七宝中学2015届高三5月份考试卷
上海市七宝中学2015年高三第二学期英语5月质量检测卷
出卷人：沈鹏审卷人：竹娉娉
I. Listening Comprehension (30’)
Section A (10’)
Directions: 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. In a library. B. In a hotel. C. In a classroom. D. In a bookstore
2. A. She thinks the man needs a vacation.
B. She thinks the man should be preparing for his tests.
C. She thinks the man doesn’t need to worry about his exams.
D. She is not interested in surfing.
3. A. She may fail the exam. B. She shouldn’t have worried.
C. She should work harder.
D. She needn’t take any more courses.
4. A. Scholarship. B. Major. C. Hobby. D. Travelling.
5. A. Thoughtful. B. Humorous. C. Careless. D. Helpful.
6. A. A rent increase. B. A bargain. C. A salary cut. D. A vacation trip.
7. A. By car. B. By bus. C. On foot. D. By train.
8. A. Only one person can come. B. There have been few responses.
C. Almost everyone can come.
D. They’re waiting for Tina’s response.
9. A. He has no interest in wild life protection.
B. He is sorry to fail in the examination.
C. He can’t join the group since he is about to graduate.
D. He’s already busy with the Student Union issue.
10. A. Because she is all wet. B. Because she is tried out.
C. Because she walked a long distance.
D. Because she left something in the school.
Section B (12’)
Directions: In Section B, you will hear two short passages, and you will be asked three questions on each passage. The passage 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. Functions of Facial Expressions. B. Types of Printed Words.
C. Means of Communication.
D. Importance of Language.
12. A. It was the first invention of mankind.
B. It is a must for man’s survival.
C. It makes other inventions possible.
D. It helps people to know the modern world.
13. A. Man would have to use signals only.
B. The modern world couldn’t function well.
C. Man would keep on inventing things.
D. Man wouldn’t be able to live with his fellow beings.
Questions 14 through 16 are based on the following passage.
14. A. The design of the laboratory. B. The laboratory experiment.
C. The workbook for the laboratory course.
D. A piece of equipment in the laboratory.
15. A. Homework must be handed in on time.
B. A great deal of equipment is available.
C. The students must follow all instructions exactly.
D. The students can make choices about the lab work.
16. A. The activities take less time.
B. The activities are to be done in class.
C. Few instructions are given for the activities.
D. Students are not required to do the activates.
Section C (8’)
Directions:In Section C, you will hear two longer conversations. The conversation will be read twice. After you hear the 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.
Blanks 21 through 24 are based on the following conversation.
II. Grammar (16’)
Directions: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.
As a big fan of Manchester United, it is always hard for me to believe that Man Utd should finish seventh in the final Premier League table (英超联赛积分榜) last season. To be frank, that result [25]_______ never be more disappointing and frustrating for me. If there is someone who is [26]________ (blame) for this, it must be the Manager David Moyes.So at the end of last season, everyone knew that it was only a matter of time before he [27]________ (dismiss) and to [28]________ Man Utd should hand the task of getting the team back on track became a matter of concern.
When the news came on the night of Wednesday 16 July [29]________ Louis van Gaal was appointed the new Manager of Man Utd, I knew he could be the one to restore the Red Devils to their former glories, [30]________ some claims that this decision was even more risky since Louis is [31]________ (familiar) with the league compared with Man Utd’s ill-fated former Manager David Moyes, who at least has worked in the league for years. “ Experienced [32]________ Louis van Gaal is,” Gary Neville, currently [33]________ occasional sports columnist for the Daily Mail (每日邮报), wrote in his column, “it is apparently unlikely for this new comer to win the title this year.” And some of the concerns were right, especially when Louis [34]________ admitted that it would take 2 [35]________ 3 months to get fully acquainted with the Premier League. Thus, Man Utd’s failure to stay on top of the Premier League table before Christmas, [36]________ used to be a rare case, didn’t come as a surprise to me.
But in the last two months, things have changed. Man Utd has gained six successive victories against different rivals [37]________ (include) its noisy neighbor—Manchester City, [38]________ ________ which the team has now climbed from rock bottom to No. 3 in the table.
With only 5 matches [39]________ (leave) and Man Utd temporarily ranking No. 3 (last season No. 7) at the league table, now everyone can agree on one thing that [40]________ ________ ________ this season ends eventually, the decision to replace David Moyes with Louis van Gaal in the last summer was a right one.
III. Vocabulary (10’)
Directions:Complete the following passage by using the words in the box. Each word can only be used once. Do note that there is one word more than you need.
My Reflection on Johnnie To’s Running on Karma(大隻佬) Recently I have seen the film Running on Karma again, a controversial film that has long been taken as a courageous attempt of Johnnie To’s and also a significant [41]________ from his other works. Those [42]________ plots which used to limit my understanding of the film now start to make sense. It just feels as if I were [43]________ with an old acquaintance whom I once misunderstood.
If there is one line that can represent what To really wants to [44]________ to his audience, it
must be the saying that all but one’s karma(佛教用语：业) can be cast away, which [45]________ appears in the film.
As the theme’s finishing touch, not only does the above saying reveal some [46]________ thoughts hidden in the film, but it also throws a light on To’s [47]________ of responsibility. Karma means “act or deed.” What was sown before is now reaped. But as sowing also takes place in the present, it [48]________ involves responsibility towards the future. Since nothing can be done to alter the past, what one should be concerned about is not yesterday’s cause, but how to sow his or her karma today—which will [49]________ fruit tomorrow.
To put it in another way, the idea of the film is that no matter what one has done, once it has been done, it just becomes water under the bridge. So what truly matters is to [50]________ the responsibility for the future, since that is something one can make a difference to.
IV. Cloze (15’)
Directions:For each blank in the following passage there are four words marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.
Many theories concerning the causes of juvenile delinquency (crimes committed by young people) focus either on the individual or on society as the major contributing influence. Theories centering on the individual suggest that children [51]_______ criminal behavior because they were not sufficiently [52]________ for previous misbehaviors or that they have learned criminal behavior through interaction with others. Theories focusing on the role of society suggest that children commit crimes in [53]________ to their failure to rise above their socioeconomic status or as a rejection of middle-class values.
