高考真题[精品解析]2019年浙江省高考英语试卷（解析版）

高考真题【精品解析】2019年浙江省高考英语试卷（解析版）

2019年6月普通高等学校招生全国统一考试(浙江卷)

英 语

选择题部分

第一部分 听力(共两节，满分30分)

做题时，先将答案标在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。

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，从题中所给的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。

例:How much is the shirt?

A. £19.15. B. £9.18. C. £9.15.

答案是C。

1.Where does this conversation take place?【此处有音频，请去附件查看】

A. In a classroom. B. In a hospital. C. In a museum.

【答案】B

【解析】

【详解】W: Excuse me, sir, visiting hours are over now. Your wife must get some rest.

M: Oh, I’m sorry, doctor. I didn’t hear the bell, or I would’ve left earlier.

2.What does Jack want to do?【此处有音频，请去附件查看】

A. Take fitness classes.

B. Buy a pair of gym shoes.

C. Change his work schedule.

【答案】A

【解析】

【详解】M: Hello, my name is Jack. I need to get in shape. How do I register for the classes?

W: We’ll need you to join the gymword/media/image1_1.png and then you can find out which classes fit your schedule the best.

3.What are the speakers talking about?【此处有音频，请去附件查看】

A. What to drink. B. Where to meet. C. When to leave.

【答案】B

【解析】

【详解】W: I’ll see you at the theatre.

M: Better still, let’s meet in the Red Lion bar to have a little nice talk.

W: Good idea, and I’d love to have a drink there.

4.What is the relationship between the speakers?【此处有音频，请去附件查看】

A. Colleges. B. Classmates. C. Strangers.

【答案】C

【解析】

【详解】M: Hello, my name is John Arber. And I’m calling to ask about the position advertised in Friday’s Dailymail.

W: Yes, the position is still open. You could come over and have a talk with us.

5.Why is Emily mentioned in the conversation?【此处有音频，请去附件查看】

A. She might want a ticket.

B. She is looking for the man.

C. She has an extra ticket.

【答案】A

【解析】

【详解】M: I have an extra ticket to the concert tonight. Would you like to join me?

W: Thanks, but I already have one. You can ask Emily. She might be interested.

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。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。

听下面一段较长对话，回答以下小题。【此处有音频，请去附件查看】

6. How long did James run his business？

A. 10 years. B. 13years. C. 15 years.

7. How does the woman feel about James' situation？

A. Embarrassed. B. Concerned. C. Disappointed.

【答案】6. C 7. B

【解析】

W: Did you know James went out of business?

M: Really? When was that?

W: Last month.

M: That’s too bad! He had owned that business for 15 years. What happened?

W: I don’t know. But life must be pretty tough for his family now. His sons are still so young. One is 13 and the other is 10.

M: Well, maybe things are not as bad as they seem to be.

W: I hope so.

【6题详解】

此为听力题，解析略。

【7题详解】

此为听力题，解析略。

听下面一段较长对话，回答以下小题。【此处有音频，请去附件查看】

8. What has Kate's mother decided to do？

A. Return to school. B. Change her job. C. Retire from work.

9. What did Kate's mother study at college？

A. Oil painting. B. Art history. C. Business administration.

10. What is Kate's attitude toward her mother's decision?

A. Disapproving. B. Ambiguous. C. Understanding.

【答案】8. A 9. C 10. C

【解析】

W: Guess what? My mother’s decided to go back to school.

M: Why?

W: Well, she always loved art, but learned business admistration at college, because her parents thought it was difficult for an artist to find a job.

M: So she wants to study art now?

W: Yeah, oil paining. It’s been her dream for a long time.

M: It’s nice to return to learn what she loves. But, Kate, I still think old age should be about peace and relaxation. Hurrying to school every day and having to pass exams sounds a bit too much for her.

W: You know, she retired last year and I’m leaving for the university soon. She needs to find something interesting to do.

M: Well, maybe, if it’s what she wants.

【8题详解】

此为听力题，解析略。

【9题详解】

此为听力题，解析略。

【10题详解】

此为听力题，解析略。

听下面一段较长对话，回答以下小题。【此处有音频，请去附件查看】

11. What is the man doing？

A. Chairing a meeting.

B. Hosting a radio program.

C. Conducting a job interview.

12. What benefits Mary most in her job？

A. Her wide reading. B. Her leaders' guidance. C. Her friends' help

13. Who will Mary talk about next？

A. Her teacher. B. Her father C. Her mother.

【答案】11. B 12. A 13. C

【解析】

M: Dear listeners, for today’s show, I have with me, my colleague, Mary Lenny. She has been a radio and TV reporter for many years. Mary, welcome to our show!

W: It’s a pleasure to be here.

M: Would you please tell our listeners who most influenced your decision to become a reporter?

Both my parents had a great influence on my choice of work, instead of trying to pick out a job for me, they helped me learn those things that led me to it.

M: How did they do that?

W: My father always told me that an education was one of the greatest advantages I could have, one that would always stay with me. He used to tell me that readers were leaders, and encouraged me to read all I could. As a result, I’ve always kept up with the newspapers, faithfully read magazines and learned to really enjoy books, all of which have been a valuable help to me in radio and television reporting.

M: What about your mother?

W: Well, my mother helped me in a much different way.

【11题详解】

此为听力题，解析略。

【12题详解】

此为听力题，解析略。

【13题详解】

此为听力题，解析略。

听下面一段较长对话，回答以下小题。【此处有音频，请去附件查看】

14. Why does the man seldom do exercise？

A. He lacks motivation.

B. He has a heart problem.

C. He works all the time.

15. What does Jacob Sattelmair probably do？

A. He's an athlete. B. He's a researcher. C. He's a journalist.

16. Why does the woman speak of a study？

A. To encourage the man.

B. To recommend an exercise.

C. To support her findings.

17. How much time will the man probably spend exercising weekly？

A. 300 minutes. B. 150 minute. C. 75 minutes.

【答案】14. A 15. B 16. A 17. C

【解析】

M: We all know that exercise is good for us, but sometimes it seems too hard to leave the sofa.

W: I can see that. You seldom do exercise.

M: Plus, having the doctor tell us to get two and a half hours’ exercise a week doesn’t really help our motivation much.

W: Don’t be discouraged. Now a new study suggests getting benefits from exercise doesn’t have to be that demanding. Jacob Sattelmair from Harvard University has done a study into how much exercise is needed to lower the risk of heart attacks.

M: Mmm…, interesting!

W: The study showed that people who put in 300 minutes a week of exercise had a 20% lower risk of death due to heart disease. Still, the people who exercise 115 minutes a week did pretty well, too, lowering their death risk by 14 %.

M: And what about the people who exercise half as much as that, like what I probably do? Does that help?

