The British and Swedish governments have introduced a socalled "traffic light system" to 46foods as healthy or unhealthy. This means that customers can see at a glance how much fat, sugar, and salt each product contains 47by looking at the lights on the package. A green light48that the amounts of the three nutrients are healthy; yellow indicates that the customer should be49; and red means that the food is high in at least one of the three nutrients and should be eaten in50. The customer is given important health information, but is still free to decide what to choose.III. Reading prehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Research has shown that twothirds of human conversation is taken up not with discussion of the cultural or political problems of the day, not heated debates about films we've just watched or books we've just finished reading, but plain and simple51.Language is our greatest treasure as a species, and what do we52do with it? We gossip. About others' behaviour and private lives, such as who's doing what with whom, who's in and who's outand why; how to deal with difficult53situations involving children, lovers, and col-leagues.So why are we keen on gossiping? Are we just natural54, of both time and words? Or do we talk a lot about nothing in particular simply to avoid facing up to the really important issues of life? It's not the case according to Professor Robin Dunbar. In fact, in his latest book, Grooming, Gossip and the Evolution of Language, the psychologist says gossip is one of these really55 issues.Dunbar56the traditional view that language was developed by the men at the early stage of social development in order to organize their manly hunting activities more effectively, or even to promote the exchange of poetic stories about their origins and the supernatural. Instead he suggests that language evolved among women. We don't spend twothirds of our time gossip-ing just because we can talk, argues Dunbar—57, he goes on to say, language evolved spe-cifically to allow us to gossip.Dunbar arrived at his cheery theory by studying the58of the higher primates(灵长类动物)like monkeys. By means of groomingcleaning the fur by brushing it, monkeys form groups with other individuals on whom they can rely for support in the event of some kind of conflict within the group or59from outside it.As we human beings evolve from a particular branch of the primate family, Dunbar 60 that at one time in our history we did much the same. Grouping together made sense because the bigger the group, the greater the 61it provided; on the other hand, the bigger the group, the greater the stresses of living close to others. Grooming helped to62the pressure and calmeverybody down.But as the groups got bigger and bigger, the amount of time spent in grooming activities also had to be63to maintain its effectiveness. Clearly, a more64kind of grooming was needed, and thus language evolved as a kind of vocal(有声的)grooming which allowed humans to develop relationship with everlarger groups by exchanging information over a wider network of individuals than would be possible by onetoone 65contact.51.A. claim B. description C. gossip D. language52.A. occasionally B. habitually C. independently D. originally53.A. social B. political C. historical D. cultural54.A. admirers B. masters C. users D. wasters55.A. vital B. sensitive C. ideal D. difficult56.A. confirms B. rejects C. outlines D. broadens57.A. for instance B. in addition C. on the contrary D. as a result58.A. motivation B. appearance C. emotion D. behaviour59.A. attack B. contact C. inspection D. assistance60.A. recalls B. denies C. concludes D. confesses61.A. prospect B. responsibility C. leadership D. protection62.A. measure B. show C. maintain D. ease63.A. saved B. extended C. consumed D. gained64.A. mon B. efficient C. scientific D. Thoughtful65.A. indirect B. daily C. physical D. secretSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Most people agree that honesty is a good thing. But does Mother Nature agree?Animals can't talk, but can they lie in other ways? Can they lie with their bodiesand behavior? Animal experts may not call it lying, but they do agree that manyanimals, from birds to chimpanzees, behave dishonestly to fool other animals. Why? Dishonesty often helps them survive.Many kinds of birds are very successful at fooling other animals. For example, a bird called the plover sometimes pretends to be hurt in order to protect its young. When a predator(猎食动物)gets close to its nest, the plover leads the predator away from the nest. How? It pretends to have a broken wing. The predator follows the "hurt" adult, leaving the baby birds safe in the nest.Another kind of bird, the scrub jay, buries its food so it always has something to eat. Scrub jays are also thieves. They watch where others bury their food and steal it. But clever scrub jays seem to know when a thief is watching them. So they go back later, unbury the food, and bury it again somewhere else.Birds called cuckoos have found a way to have babies without doing much work. How? They don't make nests. Instead, they get into other birds' nests secretly. Then they lay their eggs and fly away. When the baby birds e out, their adoptive parents feed them.Chimpanzees, or chimps, can also be sneaky. After a fight, the losing chimp will give its hand to the other. When the winning chimp puts out its hand, too, the chimps are friendly again. But an animal expert once saw a losing chimp take the winner's hand and start fighting again.Chimps are sneaky in other ways, too. When chimps find food that they love, such as bana-nas, it is natural for them to cry out. Then other chimps e running. But some clever chimps learn to cry very softly when they find food. That way, other chimps don't hear them, and they don't need to share their food.As children, many of us learn the saying "You can't fool Mother Nature." But maybe you can't trust her, either.66.A plover protects its young from a predator by______.A. getting closer to its youngB. driving away the adult predatorC. leaving its young in another nestD. pretending to be injured67.By "Chimpanzees, or chimps, can also be sneaky" (paragraph 5), the author means______.A. chimps are ready to attack othersB. chimps are sometimes dishonestC. chimps are jealous of the winnersD. chimps can be selfish too68.Which of the following is true according to the passage?A. Some chimps lower their cry to keep food away from others.B. The losing chimp won the fight by taking the winner's hand.C. Cuckoos fool their adoptive parents by making no nests.D. Some clever scrub jays often steal their food back.69.Which of the following might be the best title of the passage?A. Do animals lie?B. Does Mother Nature fool animals?C. How do animals learn to lie?D. How does honesty help animals survive?（B）Let's say you want to hit the gym more regularly this year. How do you make that happen? Consider putting the habit loop to use.Here's how it works:A habit is a 3step process. First, there's a cue, something that tells your brain to operate auto-matically. Then there's a routine. And finally, a reward, which helps your brain learn to desire the behavior. It's what you can use to createor breakhabits of your own.Here's how to apply it:Choose a cue, like leaving your running shoes by the door, then pick. a rewardsay, a piece of chocolate when you get home from the gym. That way, the cue and the reward bee interconnected. Finally, when you see the shoes, your brain will start longing for the reward, which will make it easier to work out day after day. The best part? In a couple of weeks, you won't need the chocolate at all. Your brain will e to see the workout itself as the reward. Which is the whole point, right?70.Which of the following best fits in the box with a “?”in THE HABIT LOOP?A. Pick a new cue.B. Form a new habit.C. Choose a new reward.D. Design a new resolution.71.According to THE HABIT LOOP, you can stick to your plan most effectively by______.A. changing the routineB. trying it for a weekC. adjusting your goalD. writing it down72.What's the purpose of putting the habit loop to use?A. To test out different kinds of cues.B. To do something as a habit even without rewards.C. To work out the best New Year's resolution.D. To motivate yourself with satisfactory rewards.73.“This year when I see the Harry Potter poster, I will read 30 pages of an English novel or anEnglish newspaper in order to watch TV for half an hour." What is the cue in this resolution?A. The Harry Potter poster.B. Reading 30 pages of an English novel.C. An English newspaper.D. Watching TV for half an hour.(C)If you could be anybody in the world, who would it be? Your neighbour or a super star? A few people have experienced what it might be like to step into the skin of another person, thanks to an unusual virtual reality(虚拟现实)device. Rikke Wahl, an actress, model and artist, was one of the participants in a body swapping experiment at the Be Another lab, a project developed by a group of artists based in Barcelona. She swapped with her partner, an actor, using a machine called The Machine to Be Another and temporarily became a man. "As I looked down, I saw my whole body as a man, dressed in my partner's pants," she said. "That's the picture I remember best."The setup is relatively simple. Both users wear a virtual reality headset with a camera on the top. The video from each camera is sent to the other person, so what you see is the exact view of your partner. If she moves her arm, you see it. If you move your arm, she sees it.To get used to seeing another person's body without actually having control of it, participants start by raising their arms and legs very slowly, so that the other can follow along. Eventually, this kind of slow synchronised(同步的)movement bees fortable, and participants really start to feel as though they are living in another person's body.Using such technology promises to alter people's behaviour afterwardspotentially for the bet-ter. Studies have shown that virtual reality can be effective in fighting racismthe bias(偏见)that humans have against those who don't look or sound like them. Researchers at the University of Barcelona gave people a questionnaire called the Implicit Association Test, which measures the strength of people's associations between, for instance, black people and adjectives such as good,bad, athletic or awkward. Then they asked them to control the body of a dark skinned digital character using virtual reality glasses, before taking the test again. This time, the participants' bias scores were lower. The idea is that once you've "put yourself in another's shoes" you're less likely to think ill of them, because your brain has internalised the feeling of being that person.The creators of The Machine to Be Another hope to achieve a similar result. "At the end of body swapping, people feel like holding each other in their arms," says Arthur Pointeau, a pro-grammer with the project. "It's a really nice way to have this kind of experience. I would really, really remend it to everyone."74.The word "swapping" (paragraph 1) is closest in meaning to______.A. buildingB. exchangingC. controllingD. transplanting75.We can infer from the experiment at the Be Another lab that______.A. our feelings are related to our bodily experienceB. we can learn to take control of other people's bodiesC. participants will live more passionately after the experimentD. The Machine to Be Another can help people change their sexes76.In the Implicit Association Test, before the participants used virtual reality glasses to control a dark skinned digital character, ______.A. they fought strongly against racismB. they scored lower on the test for racismC. they changed their behaviour dramaticallyD. they were more biased against those unlike them77.It can be concluded from the passage that______.A. technology helps people realize their dreamsB. our biases could be eliminated through experimentsC. virtual reality helps promote understanding among peopleD. our points of view about others need changing constantlySection CDirections: Read the passage carefully. Then answer the questions or plete the statements in the fewest possible words.More and more corporations are taking an interest in corporate social responsibility (CSR).CSR is made up of three broad layers. The most basic is traditional corporate charity work. panies typically spend about 1% of pretax profits on worthy projects. But many feel that simply writing cheques to charities is no longer enough. In some panies, shareholders want to know that their money is being put to good use, and employees want to be actively involved in good works.Money alone is not the answer when panies e under attack for their behavior. Hence the sec-ond layer of CSR, which is a branch of risk management. Starting in the 1980s, with environmen-tal disasters such as the explosion at Bhopal and the Exxon V aldez oil spill, industry after industry has suffered blows to its reputation.So, panies often responded by trying to manage the risks. They talk to nongovernmental or-ganisations (NGOs) and to governments, create codes of conduct(行为准则) and devote them-selves to more transparency(透明)in their operations. Increasingly, too. they, along with their pet-itors, set mon rules to spread risks.All this is largely defensive, but there are also opportunities for those that get ahead of the game. The emphasis on opportunity is the third layer of CSR: the idea that it can help to create value. If approached in a strategic way, CSR could bee part of a pany's petitive advantage. That is just the sort of thing chief executives like to hear. The idea of "doing well by doing good" has bee popular.Nevertheless, the business of trying to be good is bringing difficult questions to executives. Can you measure CSR performance? Should you be cooperating with NGOs and you’re your pet-itors? Is there any really petitive advantage to be had from a green strategy?Corporate social responsibility is now seen as a mainstream. Big panies want to tell the world about their good citizenship with their devotion to social responsibilities. Done badly, CSR is of-ten just windowdressing and can be positively harmful. Done well, though, it is not some separate activity that panies do on the side, a corner of corporate life reserved for virtue(美德)：it is just good business.(Note: Answer the questions or plete the statements in NO MORE THAN TEN WORDS)78.Both _________ in some panies find it no longer enough to simply donate money to charities.79.Give one example of the defensive measures of risk management according to the passage.80.With the emphasis on opportunity, the third layer of CSR is meant to_________.81.According to the passage, "good business" (paragraph 6) means that corporations ________while making profits.第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 我习惯睡前听点轻音乐。