Most theories of juvenile delinquency have focused on children from disadvantaged families, [54]________ the fact that children from wealthy homes also commit crimes. The latter may commit crimes for lack of adequate control from parents. All [55]________, however, are uncertain or unimproved and are of course challenged with criticism.
Changes in the social structure may indirectly [56]________ juvenile crime rates. For example, changes in the economy that [57]________ to fewer job opportunities for youth and rising unemployment [58]________ make gainful employment increasingly difficult to obtain. This results in dissatisfaction among youths and may in [59]________ lead more youths into criminal behavior.
Families have also experienced [60]________ these years. More families consist of one parent households or two working parents; [61]________, children are likely to have less supervision at home than was common in the traditional family [62]________. This lack of parental supervision is thought to be an influence on juvenile crime rates. Other noticeable
[63]________ of offensive acts include unfavorable experience or failure in school, the
[64]________ availability of drugs and alcohol, and the growing phenomenon of child abuse and child neglect. All these conditions tend to increase the [65]________ of a child committing a criminal act, although a direct cause and effect relationship has not yet been established.
51. A. refer to B. know about C. engage in D. learn of
52. A. punished B. forgiven C. forgotten D. excused
53. A. return B. contact C. reference D. response
54. A. considering B. ignoring C. highlighting D. believing
55. A. values B. misbehaviors C. criminals D. theories
56. A. affect B. reduce C. prevent D. reflect
57. A. point B. lead C. come D. add
58. A. in general B. on average C. by contrast D. at last
59. A. case B. short C. turn D. essence
60. A. failure B. miseries C. development D. changes
61. A. contrarily B. consequently C. similarly D. occasionally
62. A. education B. concept C. structure D. economy
63. A. suggestions B. causes C. ideas D. reports
64. A. increased B. restricted C. reasonable D. popular
65. A. knowledge B. aspect C. strength D. probability
V. Reading Comprehension (2*16)
Section A (2’*12)
Directions: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)
Pride and Prejudice for the Modern Woman
Let us imagine how Pride and Prejudice, Jane Austen’s most fa mous work, might be updated, 200 years on.
Austen’s popularity is rooted in her intelligence. But today she would certainly have had a very different life, as would her character s. Here’s my own suggestion.
It is a truth finally and universally acknowledged that a single woman with brains deserves to have equal opportunities to men, however disadvantaged she may feel by sexism.
“My dear husband,”said his hopeful wife one day, “have you heard that the local store, standing empty for so long, is taken over b y a bright young businesswoman?”
Her dull and indifferent husband replied that he had not. “But it is, it is,” she replied excitedly. Mr. Dull-Husband made no reply.
“Don’t you want to know her plans?” she cried with some impatience.
“Well, clearly you think it matters to your silly little head... so I’d better listen.”
“Well, my dear, the rumour is that she has already set up a string of successful businesses in northern England, though how a woman can know anything about that is beyond me. She will move in herself next month.
“What is her name?”“Bingley.”
“Is she married or single?”
“What a question! And none of your business.” But her coming will be a fine thing for our five boys. “How so? H ow can it possibly affect them?”
“My dear love; those lazy boys need something to wake them up. There are bound to be jobs going.”
“Is that her point in settling here? Surely as a woman she has simply taken a fancy to the place.”
“Nonsense, my love, how little you’ve noticed the world has changed. She’s got a first-rate degree and some sort of business qualification, I’m told. She surely needs one of our boys! Per haps you might give her a call.”
“Me? No. Perhaps you can take an interest. You still have your looks, after all. She may even offer you a job.”
“Oh, that’s not likely. These new chances belong to the younger generation. But now you mention it, I think I’ll go along all the same.”
And Mrs. Bennet went along. That was 10 years ago. She is now managing director of a FTSE(英国富时指数)-listed company.
... It would remain the case, of course, that Mrs. Bennet would be one of very few women on the company board, that her salary would be lower than her male colleagues, her bonus of a more “female” dimension and her lifespan among the city’s business leaders shorter than theirs. Still, she’d no doubt have enjoyed Davos(达沃斯论坛)—and might even have hobnobbed (攀谈) with influential figures.
66. Which of the following is TRUE according to the passage?
A. Austen was born 200 years age.
B. Austen rewrote Pride and Prejudice.
C. Austen’s success lies in her wisdom.
D. Austen’s updated work gains popularity.
67. The underlined part in the passage suggests that Mrs. Bennet ________.
A. had mixed feelings of admiration and surprise about Bingley
B. felt kind of worried and doubtful about Bingley
C. was extremely anxious to meet Bingley
D. had a great curiosity about Bingley
68. In the eyes of Mrs. Bennet, Bingley surely needed one of their boys to ________.
A. get married to
B. work for her
C. help her move in
D. take over her store
69. What does the writer intend to tell us?
A. Women with brains can also be as successful as men.
B. Women have to pay a high price for success.
C. A judgment must be made free from prejudice.
D. Sex discrimination still exists nowadays.
(B)
Shanghai is filled with interesting museums, and they will educate, intrigue and delight children with exhibitions of animation characters, insects and chopsticks, to name a few. Here are some lesser-known, non-art museum scattered around the city.
Animation Museum
Children will love this museum covering the world history of cartoons and animations. The first floor covers history, from China’s shadow puppets to Disney’s characters. The main hall is filled with posters and life-sized statues. Short animation is screened.
In a second-floor studio, children can dub(配音) voices for favorite characters.
Tel: 5895-7998
Address: 69 Zhangjiang Rd, Pudoing New Area
Opening hours: 10am-5pm, closed on Mondays
Admission: 30 yuan
Brush and Ink Museum
The one-room museum covers the history of ink, inkstones and brushes. It explains how to make ink and features stories about Shanghai and its calligraphers. Brushes and inkstones are displayed, each with an English audio explanation.
Tel: 5169-8918
Address: 2/F, 429 Fujiang Rd, Huangpu District
Opening hours: 9:30am-5:30pm, daily
Admission: Free
Chopsticks Museum
This is one of the city’s smallest museums. It’s the personal exhibition of Lan Xiang, who has collected 2,000 pairs of chopsticks from around Asia. Lan, 81, lives upstairs. The prized pair is a gilded silver set from the Tang Dynasty (AD 618-907).