W: Of course, even 15 minutes would help.

【14题详解】

此为听力题，解析略。

【15题详解】

此为听力题，解析略。

【16题详解】

此为听力题，解析略。

【17题详解】

此为听力题，解析略。

听下面一段独白，回答以下小题。【此处有音频，请去附件查看】

18. What did the scientists do to the road？

A. They repaired it. B. They painted it. C. They blocked it

19. Why are young birds drawn to the road surface？

A. It's warm. B. It's brown. C. It's smooth.

20. What is the purpose of the scientists' experiment？

A. To keep the birds there for a whole year.

B. To help students study the birds wellword/media/image2_1.png

C. To prevent the birds from being killed.

【答案】18. B 19. A 20. C

【解析】

Here is a piece of news for bird lovers. Scientists have painted a long road, red, yellow and white. They help to discourage the sea birds from wandering onto the highway. The area is home to large crowds of birds that come to stay for the season. Young birds are often attracted to the warm roads’ surface and get killed by the traffic. Biology student, Hannah tells the broadcaster. The youngster’s feathers are brown in color. The dark-colored road surface makes the youngster hard to be noticed. As the number of tourists has grown, so has the amount of traffic on the roads. Biologist Christen says the plan is to see how the birds respond to the multi-colored road this summer, and if it works, the idea could spread to other parts of the country.

【18题详解】

此为听力题，解析略。

【19题详解】

此为听力题，解析略。

【20题详解】

此为听力题，解析略。

第二部分 阅读理解(共两节，满分35分)

第一节(共10小题；每小题2.5分，满分25分)

阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题纸上将该项涂黑。

A

Zachariah Fike has an unusual hobby. He finds old military(军队的)medals for sale in antique stores and on the Internet.But unlike most collectors, Zac tracks down the medals’ rightful owners, and returns them.

His effort to reunite families with lost medals began with a Christmas gift from his mother, a Purple Heart with the name Corrado A. G. Piccoli, found in an antique shop. Zac knows the meaning of a Purple Heart-he earned one himself in a war as a soldier. So when his mother gave him the medal, he knew right away what he had to do.

Through the Internetword/media/image1_1.png Zac tracked down Corrado’s sister Adeline Rockko. But when he finally reached her, the woman flooded him with questions: "Who are you？What antique shop？" However, when she hung up, she regretted the way she had handled the call. So she called Zac back and apologized. Soon she drove to meet Zac in Watertown, N.Y. "At that point, I knew she meant business, " Zac says. "To drive eight hours to come to see me."

The Piccolis grew up the children of Italian immigrants in Watertown. Corrado, a translator for the Army during WWII, was killed in action in Europe.

Before hearing from Zac, Adeline hadn’t realized the medal was missing. Like many military medals, the one Zac’s mother had found was a family treasure." This medal was very precious to my parents. Only on special occasions(场合)would they take it out and let us hold it in our hands," Adeline says.

As a child, Adeline couldn't understand why the medal was so significant. “But as I grew older,” Adeline says, "and missed my brother more and more, I realized that was the only thing we had left." Corrado Piccoli’s Purple Heart medal now hangs at the Italian American Civic Association in Watertown.

Zac recently returned another lost medal to a family in Alabama. Since he first reunited Corrado’s medal, Zac says his record is now 5 for 5.

21. Where did Zac get a Purple Heart medal for himself？

A. In the army.

B. In an antique shop.

C. From his mother.

D. From Adeline Rockko.

22. What did Zac realize when Adeline drove to meet him？

A. She was very impolite.

B. She was serious about the medal.

C. She suspected his honesty.

D. She came from a wealthy family.

23. What made Adeline treasure the Purple Heart?

A. Her parents’ advice.

B. Her knowledge of antiques.

C. Her childhood dream.

D. Her memory of her brother.

【答案】21. A 22. B 23. D

【解析】

这是一篇记叙文。Zachariah Fike有一个不同寻常的业余爱好：他在网上和古董店里寻找旧的军队勋章，然后将这些勋章归还它们的合法主人。文章主要叙述了他这一爱好的起源。

【21题详解】

细节理解题。根据第二段中的“Zac knows the meaning of a Purple Heart—he earned one himself in a war as a soldier”可知，当Zac还是一名士兵的时候，在一次战争中他获得了一枚Purple Heart。故A选项正确。

【22题详解】

推理判断题。根据第三段中的“To drive eight hours to come to see me”可以推知，Adeline为了那枚Purple Heart开车八个小时来见Zac，由此可知，她对于这件事是认真地。因此，At that point, I knew she meant business应该指的是Zac意识到Adeline对这枚勋章是认真的。故B选项正确。

【23题详解】

推理判断题。根据第四段中的“Corrado, a translator…was killed in action in Europe”和倒数第三段中的“as I grew older…and missed my brother more and more, I realized that was the only thing we had left ”这枚勋章寄托了Adeline对于去世的哥哥Corrado的回忆和思念，这是他们家留下的唯一关于哥哥的东西了。因此她很珍惜这枚勋章。故D选项正确。

B

Money with no strings attached. It’s not something you see every day. But at Union Station in Los Angeles last month, a board went up with dollar bills attached to it with pins and a sign that read, "Give What You Can, Take What You Need."

People quickly caught on. And while many took dollars, many others pinned their own cash to the board. “People of all ages, races, and socio-economic(社会经济的)backgrounds gave and took, ”said Tyler Bridges of The Toolbox, which created the project. "We even had a bride in her wedding dress come up to the board and take a few dollars." Most of the bills on the board were singles, but a few people left fives, tens and even twenties. The video clip(片段)shows one man who had found a $ 20 bill pinning it to the board.

“What I can say for the folks that gave the most, is that they were full of smiles,” Bridges said. “There’s a certain feeling that giving can do for you and that was apparent in those that gave the most." Most people who took dollars took only a few, but Bridges said a very small number took as much as they could.

While the clip might look like part of a new ad campaign, Bridges said the only goal was to show generosity and sympathy. He added that he hopes people in other cities might try similar projects and post their own videos on the Internet.

“After all, everyone has bad days and good days," he said. “Some days you need a helping hand and some days you can be the one giving the helping hand.”

