【英语】2018-2019学年复旦附中高二上

【英语】2018-2019学年复旦附中高二上
【英语】2018-2019学年复旦附中高二上

复旦大学附属中学2018学年第一学期

高二年级英语期末考试试卷

II.Grammar and Vocabulary

Section A

21.The real art of conversation is not only to say the right thing at the right place but to leave ________the wrong thing at the ________ moment.

A.unsay … tempted

B.unsay … tempting

C.unsaid … tempted

D.unsaid … tempting

22.Though he never disguised his leadership ambitions, he continued to deny that ________ to challenge the Prime Minister.

A.he had no intention

B.he had every intention

C.it was not his intention

D.it was his intention

23.Studying is the action of ________ to acquire knowledge, either by directly observing phenomena of interest, or by reading the writings of others about these phenomena.

A.proceeding

B.attempting

C.tending

D.managing

24.Some Western countries have long ________ that Iran aims to create a nuclear bomb, but Teheran said the materials were only for civil use.

A.suspected

B.doubted

C.wondered

D.convinced

25.Privilege comes from Latin privilegium, meaning a law for just one person, and means a benefit enjoyed by an individual or group ________ what’s available to others.

A.within

B.considering

C.despite

D.beyond

26.Think to yourself that every day is your last and the hour to which you do not look forward may come as a(n) ________ surprise.

A.welcomed

B.welcoming

C.welcome

D.unwelcome

27.Among all pastimes, gathering around and listening to mother or father read a good story can almost bring a family ________ together.

A.closer

B.closest

C.the closer

D.close

28.I’m afraid your type of humor might be a little ________ in such a formal meeting.

A.out of character

B.out of context

C.out of use

D.out of place

29.He had one mistress to whom he was faithful to the day of his death: Music. Not for ________ moment did he ever give up what he believed, or what he loved.

A.a single

B.the slightest

C.quite a

D.the very

30.The most striking trait of Americans is that they always seem to be in a hurry. ________ is this more evident than in their eating habits – sitting down to a leisurely meal seems to be a luxury.

A.Barely

B.Only

C.Nowhere

D.Eventually

31.Crying and talking about emotional pain are the most effective ways to get rid of the heavy feeling that haunts you, so don’t ________ your tears or zip your lips about your distress.

A.hold back

B.set back

https://www.360docs.net/doc/197299657.html,ugh away

D.burst into

32.The autobiography(自传) of the happiest man would not be a record of sensational or exciting experiences, but ________ composed of simple and plain incidents or routines.

A.it is

B.which is

C.one that

D.one

33.General Eisenhower once told his soldiers that what ________ not necessarily the size of the dog in the fight – it’s the size of the fight in the dog.

A.is counted

B.counts is

C.is counted is

D.to count is 上海高中生

34.Scientists have suggested a solution to cutting down greenhouse effect: planting an area ________ the US with trees, which, when mature, would consume as much carbon dioxide as is being released.

A.of the size of

B.the size of

C.as the same size as

D.the same size of

35.________ to a colorful campus culture, students should draw a line between what is their major concern and what is of ________ importance.

A.Exposing … the least

B.Having exposed … least

C.Having been exposed … the less

D.Exposed … less

36.The use of the telescope to observe the heavens close up has made ________ great increase of our knowledge of the starts.

A.possible

B.it possible

C.possibly

D.it possibly

37.China is a racially mixed country, in which various ethnic(民族) groups bring their own unique flavors to each corner of the country, which adds ________ people’s table.

A.to great variety of

B.great variety to

C.to a great variety of

D.the great variety to

38.Once upon a time, with roots that go back to medieval marketplaces ________ stalls(货摊) that functioned as stores, shopping offered a way for people to get socially connected.

A.featuring

B.featuring in

C.featured

D.featured in

39.The development of pills often owe ________ to science – we started with a drug that we hoped would be effective in heart disease and we ended up with a medicine that was highly effective against nerve disorder.

A.much chance

B.much chance as

C.much to chance as

D.as much to chance as

40.Which of the following sentence have “save ” of the same meaning as that in “The grownups, less excitable, save their own presents till breakfast time.”

A.I had a bottle of champagne which I’d been saving for a special occasion.

B.Your eyes don’t water with fresh air, which saves you a lot in paper tissues.