Tel: 5671-7528
Address: 191 Duolun Rd, Hongkou District
Opening hours: Call in advance
Admission: Free
Insect Museum
The museum contains more than a million specimens(标本) of insects from around the world, many rare and beautiful, some extinct. The museum was founded in 1868 and once called the British Museum in Asia. Today it’s in a modern building.
Tel: 5492-4191
Address: 300 Fenglin Rd, Xuhui District
Opening hours: 9am-4pm
Admission: 15 yuan for adults (18+), 10 yuan for children
Postal Museum
This is a wonderful free museum with a beautiful Baroque clock tower, rooftop garden and glassed-in courtyard. The 1924 landmark building was the original Shanghai Postal Museum and explains the history of the postal service in China. It’s filled with interesting exhibits, concession-period post marks, clay seals and postage stamps.
Tel: 6393-6666 ext. 1280
Address: 250 Suzhou Rd, Hongkou District
Opening hours: Wednesday, Thursdays, Saturdays and Sundays, 9am-5pm
70. Children can do the following in the Animation Museum EXCEPT ________.
A. making shadow puppets
B. dubbing in the studio
C. learning the history of cartoons
D. watching the short animation
71. What do the Chopsticks Museum and the Postal Museum have in common?
A. They are closed on Mondays.
B. They are private museums.
C. They offer excellent views.
D. They are admission free.
72. If a 40-year-old man takes three of his nephews (aged 4, 13 and 19) to the Insect Museum, he
needs to pay ________ for admission fees.
A. 60 yuan
B. 50 yuan
C. 45 yuan
D. 40 yuan
73. An American who is fond of learning some traditional Chinese culture but knows little Chinese
is advised to dial ________.
A. 5492-4191
B. 5895-7998
C. 5671-7528
D. 5169-8918
(C)
Just five one-hundredths of an inch thick, light golden in color and with a perfect “saddle curl,” the Lay’s potato chip(乐事薯片) seems an unlikely weapon for global domination. But its maker, Frito-Lay, thinks otherwise. “Potato chips are a snack food for the world,”said Salman Amin, the company’s head of global marketing. Amin believes there is no corner of the world that can resist the charms of a Frito-Lay potato chip.
Frito-Lay is the biggest snack maker in America owned by PepsiCo(百事公司) and accounts for over half of the parent company’s $3 billion annual profits. But the U.S. snack food market is largely saturated(饱和), and to grow the company has to look overseas.
Its strategy rests on two beliefs: first a global product offers economies of scale with which local brands cannot compete. And second, consumers in the 21st century are drawn to “global” as a concept. “Global” does not mean products that are consciously identified as American, but ones that consumers—especially young people—see as part of a modern, innovative world in which people are linked across cultures by shared beliefs and tastes. Potato chips are an American invention, but most Chinese, for instance, do not know that Frito-Lay is an American company. Instead, Riskey, the company’s research and development head, would hope they associate the brand with the new world of global communications and business.
With brand perception a crucial factor, Riskey ordered a redesign of the Frito-Lay logo. The logo, along with the company’s long-held marketing image of the “irresistibility”of its chips, would help facilitate the company’ global expansion.
The executives acknowledge that they try to swing national eating habits to a food created in America, but they deny that amounts to economic imperialism. Rather, they see Frito-Lay as spreading the benefits of free enterprise across the world. “We’re making products in those countries, we’re adapting them to the tastes of those countries, building business and employing people and changing lives,” said Steve Reinemund, PepsiCo’s chief executive.
74. It is the belief of Frito-Lay’s head of global marketing that ________.
A. Potato chips can hardly be used as a weapon to dominate the world market
B. Their company must find new ways to promote domestic sales
C. The light golden color enhances the charm of their company’s potato chips
D. People over the world enjoy eating their company’s potato chips
75. One of the assumptions on which Frito-Lay bases its development strategy is that ________.
A. consumers worldwide today are attracted by global brands
B. local brands cannot compete successfully with American brands
C. products suiting Chinese consumers’ needs bring more profits
D. products identified as American will have promising market value
76. Why did Riskey have the Frito-Lay logo redesigned?
A. To suit changing tastes of young consumers.
B. To promote the company’s strategy of globalization.
C. To change the company’s long-held marketing image.
D. To compete with other American chip producers.
77. Frito-Lay’s executives claim that the promoting of American food in the international market
________.
A. won’t affect the eating habits of the local people
B. will lead to economic imperialism
C. will be in the interest of the local people
D. won’t spoil the taste of their potato chips
Section B (2’*4)
Directions: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.
Oscar-winning director Ang Lee’s new epic Life of Pi reveals the relationship between a teenage Indian boy and a Bengal tiger. But in reality, the predators(肉食性动物) are under increasing threat from humans. Animal rights group PETA is hoping to use the popularity of the film to focus people’s attention on the real life of Bengal tigers.
With the rising demand for tiger parts from East Asia, illegal hunting remains a tremendous danger for the remaining cat population. Back in 1947, there were 40,000 tigers in India, but the number is experiencing a sharp decline to 1,707 despite campaigns to protect the animal.
Rising man-animal conflict is also one of the leading causes of decline in tiger numbers. In one of numerous reported attacks on the endangered big cats, villagers near the Bangladesh-India border, armed with sticks and boat oars, set upon the animal suspected to have attacked a local fisherman and beat it to death earlier this month. So far this year, 58 tigers deaths have been reported in the country.
“The first instinct when a tiger is spotted is to just kill it,” grieved Gurmeet Sapal, a wildlife filmmaker. “The feeling of fear and revenge is so strong that is shuts out any other emotion.”What we don’t realize is that the tiger never attacks humans until it is forced to.”
India has been struggling to stop tiger’s decline in the face of the loss of habitat as well that encourages the animals to leave the forest for food. “The tiger’s rapidly exhausted prey base causes the predator to go all out to get its food. Consequently, livestock and human beings become easy prey, which leads inevitably to conflicts,” says a wildlife conservationist.
Filmmakers Sapal says it is only normal for people to think of the tiger as a dangerous animal, but its image as a human killer bears some injustice. “Tigers never kill for sport nor store meat. They kill their prey only in case of hunger.”