浙江省2014年高考语文试题一、语言文字运用（共24分，其中选择题每小题3分）1．下列词语中，加点字的注音全都正确的一项是A．摭．（zhí）拾哄．（hōng）笑擎．（qín）天柱钻．（zuān）木取火B．屏．（bǐng）息包扎．（zhā）夹（jiā）克衫言之凿凿（záo）C．孱（càn）弱牌坊（fāng）干．（gàn）细胞铩．（shā）羽而归D．吟哦．（é）皲．（jūn）裂胳．（gā）肢窝蜚．（fēi）声中外2．下列各句中，没有错别字的一项是A．这个节目融合了京剧、粤剧、秦腔等中国戏曲的精萃，舞者多变的动作和戏剧化的表情，淋漓尽致地表达了喜怒哀乐的情绪。

B．城郊的这座园林，亭台楼阁错落有致，溪流小径曲折萦纡，到了春天，杂花生树，草长莺飞，真是一处世外桃源。

C．在全球一体化进程中，有些备受国人青睐的外国名品，其实是用中国的原料，在中国的流水线上生产出来的，已不是地道的泊来品。

D．该公司在把握市场脉搏的基础上，另辟蹊径，依靠独树一帜的管理理念以及出奇不意的营销策略赢得了商机，获得了发展。

3．下列各句中，加点的词语运用正确的一项是A．从小到大，母亲一直是你的守护天使，当母亲需要你的时候，不要推托．．工作繁忙，久不回家，哪怕是一句问候，也是给母亲最好的安慰。

B．社会需要个体的行动，每个人都应该从身边做起，从实事做起，不需要太多的空话，赞同这种观点的，远不只．．一个人。

C．相比于持续火爆的住宅市场，多年来，写字楼市场一直处于不瘟不火．．．．的状态，与同地段的住宅楼相比，写字楼的销量要小得多。

D．解决问题一般有两种思路：一种是将问题变小，小意味着成本低，好办事；另一种是把问题变大，大而化之．．．．，放大了才能解决。

4．下列各句中，没有语病的一项是A．一项好的政策照理会带来好的效果，但在现阶段，必须强化阳光操作、民主监督等制约措施，因为好经也要提防不被念歪。

2014 年普通高等学校招生全国统一考试英语(一）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 10 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。