C.If you lent me £5, it would save me a trip to the bank.

D.Safety may mean more time and trouble but it may save a lot of heartbreak in the home.

Attitudes toward new technologies often fall along generational lines. That is, generally, younger people tend to (41)________ older people on the front end of a technological shift.

It is not always the case, though. When you look at attitudes toward driverless cars, there doesn’t seem to be a clear (42)________ divide. The public overall is split on whether they’d like to use a driverless car. In a study last year, of all people surveyed, 48 percent said they wanted to ride in one, while 50 percent did not.

The fact that attitudes toward self-driving cars appear to be so (43)________ across generations suggests how transformative the shift to driverless cars could be. Not everyone wants a driverless car now—and no one can get one yet—but among those who are open to them, every age group is (44)________ engaged.

Actually, this isn’t surprising. Whereas older generations are sometimes reluctant to adopt new technologies, driverless cars (45)________ real value to these age groups, especially to those with

(46)________ mobility or difficulty driving on their own.

This is especially interesting when you consider that younger people are generally more interested in travel-related (47)________ than older ones.

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When it comes to driverless cars, differences in attitude are more (48)________ based on factors not related to age. College graduates, for example, are particularly interested in driverless cars compared with those who have less education: 59 percent of college graduates said they would like to use a driverless car compared with 38 percent of those with a high-school diploma or less.

Where a person lives (49)________, too. More people who lived in cities and suburbs said they wanted to try driverless cars than those who lived in rural areas.

While there’s reason to believe that interest in self-driving cars is going up across the board, a person’s age will have little to do with how self-driving cars can become (50)________. Once driverless cars are actually available for sale, the early adopters will be the people who can afford to buy them.

III.Reading Comprehension

Section A Cloze Test.

Technological life is and will be a series of upgrades and the rate of advancement is increasing. If we are honest, we must admit that one aspect of the __51__ upgrades and eternal becoming of the technium(技术元素) is to make holes in our heart. One day not too long ago we (all of us) decided that we could not live another day __52__ we had a smart phone; a dozen years earlier this need would have __53__ us. Now we get angry if the network is slow, but before, when we were __54__, we had no thoughts of the network at all. We keep inventing new things that make new __55__, new holes that must be filled.

Some people are furious that our hearts are pierced(刺穿) __56__ by the things we make. They see this ever-neediness as a devaluing of human nobility, the source of our __57__ discontent. I agree that technology is the source. The momentum of technologies pushes us to chase the __58__, which are always disappearing beneath the arrival of the next newer thing, so satisfaction continues to retreat from our __59__.

But I celebrate the never-ending discontent that technology brings. We are different from our animal ancestors in that we are not __60__ to merely survive, but have been incredibly busy __61__ new itches that we have to scratch, new desires we’ve never had before. This is the trigger for our ingenuity and growth.

We cannot expand our self, and our collective self, __62__ making holes in our heart. We are __63__ our boundaries and widening the small container that holds our identity. It can be painful. Of course, there will be rips and tears. Late-night infomercials(信息广告) and endless web pages of about-to-be-out-of-date gizmos(新玩意儿) are hardly uplifting techniques, and the path to our __64__ is very boring, and everyday. When we imagine a better future, we should factor in this constant __65__. 51.

A. ceaseless

B.effortless

C.meaningless

D.regardless 52.

A. whether

B.once

C.while

D.unless 53.

A. dismayed

B.astonished

C.delighted

D.bothered 54.

A. tactless

B.humble

C.innocent

D.suspicious 55.

A. longings

B.findings

C.understanding

D.warnings 56.

A. thus

B.yet

C.even

D.rather 57.

A. half-hearted

B.continual

C.peculiar

D.social 58.

A. wildest

https://www.360docs.net/doc/197299657.html,tter

C.newest

D.utmost 59.

A. grasp

B.era

C.sight

D.share 60.

A. allowed

B.content

C.privileged

D.spontaneous 61.

A. wrapping up

B.smoothing over

C.carrying out

D.making up 62.

A. through

B.against

C.without

D.despite 63.

A. defining

B.stretching

C.overstepping

D.marking 64.