(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)
78. PETA hopes Life of Pi can _____________________________________________________.
79. Why did villagers beat the tiger to death?
80. The main reasons for the decline in tiger numbers are ____________________________ and
__________________________.
81. When will tigers attack and kill people according to the article?
VI. Translation (3’+4’+5’+5’+5’ = 22’)
Directions: Translate the following sentences into English, using the words given in the brackets.
1. 公司明确表示只有精通计算机技能的人才能申请这个职位。(clear)
2. 所有与会的人都对Malala, 这个为了女性教育权利抗争的诺贝尔和平奖获得者，表示了敬
意。(present)
3. 尽管他的尝试均以失败告终，但他仍然不遗余力地要去实现自己打破世界纪录的梦想而
不是轻言放弃。(end v.)
4. 淘宝(TaoBao) 是中国最大的购物网站之一，在那儿你不仅可以淘到许多便宜货还能靠经
营自己的网店来挣钱。(where)
5. 我一进会议室他就向我保证这次的研讨将会在三点前结束，这样我就可以赶上最后一班
去丽江的飞机。(No sooner…)
VII. Writing (25’)
Directions: Write an English composition in 120-150 words. The composition must be based on the information given below.
现在，有些学生认为和老师之间存在代沟，很难与之沟通。而有些学生则认为现在的师生关系更像是平等的朋友关系。请以My teacher and I 为题描述一件你和老师之间发生的令人印象深刻的事情，并就上述观点谈谈你的看法和理由
Answer Sheet
I. Listening Comprhension (8’)
17. ____________ 18. ____________ 19. ____________ 20. ____________
21. ____________ 22. ____________ 23. ____________ 24. ____________
II. Grammar (16’)
25. ____________ 26. ____________ 27. ____________ 28. ____________
29. ____________ 30. ____________ 31. ____________ 32. ____________
33. ____________ 34. ____________ 35. ____________ 36. ____________
37. ____________ 38. ____________ ____________ 39. ____________
40. ____________ ____________ ____________
V. Reading Comprehension (8’)
78. ____________________________________________________________________________
79. ____________________________________________________________________________
80. ____________________________________________________________________________
81. ____________________________________________________________________________
VI. Translation (3’+4’+5’+5’+5’ = 22’)
1. ____________________________________________________________________________ ____________________________________________________________________________
2. ____________________________________________________________________________ ____________________________________________________________________________
3. ____________________________________________________________________________ ____________________________________________________________________________
4. ____________________________________________________________________________ ____________________________________________________________________________
5. ____________________________________________________________________________ ____________________________________________________________________________
VII. Writing (25’)
_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________
【全国百强校】上海市七宝中学2019届高三上学期期中考试数学试题
【全国百强校】上海市七宝中学2019届高三上学期 期中考试数学试题 学校_________ 班级__________ 姓名__________ 学号__________ 一、填空题 1. 集合的真子集有________个 2. 设全集，，，则图中阴影部分所表示的集合是________（用区间表示） 3. 命题“若实数、满足，则或”是________命题（填“真”或“假”） 4. 某个时钟时针长6，则在本场考试时间内，该时针扫过的面积是 ________ 5. 函数是奇函数，则实数的值为________ 6. 函数在上单调递增，则实数的取值范围为________ 7. 在△中，角、、所对的边分别为、、，若，，，则△的面积为________ 8. 已知函数，则的解集是________
9. 若关于的不等式在上恒成立，则正实数的取值范围为________ 10. 已知常数，函数的图象经过点， ．若，则______． 11. 已知函数，若，则 的最大值是________ 12. 已知函数，如果函数恰有三个不同的零点，那么实数的取值范围是________ 二、单选题 13. “函数存在反函数”是“函数在上为增函数”的（）A．充分而不必要条件B．必要而不充分条件 C．充分必要条件D．既不充分也不必要条件 14. 若函数的反函数为，则函数与的图象可能是 A．B．C．D． 15. 在△中，角、、所对的边分别为、、，给出四个命题：（1）若，则△为等腰三角形； （2）若，则△为直角三角形； （3）若，则△为等腰直角三角形；
（4）若，则△为正三角形； 以上正确命题的个数是（） A．1 B．2 C．3 D．4 16. 是定义在上的函数，且，若的图像绕原点逆时针旋转 后与原图像重合，则在以下各项中，的可能取值只能是（）A．0 B．1 C．2 D．3 三、解答题 17. 已知锐角和钝角的终边分别与单位圆交于、两点，其中点坐标 . （1）求的值； （2）若，求点坐标. 18. 如图，某公园有三个警卫室、、有直道相连，千米，千米，千米. （1）保安甲沿从警卫室出发行至点处，此时，求的直线距离；（2）保安甲沿从警卫室出发前往警卫室，同时保安乙沿从警卫室出发 前往警卫室，甲的速度为1千米/小时，乙的速度为2千米/小时，若甲乙两人通过对讲机联系，对讲机在公园内的最大通话距离不超过3千米，试问有多 长时间两人不能通话？（精确到0.01小时） 19. 问题：正数、满足，求的最小值. 其中一种解法是：，当且仅当
上海市七宝中学高一入学分班数学考试卷及答案
1 2016学年第一学期七宝中学高一新生入学摸底考试数学试卷 一、选择题（每小题有仅一个正确答案，每题 3 分） 1. 已知0a b ，则下列不等式不一定成立的是（ ）． （A ）2ab b （B ）a c b c （C ） 11 a b （D ）ac bc 2. 若不等式组21 13 x x a 的解集为2x ，则a 的取值范围是（ ）． （A ）2a （B ）2a （C ）2a （D ）2a 3. 若11,2M y ，21,4N y ，31,2P y 三点都在函数k y x （0k ）的图像上，则123 y y y 、、的大小关系为（ ）． （A ）213y y y （B ）231y y y （C ）312y y y （D ）321y y y 4. 已知22y x 的图像是抛物线，若抛物线不动，把 x 轴、 y 轴分别向上、向右平移 2 个单位， 那么在新坐标系下抛物线的解析式是（ ）． （A ） 2 222y x （B ） 2 222y x （C ） 2222y x （D ） 2 222y x 5. 中央电视台“幸运 52”栏目中的“百宝箱”互动环节，是一种竞猜游戏，游戏规则如下：在 20个商标中，有 5 个商标牌的 背面注明了一定的奖金额，其余商标的背面是一张苦脸，若翻到它就不得奖、参加这个游戏的观众有三次翻牌的机会．某观众前两次翻牌均得若干奖金，如果翻过的牌不能再翻，那么这位观众第三次翻牌获奖的概率是（ ）． （A ）14 （B ）16 （C ）15 （D ）3 20 6. 将水匀速注入一个容器，时间（t ）与容器水位（h ）的关系如图所示，则容器的形状是（ ）． （A ） （B ） （C ） （D ）
上海市七宝中学2016届高三考前模拟英语试题(一) Word版含答案