例： What is the man going to rend? A. A newspaperB. A magazineC. A book答案是 A1. What room does the man want?A. SimpleB. DoubleC. Twin2. What will the man buy?A. VegetableB. MeatC. Bread3. What does the man plan to do?A. Go fishingB. Go joggingC. Go camping4. How much is the change?A. $8B. $ 42C. $505. What’s the weather like this afternoon?第二节（共 10 小题；每小题 1.5 分，共 15 分）听下面 4 段对话或独白。

每段对话或独白后有几道小题，从每题所给的 A、B、C 三个选项中选出最佳选项。

听每段对话或独白前，你将有 5 秒钟的时间阅读每小题。

听完后，每小题将给出 5 秒钟的作答时间。

每段对话或独白你将听两遍。

听第 6 段材料，回答第 6 至 7 题。

6. When will the woman go to see the movie? A. Friday. B. Saturday C. Sunday7. Where will the woman sit for the movie?A. In the front.B. In the middleC. At the back听第 7 段材料，回答第 8 至 9 题。

2014年全国统一高考数学试卷（理科）（新课标Ⅱ）一、选择题：本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一个选项符合题目要求.1．（5分）设集合M={0，1，2}，N={x|x2﹣3x+2≤0}，则M∩N=（）A．{1}B．{2}C．{0，1}D．{1，2} 2．（5分）设复数z1，z2在复平面内的对应点关于虚轴对称，z1=2+i，则z1z2=（）A．﹣5B．5C．﹣4+i D．﹣4﹣i3．（5分）设向量，满足|+|=，|﹣|=，则•=（）A．1B．2C．3D．54．（5分）钝角三角形ABC的面积是，AB=1，BC=，则AC=（）A．5B．C．2D．15．（5分）某地区空气质量监测资料表明，一天的空气质量为优良的概率是0.75，连续两天为优良的概率是0.6，已知某天的空气质量为优良，则随后一天的空气质量为优良的概率是（）A．0.8B．0.75C．0.6D．0.456．（5分）如图，网格纸上正方形小格的边长为1（表示1cm），图中粗线画出的是某零件的三视图，该零件由一个底面半径为3cm，高为6cm的圆柱体毛坯切削得到，则切削掉部分的体积与原来毛坯体积的比值为（）A．B．C．D．7．（5分）执行如图所示的程序框图，若输入的x，t均为2，则输出的S=（）A．4B．5C．6D．78．（5分）设曲线y=ax﹣ln（x+1）在点（0，0）处的切线方程为y=2x，则a=（）A．0B．1C．2D．39．（5分）设x，y满足约束条件，则z=2x﹣y的最大值为（）A．10B．8C．3D．210．（5分）设F为抛物线C：y2=3x的焦点，过F且倾斜角为30°的直线交C于A，B两点，O为坐标原点，则△OAB的面积为（）A．B．C．D．11．（5分）直三棱柱ABC﹣A1B1C1中，∠BCA=90°，M，N分别是A1B1，A1C1的中点，BC=CA=CC1，则BM与AN所成角的余弦值为（）A．B．C．D．12．（5分）设函数f（x）=sin，若存在f（x）的极值点x0满足x02+[f（x0）]2＜m2，则m的取值范围是（）A．（﹣∞，﹣6）∪（6，+∞）B．（﹣∞，﹣4）∪（4，+∞）C．（﹣∞，﹣2）∪（2，+∞）D．（﹣∞，﹣1）∪（1，+∞）二、填空题：本大题共4小题，每小题5分.（第13题~第21题为必考题，每个试题考生都必须作答，第22题~第24题为选考题，考生根据要求作答）13．（5分）（x+a）10的展开式中，x7的系数为15，则a=．14．（5分）函数f（x）=sin（x+2φ）﹣2sinφcos（x+φ）的最大值为．15．（5分）已知偶函数f（x）在[0，+∞）单调递减，f（2）=0，若f（x﹣1）＞0，则x的取值范围是．16．（5分）设点M（x0，1），若在圆O：x2+y2=1上存在点N，使得∠OMN=45°，则x0的取值范围是．三、解答题：解答应写出文字说明，证明过程或验算步骤.17．（12分）已知数列{a n}满足a1=1，a n+1=3a n+1．（Ⅰ）证明{a n+}是等比数列，并求{a n}的通项公式；（Ⅱ）证明：++…+＜．18．（12分）如图，四棱锥P﹣ABCD中，底面ABCD为矩形，PA⊥平面ABCD，E为PD的中点．（Ⅰ）证明：PB∥平面AEC；（Ⅱ）设二面角D﹣AE﹣C为60°，AP=1，AD=，求三棱锥E﹣ACD的体积．19．（12分）某地区2007年至2013年农村居民家庭人均纯收入y（单位：千元）的数据如表：年份2007200820092010201120122013年份代号t1234567人均纯收入y 2.9 3.3 3.6 4.4 4.8 5.2 5.9（Ⅰ）求y关于t的线性回归方程；（Ⅱ）利用（Ⅰ）中的回归方程，分析2007年至2013年该地区农村居民家庭人均纯收入的变化情况，并预测该地区2015年农村居民家庭人均纯收入．附：回归直线的斜率和截距的最小二乘估计公式分别为：=，=﹣．20．（12分）设F1，F2分别是C：+=1（a＞b＞0）的左，右焦点，M是C 上一点且MF2与x轴垂直，直线MF1与C的另一个交点为N．（1）若直线MN的斜率为，求C的离心率；（2）若直线MN在y轴上的截距为2，且|MN|=5|F1N|，求a，b．21．（12分）已知函数f（x）=e x﹣e﹣x﹣2x．（Ⅰ）讨论f（x）的单调性；（Ⅱ）设g（x）=f（2x）﹣4bf（x），当x＞0时，g（x）＞0，求b的最大值；（Ⅲ）已知1.4142＜＜1.4143，估计ln2的近似值（精确到0.001）．请考生在第22、23、24三题中任选一题作答，如果多做，则按所做的第一题计分，作答时请写清题号.【选修4-1：几何证明选讲】22．（10分）如图，P是⊙O外一点，PA是切线，A为切点，割线PBC与⊙O相交于点B，C，PC=2PA，D为PC的中点，AD的延长线交⊙O于点E，证明：（Ⅰ）BE=EC；（Ⅱ）AD•DE=2PB2．【选修4-4：坐标系与参数方程】23．在直角坐标系xOy中，以坐标原点为极点，x轴正半轴为极轴建立极坐标系，半圆C的极坐标方程为ρ=2cosθ，θ∈[0，]（Ⅰ）求C的参数方程；（Ⅱ）设点D在半圆C上，半圆C在D处的切线与直线l：y=x+2垂直，根据（1）中你得到的参数方程，求直线CD的倾斜角及D的坐标．六、解答题（共1小题，满分0分）24．设函数f（x）=|x+|+|x﹣a|（a＞0）．（Ⅰ）证明：f（x）≥2；（Ⅱ）若f（3）＜5，求a的取值范围．2014年全国统一高考数学试卷（理科）（新课标Ⅱ）参考答案与试题解析一、选择题：本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一个选项符合题目要求.1．（5分）设集合M={0，1，2}，N={x|x2﹣3x+2≤0}，则M∩N=（）A．{1}B．{2}C．{0，1}D．{1，2}【考点】1E：交集及其运算．【专题】5J：集合．【分析】求出集合N的元素，利用集合的基本运算即可得到结论．【解答】解：∵N={x|x2﹣3x+2≤0}={x|（x﹣1）（x﹣2）≤0}={x|1≤x≤2}，∴M∩N={1，2}，故选：D．【点评】本题主要考查集合的基本运算，比较基础．2．（5分）设复数z1，z2在复平面内的对应点关于虚轴对称，z1=2+i，则z1z2=（）A．﹣5B．5C．