24. What does the expression "money with no strings attached" in paragraph 1 mean?

A. Money spent without hesitation.

B. Money not legally made.

C. Money offered without conditions.

D. Money not tied together.

25. What did Bridges want to show by mentioning the bride?

A. Women tended to be more sociable.

B. The activity attracted various people.

C. Economic problems were getting worse.

D. Young couples needed financial assistance.

26. Why did Bridges carry out the project?

A. To do a test on people’s morals.

B. To raise money for his company.

C. To earn himself a good reputation.

D. To promote kindness and sympathy.

【答案】24. C 25. B 26. D

【解析】

这是一篇新闻报道。短文报道了上个月在洛杉矶的联合车站,一块牌子上别针别满了美元，上面写着“给予你所能给与的，拿走你所需要的”。这样的活动吸引了各种各样的人，组织者希望通过这样的活动来提倡仁慈和同情。

【24题详解】

词义猜测题。由第一段“But at Union Station in Los Angeles last month, a board went up with dollar bills attached to it with pins and a sign that read, "Give What You Can, Take What You Need.”可知，但是上个月在洛杉矶的联合车站，一块牌子上别针别满了美元，上面写着“给予你所能给与的，拿走你所需要的”。所以通过下文的语境，判断出第1段中的money with no strings attached是“无条件提供的钱”的意思。故B选项正确。

【25题详解】

推理判断题。由第二段““People of all ages, races, and socio-economic（社会经济的）backgrounds gave and took, ”said Tyler Bridges of The Toolbox, which created the project. "We even had a bride in her wedding dress come up to the board and take a few dollars.”可知，发起该项活动的泰勒·布里奇斯说:“所有年龄、种族和社会经济背景的人都会付出和索取。”甚至有一位穿着婚纱的新娘来到了牌子前，拿走了一些钱。所以通过泰勒·布里奇斯所说的，可以判断出，他提到新娘就是想说明这项活动吸引了各种各样的人。故B选项正确。

【26题详解】

细节理解题。由倒数第二段“While the clip might look like part of a new ad campaign, Bridges said the only goal was to show generosity and sympathy”可知，尽管这段视频看起来像是一项新的广告活动的一部分，但是布里奇斯说这次活动唯一的目标是表现出慷慨和同情。所以布里奇斯实施这个活动是为了提倡仁慈和同情。故D选项正确。

C

California has lost half its big trees since the 1930s, according to a study to be published Tuesday and climate change seems to be a major factor(因素).

The number of trees larger than two feet across has declined by 50 percent on more than 46, 000 square miles of California forests, the new study finds. No area was spared or unaffected, from the foggy northern coast to the Sierra Nevada Mountains to the San Gabriels above Los Angeles. In the Sierra high country, the number of big trees has fallen by more than 55 percent; in parts of southern California the decline was nearly 75 percent.

Many factors contributed to the decline, said Patrick Mclntyre, an ecologist who was the lead author of the study. Woodcutters targeted big trees. Housing development pushed into the woods. Aggressive wildfire control has left California forests crowded with small trees that compete with big trees for resources(资源).

But in comparing a study of California forests done in the 1920s and 1930s with another one between 2001 and 2010, Mclntyre and his colleagues documented a widespread death of big trees that was evident even in wildlands protected from woodcutting or development.

The loss of big trees was greatest in areas where trees had suffered the greatest water shortage. The researchers figured out water stress with a computer model that calculated how much water trees were getting in comparison with how much they needed, taking into account such things as rainfall, air temperature, dampness of soil, and the timing of snowmelt(融雪).

Since the 1930s, Mclntyre said, the biggest factors driving up water stress in the state have been rising temperatures, which cause trees to lose more water to the air, and earlier snowmelt, which reduces the water supply available to trees during the dry season.

27. What is the second paragraph mainly about?

A. The seriousness of big-tree loss in California.

B. The increasing variety of California big trees.

C. The distribution of big trees in California forests.

D. The influence of farming on big trees in California.

28. Which of the following is well-intentioned but may be bad for big trees?

A. Ecological studies of forests.

B. Banning woodcutting.

C. Limiting housing development.

D. Fire control measures.

29. What is a major cause of the water shortage according to Mclntyre?

A. Inadequate snowmelt. B. A longer dry season.

C. A warmer climate. D. Dampness of the air.

30. What can be a suitable title for the text?

A. California's Forests: Where Have All the Big Trees Gone?

B. Cutting of Big Trees to Be Prohibited in California Soon

C. Why Are the Big Trees Important to California Forests?

D. Patrick Mclntyre: Grow More Big Trees in California

【答案】27. A 28. D 29. C 30. A

【解析】

本文为说明文，根据一项研究表明，自20世纪30年代以来，加州已经失去了一半的大树，气候变化似乎是其主要因素。

【27题详解】

主旨大意题。在第二段中，作者用具体数据说明了大树损失在各个地区的严重程度，没有任何地区幸免或不受影响，故选A。

【28题详解】

推理判断题。根据第三段最后一句Aggressive wildfire control has left California forests crowded with small trees that compete with big trees for resources（资源）.可知，野火控制在控制了森林大火的同时，使得加利福尼亚的森林里挤满了小树，它们与大树争夺资源，这对大树产生了不利的影响，故选D。

【29题详解】

细节理解题。根据最后一段the biggest factors driving up water stress in the state have been rising temperatures, …, and earlier snowmelt, …可知，造成加州水资源短缺的最大因素是气温的上升，以及较早的融雪，故选C。

【30题详解】

主旨大意题。通读全文可知，自20世纪30年代以来，加州已经失去了一半的大树，文章分析了引起该现象的几个主要因素。全文围绕“加州森林的大树都去哪儿了”话题展开，故选项A符合题意。

第二节(共5小题；每小题2分，满分10分)

根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。

Rock music consists of many different styles. Even though there is a common spirit among all music groups, they make very different music. ___31___ At that time the Beatles entered the world of music from Liverpool.

After they were given an invitation to appear live on BBC, the Beatles quickly became famous in Britain with nationwide tours. By mid-1963, the Beatles had been extremely popular in England. ___32___ They held large concerts and performed at clubs. They became the hottest thing on the pop music scene in England. They began as a modestly successful musician group and ended the year as show business legends(传说). John Lennon and Paul McCartney were named composers of the year.