2016高三英语模拟考试 II. Grammar and Vocabulary Section A Directions: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) Once just a science fiction idea, VR has now become more accessible than ever. (25) _________ (wear) a pair of VR goggles connected to your computer and you can experience a lot of things without stepping out of the room. From climbing (26) _________ (high) mountain in the world to flying a spacecraft, the things you can experience with VR are limitless. This new 'reality ' is starting to takeover China. The Report on Chinese VR Users' Behavior was released on March 18 during the 12th TFC Global Mobile Game Conference & Intelligent Entertainment Expo held in Beijing. The report is based on a survey of 5,626 people, (27) _________ (age) between 15 and 39, from across the country. It shows that up to 68.5 percent of people have heard of or are interested in VR products. But surprisingly, it isn't new technology that has made VR so popular. 'VR has been (28) _________ for many years, but it will stick this time because there's enough computer power and the price will just keep going down,' Todd Richmond, a VR group member with the Institute of Electrical and Electronic Engineers in the US, told USA Today. VR (29) _________ (expect) to change various different fields. For example, VR could be used to train pilots and miners before they had to actually risk their lives in highly dangerous working environments, or to treat patients with acrophobia(恐高症）by making them think they were standing on top of a high building. 'If you have perfect virtual reality, (30) _________ you'll be able to simulate everything that a human can experience or imagine experiencing,it's hard to imagine where you go from there,' Palmer Luckey, 23 inventor of the Oculus VR goggles, told NPR. But the technology is still far from perfect. Users report experiencing motion sickness, headaches and other discomfort while wearing VR goggles. Also, (31) _________ more and more tools are flooding the market, the software that runs VR games and simulators has yet to catch up with all the new advancements. It could take (32) _________ while for VR to be widely accepted. When every new technology is first introduced, the technology (33) _________ is the driving force. But for it to really blend into people's lives, meeting basic and practical needs should be the main aim. (B) It has become the talk of the town: A stranger allegedly attacked a woman in a Beijing hotel at night on April 3. The man is said to have clutched her by the neck and attempted to drag her into the elevator. Lodgers passed by, but no one tried to intervene until one woman did. Her actions are believed to (34) _________ (save) the victim from whatever was going to happen to her. The incident has pushed the risks of solo traveling into the spotlight. Online forums like Sina Weibo (35) _________ (flood) with advice for how women (36) _________ protect themselves
上海市七宝中学2017届高三10月月考数学试题
七宝中学高三月考数学卷 2016.10 一. 填空题 1. 已知函数()f x 的定义域是[1,2]-，则()()y f x f x =+-的定义域是 2. 若25x y -<<<，则x y -的取值范围是 3. 锐角△ABC 中，角,A B 所对的边长分别为,a b ，若2sin a B b =，则A = 4. 二项式921()x x -的展开式中常数项为 (结果用数值表示) 5. 若函数cos(2)y x ?=+(||)2π?<的图像关于点4(,0)3 π中心对称，则?= 6. 若12 2log (42)0ax x a -+-<对任意x R ∈恒成立，则实数a 的取值范围是 7. 已知0x >，0y >，1211 x y +=+，则x y +的最小值为 8. 已知向量AB 与AC 的夹角为120，且||2AB =，||3AC =，若AP AB AC λ=+， 且AP BC ⊥，则实数λ的值为 9. 某微信群中甲、乙、丙、丁、戊五名成员先后抢4个不相同的红包，每人最多抢一个红 包，且红包全被抢光，则甲乙两人都抢到红包的情况有 种 10. 设函数()min{||,||}f x x x t =+的图像关于 直线3x =-对称，其中min{,}a b 表示,a b 中的 最小值，则实数t = 11. 右侧程序框图的运行结果：S = 12. 已知函数1,0()42,0 x x x x f x x --?+>?=?-≤??，若函数 (32)y f x a =--恰有三个不同的零点，则实 数a 的取值范围是 13. 等差数列{}n a 的前n 项和为n S ，已知31819992017(1)2016(5)sin()3a a π-+-=-， 31999182017(5)2016(1)cos()6 a a π-+-=-，则2016S = 14. 正方体1111D C B A ABCD -的棱长为3，以顶点A 为球心，2为半径作一个球，则球面与正方体的表面相交所得到的所有弧长之和等于
详解及答案-2019年上海市闵行区七宝中学高考数学一模试卷
2019年上海市闵行区七宝中学高考数学一模试卷 一、选择题（本大题共4小题） 1.设集合P1={x|x2+ax+1＞0}，P2={x|x2+ax+2＞0}，其中a∈R，下列说法正确的是（） A. 对任意a，P1是P2的子集 B. 对任意a，P1不是P2的子集 C. 存在a，使得P1不是P2的子集 D. 存在a，使得P2是P1的子集 【答案】A 【解析】 【分析】 由不等式的性质得：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0，由x2+ax+2＞0，不能推出x2+ax+1＞0，由集合间的关系得：P1P2，得解． 【详解】解：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0， 由x2+ax+2＞0，则有x2+ax+1=x2+ax+2-1＞-1，不能推出x2+ax+1＞0， 即P1P2， 故选：A． 【点睛】本题考查了集合间的关系，不等式的性质，属简单题． 2.△ABC中，a2：b2=tan A：tan B，则△ABC一定是（） A. 等腰三角形 B. 直角三角形 C. 等腰直角三角形 D. 等腰或直角三角形 【答案】D 【解析】 【分析】 由已知a2：b2=tan A：tan B，利用正弦定理及同角基本关系对式子进行化简，然后结合二倍角公式在进行化简即可判断. 【详解】解：∵a2：b2=tan A：tan B， 由正弦定理可得， ∵sin A sin B≠0 ∴
∵sin A cosA=sin B cosB即sin2A=sin2B ∵2A=2B或2A+2B=π ∵A=B或A+B=，即三角形为等腰或直角三角形 故选：D． 【点睛】本题考查同角三角函数的基本关系，正弦定理的应用，式子变形是解题的关键和难点． 3.抛物线y=2x2上有一动弦AB，中点为M，且弦AB的长度为3，则点M的纵坐标的最小值为（） A. B. C. D. 1 【答案】A 【解析】 【分析】 由题意设，，直线的方程为，代入抛物线方程，写出韦达定理关系式及弦长 与点的纵坐标关系式，通过基本不等式确定最小值. 【详解】由题意设，，，直线的方程为， 联立方程，整理得 ，∵∵ 点M的纵坐标∵ 弦的长度为 ，即 ∵ 整理得，即 根据基本不等式∵，当且仅当∵时取等，即∵ ∵点的纵坐标的最小值为. 故选A. 【点睛】本题考查直线与抛物线位置关系，考查基本不等式在圆锥曲线综合问题中的应用∵解题时要认真审题，注意等价转化思想的合理运用.