﹣4+i D．﹣4﹣i【考点】A5：复数的运算．【专题】5N：数系的扩充和复数．【分析】根据复数的几何意义求出z2，即可得到结论．【解答】解：z1=2+i对应的点的坐标为（2，1），∵复数z1，z2在复平面内的对应点关于虚轴对称，∴（2，1）关于虚轴对称的点的坐标为（﹣2，1），则对应的复数，z2=﹣2+i，则z1z2=（2+i）（﹣2+i）=i2﹣4=﹣1﹣4=﹣5，故选：A．【点评】本题主要考查复数的基本运算，利用复数的几何意义是解决本题的关键，比较基础．3．（5分）设向量，满足|+|=，|﹣|=，则•=（）A．1B．2C．3D．5【考点】9O：平面向量数量积的性质及其运算．【专题】5A：平面向量及应用．【分析】将等式进行平方，相加即可得到结论．【解答】解：∵|+|=，|﹣|=，∴分别平方得+2•+=10，﹣2•+=6，两式相减得4•=10﹣6=4，即•=1，故选：A．【点评】本题主要考查向量的基本运算，利用平方进行相加是解决本题的关键，比较基础．4．（5分）钝角三角形ABC的面积是，AB=1，BC=，则AC=（）A．5B．C．2D．1【考点】HR：余弦定理．【专题】56：三角函数的求值．【分析】利用三角形面积公式列出关系式，将已知面积，AB，BC的值代入求出sinB的值，分两种情况考虑：当B为钝角时；当B为锐角时，利用同角三角函数间的基本关系求出cosB的值，利用余弦定理求出AC的值即可．【解答】解：∵钝角三角形ABC的面积是，AB=c=1，BC=a=，∴S=acsinB=，即sinB=，当B为钝角时，cosB=﹣=﹣，利用余弦定理得：AC2=AB2+BC2﹣2AB•BC•cosB=1+2+2=5，即AC=，当B为锐角时，cosB==，利用余弦定理得：AC2=AB2+BC2﹣2AB•BC•cosB=1+2﹣2=1，即AC=1，此时AB2+AC2=BC2，即△ABC为直角三角形，不合题意，舍去，则AC=．故选：B．【点评】此题考查了余弦定理，三角形面积公式，以及同角三角函数间的基本关系，熟练掌握余弦定理是解本题的关键．5．（5分）某地区空气质量监测资料表明，一天的空气质量为优良的概率是0.75，连续两天为优良的概率是0.6，已知某天的空气质量为优良，则随后一天的空气质量为优良的概率是（）A．0.8B．0.75C．0.6D．0.45【考点】C8：相互独立事件和相互独立事件的概率乘法公式．【专题】5I：概率与统计．【分析】设随后一天的空气质量为优良的概率为p，则由题意可得0.75×p=0.6，由此解得p的值．【解答】解：设随后一天的空气质量为优良的概率为p，则由题意可得0.75×p=0.6，解得p=0.8，故选：A．【点评】本题主要考查相互独立事件的概率乘法公式的应用，属于基础题．6．（5分）如图，网格纸上正方形小格的边长为1（表示1cm），图中粗线画出的是某零件的三视图，该零件由一个底面半径为3cm，高为6cm的圆柱体毛坯切削得到，则切削掉部分的体积与原来毛坯体积的比值为（）A．B．C．D．【考点】L!：由三视图求面积、体积．【专题】5F：空间位置关系与距离．【分析】由三视图判断几何体的形状，通过三视图的数据求解几何体的体积即可．【解答】解：几何体是由两个圆柱组成，一个是底面半径为3高为2，一个是底面半径为2，高为4，组合体体积是：32π•2+22π•4=34π．底面半径为3cm，高为6cm的圆柱体毛坯的体积为：32π×6=54π切削掉部分的体积与原来毛坯体积的比值为：=．故选：C．【点评】本题考查三视图与几何体的关系，几何体的体积的求法，考查空间想象能力以及计算能力．7．（5分）执行如图所示的程序框图，若输入的x，t均为2，则输出的S=（）A．4B．5C．6D．7【考点】EF：程序框图．【专题】5K：算法和程序框图．【分析】根据条件，依次运行程序，即可得到结论．【解答】解：若x=t=2，则第一次循环，1≤2成立，则M=，S=2+3=5，k=2，第二次循环，2≤2成立，则M=，S=2+5=7，k=3，此时3≤2不成立，输出S=7，故选：D．【点评】本题主要考查程序框图的识别和判断，比较基础．8．（5分）设曲线y=ax﹣ln（x+1）在点（0，0）处的切线方程为y=2x，则a=（）A．0B．1C．2D．3【考点】6H：利用导数研究曲线上某点切线方程．【专题】52：导数的概念及应用．【分析】根据导数的几何意义，即f′（x0）表示曲线f（x）在x=x0处的切线斜率，再代入计算．【解答】解：，∴y′（0）=a﹣1=2，∴a=3．故选：D．【点评】本题是基础题，考查的是导数的几何意义，这个知识点在高考中是经常考查的内容，一般只要求导正确，就能够求解该题．在高考中，导数作为一个非常好的研究工具，经常会被考查到，特别是用导数研究最值，证明不等式，研究零点问题等等经常以大题的形式出现，学生在复习时要引起重视．9．（5分）设x，y满足约束条件，则z=2x﹣y的最大值为（）A．10B．8C．3D．2【考点】7C：简单线性规划．【专题】59：不等式的解法及应用．【分析】作出不等式组对应的平面区域，利用目标函数的几何意义，利用数形结合确定z的最大值．【解答】解：作出不等式组对应的平面区域如图：（阴影部分ABC）．由z=2x﹣y得y=2x﹣z，平移直线y=2x﹣z，由图象可知当直线y=2x﹣z经过点C时，直线y=2x﹣z的截距最小，此时z最大．由，解得，即C（5，2）代入目标函数z=2x﹣y，得z=2×5﹣2=8．故选：B．【点评】本题主要考查线性规划的应用，结合目标函数的几何意义，利用数形结合的数学思想是解决此类问题的基本方法．10．（5分）设F为抛物线C：y2=3x的焦点，过F且倾斜角为30°的直线交C于A，B两点，O为坐标原点，则△OAB的面积为（）A．B．C．D．【考点】K8：抛物线的性质．【专题】5D：圆锥曲线的定义、性质与方程．【分析】由抛物线方程求出焦点坐标，由直线的倾斜角求出斜率，写出过A，B 两点的直线方程，和抛物线方程联立后化为关于y的一元二次方程，由根与系数关系得到A，B两点纵坐标的和与积，把△OAB的面积表示为两个小三角形AOF与BOF的面积和得答案．【解答】解：由y2=2px，得2p=3，p=，则F（，0）．∴过A，B的直线方程为y=（x﹣），即x=y+．联立，得4y2﹣12y﹣9=0．设A（x1，y1），B（x2，y2），则y 1+y 2=3，y 1y 2=﹣．∴S△OAB =S △OAF +S△OFB =×|y 1﹣y 2|==×=．故选：D ．【点评】本题考查直线与抛物线的位置关系，考查数学转化思想方法，涉及直线和圆锥曲线关系问题，常采用联立直线和圆锥曲线，然后利用一元二次方程的根与系数关系解题，是中档题．11．（5分）直三棱柱ABC ﹣A 1B 1C 1中，∠BCA=90°，M ，N 分别是A 1B 1，A 1C 1的中点，BC=CA=CC 1，则BM 与AN 所成角的余弦值为（ ） A ．B ．C ．D ．【考点】LM ：异面直线及其所成的角．【专题】5F ：空间位置关系与距离．【分析】画出图形，找出BM 与AN 所成角的平面角，利用解三角形求出BM 与AN 所成角的余弦值．【解答】解：直三棱柱ABC ﹣A 1B 1C 1中，∠BCA=90°，M ，N 分别是A 1B 1，A 1C 1的中点，如图：BC 的中点为O ，连结ON ，，则MN0B 是平行四边形，BM 与AN 所成角就是∠ANO ，∵BC=CA=CC 1，设BC=CA=CC 1=2，∴CO=1，AO=，AN=，MB===， 在△ANO 中，由余弦定理可得：cos ∠ANO===．故选：C ．【点评】本题考查异面直线对称角的求法，作出异面直线所成角的平面角是解题的关键，同时考查余弦定理的应用．12．（5分）设函数f（x）=sin，若存在f（x）的极值点x0满足x02+[f（x0）]2＜m2，则m的取值范围是（）A．（﹣∞，﹣6）∪（6，+∞）B．（﹣∞，﹣4）∪（4，+∞）C．（﹣∞，﹣2）∪（2，+∞）D．（﹣∞，﹣1）∪（1，+∞）【考点】H4：正弦函数的定义域和值域．