A. enlargement

B.formation

C.sensation

D.pleasure 65. A. demand B.tolerance https://www.360docs.net/doc/197299657.html,panion D.discomfort

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Section B

(A)

Westley said to me in a whisper: “God damn! I’m tired of sitting here. Let’s get up and be saved.” So he got up and was saved.

Then I was left alone on the mourners’ bench. My aunt came and knelt at my knees and cried, while prayers and songs circled, all around me in the little church. The whole room prayed for me alone. And I kept waiting quietly for Jesus, waiting, waiting – but he didn’t come. I want to see him, but nothing happened to me. Nothing!

“Langston, why don’t you come? Why don’t you come and be saved? Oh, Lamb of God! Why don’t you come?”

Now it was really getting late. I began to be ashamed of myself, holding everything up so long. I began to wonder what God thought about Westley, who certainly hadn’t seen Jesus either, but who was now sitting proudly on the platform, swinging his legs and grinning down at me, surrounded by deacons(教堂执事) and old women on their knees praying. God had not struck Westley dead for lying in the temple. So I decided that maybe to save further trouble, I’d better lie, too, and say that Jesus had come, and get up and be saved. So I got up.

Suddenly the whole room broke into a sea of shouting, as they saw me rise. Waves of rejoicing swept the place. Women leaped in the air. My aunt threw her arms around me. The minister(牧师) took me by the hand and led me to the platform.

When things quieted down, in a hushed silence, interrupted by a few joyous “Amens,” all the new young lambs were blessed in the name of God. Then happy singing filled the room.

That night, for the last time in my life but one – for I was a big boy twelve years old – I cried. I cried, in bed alone, and couldn’t stop. I buried my head under the quilts, but my aunt heard me. She woke up and told my uncle I was crying because the Holy Ghost had come into my life, but I was really crying because I couldn’t bear to tell her that I deceived everybody in the church, that I hadn’t seen Jesus, and that now I didn’t believe there was a Jesus any more, since he didn’t come to help me.

66.I attended a special ceremony ________.

A.to be saved by Jesus and blessed

B.to become a member of the church

C.to celebrate the appearance of Jesus

D.to be given judgment for my sin

67.________, I got up at last.

A. Afraid of being struck dead by God

B.Eager to join Westley sitting on the platform

C. Ashamed of delaying the coming of God

D.Guilty of causing trouble to all the others

68.What can be inferred about the new young lambs in the service?

A.There were all saved by the God.

B.They all committed a sin.

C.They all saw Jesus except Westley and me.

D.They all deserved God’s blessing.

69.I cried that night because I was _________.

A.forced to accept a merciless God

B.conscience-stricken at cheating before God

C.more a saved lamb than a liar

D.deprived of my belief in the existence of Jesus

(B) Finally, a dictionary with a soul.

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Our dictionary was written for humans, by humans. Look up a word, and you’ll read a friendly explanation that you’ll actually remember. It’s as if your favorite teacher were explaining it to you.

Real world examples, hot off the press.

Read thousands of example sentences from current newspapers, magazines, and literature. We show you how words live in the wild and give you usage tips so that you’re more confident about using the words you learn.

Try the world’s smartest, fastest dictionary.

Find the word you’re looking for faster than with any other online dictionary. Just start typing a word and our dictionary will display the most likely results. We want you to find the word’s definition as quickly as possible, without having to look through a lot of clutter.

Start playing

As you play V https://www.360docs.net/doc/197299657.html,, we figure out which words you know and which ones you need a little help with. We keep practicing with you until you master the tough ones.

Let us know which words you want to focus on, and we’ll prioritize those.

As your vocabulary grows, https://www.360docs.net/doc/197299657.html, grows with you.

V https://www.360docs.net/doc/197299657.html, is a platform for lifelong learning, growing with you every step of the way. As you improve, the words that you learn will become more and more advanced. And, with our easy-to-use progress-

70.Each word item in V https://www.360docs.net/doc/197299657.html, is explained in a(n) _________ way.

A. clear and precise

B. easy-to-understand-and-remember

C. in-depth and thoughtful

D. humorous and thought-provoking

71.When a user types a word in the search box, V https://www.360docs.net/doc/197299657.html, will give is list of _________.

A. likely results for the user to choose

B. useful tips on word usages

C. most likely definitions

D. real-world examples

72.Regular users of V https://www.360docs.net/doc/197299657.html, can enjoy a(n) ________ vocabulary improvement.