2020-2021学年上海市闵行区七宝中学高三英语上学期10月月考试卷-难易度及易错题分析版
2020-2021学年上海市闵行区七宝中学 高三英语上学期10月月考试卷 I. Listening Comprehension(略) II. Grammar and Vocabulary (20分) Section A Directions: After reading the passage below, fill in the blanks to make the passage 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. Challenging work that requires lots of analytical thinking, planning and other managerial skills might help your brain stay sharp (21) you age, a study published Wednesday in the journal Neurology suggests. Researchers from the University of Leipzig in Germany gathered more than 1, 000 retired workers who were over age 75 and had the volunteers’ memory and thinking skills (22) (assess)through a battery of tests. Then, for eight years, the scientists asked the same group to come back to the lab every 18 months (23) (take) the same sorts of tests. Those who (24) (hold)mentally stimulating, demanding jobs before retirement tended to do the best on the tests. And they tended to lose cognitive（认知）function (25) a much slower rate than those with the least mentally challenging jobs. The results held true even after the scientists accounted for the participants’ overall health status. “This works just like physical exercise,” says Francisca Then, who led the study. “After a long run, you may feel like you’re in pain, you may feel tired. But it makes you fit. After a long day at work — sure, you will feel tired, (27) it can help your brain stay healthy. ” It’s not just corporate jobs, or even paid work (26) can help keep your brain fit, Then points out. A waiter’ s job, for example, (28) ( require) multitasking, teamwork and decision-making could be just as stimulating as any high-level office work. And “running a family household requires high-level planning and coordinating（协调）,” she says. “You (29) _______ ________organize the activities of the children and take care of the bills and groceries.” Of course, our brains can decline as we grow older for lots of reasons — including other environmental influences or genetic factors. Still, continuing to challenge (30) mentally and keeping your mind busy can only help. 【答案】 21. as 22. assessed23. to take 24.had held25. at26. that 27. but28.requiring 29. have to30. yourself 【难度】中等
2020届上海市七宝中学高三三模数学试题
2020届上海市七宝中学高三三模数学试题 注意事项： 1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上 第I 卷（选择题） 请点击修改第I 卷的文字说明 一、单选题 1．设a 、b 分别是直线a 、b 的方向向量，则“a ∥b ”是“a ∥b ”的（ ） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件 D ．既非充分又非必要条件 2．某学校有2500名学生，其中高一600人，高二800人，高三1100人，为了了解学生的身体健康状况，采用分层抽样的方法，若从本校学生中抽取100人，从高一和高二抽取样本本数分别为a 、b ，且直线480ax by ++=与以(1,1)A -为圆心的圆交于B 、 C 两点，且120BAC ∠=?，则圆C 的方程为（ ） A ．22(1)(1)1x y -++= B ．22(1)(1)9x y -++= C ．22(1)(1)4x y -++= D ．22(1)(1)3x y -++= 3．函数2cos(2)26 y x π =+ -的图像按向量a 平移后所得图像的函数解析式为 ()y f x =，当函数()f x 为奇函数时，向量a 可以等于（ ） A ．(,26 )π - B ．(),26 π - C ．( 212 ,)π - D ．()212 ,π - 4．已知F 为抛物线2 4y x =的焦点，A 、B 、C 为抛物线上三点， 当0FA FB FC ++=时，则存在横坐标2x >的点A 、B 、C 有（ ） A ．0个 B ．2个 C ．有限个，但多于2个 D ．无限多个 第II 卷（非选择题）
2017-2018年上海市七宝中学高一下开学考数学试卷及答案
2018年七宝中学高一下开学考试卷 2018.03 一. 填空题 1. 函数()lg(23)x x f x =-的定义域为 2. 已知集合{1,0,}A a =-，{||1|1}B x x =-<，若A B ≠?，则实数a 的取值范围是 3. 函数2 1 46 y x x = -+的值域为 4. 不等式33(1log )(log )0x a x +->的解集是1(,9)3 ，则实数a 的值为 5. 若函数()f x 的图像过点(1,2)，则1 ()1f x --的图像经过点 6. 设m R ∈，若43 ()(1)1f x m x mx =+++是偶函数，则()f x 的单调递减区间是 7. 关于x 的方程9(4)310x x a ++?+=有实数解，则实数a 的取值范围为 8. 已知函数1 ()ln(1) 1 a x f x x x ?≥? =? -且1a ≠，b R ∈），()1 g x x =+，若对任意实数x 均有 ()()0f x g x ?≤，则有 13 a b +的最小值为 11. 211 {|,1}k A y y kx x kx k ==+ ≤≤，其中2,3,,2018k =???，则所有k A 的交集为 12. 设单调函数()y p x =的定义域为D ，值域为A ，如果单调函数()y q x =的值域是 D ， 函数(())y p q x =的值域是A ，则称函数()y q x =是函数()y p x =的一个“保值域函数”， 已知定义域为[,]a b 的函数2 ()|3| h x x = -，函数()f x 与()g x 互为反函数，且()h x 是 ()f x 的一个“保值域函数”， ()g x 是()h x 的一个“保值域函数”，则b a -=