【专题】57：三角函数的图像与性质．【分析】由题意可得，f（x0）=±，且=kπ+，k∈Z，再由题意可得当m2最小时，|x0|最小，而|x0|最小为|m|，可得m2 ＞m2+3，由此求得m的取值范围．【解答】解：由题意可得，f（x0）=±，即=kπ+，k∈z，即x0=m．再由x02+[f（x0）]2＜m2，即x02+3＜m2，可得当m2最小时，|x0|最小，而|x0|最小为|m|，∴m2 ＞m2+3，∴m2＞4．求得m＞2，或m＜﹣2，故选：C．【点评】本题主要正弦函数的图象和性质，函数的零点的定义，体现了转化的数学思想，属于中档题．二、填空题：本大题共4小题，每小题5分.（第13题~第21题为必考题，每个试题考生都必须作答，第22题~第24题为选考题，考生根据要求作答）13．（5分）（x+a）10的展开式中，x7的系数为15，则a=．【考点】DA：二项式定理．【专题】5P：二项式定理．【分析】在二项展开式的通项公式中，令x的幂指数等于3，求出r的值，即可求得x7的系数，再根据x7的系数为15，求得a的值．【解答】解：（x+a）10的展开式的通项公式为T r=•x10﹣r•a r，+1令10﹣r=7，求得r=3，可得x7的系数为a3•=120a3=15，∴a=，故答案为：．【点评】本题主要考查二项式定理的应用，二项展开式的通项公式，求展开式中某项的系数，二项式系数的性质，属于中档题．14．（5分）函数f（x）=sin（x+2φ）﹣2sinφcos（x+φ）的最大值为1．【考点】GP：两角和与差的三角函数；HW：三角函数的最值．【专题】56：三角函数的求值．【分析】由条件利用两角和差的正弦公式、余弦公式化简函数的解析式为f（x）=sinx，从而求得函数的最大值．【解答】解：函数f（x）=sin（x+2φ）﹣2sinφcos（x+φ）=sin[（x+φ）+φ]﹣2sinφcos （x+φ）=sin（x+φ）cosφ+cos（x+φ）sinφ﹣2sinφcos（x+φ）=sin（x+φ）cosφ﹣cos（x+φ）sinφ=sin[（x+φ）﹣φ]=sinx，故函数f（x）的最大值为1，故答案为：1．【点评】本题主要考查两角和差的正弦公式、余弦公式的应用，正弦函数的最值，属于中档题．15．（5分）已知偶函数f（x）在[0，+∞）单调递减，f（2）=0，若f（x﹣1）＞0，则x的取值范围是（﹣1，3）．【考点】3N：奇偶性与单调性的综合．【专题】51：函数的性质及应用．【分析】根据函数奇偶性和单调性之间的关系将不等式等价转化为f（|x﹣1|）＞f（2），即可得到结论．【解答】解：∵偶函数f（x）在[0，+∞）单调递减，f（2）=0，∴不等式f（x﹣1）＞0等价为f（x﹣1）＞f（2），即f（|x﹣1|）＞f（2），∴|x﹣1|＜2，解得﹣1＜x＜3，故答案为：（﹣1，3）【点评】本题主要考查函数奇偶性和单调性之间的关系的应用，将不等式等价转化为f（|x﹣1|）＞f（2）是解决本题的关键．16．（5分）设点M（x0，1），若在圆O：x2+y2=1上存在点N，使得∠OMN=45°，则x0的取值范围是[﹣1，1] ．【考点】J9：直线与圆的位置关系．【专题】5B：直线与圆．【分析】根据直线和圆的位置关系，画出图形，利用数形结合即可得到结论．【解答】解：由题意画出图形如图：点M（x0，1），要使圆O：x2+y2=1上存在点N，使得∠OMN=45°，则∠OMN的最大值大于或等于45°时一定存在点N，使得∠OMN=45°，而当MN与圆相切时∠OMN取得最大值，此时MN=1，图中只有M′到M″之间的区域满足MN≤1，∴x0的取值范围是[﹣1，1]．【点评】本题考查直线与圆的位置关系，直线与直线设出角的求法，数形结合是快速解得本题的策略之一．三、解答题：解答应写出文字说明，证明过程或验算步骤.17．（12分）已知数列{a n}满足a1=1，a n+1=3a n+1．（Ⅰ）证明{a n+}是等比数列，并求{a n}的通项公式；（Ⅱ）证明：++…+＜．【考点】87：等比数列的性质；8E：数列的求和．【专题】14：证明题；54：等差数列与等比数列．【分析】（Ⅰ）根据等比数列的定义，后一项与前一项的比是常数，即=常数，又首项不为0，所以为等比数列；再根据等比数列的通项化式，求出{a n}的通项公式；（Ⅱ）将进行放大，即将分母缩小，使得构成一个等比数列，从而求和，证明不等式．【解答】证明（Ⅰ）==3，∵≠0，∴数列{a n+}是以首项为，公比为3的等比数列；∴a n+==，即；（Ⅱ）由（Ⅰ）知，当n≥2时，∵3n﹣1＞3n﹣3n﹣1，∴＜=，∴当n=1时，成立，当n≥2时，++…+＜1+…+==＜．时，++…+＜．∴对n∈N+【点评】本题考查的是等比数列，用放缩法证明不等式，证明数列为等比数列，只需要根据等比数列的定义就行；数列与不等式常结合在一起考，放缩法是常用的方法之一，通过放大或缩小，使原数列变成一个等比数列，或可以用裂项相消法求和的新数列．属于中档题．18．（12分）如图，四棱锥P﹣ABCD中，底面ABCD为矩形，PA⊥平面ABCD，E为PD的中点．（Ⅰ）证明：PB∥平面AEC；（Ⅱ）设二面角D﹣AE﹣C为60°，AP=1，AD=，求三棱锥E﹣ACD的体积．【考点】LF：棱柱、棱锥、棱台的体积；LS：直线与平面平行；MJ：二面角的平面角及求法．【专题】5F：空间位置关系与距离．【分析】（Ⅰ）连接BD交AC于O点，连接EO，只要证明EO∥PB，即可证明PB∥平面AEC；（Ⅱ）延长AE至M连结DM，使得AM⊥DM，说明∠CMD=60°，是二面角的平面角，求出CD，即可三棱锥E﹣ACD的体积．【解答】（Ⅰ）证明：连接BD交AC于O点，连接EO，∵O为BD中点，E为PD中点，∴EO∥PB，（2分）EO⊂平面AEC，PB⊄平面AEC，所以PB∥平面AEC；（6分）（Ⅱ）解：延长AE至M连结DM，使得AM⊥DM，∵四棱锥P﹣ABCD中，底面ABCD为矩形，PA⊥平面ABCD，∴CD⊥平面AMD，∴CD⊥MD．∵二面角D﹣AE﹣C为60°，∴∠CMD=60°，∵AP=1，AD=，∠ADP=30°，∴PD=2，E为PD的中点．AE=1，∴DM=，CD==．三棱锥E﹣ACD的体积为：==．【点评】本题考查直线与平面平行的判定，几何体的体积的求法，二面角等指数的应用，考查逻辑思维能力，是中档题．19．（12分）某地区2007年至2013年农村居民家庭人均纯收入y（单位：千元）的数据如表：年份2007200820092010201120122013年份代号t1234567人均纯收入y 2.9 3.3 3.6 4.4 4.8 5.2 5.9（Ⅰ）求y关于t的线性回归方程；（Ⅱ）利用（Ⅰ）中的回归方程，分析2007年至2013年该地区农村居民家庭人均纯收入的变化情况，并预测该地区2015年农村居民家庭人均纯收入．附：回归直线的斜率和截距的最小二乘估计公式分别为：=，=﹣．【考点】BK：线性回归方程．【专题】11：计算题；5I：概率与统计．【分析】（Ⅰ）根据所给的数据，利用最小二乘法可得横标和纵标的平均数，横标和纵标的积的和，与横标的平方和，代入公式求出b的值，再求出a的值，写出线性回归方程．（Ⅱ）根据上一问做出的线性回归方程，代入所给的t的值，预测该地区2015年农村居民家庭人均纯收入，这是一个估计值．【解答】解：（Ⅰ）由题意，=×（1+2+3+4+5+6+7）=4，=×（2.9+3.3+3.6+4.4+4.8+5.2+5.9）=4.3，∴== =0.5，=﹣=4.3﹣0.5×4=2.3．∴y关于t的线性回归方程为=0.5t+2.3；（Ⅱ）由（Ⅰ）知，b=0.5＞0，故2007年至2013年该地区农村居民家庭人均纯收入逐年增加，平均每年增加0.5千元．将2015年的年份代号t=9代入=0.5t+2.3，得：=0.5×9+2.3=6.8，故预测该地区2015年农村居民家庭人均纯收入为6.8千元．