___33___ They were not sure how the Americans would react to the new type of music. Beatlemania hit New York on February 7, 1964. Hundreds of fans jammed the airport to greet them. ___34___ The concert was broadcast live and attracted the largest one night audience in the history of television up to that time. The Beatles were described as a British invasion(入侵)by local and nationwide newspapers at that time. Their victory in America was still remembered as a major turning point in the history of rock and roll. Thanks to the Beatles, a lot of opportunities were opened up to new faces on the market. ___35___

A. They decided on a tour to the United States in 1964.

B. Even their hairstyles became major trends at that time.

C. Rock music developed in the 1950s and the early 1960s.

D. However, their songs changed the lives of generations to come.

E. Many rock bands were able to follow in the footsteps of the Beatles.

F. They appeared in the films A Hard Day's Night(1964)and Help！(1965).

G. They performed their first concert in America at CBS television's 53rd street studio.

【答案】31. C 32. B

33. A 34. G

35. E

【解析】

本文是一篇说明文。文中讲述了披头士的发展和影响，引领了一种潮流趋势。

【31题详解】

第一段讲述摇滚音乐，根据空后的at that time可知前句提到了时间，而且与rock music有关，选项中只有C 项讲的是摇滚音乐，并且讲述了其发展的时间，故选C。

word/media/image3_1.png32题详解】

空前后都是讲述披头士的出名程度，根据空前extremely popular in England, 以及后文的they became the hottest thing可知此处描述了他们的影响，选项B （甚至他们的发型在那时也成为了一种潮流）符合文意，且关键词even是一个提示，故选B。

【33题详解】

根据空后They were not sure how the Americans would react to the new type of music.（他们不确定美国人怎样反应），可知他们首次来美国演出，所以A项（决定首次到美国开巡回演出）符合文意，故选A。

【34题详解】

根据空后The concert was broadcast live…可知前句中应该出现concert，选项G中的关键词their first concert 前后呼应。故选G。

【35题详解】

根据空前（由于披头士，市场上出现了很多机会），E项（很多新乐队（新面孔）都是模仿披头士），符合逻辑。故选E。

第三部分 语言运用(共两节，满分45分)

第一节 完形填空(共20小题；每小题1.5分，满分30分)

阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空白处的最佳选项，并在答题纸上将该项涂黑。

There are lots of ways to raise awareness for a cause. Usually, the ___36___ the idea is, the more it gets noticed. And that’s precisely why one ___37___ Frenchman has caught our attention.

Baptiste Dubanchet is biking across Europe，surviving ___38___ on discarded(丢弃)food. The three-monthword/media/image1_1.png 1 900-mile journey from Paris to Warsaw is Dubanchet’s ___39___ of raising awareness of food waste in Europe and throughout the world.

As you can ___40___, the trip is no piece of cake. While restaurants ___41___ tons of food each year, much of it remains inaccessible because of ___42___ garbage containers, health regulations, or business policies. Only about one in ten places ___43___ him food that would otherwise be discarded.

For legal ___44___, most restaurants have a policy against ___45___ food waste. "Some people have even ___46___ their jobs by giving me food," Dubanchet said.

What's ___47___ interesting is the attitude various cities have toward Dubanchet’s cause. Berlin has been the ___48___ while the most difficult was the Czech town of Pilsen. There, he had to ___49___ at some ___50___ different stores or restaurants before finding food. The 50 is all the more serious when you consider the ___51___ exercise required to bike from France to Poland.

"I have to get food ___52___ because after all the biking I am tired and I need the ___53___,"

Dubanchet explained. "Is my ___54___ full or empty? That is the most important thing, not what I am eating."

He aims to ___55___ his journey by mid-July. With any luck, he’ll turn a few more heads in the process.

36. A. cleverer B. older C. stranger D. simpler

37. A. garbage-eating B. sports-loving C. food-wasting D. law-breaking

38. A. secretly B. finally C. entirely D. probably

39. A. purpose B. way C. opinion D. dream

40. A. observe B. imagine C. suggest D. remember

41. A. store B. cook C. shop for D. throw away

42. A. locked B. damaged C. connected D. abandoned

43. A. bought B. offered C. ordered D. sold

44. A. reasons B. rights C. fees D. aids

45. A. begging for B. giving away C. hiding D. causing

46. A. did B. kept C. accepted D. risked

47. A. hardly B. usually C. particularly D. merely

48. A. easiest B. nearest C. biggest D. richest

49. A. work B. shout C. ask D. jump

50. A. competition B. conversation C. conflict D. challenge

51. A. adequate B. rewarding C. demanding D. suitable

52. A. again B. alone C. later D. fast

53. A. spirit B. energy C. time D. effort

54. A. stomach B. hand C. pocket D. basket

55. A. arrange B. restart C. report D. finish

【答案】36. C 37. A 38. C 39. B 40. B 41. D 42. A 43. B 44. A 45. B 46. D 47. C 48. A 49. C 50. D 51. C 52. D 53. B 54. A 55. D

【解析】

这是一篇夹叙夹议的文章。文章主要讲了一个吃垃圾的法国人引起了我们的注意，Baptiste Dubanchet骑着自行车穿越欧洲，完全靠丢弃的食物生存。

【36题详解】

考查形容词辨析。根据Usually, the 36 the idea is, the more it gets noticed.可知这里意思是通常，这个观点越奇怪，它就会越受到关注。A. cleverer更聪明的；B. older更老的；C. stranger更奇怪；D. simpler更简单的，故选C。

【37题详解】

考查形容词辨析。根据Baptiste Dubanchet is biking across Europe, surviving 38 on discarded(丢弃) food.可知这里意思是那就是为什么一个吃垃圾的法国人引起了我们的注意。A. garbage-eating吃垃圾的；B. sports-loving爱好体育的；C. food-wasting浪费食物的； D. law-breaking破坏法律的，故选A。

【38题详解】

考查副词辨析。句意：Baptiste Dubanchet骑着自行车穿越欧洲，完全靠丢弃的食物生存。A.secretly 秘密地；B. finally 最后；C. entirely完全地；D. probably很可能，故选C。

【39题详解】

考查名词辨析。句意：从巴黎到华沙历时三个月、1900英里的旅程，是Dubanchet引起欧洲和全世界对食物残羹注意的道路。A.purpose目的；B.way道路；C.opinion意见；D. dream梦想，故选B。

【40题详解】

考查动词辨析。句意：你可以想象，这次旅行不是小菜一碟。A. observe观察；B. imagine想象；C. suggest建议；D. remember记得，故选B。

【41题详解】

考查动词短语辨析。句意：虽然餐馆每年扔掉大量的食物，但由于垃圾容器上锁、卫生规定或商业政策，很多食物仍然难以接近。A . store存储；B.cook做饭；C. shop for购买某物；D. throw away扔掉，故选D。

【42题详解】

考查形容词辨析。根据it remains inaccessible可知这里意思是垃圾容器上锁。A.locked上锁的；B . damaged被损坏的；C.connected连接的；D. abandoned被抛弃的，故选A。

【43题详解】

考查动词辨析。句意：只有大约十分之一的地方给他提供了食物，否则就会被丢弃。A.bought买；B. offered提供；C . ordered命令；D. sold销售，故选B。

【44题详解】

考查名词辨析。句意：由于法律原因，大多数餐馆都有禁止浪费食物的政策。A.reasons原因；B. rights权利；C.fees费用；D. aids援助，故选A。

【45题详解】

考查动词短语辨析。句意：由于法律原因，大多数餐馆都有禁止分发食物残渣的政策。A. begging for乞求； B. giving away分发；C . hiding隐藏；D. causing造成，故选B。