上海市七宝中学2018-2019学年高一上学期10月月考数学试题
上海市七宝中学2018-2019学年高一上学期10月月 考数学试题 学校_________ 班级__________ 姓名__________ 学号__________ 一、填空题 1. 不等式的解集为________； 2. 已知集合，，则_________. 3. 设，则是成立的________条件； 4. 不等式的解集为________； 5. 已知集合，，若，则实数a的取值范围是____________. 6. 已知，若，则或”是_______命题（填“真”或“假”）. 7. 关于的不等式的解集为，则实数的取值范围是 __________ 8. 已知，，若，则实数的取值范围是________； 9. 已知关于的不等式有解，则实数的取值范围是 ________；
10. 已知关于的方程的两个根，，且在区间上恰好有两个正整数解，则实数的取值范围是________. 11. 定义区间，，，的长度均为，多个区间并集的长度为各区间长度之和，例如的长度，设，，其中表示不超过的最大整数， ．若用表示不等式解集区间的长度，则当 时，________； 12. 对于集合，定义函数，对于两个集合，，定义集合．已知，，用 表示有限集合中的元素个数，则对于任意集合，的最小值为________； 二、单选题 13. 已知为非零实数，且，则下列命题成立的是 A．B． C．D． 14. 设集合A=若A B,则实数a,b必满足 A．B． C．D． 15. 已知函数，且，，集合 ，则下列结论中正确的是（） A．任意，都有B．任意，都有 C．存在，都有D．存在，都有
16. 设，，.记集合，，若、分别表示集合，的元素个数，则下列结论不可能的是（） A．，B．， C．，D．， 三、解答题 17. 已知关于的不等式：． （1）当时，求此不等式的解集； （2）当时，求此不等式的解集． 18. 命题甲：关于的方程有两个相异负根；命题乙：不等式 对恒成立． （1）若这两个命题至少有一个成立，求实数的取值范围； （2）若这两个命题有且仅有一个成立，求实数的取值范围． 19. 若存在满足下列三个条件的集合，，，则称偶数为“萌数”： ①集合，，为集合的个非空子集，，，两两之间的交集为空集，且；②集合中的所有数均为奇数，集合中的所有数均为偶数，所有的倍数都在集合中；③集合，，所有元素的 和分别为，，，且．注：． （1）判断：是否为“萌数”？若为“萌数”，写出符合条件的集合，，，若不是“萌数”，说明理由． （2）证明：“”是“偶数为萌数”成立的必要条件． 20. 已知集合，． （1）求集合； （2）若，求实数的取值范围； （3）若，求实数的取值范围；
19年上海高三英语4+19七宝中学高三英语试题解析
2019届七宝中学高三英语模考卷 ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ ________ ________ ________ ________ ________ ________ ________ ________ _________ 核心词汇词性转换 1. distribute [dis’tribju:t] vt.分发;分布——_______________(n.) 2. disturb [dis’t?:b] vt.打扰,扰乱——________________(n.) [da?’v??s] a.不一样的,相异的——________________(n.) [d?’mestik] a.本国的;家庭的——________________(v.驯养) [drai] a/vt 干的，弄干——_________________(n.干旱) ‘i:g?/ a.渴望的——________________(n.) i’fi??nt/ a.效率高的——________________(n.) ‘emf?saiz/ vt.强调，着重——________________(n.) in’dju?/ vt.忍受;容忍——________________(n.) 10. enthusiasm/ in’θju:zi?z?m/ n.热情——________________(n.激情者)——________________(a.) 11. environment/ in’vai?r?nm?nt/ n.环境——________________(n.环保人士) 12. establish/ is’t?bli?/ vt.建立，设立;确立——________________(n.)——________________(a.) 13. evolve/ i’v?lv/ vt.使进化——________________(n.) 14. e xceed/ ik’si:d/ vt.超过，胜过——________________(n.)——________________(a.) 15. exist/ ig’zist/ vi.存在——________________(n.)——________________(a.) 16. expose/ iks’p?uz/ vt.使暴露——________________(n.) 17. fertile [?f?:ta?l] a.肥沃的——________________(v.施肥)——________________(n.肥料)
2019-2020年上海市七宝中学高一上期中数学试卷
2019-2020年上海市七宝中学高一上期中 一. 填空题 1. 已知集合，，且，则实数的取值范围是{|2019}A x x =≤{|}B x x a =>A B =R U a 2. 若集合，，若，则实数 {1,3}M =-2{3,21,2}N a a a =-++{3}M N =-I a =3. 命题“若不为零，则、都不为零”的否命题是 a b ?a b 4. 科技节期间，高一年级的某同学发明了一个魔术盒，当任意实数对进入其中时，会(,)a b 得到一个新的实数：，如把放入其中，就会得到，现将21a b +-(3,2)-23(2)13?+--=实数对放入其中，得到实数，则 (,3)m m -9-m =5. 设函数，若，则 211()211 x x f x x x ?+≤=?+>?0()3f x =0x = 6. 已知函数，则 () f x =() g x =()()f x g x ?=7. 已知不等式的解集中有且只有5个整数，则实数的取值范围是 |1|x m -
2020届上海市七宝中学2017级高三上学期期中考试英语试卷及解析
2020届上海市七宝中学2017级高三上学期期中考试 英语试卷 ★祝考试顺利★ Ⅱ. Grammar Directions: After reading the passage below, fill in he blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blanks with the proper form of the given word; for the blanks,use one word that best fits each blank. When I worked part-time in a local bookstore at my early age -- so easily - pictured, if you do not work in one, as a kind of paradise where not only ____1____ one read his own favorite books but also encounter charming young ladies (one of my personal fantasies) who browse eternally among Toni Morrison or Ernest Hemingwast thing that chiefly struck me