【点评】本题考查线性回归分析的应用，本题解题的关键是利用最小二乘法认真做出线性回归方程的系数，这是整个题目做对的必备条件，本题是一个基础题．20．（12分）设F1，F2分别是C：+=1（a＞b＞0）的左，右焦点，M是C 上一点且MF2与x轴垂直，直线MF1与C的另一个交点为N．（1）若直线MN的斜率为，求C的离心率；（2）若直线MN在y轴上的截距为2，且|MN|=5|F1N|，求a，b．【考点】K4：椭圆的性质．【专题】5E：圆锥曲线中的最值与范围问题．【分析】（1）根据条件求出M的坐标，利用直线MN的斜率为，建立关于a，c的方程即可求C的离心率；（2）根据直线MN在y轴上的截距为2，以及|MN|=5|F1N|，建立方程组关系，求出N的坐标，代入椭圆方程即可得到结论．【解答】解：（1）∵M是C上一点且MF2与x轴垂直，∴M的横坐标为c，当x=c时，y=，即M（c，），若直线MN的斜率为，即tan∠MF1F2=，即b2==a2﹣c2，即c2+﹣a2=0，则，即2e2+3e﹣2=0解得e=或e=﹣2（舍去），即e=．（Ⅱ）由题意，原点O是F1F2的中点，则直线MF1与y轴的交点D（0，2）是线段MF1的中点，设M（c，y），（y＞0），则，即，解得y=，∵OD是△MF1F2的中位线，∴=4，即b2=4a，由|MN|=5|F1N|，则|MF1|=4|F1N|，解得|DF1|=2|F1N|，即设N（x1，y1），由题意知y1＜0，则（﹣c，﹣2）=2（x1+c，y1）．即，即代入椭圆方程得，将b2=4a代入得，解得a=7，b=．【点评】本题主要考查椭圆的性质，利用条件建立方程组，利用待定系数法是解决本题的关键，综合性较强，运算量较大，有一定的难度．21．（12分）已知函数f（x）=e x﹣e﹣x﹣2x．（Ⅰ）讨论f（x）的单调性；（Ⅱ）设g（x）=f（2x）﹣4bf（x），当x＞0时，g（x）＞0，求b的最大值；（Ⅲ）已知1.4142＜＜1.4143，估计ln2的近似值（精确到0.001）．【考点】6B：利用导数研究函数的单调性．【专题】16：压轴题；53：导数的综合应用．【分析】对第（Ⅰ）问，直接求导后，利用基本不等式可达到目的；对第（Ⅱ）问，先验证g（0）=0，只需说明g（x）在[0+∞）上为增函数即可，从而问题转化为“判断g′（x）＞0是否成立”的问题；对第（Ⅲ）问，根据第（Ⅱ）问的结论，设法利用的近似值，并寻求ln2，于是在b=2及b＞2的情况下分别计算，最后可估计ln2的近似值．【解答】解：（Ⅰ）由f（x）得f′（x）=e x+e﹣x﹣2，即f′（x）≥0，当且仅当e x=e﹣x即x=0时，f′（x）=0，∴函数f（x）在R上为增函数．（Ⅱ）g（x）=f（2x）﹣4bf（x）=e2x﹣e﹣2x﹣4b（e x﹣e﹣x）+（8b﹣4）x，则g′（x）=2[e2x+e﹣2x﹣2b（e x+e﹣x）+（4b﹣2）]=2[（e x+e﹣x）2﹣2b（e x+e﹣x）+（4b﹣4）]=2（e x+e﹣x﹣2）（e x+e﹣x+2﹣2b）．①∵e x+e﹣x＞2，e x+e﹣x+2＞4，∴当2b≤4，即b≤2时，g′（x）≥0，当且仅当x=0时取等号，从而g（x）在R上为增函数，而g（0）=0，∴x＞0时，g（x）＞0，符合题意．②当b＞2时，若x满足2＜e x+e﹣x＜2b﹣2即，得，此时，g′（x）＜0，又由g（0）=0知，当时，g（x）＜0，不符合题意．综合①、②知，b≤2，得b的最大值为2．（Ⅲ）∵1.4142＜＜1.4143，根据（Ⅱ）中g（x）=e2x﹣e﹣2x﹣4b（e x﹣e﹣x）+（8b﹣4）x，为了凑配ln2，并利用的近似值，故将ln即代入g（x）的解析式中，得．当b=2时，由g（x）＞0，得，从而；令，得＞2，当时，由g（x）＜0，得，得．所以ln2的近似值为0.693．【点评】1．本题三个小题的难度逐步增大，考查了学生对函数单调性深层次的把握能力，对思维的要求较高，属压轴题．2．从求解过程来看，对导函数解析式的合理变形至关重要，因为这直接影响到对导数符号的判断，是解决本题的一个重要突破口．3．本题的难点在于如何寻求ln2，关键是根据第（2）问中g（x）的解析式探究b的值，从而获得不等式，这样自然地将不等式放缩为的范围的端点值，达到了估值的目的．请考生在第22、23、24三题中任选一题作答，如果多做，则按所做的第一题计分，作答时请写清题号.【选修4-1：几何证明选讲】22．（10分）如图，P是⊙O外一点，PA是切线，A为切点，割线PBC与⊙O相交于点B，C，PC=2PA，D为PC的中点，AD的延长线交⊙O于点E，证明：（Ⅰ）BE=EC；（Ⅱ）AD•DE=2PB2．【考点】N4：相似三角形的判定；NC：与圆有关的比例线段．【专题】17：选作题；5Q：立体几何．【分析】（Ⅰ）连接OE，OA，证明OE⊥BC，可得E是的中点，从而BE=EC；（Ⅱ）利用切割线定理证明PD=2PB，PB=BD，结合相交弦定理可得AD•DE=2PB2．【解答】证明：（Ⅰ）连接OE，OA，则∠OAE=∠OEA，∠OAP=90°，∵PC=2PA，D为PC的中点，∴PA=PD，∴∠PAD=∠PDA，∵∠PDA=∠CDE，∴∠OEA+∠CDE=∠OAE+∠PAD=90°，∴OE⊥BC，∴E是的中点，∴BE=EC；（Ⅱ）∵PA是切线，A为切点，割线PBC与⊙O相交于点B，C，∴PA2=PB•PC，∵PC=2PA，∴PA=2PB，∴PD=2PB，∴PB=BD，∴BD•DC=PB•2PB，∵AD•DE=BD•DC，∴AD•DE=2PB2．【点评】本题考查与圆有关的比例线段，考查切割线定理、相交弦定理，考查学生分析解决问题的能力，属于中档题．【选修4-4：坐标系与参数方程】23．在直角坐标系xOy中，以坐标原点为极点，x轴正半轴为极轴建立极坐标系，半圆C的极坐标方程为ρ=2cosθ，θ∈[0，]（Ⅰ）求C的参数方程；（Ⅱ）设点D在半圆C上，半圆C在D处的切线与直线l：y=x+2垂直，根据（1）中你得到的参数方程，求直线CD的倾斜角及D的坐标．【考点】QH：参数方程化成普通方程．【专题】5S：坐标系和参数方程．【分析】（1）利用即可得出直角坐标方程，利用cos2t+sin2t=1进而得出参数方程．（2）利用半圆C在D处的切线与直线l：y=x+2垂直，则直线CD的斜率与直线l的斜率相等，即可得出直线CD的倾斜角及D的坐标．【解答】解：（1）由半圆C的极坐标方程为ρ=2cosθ，θ∈[0，]，即ρ2=2ρcosθ，可得C的普通方程为（x﹣1）2+y2=1（0≤y≤1）．可得C的参数方程为（t为参数，0≤t≤π）．（2）设D（1+cos t，sin t），由（1）知C是以C（1，0）为圆心，1为半径的上半圆，∵直线CD的斜率与直线l的斜率相等，∴tant=，t=．故D的直角坐标为，即（，）．【点评】本题考查了把极坐标方程化为直角坐标方程、参数方程化为普通方程、直线与圆的位置关系，考查了推理能力与计算能力，属于中档题．六、解答题（共1小题，满分0分）24．设函数f（x）=|x+|+|x﹣a|（a＞0）．（Ⅰ）证明：f（x）≥2；（Ⅱ）若f（3）＜5，求a的取值范围．【考点】R5：绝对值不等式的解法．【专题】59：不等式的解法及应用．【分析】（Ⅰ）由a＞0，f（x）=|x+|+|x﹣a|，利用绝对值三角不等式、基本不等式证得f（x）≥2成立．（Ⅱ）由f（3）=|3+|+|3﹣a|＜5，分当a＞3时和当0＜a≤3时两种情况，分别去掉绝对值，求得不等式的解集，再取并集，即得所求．【解答】解：（Ⅰ）证明：∵a＞0，f（x）=|x+|+|x﹣a|≥|（x+）﹣（x﹣a）|=|a+|=a+≥2=2，故不等式f（x）≥2成立．（Ⅱ）∵f（3）=|3+|+|3﹣a|＜5，∴当a＞3时，不等式即a+＜5，即a2﹣5a+1＜0，解得3＜a＜．当0＜a≤3时，不等式即6﹣a+＜5，即a2﹣a﹣1＞0，求得＜a≤3．综上可得，a的取值范围（，）．【点评】本题主要考查绝对值三角不等式，绝对值不等式的解法，体现了转化、分类讨论的数学思想，属于中档题．。