【46题详解】

考查动词辨析。上文说由于法律原因，大多数餐馆都有禁止分发食物残渣的政策。可知这里意思是有些人甚至冒着失业的危险给我食物。A.did做；B. kept保持；C.accepted接受；

D. risked冒…的危险，故选D。

【47题详解】

考查副词辨析。句意：特别有趣的是各个城市对Dubanchet事件的态度。A.hardly几乎不；

B. usually 通常；C . particularly特别是；D . merely仅仅，故选C。

【48题详解】

考查形容词辨析。根据while the most difficult was the Czech town of Pilsen.可知这里意思是柏林是最容易的。A.easiest最容易的；B . nearest最近的；C . biggest最大的；D. richest最富有的，故选A。

【49题详解】

考查动词辨析。句意：在那里，他必须在大约50家不同的商店或餐馆询问，才能找到食物。A.work工作；B. shout 呼喊；C.ask询问；D. jump跳跃，故选C。

【50题详解】

考查名词辨析。句意：当你考虑到从法国骑自行车到波兰所需要的高强度运动时，挑战就更加严峻了。A. competition竞赛；B. conversation会话；C. conflict冲突；D. challenge挑战，故选D。

【51题详解】

考查形容词辨析。句意：当你考虑到从法国骑自行车到波兰所需要的高强度运动时，挑战就更加严峻了。A. adequate充足的；B. rewarding有益的；C. demanding要求高的；D. suitable适当的，故选C。

【52题详解】

考查副词辨析。句意：我必须快点吃东西，因为骑了那么多自行车，我累了，我需要能量。A.again再一次；B. alone独自地；C . later后来；D. fast迅速地，故选D。

【53题详解】

考查名词辨析。根据because after all the biking I am tired可知我需要能量。A.spirit精神；

B . energy能量；C.time时间；D. effort努力，故选B。

【54题详解】

考查名词辨析。根据That is the most important thing, not what I am eating.可知这里意思是我的胃是满的还是空的。A. stomach胃；B. hand手；C. pocket口袋；D. basket篮子，故选A。

【55题详解】

考查动词辨析。根据With any luck, he'll tum a few more heads in the process.可知这里意思是他计划在七月中旬结束他的旅行。A.arrange安排；B . restart重新开始；C. report报告；

D. finish结束，故选D。

非选择题部分

第三部分 语言运用(共两节，满分45分)

第二节(共10小题:每小题1.5分，满分15分)

阅读下面材料，在空白处填入适当的内容(1个单词)或括号内单词的正确形式。

There are several reasons why school uniforms are good idea. First of all, uniforms help the school look smart. The students feel that they belong to a particular group. When every pupil in the school wears the uniform, nobody ___56___ (have) to worry about fashion(时尚). Everybody wears___57___ same style of clothes. Uniforms can be useful in unexpected ways, A school in Ireland has introduced an interesting new uniform. On the edge of the jacket, there is a piece of cloth ___58___gives off light in the dark. When the children are walking or ___59___ (cycle) to school on dark mornings, car drivers can ___60___ (easy) see them.

But can uniforms help improve school standards? The answer ___61___ this question is not clear. One study in America found that students' grades ___62___ (improve) a little after the school introduced uniforms. But some students didn't want ___63___ (wear) the uniform. Other American studies showed no ___64___(connect) between uniforms and school performance.

School uniforms are ___65___ (tradition) in Britain, but some schools are starting to get rid of them. Some very good schools don't have a uniform policy. However, uniforms are still popular. Pupils at about 90 percent of British secondary schools wear uniforms.

【答案】56. has/will have

57. the 58. that/which

59. cycling

60. easily 61. to

62. improved

63. to wear

64. connection/connections

65. traditional

【解析】

这是一篇说明文。文章主要介绍了学生穿校服的几个好处。

【56题详解】

考查时态。句意：当每个学生在校穿校服时，没有人会担心时尚问题。本句是when引导的时间状语从句，遵循主将从现原则，因此，主句可以使用将来时will do；根据语境可知，本文叙述的是客观事实，因此，本句亦可用一般现在时，主语是nobody，谓语用has。故填will have/has。

【57题详解】

考查冠词。句意：每个人都穿相同风格的衣服。same是形容词，意思是“相同的”，常与the连用修饰名词。故填the。

【58题详解】

考查定语从句。这是个限制性定语从句，先行词是cloth，指物，从句中缺少主语，因此，可以用that或which引导。故填that/which。

【59题详解】

考查非谓语动词。句意：当孩子们在黑暗的早晨步行或骑车上学时，汽车司机很容易看到它们。or连接两个并列成分，根据or前的walking可知，此处要用cycling。故填cycling。

【60题详解】

考查副词。分析句式可知，设空处所给词是修饰动词see，修饰动词要用副词，因此，用easy的副词形式。故填easily。

【61题详解】

考查介词。句意：这个问题的答案不清楚。the key/answer to ...这是固定搭配，“……的答案是……”。故填to。

【62题详解】

考查时态。句意：美国的一项研究发现，在学校引入校服后，学生的成绩有所提高。本句是after引导的时间状语从句，前后时态保持一致，从句使用了一般过去式，主句用一般过去式。故填improved。

【63题详解】

考查非谓语动词。句意：但是，有一些学生不想穿学生服。want to do sth想要做某事，这是want的固定用法。故填to wear。

【64题详解】

考查名词。句意：其他的美国研究表明校服和学校表现之间没有联系。no是形容词，形容词修饰名词，位于名词前，名词可用复数也可用单数形式。connect是动词，“联系”的意思，因此，要用其名词形式。故填connection/connections。

【65题详解】

考查形容词。句意：穿校服在英国是一个传统，但是一些学校开始允许学生上学不用穿校服。are是系动词，其后常用形容词作表语，tradition是名词，“传统”的意思，因此，用其形容词形式。故填traditional。

第四部分 写作(共两节，满分40分)

第一节 应用文写作(满分15分)

66.假定你是李华，经常帮助你学习英语的朋友Alex即将返回自己的国家。请给他写一封邮件，内容包括:

1.表示感谢；

2.回顾Alex对你的帮助；

3.临别祝愿。

注意:

1.词数80左右；

2可适当增加细节，以使行文连贯。

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

【答案】参考范文略

【解析】

【详解】本题解析略。

第二节 读后续写(满分25分)

67.阅读下面短文，根据其内容写一篇60词左右的内容概要。

Parents everywhere praise their kids. Jenn Berman, author of The A to Z Guide to Raising Happy and Confident Kids, says, "We've gone to the opposite extreme of a few decades ago when parents tended to be more strict." By giving kids a lot of praise, parents think they're building their children's confidence, when, in fact, it may be just the opposite. Too much praise can backfire and, when given in a way that's insincere, make kids afraid to try new things or take a risk for fear of not being able to stay on top where their parents' praise has put them.