was that really bookish people are a rarity, ____2____ there are vast numbers of those who consider themselves to be such. Often they will introduce themselves when they enter the bookshop ____3____ ‘book people’ and insist on telling you that ‘we love books’. They will wear T-shirts or carry bags with slogans explaining exactly how much they think they adore books. It is clear that the was they dress themselves is quite similar to that of us bookish people, but that is ____4____ the similarities between them and us begin and end. And ____5____ (sure) means of identifying them is that they never, ever buy books. These days it is so rare that I find time to read that, when I do, it feels like indulgence, more so than any, other sensory experience. When an important relationship in my twenties ____6____ (break) up the only thing I could do was to read, and I amassed a pile of books ___7___ I sank and escaped from the world around me and inside me. The landscapes of Yu Hua,
2021届上海市闵行区七宝中学高三上学期期中考试数学试题(解析版)
2020-2021年七宝中学高三期中考数学试卷 一、填空题 1.已知全集U R =，集合{} 12A x x =->，则U C A =_________. 2.若函数2()(4)4,(5)f x x x =-+≥，则1 (5)f -=_________. 3. () 2 14732lim n n n →∞ +++ +-=_________. 4.已知数列{}n a 为等差数列，且191,25a a ==-，则5a =_________. 5.设函数2 ()41f x x mx =-+在(],2-∞上是减函数，则实数的取值范围是_________. 6.已知222a b +=，则a b +的取值范围是_________. 7.若函数()2sin sin 2f x x x =-在区间[]0,a 上的零点个数为3个，则实数a 的取值范围是_________. 8.已知两变量x 、y 之间的关系为lg()lg lg y x y x -=-，则以x 为自变量的函数y 的最小值是_________. 9.已知函数()x f x a b =-（0a >且1,a b R ≠∈），()1 g x x =+若对任意实数x 均有()()0f x g x ?≤，则 14 a b +的最小值为_________. 10.设函数()sin()(0,0)6 f x A x A π ωω=- >>，[]0,2x π∈若()f x 恰有4个零点，则下述结论中：① 0()()f x f x ≥恒成立，则0x 的值有且仅有2个；②存在0ω>，使得()f x 在80,19π?? ???? 上单调递增；③方 程1 ()2 f x A = 一定有4个实数根，其中真命题的序号为_________. 11.函数11 ()22 f x x =- ≤≤的图像绕着原点旋转弧度θ(0)θπ≤≤，若得到的图像仍是函数图像，则θ可取值的集合为_________.
2019届上海市七宝中学高三上学期摸底考试数学试题(解析版)
2019届上海市七宝中学高三上学期摸底考试数学试题 一、单选题 1．若,a b 为实数，则“01ab <<”是“1 b a <”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 【答案】D 【解析】【详解】 若“0＜ab ＜1”，当a ，b 均小于0时，b ＞1a 即“0＜ab ＜1”?“b ＜1 a ”为假命题； 若“b ＜ 1a 当a ＜0时，ab ＞1，即“b ＜1a ”?“0＜ab ＜1”为假命题，综上“0＜ab ＜1”是“b ＜1 a ”的既不充分也不必要条件，故选D 2．若函数()2sin()f x x ω=在区间[,]54 ππ -上存在最小值2-,则非零实数ω的取值范围是（ ） A ．(,2]-∞- B ．[6,)+∞ C ．5(,2][,)2-∞-+∞U D ．15 (,][6,)2 -∞-+∞U 【答案】C 【解析】先根据x 的范围求出x ω的范围,根据函数()f x 在区间[,]54 ππ -上存在最小值2-,然后对ω大于 0和小于0两种情况讨论最值,即可求得非零实数ω的取值范围. 【详解】 Q 函数()2sin()f x x ω=在区间[,]54 ππ - ①当0>ω时,,54x ππωωω?? ∈- ??? ? Q 函数()2sin()f x x ω=在区间[,]54 ππ -上存在最小值2- ∴ 5 2 π π ω- ≤- 可得:52 ω∴≥ ②当0ω<时,,4 5x π πωωω??∈-? ??? Q 函数()2sin()f x x ω=在区间[,]54 ππ -上存在最小值2- ∴ 4 2 π π ω≤- 可得:2ω≤-
【市级联考】上海市七宝中学2018-2019学年高一上学期数学期中考试
【市级联考】上海市七宝中学2018-2019学年高一 上学期数学期中考试 学校_________ 班级__________ 姓名__________ 学号__________ 一、填空题 1. 函数的定义域为________ 2. 已知集合，，则________ 3. 不等式的解集是________ 4. “若且，则”的否命题是__________________． 5. 已知，则的取值范围是________ 6. 若，，且，则的取值范围是_ 7. 若关于的不等式对一切实数都成立，则实数a 的取值范围是_________________． 8. 若函数，则________ 9. 若关于的不等式在上恒成立，则实数的最小值是__
10. 已知函数，（），若不存在实数使得和同时成立，则的取值范围是________ 11. 当时，可以得到不等式，，，由此可以推广为，则________ 12. 已知数集（，）具有性质：对任意、（），与两数中至少有一个属于集合，现给出以下四个命题：①数集具有性质；②数集具有性质；③若数集具有性质，则；④若数集 （）具有性质，则；其中真命题有________（填写序号） 二、单选题 13. 如图，为全集，、、是的三个子集，则阴影部分所表示的集合是（） A．B． C．D． 14. 下列各组函数中，表示同一函数的是（） A．与 B．与 C．与 D．（）与（）
15. “若a，b∈R＋，a2＋b2<1”是“ab＋1>a＋b”的( ) A．充要条件B．必要不充分条件 C．充分不必要条件D．既不充分也不必要条件 16. 汽车的“燃油效率”是指汽车每消耗1升汽油行驶的里程，下图描述了甲、乙、丙三辆汽车在不同速度下的燃油效率情况. 下列叙述中正确的是 （） A．消耗1升汽油，乙车最多可行驶5千米 B．以相同速度行驶相同路程，三辆车中，甲车消耗汽油最多 C．甲车以80千米/小时的速度行驶1小时，消耗10升汽油 D．某城市机动车最高限速80千米/小时. 相同条件下，在该市用丙车比用乙车更省油 三、解答题 17. 设集合，集合. （1）若“”是“”的必要条件，求实数的取值范围； （2）若中只有一个整数，求实数的取值范围. 18. 练习册第21页的题“，，求证：”除了用比较法证明外，还可以有如下证法： （当且仅当时等号成立），∴.