2014年全国高考语文真题第I卷阅读题甲必考题一、现代文阅读（9分，每小题3分）阅读下面的文字，完成1-3题。

周代，尽管关于食品安全事件的记载不多，但我们还是看到，由于食品安全关系重大，统治者对此非常重视并作出了特别规定。

周代的食品交易是以直接收获采摘的初级农产品为主，所以对农产品的成熟度十分关注．据《礼记》记栽，周代对食品交易的规定有：‚五谷不时，果实未熟，不鬻于市。

‛这是我国历史上最早的关于食品安全管理的记录．汉唐时期，食品交易活动非常频繁，交易品种十分丰富。

为杜绝有毒有害食品流入市场，国家在法律上作出了相应的规定。

汉朝《二年律令》规定：‚诸食脯肉，脯肉毒杀、伤、病人者，亟尽孰燔其余……当燔弗燔，及吏主者，皆坐脯肉赃，与盗同法。

‛即肉类因腐坏等因素可能导致中毒者，应尽快焚毁，否则将处罚当事人及相关官员。

唐朝《唐律》规定：‚脯肉有毒，曾经病人，有余者速焚之，违者杖九十。

若故与人食并出卖，令人病者，徒一年；以故致死者，绞。

即人自食致死者，从过失杀人法。

‛从《唐律》中可以看到，在唐代，知脯肉有毒不速焚而构成的刑事犯罪分为两种情况，处罚各不相同：一是得知脯肉有毒时，食品的所有者应当立刻焚毁所剩有毒食品，以绝后患，否则杖九十；二是明知脯肉有毒而不立刻焚毁，致人中毒，则视情节及后果以科罚。