Still, don't go too far in the other direction. Not giving enough praise can be just as damaging gas giving too much. Kids will feel like they're not good enough or that you don't care and, as a result, may see no point in trying hard for their accomplishments.

So what is the right amount of praise? Experts say that the quality of praise is more important than the quantity. If praise is sincere and focused on the effort not the outcome, you can give it as often as your child does something that deserves a verbal reward." We should especially recognize our children's efforts to push themselves and work hard to achieve a goal, "says Donahue, author of Parenting Without Fear: Letting Go of Worry and Focusing on What Really Matters. "One thing to remember is that it's the process not the end product that matters."

Your son may not be the best basketball player on his team. But if he's out there every day and playing hard, you should praise his effort regardless of whether his team wins or loses. Praising the effort and not the outcome can also mean recognizing your child when she has worked hard to clean the yard, cook dinner, or finish a book report. But whatever it is, praise should be given on a case-by-case basis and be proportionate(相称的)to the amount of effort your child has put into it.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

【答案】参考范文略

【解析】

【详解】本题解析略。

高考真题【精品解析】2019年全国统一高考数学试卷（文科）（新课标Ⅱ）（解析版）

绝密★启用前

2019年普通高等学校招生全国统一考试

文科数学

本试卷共5页。考试结束后，将本试卷和答题卡一并交回

注意事项：

1．答题前，考生先将自己的姓名、准考证号码填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

3．请按照题号顺序在答题卡各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试卷上答题无效。

4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。

5．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。

一、选择题：本题共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.已知集合，，则A∩B=

A. (–1，+∞) B. (–∞，2)

C. (–1，2) D.

【答案】C

【解析】

【分析】

本题借助于数轴，根据交集的定义可得．

【详解】由题知，，故选C．

【点睛】本题主要考查交集运算，容易题，注重了基础知识、基本计算能力的考查．易错点是理解集合的概念及交集概念有误，不能借助数轴解题．

2.设z=i(2+i)，则=

A. 1+2i B. –1+2i

C. 1–2i D. –1–2i

【答案】D

【解析】

【分析】

本题根据复数的乘法运算法则先求得，然后根据共轭复数的概念，写出．

【详解】，

所以，选D．

【点睛】本题主要考查复数的运算及共轭复数，容易题，注重了基础知识、基本计算能力的考查．理解概念，准确计算，是解答此类问题的基本要求．部分考生易出现理解性错误．

3.已知向量a=(2，3)，b=(3，2)，则|a–b|=

A. B. 2

C. 5 D. 50

【答案】A

【解析】

【分析】

本题先计算，再根据模的概念求出．

【详解】由已知，，

所以，

故选A

【点睛】本题主要考查平面向量模长的计算，容易题，注重了基础知识、基本计算能力的考查．由于对平面向量的坐标运算存在理解错误，从而导致计算有误；也有可能在计算模的过程中出错．

4.生物实验室有5只兔子，其中只有3只测量过某项指标，若从这5只兔子中随机取出3只，则恰有2只测量过该指标的概率为

A. B.

C. D.

【答案】B

【解析】

【分析】

本题首先用列举法写出所有基本事件，从中确定符合条件的基本事件数，应用古典概率的计算公式求解．

【详解】设其中做过测试的3只兔子为，剩余的2只为，则从这5只中任取3只的所有取法有，共10种．其中恰有2只做过测试的取法有共6种，

所以恰有2只做过测试的概率为，选B．

【点睛】本题主要考查古典概率的求解，题目较易，注重了基础知识、基本计算能力的考查．应用列举法写出所有基本事件过程中易于出现遗漏或重复，将兔子标注字母，利用“树图法”，可最大限度的避免出错．

5.在“一带一路”知识测验后，甲、乙、丙三人对成绩进行预测．

甲：我的成绩比乙高．

乙：丙的成绩比我和甲的都高．

丙：我的成绩比乙高．

成绩公布后，三人成绩互不相同且只有一个人预测正确，那么三人按成绩由高到低的次序为

A. 甲、乙、丙 B. 乙、甲、丙

C. 丙、乙、甲 D. 甲、丙、乙

【答案】A

【解析】

【分析】

利用逐一验证的方法进行求解.

【详解】若甲预测正确，则乙、丙预测错误，则甲比乙成绩高，丙比乙成绩低，故3人成绩由高到低依次为甲，乙，丙；若乙预测正确，则丙预测也正确，不符合题意；若丙预测正确，则甲必预测错误，丙比乙的成绩高，乙比甲成绩高，即丙比甲，乙成绩都高，即乙预测正确，不符合题意，故选A．

【点睛】本题将数学知识与时政结合，主要考查推理判断能力．题目有一定难度，注重了基础知识、逻辑推理能力的考查．

6.设f(x)为奇函数，且当x≥0时，f(x)=，则当x<0时，f(x)=

A. B.

C. D.

【答案】D

【解析】

【分析】

先把x<0，转化为-x>0,代入可得，结合奇偶性可得.

【详解】是奇函数，．当时，，，得．故选D．

【点睛】本题考查分段函数的奇偶性和解析式，渗透了数学抽象和数学运算素养．采取代换法，利用转化与化归的思想解题．

7.设α，β为两个平面，则α∥β的充要条件是

A. α内有无数条直线与β平行

B. α内有两条相交直线与β平行

C. α，β平行于同一条直线

D. α，β垂直于同一平面

【答案】B

【解析】

【分析】

本题考查了空间两个平面的判定与性质及充要条件，渗透直观想象、逻辑推理素养，利用面面平行的判定定理与性质定理即可作出判断．

【详解】由面面平行的判定定理知：内两条相交直线都与平行是的充分条件，由面面平行性质定理知，若，则内任意一条直线都与平行，所以内两条相交直线都与平行是的必要条件，故选B．

【点睛】面面平行的判定问题要紧扣面面平行判定定理，最容易犯的错误为定理记不住，凭主观臆断，如：“若，则”此类的错误．

8.若x1=，x2=是函数f(x)= ( >0)两个相邻的极值点，则=

A. 2 B.

C. 1 D.

【答案】A

【解析】

【分析】

从极值点可得函数word/media/image54_1.png周期，结合周期公式可得.