A. progressive

B. personal

C. privileged

D. instant

73.What people is V https://www.360docs.net/doc/197299657.html, most suitable for to use?

A. Those who attempt long-term English learning.

B. Advanced English learners with a large vocabulary.

C.English learners who need a dictionary near at hand.

D.English teachers who want to monitor students’ progress.

(C)

Countries are failing to take the action needed to stave off the worst effects of climate change, a UN climate report has found, and the commitments made in the 2015 Paris agreement will not be met unless governments introduce additional measures as a matter of urgency.

New taxes on fossil fuels, investment in clean technology and much stronger government policies to bring down emissions are likely to be necessary. Governments must also stop subsidizing(补贴) fossil fuels, directly and indirectly, the report said.

Greenhouse gas emissions continued their long-term rise last year, according to the report, but they could be brought under control. There are promising signs, such as investment from the private sector in renewable energy and other technologies to cut carbon, but these are currently insufficient to meet scientific advice.

Global emissions have reached what the UN has called “historic levels” of 53.5 gigatonnes(十亿吨) of carbon dioxide equivalent, and are showing no signs of peaking, despite a leveling off in the past decade.

Joyce Msuya, deputy executive director of UN Environment, said: “The science is clear: for all the ambitious climate action we’ve seen, governments need to move faster and with greater urgency. We’re feeding this fire, while the means to extinguish it are within reach.”

Last month, the Intergovernmental Panel on Climate Change (IPCC) warned of the dire effects of allowing global warming to reach 1.5℃ above pre-industrial levels. The world has a little over a decade to bring down greenhouse gas emissions before such dangerous levels of warming become inevitable.

Only 57 countries, representing 60% of global greenhouse gas emissions, are on track to cause their emissions to peak before 2030. If emissions are allowed to rise beyond that, the IPCC has said countries are likely to breach the 1.5℃ limit, which will trigger sea-level rises, droughts, floods and other extreme weather events.

According to the Paris agreement, the first global pact to bind both developed and developing countries to a specific temperature goal, governments must do all they can to stop warming reaching 2℃ above pre-industrial levels, with an aspiration to limit warming to no more than 1.5℃.

Jian Liu, the chief scientist at UN Environment, said some of the necessary policies were clear and available, if there was political will to implement them. “When governments embrace fiscal(财政的) policy measures to subsidize low-carbon alternatives and tax fossil fuels, they can stimulate the right investments in the energy sector and significantly reduce carbon emissions. If all fossil fuel subsidies were phased out, global carbon emissions could be reduced by up to 10% by 2030.” 74.Which of the following ideas is NOT included in the UN climate report?

https://www.360docs.net/doc/197299657.html,ernments should stop their subsidy to the coal and petroleum industry.

B.The efforts made by the government showed some promising signs.

C.Man has been breaking the historical records of global emissions.

D.There is still hope for us to control Greenhouse gas emission.

75.How do you interpret the underlined sentence in paragraph 5?

A.The situation is dangerous and we need to do something to bring it under control.

B.Immediate fire-fighting measures should be taken to keep the fire under control.

C.We are making climate efforts but the achieved effects can be easily reversed.

D.To reduce emissions, we need to close down the fossil-fuel-powered plants.

76.Which of the following statements is True according to the Paris agreement?

A.It is desirable for humanity to limit the temperature rise within 1.5℃.

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B. Countries need to control the temperature rise within 2℃ above prehistoric level.

C. Developed and developing countries are bound by their own temperature goals.

D. Disastrous climate change will be irrecoverable if we exceed the 1.5℃ limit.

77. What does the word “dire ” mean in paragraph 4?

A. upcoming

B. hazardous

C. crucial

D. convincing

78. What’s the primary purpose of this article?

A. To show a huge gap between words and deeds in fighting global warning.

B. To present a clear picture of how Paris agreement is implemented.

C. To appeal for further global commitment to avoid disastrous climate.

D. To warn of worsening climate caused by lack of combined human effort.

Franz Kafka wrote that “a book must be the ax(斧子) for the frozen sea inside us”. I once shared this sentence with a class of seventh graders, when we’d just finished John Steinbeck’s novel Of Mice and Men . Reading the end together out loud in class, my toughest boy, a star basketball player, wept a little. They understood. When George shoots Lennie, the tragedy is that they realize it was always going to happen. In my 14 years of teaching in a New York City public middle school, I’ve taught kids with imprisoned parents, abusive parents, irresponsible parents; kids who are parents themselves; kids who are homeless; kids who grew up in violent neighborhoods. (79)_________