宋代，饮食市场空前繁荣。

孟元老在《东京梦华录》中，追述了北宋都城开封府的城市风貌，并且以大量笔墨写到饮食业的昌盛，书中共提到一百多家店铺以及相关行会。

商品市场的繁荣，不可避免地带来一些问题，一些商贩‚以物市于人，敝恶之物，饰为新奇；假伪之物，饰为真实。

如绢帛之用胶糊，米麦之增温润，肉食之灌以水，药材之易以他物‛（《袁氏世范》）。

有的不法分子甚至采用鸡塞沙，鹅羊吹气、卖盐杂以灰之类伎俩谋取利润。

为了加强对食品掺假，以次充好现象的监督和管理，宋代规定从业者必须加入行会，而行会必须对商品质量负责。

‚市肆谓之行者，因官府料索而得此名，不以其物小大，但合充用者，皆臵为行，虽医卜亦有职。

2014年普通高等学校招生全国统一考试（全国大纲卷）语文试题第Ⅰ卷一、（12分，每小题3分）1．下列词语中加点的字，读音全都正确的一组是（B）A．龃龉．（yǔ) 系．鞋带(xi) 舐．犊情深（shi) 曲．意逢迎（qū)B．倜傥．(tǎng) 纤．维素（xiān) 羽扇纶．巾(guān ) 针砭．时弊(biān)C．感喟．(kuì) 揭疮．疤（chuāng) 按捺．不住（nài) 大相径．庭（jing)D．霰．弹(xiàn ) 涮．羊肉（shuàn) 以儆．效尤（jǐng) 纵横捭．阖必（bì)2．下列各句中，加点的成语使用恰当的一项是（A）A．在评价某些历史人物时，我们不能只是简单地对他们盖棺论定．．．．，，还应该学科网特别注意研究他们的人生经历和思想变化轨迹。

B．这把吉他是我最要好的朋友出国前存在我这里的，本来说存一年，结果朋友一直没回来，这吉他到现在巳经由我敝帚自珍．．．．了十年。

C．最美的是小镇的春天，草长莺飞，风声鹤唳．．．．，走进小镇就如同置身于世外桃源，来此旅游的人一定会被这里的美丽景色深深吸引。

D．这个剧院的大型话剧、歌剧等演出票价不菲，让许多有艺术爱好而又收入不高的普通人叹为观止．．．．，无法亲临现场享受艺术大餐。

3．下列各句中，没有语病的一句是答：DA．有的人看够了城市的繁华，喜欢到一些人迹罕至的地方去游玩，但这是有风险的，近年来已经发生了多次背包客被困野山的案情。

B．他家离铁路不远，小时候常常去看火车玩儿，火车每当鸣着汽笛从他身边飞驰而过时，他就很兴奋，觉得自己也被赋予了一种力量。

学科网C．新“旅游法”的颁布实施，让很多旅行社必须面对新规定带来的各种新问题，不少旅行社正从过去拼价格向未来拼服务转型的阵痛。

D．哈大高铁施行新的运行计划后，哈尔滨至北京、上海等地的部分列车也将进一步压缩运行时间，为广大旅客快捷出行提供更多选择。

4．依次填人下面一段文字横线处的语句，衔接最恰当的一组是答：C信息时代给人们带来了一种新的极其便捷的阅读方式，那就是网络阅读。

2014高考试题及答案2014年普通高等学校招生全国统一考试语文试题及答案解析一、语文知识运用（共15小题；每小题3分，满分45分）1. 下列词语中加点的字，读音全部正确的一项是：A. 湍急（tuān）星宿（xiù）拾掇（duó）绯红（fēi）B. 峥嵘（zhēng）缜密（zhěn）筵席（yán）睥睨（nì）C. 讣告（fù）涸泽（hé）缱绻（quǎn）斡旋（wò）D. 倥偬（kǒng）缥缈（miǎo）翩跹（xiān）缄默（jiān）2. 下列各组词语中，没有错别字的一组是：A. 妨碍妨碍妨害妨碍B. 观摩观摹观磨观摩C. 妨碍妨害妨碍妨害D. 观摩观摹观磨观摹3. 依次填入下面一段文字横线处的词语，最恰当的一组是：在这个过程中，我们不仅要______新知识，还要学会______已有的知识，更要善于______和运用这些知识。

A. 吸收整合应用B. 整合吸收应用C. 应用吸收整合D. 应用整合吸收4. 下列句子中，没有语病的一项是：A. 通过这次活动，使大家对团队协作有了更深刻的认识。

B. 他的话虽然简单，但却意味深长，让人回味无穷。

C. 这本书的内容深入浅出，对于初学者来说，是一本难得的好书。

D. 为了避免不再发生类似事故，我们必须加强安全管理。

5. 根据语境，选择正确的句子填空：春天到了，______，万物复苏，处处充满了生机。

A. 冰雪融化B. 秋风萧瑟C. 夏日炎炎D. 冬雪皑皑...（此处省略其他题目）二、阅读理解（共20小题；每小题3分，满分60分）（一）现代文阅读（共5小题；每小题3分，满分15分）阅读下面的文字，完成6-10题。

6. 作者在文中提到的“绿色革命”主要是指什么？A. 农业生产方式的转变B. 环境保护意识的提升C. 可持续发展战略的实施D. 生态农业的推广7. 文章中提到的“三农”问题，具体指的是什么？A. 农业、农村、农民B. 农业、农村、粮食C. 农业、畜牧业、渔业D. 农业、农村、农产品8. 根据文章内容，以下哪项不是解决“三农”问题的措施？A. 推进农业产业化B. 加强农村基础设施建设C. 提高农产品出口量D. 完善农村社会保障体系9. 作者认为，发展农村经济的关键在于什么？A. 政府的政策支持B. 农民的自我发展能力C. 农业科技的进步D. 农产品市场的扩大10. 文章最后提到的“绿色经济”概念，主要强调的是什么？A. 经济增长与环境保护的平衡B. 资源的高效利用C. 农业的可持续发展D. 农村地区的经济发展...（此处省略其他题目）三、写作（共60分）21. 阅读下面的材料，根据要求写一篇不少于800字的文章。