【详解】由题意知，的周期，得．故选A．

【点睛】本题考查三角函数的极值、最值和周期，渗透了直观想象、逻辑推理和数学运算素养．采取公式法，利用方程思想解题．

9.若抛物线y2=2px（p>0）的焦点是椭圆的一个焦点，则p=

A. 2 B. 3

C. 4 D. 8

【答案】D

【解析】

【分析】

利用抛物线与椭圆有共同的焦点即可列出关于的方程，即可解出，或者利用检验排除的方法，如时，抛物线焦点为（1，0），椭圆焦点为（±2，0），排除A，同样可排除B，C，故选D．

【详解】因为抛物线的焦点是椭圆的一个焦点，所以，解得，故选D．

【点睛】本题主要考查抛物线与椭圆的几何性质，渗透逻辑推理、运算能力素养．

10.曲线y=2sinx+cosx在点(π，–1)处的切线方程为

A. B.

C. D.

【答案】C

【解析】

【分析】

先判定点是否为切点，再利用导数的几何意义求解.

【详解】当时，，即点在曲线上． 则在点处的切线方程为，即．故选C．

【点睛】本题考查利用导数工具研究曲线的切线方程，渗透了直观想象、逻辑推理和数学运算素养．采取导数法，利用函数与方程思想解题．学生易在非切点处直接求导数而出错，首先证明已知点是否为切点，若是切点，可以直接利用导数求解；若不是切点，设出切点，再求导，然后列出切线方程．

11.已知a∈（0，），2sin2α=cos2α+1，则sinα=

A. B.

C. D.

【答案】B

【解析】

【分析】

利用二倍角公式得到正余弦关系，利用角范围及正余弦平方和为1关系得出答案．

【详解】，．

，又，，又，，故选B．

【点睛】本题为三角函数中二倍角公式、同角三角函数基本关系式的考查，中等难度，判断正余弦正负，运算准确性是关键，题目不难，需细心，解决三角函数问题，研究角的范围后得出三角函数值的正负，很关键，切记不能凭感觉．

12.设F为双曲线C：（a>0，b>0）的右焦点，O为坐标原点，以OF为直径的圆与圆x2+y2=a2交于P、Q两点．若|PQ|=|OF|，则C的离心率为

A. B.

C. 2 D.

【答案】A

【解析】

【分析】

准确画图，由图形对称性得出P点坐标，代入圆的方程得到c与a关系，可求双曲线的离心率．

【详解】设与轴交于点，由对称性可知轴，

又，为以为直径的圆的半径，

为圆心．

，又点在圆上，

，即．

，故选A．

【点睛】本题为圆锥曲线离心率的求解，难度适中，审题时注意半径还是直径，优先考虑几何法，避免代数法从头至尾，运算繁琐，准确率大大降低，双曲线离心率问题是圆锥曲线中的重点问题，需强化练习，才能在解决此类问题时事半功倍，信手拈来．

二、填空题：本题共4小题，每小题5分，共20分．

13.若变量x，y满足约束条件则z=3x–y的最大值是___________.

【答案】9.

【解析】

【分析】

作出可行域，平移找到目标函数取到最大值的点，求出点的坐标，代入目标函数可得.

【详解】画出不等式组表示的可行域，如图所示，

阴影部分表示的三角形ABC区域，根据直线中的表示纵截距的相反数，当直线过点时，取最大值为9．

【点睛】本题考查线性规划中最大值问题，渗透了直观想象、逻辑推理和数学运算素养．采取图解法，利用数形结合思想解题．搞不清楚线性目标函数word/media/image54_1.png几何意义致误，从线性目标函数对应直线的截距观察可行域，平移直线进行判断取最大值还是最小值．

14.我国高铁发展迅速，技术先进．经统计，在经停某站的高铁列车中，有10个车次的正点率为0.97，有20个车次的正点率为0.98，有10个车次的正点率为0.99，则经停该站高铁列车所有车次的平均正点率的估计值为___________.

【答案】0．98.

【解析】

【分析】

本题考查通过统计数据进行概率的估计，采取估算法，利用概率思想解题．

【详解】由题意得，经停该高铁站的列车正点数约为，其中高铁个数为10+20+10=40，所以该站所有高铁平均正点率约为．

【点睛】本题考点为概率统计，渗透了数据处理和数学运算素养．侧重统计数据的概率估算，难度不大．易忽视概率的估算值不是精确值而失误，根据分类抽样的统计数据，估算出正点列车数量与列车总数的比值．

15.的内角A，B，C的对边分别为a，b，c.已知bsinA+acosB=0，则B=___________.

【答案】.

【解析】

【分析】

先根据正弦定理把边化为角，结合角的范围可得.

【详解】由正弦定理，得．，得，即，故选D．

【点睛】本题考查利用正弦定理转化三角恒等式，渗透了逻辑推理和数学运算素养．采取定理法，利用转化与化归思想解题．忽视三角形内角的范围致误，三角形内角均在范围内，化边为角，结合三角函数的恒等变化求角．

16.中国有悠久的金石文化，印信是金石文化的代表之一．印信的形状多为长方体、正方体或圆柱体，但南北朝时期的官员独孤信的印信形状是“半正多面体”（图1）.半正多面体是由两种或两种以上的正多边形围成的多面体.半正多面体体现了数学的对称美．图2是一个棱数为48的半正多面体，它的所有顶点都在同一个正方体的表面上，且此正方体的棱长为1．则该半正多面体共有________个面，其棱长为_________．

【答案】 (1). 共26个面. (2). 棱长为.

【解析】

【分析】

第一问可按题目数出来，第二问需word/media/image125_1.png正方体中简单还原出物体位置，利用对称性，平面几何解决．

【详解】由图可知第一层与第三层各有9个面，计18个面，第二层共有8个面，所以该半正多面体共有个面．

如图，设该半正多面体的棱长为，则，延长与交于点，延长交正方体棱于，由半正多面体对称性可知，为等腰直角三角形，

，

，即该半正多面体棱长为．

【点睛】本题立意新颖，空间想象能力要求高，物体位置还原word/media/image137_1.png关键，遇到新题别慌乱，题目其实很简单，稳中求胜是关键．立体几何平面化，无论多难都不怕，强大空间想象能力，快速还原图形．

三、解答题：共70分。解答应写出文字说明、证明过程或演算步骤。第17～21题为必考题，每个试题考生都必须作答．第22、23题为选考题，考生根据要求作答．

（一）必考题：共60分。

17.如图，长方体ABCD–A1B1C1D1的底面ABCD是正方形，点E在棱AA1上，BE⊥EC1.

（1）证明：BE⊥平面EB1C1；

（2）若AE=A1E，AB=3，求四棱锥的体积．

【答案】（1）见详解；（2）18

【解析】

【分析】

（1）先由长方体得，平面，得到，再由，根据线面垂直的判定定理，即可证明结论成立；

（2）先设长方体侧棱长为，根据题中条件求出；再取中点，连结，证明平面，根据四棱锥的体积公式，即可求出结果.