For the last seven years, I have worked as a reading enrichment teacher, reading classic works of literature with small groups of students from grades six to eight. I originally proposed this idea to my headmaster after learning that a former excellent student of mine had transferred out of a selective high school-one that often attracts the literary-minded children of Manhattan’s upper classes-into a less competitive setting. The daughter of immigrants, with a father in prison, she perhaps felt uncomfortable with her new classmates, who came from homes lined with bookshelves, whose parents had earned Ph. D.’s.

(80)_________

Along with Of Mice and Men , my groups read: Sounder, The Red Pony, Lord of the Flies, Romeo and Juliet and Macbeth . (81)_________ About The Red Pony, one student said, “it’s about being a man, it’s about manliness.” I had never before seen the parallels between Scarface and Macbeth, nor had I heard Lady Macbeth’s soliloquies (独白) read as raps, but both made sense; the interpretations were playful, but serious. Once introduced to Steinbeck’s writing, one boy went on to read The Grapes of Wrath and told me repeatedly how amazing it was that “all these people hate each other, and they’re all white.” (82)_________ Year after year, former students visited and told me how prepared they had felt in their first year in college as a result of the classes.

IV . Grammar

It was her notion that boys my age needed “a good thrashing” when they misbehaved. These she administered with my belt, often for what seemed to me like small offenses (1)_________ _________ coming home late for supper because I was having a good time sledding on the hill. A man had a responsibility to meet his social obligations on time. Small as she was, she (2)_________ still make the 上海高中生

snapping belt sting when it lashed across my bared legs, but I hated the indignity of these beatings so much that I refused to satisfy her with (3)_________ discreetly pretended show of tears.

My failure to cry during her “thrashings” fueled my mother’s anger, and I knew it. Tears (4)_________ (be) evidence that I had learned the lesson. My silent submission to her heaviest blows intensified her fury. If she had been a man she would have been able to make me cry for mercy, but because she was not, and because I did not weep, she struck (5)_________ (hard).

I knew that faking the tears would gratify her and end the punishment, but I refused. The injustice and humiliation of (6)_________ (beat) hurt so greatly that I deliberately accepted the worst gritted my teeth and, when the belt had fallen four or five times, muttered, “That doesn’t hurt me.” In these moments we were very close to bitter hatred of (8)_________ _________. We were two wills of iron. She was determined to break me; I was just as determined (9)_________ she would not.

In the end she was the one who always cried, and then, when she had thrown the belt aside and collapsed on a chair weeping quietly, the anger and hatred instantly drained out of me, and (10)_________ (overcome) with pity and love, I rushed to embrace and kiss her, saying “It’s all right, Mama, it’s all right. I’ll never do it again. I promise, I’ll never do it again.”

V .Summary writing

Craig Silverman, a journalist, tracked rumors circulating online in 2014 and found that shares and social interactions around fake news articles dwarfed those of the articles that debunked(戳穿) them. According to Silverman, fake news stories are engineered to appeal to people’s hopes and fears, and aren’t constrained by reality, which gives them the edge in creating shareable content.

You might think you’re immune to(对…免疫) falling for these lies, but a wealth of research disagrees. Back in the 1940s, researchers found that “the more a rumor is told, the greater is its plausibility(可信度)”. This means a rumor born out of mild suspicion can, by gaining currency, shift public thinking and opinion.

It gets worse: studies show that students tend to place enormous trust in search engines to deliver accurate results, often turning to the first result returned – a concern given that fake news can appear in the section for news stories displayed, for example, above Google’s search results.

So how can you protect yourself from digital lies? An easy step is to check who produced it. Often it is clear from the URL, that a website is pretending to be reputable by stealing the name and style of another publication. Also, take a look at the other stories on the website. Fake news websites often have nothing but fake content. If all the stories are outrageous, consider it a red flag. Finally, search for coverage of the story elsewhere, if a story is false you’ll often find it debunked on websites such as https://www.360docs.net/doc/197299657.html,. Summary: (NO MORE THAN FOUR words for each blank).