【详解】（1）因为在长方体中，平面；

平面，所以，

又，，且平面，平面，

所以平面；

（2）设长方体侧棱长为，则，

由（1）可得；所以，即，

又，所以，即，解得；

取中点，连结，因为，则；

所以平面，

所以四棱锥的体积为.

【点睛】本题主要考查线面垂直的判定，依据四棱锥的体积，熟记线面垂直的判定定理，以及四棱锥的体积公式即可，属于基础题型.

18.已知是各项均为正数的等比数列，.

（1）求的通项公式；

（2）设，求数列的前n项和.

【答案】（1）；（2）.

【解析】

【分析】

(1)本题首先可以根据数列是等比数列将转化为，转化为，再然后将其带入中，并根据数列是各项均为正数以及即可通过运算得出结果；

(2)本题可以通过数列的通项公式以及对数的相关性质计算出数列的通项公式，再通过数列的通项公式得知数列是等差数列，最后通过等差数列求和公式即可得出结果。

【详解】(1)因为数列是各项均为正数的等比数列，，，

所以令数列的公比为，，，

所以，解得(舍去)或，

所以数列是首项为、公比为的等比数列，。

(2)因为，所以，，，

所以数列是首项为、公差为的等差数列，。

本题考查数列的相关性质，主要考查等差数列以及等比数列的通项公式的求法，考查等差数列求和公式的使用，考查化归与转化思想，考查计算能力，是简单题。

19.某行业主管部门为了解本行业中小企业的生产情况，随机调查了100个企业，得到这些企业第一季度相对于前一年第一季度产值增长率y的频数分布表.

（1）分别估计这类企业中产值增长率不低于40%的企业比例、产值负增长的企业比例；

（2）求这类企业产值增长率的平均数与标准差的估计值（同一组中的数据用该组区间的中点值为代表）.（精确到0.01）

附：.

【答案】(1) 增长率超过的企业比例为，产值负增长的企业比例为；（2）平均数；标准差.

【解析】

【分析】

(1)本题首先可以通过题意确定个企业中增长率超过的企业以及产值负增长的企业的个数，然后通过增长率超过的企业以及产值负增长的企业的个数除随机调查的企业总数即可得出结果；

(2)可通过平均值以及标准差的计算公式得出结果。

【详解】(1)由题意可知，随机调查的个企业中增长率超过的企业有个，

产值负增长的企业有个，

所以增长率超过的企业比例为，产值负增长的企业比例为。

(2)由题意可知，平均值，

标准差的平方：

，

所以标准差。

【点睛】本题考查平均值以及标准差的计算，主要考查平均值以及标准差的计算公式，考查学生从信息题中获取所需信息的能力，考查学生的计算能力，是简单题。

20.已知是椭圆的两个焦点，P为C上一点，O为坐标原点．

（1）若为等边三角形，求C的离心率；

（2)如果存在点P，使得，且的面积等于16，求b的值和a的取值范围.

【答案】(1)；（2），a的取值范围为.

【解析】

【分析】

（1）先连结，由为等边三角形，得到，，；再由椭圆定义，即可求出结果；

（2）先由题意得到，满足条件的点存在，当且仅当，，，根据三个式子联立，结合题中条件，即可求出结果.

【详解】（1）连结，由为等边三角形可知：在中，，，，

于是，

故椭圆C的离心率为；

（2）由题意可知，满足条件的点存在，当且仅当，，，

即 ①

②

③

由②③以及得，又由①知，故；

由②③得，所以，从而，故；

当，时，存在满足条件的点.

故，a的取值范围为.

【点睛】本题主要考查求椭圆的离心率，以及椭圆中存在定点满足题中条件的问题，熟记椭圆的简单性质即可求解，考查计算能力，属于中档试题.

21.已知函数.证明：

（1）存在唯一的极值点；

（2）有且仅有两个实根，且两个实根互为倒数.

【答案】（1）见详解；（2）见详解

【解析】

【分析】

（1）先对函数求导，根据导函数的单调性，得到存在唯一，使得，进而可得判断函数的单调性，即可确定其极值点个数，证明出结论成立；

（2）先由（1）的结果，得到，，得到在内存在唯一实根，记作，再求出，即可结合题意，说明结论成立.

【详解】（1）由题意可得，的定义域为，

由，

得，

显然单调递增；

又，，

故存在唯一，使得；

又当时，，函数单调递增；当时，，函数单调递减；

因此，存在唯一的极值点；

（2）由（1）知，，又，

所以在内存在唯一实根，记作.

由得，

又，

故是方程在内的唯一实根；

综上，有且仅有两个实根，且两个实根互为倒数.

【点睛】本题主要考查导数的应用，通常需要对函数求导，用导数的方法研究函数的单调性、极值、以及函数零点的问题，属于常考题型.

（二）选考题：共10分．请考生在第22、23题中任选一题作答。如果多做，则按所做的第一题计分．

22.[选修4-4：坐标系与参数方程]

在极坐标系中，O为极点，点在曲线上，直线l过点且与垂直，垂足为P.

（1）当时，求及l的极坐标方程；

（2）当M在C上运动且P在线段OM上时，求P点轨迹的极坐标方程.

【答案】（1），l的极坐标方程为；（2）

【解析】

【分析】

（1）先由题意，将代入即可求出；根据题意求出直线的直角坐标方程，再化为极坐标方程即可；

（2）先由题意得到P点轨迹的直角坐标方程，再化为极坐标方程即可，要注意变量的取值范围.

【详解】（1）因为点在曲线上，

所以；

即，所以，

因word/media/image281_1.png直线l过点且与垂直，

所以直线的直角坐标方程为，即；

因此，其极坐标方程为，即l的极坐标方程为；

（2）设，则，，

由题意，，所以，故，整理得，

因为P在线段OM上，M在C上运动，所以，

所以，P点轨迹的极坐标方程为，即.

【点睛】本题主要考查极坐标方程与直角坐标方程的互化，熟记公式即可，属于常考题型.

23.[选修4-5：不等式选讲]

已知

（1）当时，求不等式的解集；

（2）若时，，求的取值范围.

【答案】（1）；（2）

【解析】

【分析】

（1）根据，将原不等式化为，分别讨论，，三种情况，即可求出结果；

（2）分别讨论和两种情况，即可得出结果.

【详解】（1）当时，原不等式可化为；

当时，原不等式可化为，即，显然成立，

此时解集为；

当时，原不等式可化为，解得，此时解集为空集；

当时，原不等式可化为，即，显然不成立；此时解集为空集；

综上，原不等式的解集为；

（2）当时，因为，所以由可得，

即，显然恒成立；所以满足题意；

当时，，因为时，显然不能成立，所以不满足题意；

综上，的取值范围是.

【点睛】本题主要考查含绝对值的不等式，熟记分类讨论的方法求解即可，属于常考题型.

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