Meeting people’s (1)________________ and freed from (2)________________, fake news is found to

(3)________________ especially when (4)________________. Worse still, students

(5)________________, particularly those (6)________________ of search results. For

(7)________________, website visitors should (8)________________ and (9)________________, or

(10)________________ for verification.

VI.Text Recitation

(A)

Because of excellent weather conditions and extremely strong signals, Venusian scientists were able to get valuable information as to (1)________ ________ ________ a manned flying saucer landing on Earth.

A press conference was held at the Venus Institute of Technology.

“We have come to the conclusion, (2)________ ________ last week’s satellite landing,” Prof. Zog said, “that there is no life on Earth.”

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“How do you know this?” the science reporter of the Venus Evening Star asked.

“For one thing, Earth’s surface in the area of Manhattan (3)________ ________ ________ solid concrete and nothing can grow there. (4)________ ________, the atmosphere is filled with carbon monoxide and other deadly gases and nobody (5)________ ________ breathe this air and survive.”

“What does this mean as far as our flying saucer program is concerned?”

“We shall have to take our own oxygen with us, which means a much heavier flying saucer than we (6)________ ________.”

(B)

Maybe it would be better to say nothing but appear to be (7)________ ________ such deep pleasure that speech had escaped me. I wasn’t sure, though. I’d seen speechless gratitude in the movies too, and it never (8)________ ________ until the actors managed to cry a few quiet tears. I doubted I could cry (9)________ ________, so I began thinking about other expressions of (10)________ ________. In front of a hand-held mirror in my bedroom I tried the whole range of expressions; mouth open and eyes wide; hands (11)________ ________ ________ both cheeks to keep the jaw from falling off; ear-to-ear grin with all teeth (12)________ ________ while hugging myself with both arms.

VII.Translations.

1.难道老师不应该对所有学生一视同仁吗?(suppose)

2.考虑到你的处境,你的确很值得同情,但坦言,你的话我远不能接受。(more than)

3.没有坚决持久的行动难成大事。正由于此,史上各个领域梦想成真的巨星,寥寥无几。(come true)

4.新建的笃志楼,现代感足,设施齐备,将解决教学空间有限的问题。在投入使用之前,欢迎师生前往参观。(welcome a.)

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参考答案

II.Grammar and Vocabulary.

Section A 21-30 DDBAD CBDAC 31-40 ADBBD ABADA

Section B 41. AD 42. C 43. B 44. ABC 45. A 46. BC 47.AB

48.BD 49. AC 50. C III.Reading Comprehension

Section A 51-55 ADBCA 56-60 ABCAB 61-65 DCBAD

Section B (A)66-69 ADBD (B)70-73 BAAA (C)74-78 BCABC

Section C 79.D 80.B 81. AB 82.C

IV .Grammar

1.such as

2.could

3.a

4.would be

5.harder

6.being beaten

7.of which

8.each other

9.that 10.overcome V .Summary

(1)psychological needs

(2)the restraint of reality (3)build up its plausibility/ win readers’ trust

(4)circulating/ gaining currency (5)trust online rumors readily/ easily

(6)high on/ heading the list (7)protection (against digital lies)

(8)check a website’s URL (9)others stories on it

(10)visit debunking website VI.Text Recitation

1.the feasibility of

2.based on

3.is composed of

4.For another

5.could possibly

6.originally planned

7.shocked into

8.really worked 9.on cue 10.speechless amazement

11.slapped firmly against 12.fully exposed

VII.Translations.

1.Aren’t teachers supposed to treat all (the) students alike?

2.Considering the position/ situation you are in, you really deserve to be sympathized with, but quite frankly/ honestly, your remark is far more than I can take.

3.It’s hard to achieve anything great without firm and consistent/ constant action, because of/ owing to which great/ big stars in various fields in history are very few, whose dreams have come true.

4.The newly built Duzhi Building, of modern design and fully-equipped/ fully furnished will solve the problem of the limited space for educational use. Teachers and students are welcome to pay a visit before it is put to use. 上海高中

【12份试卷合集】上海市复旦附中2019年高二下学期物理期末模拟试卷

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复旦附中2017-2018高一下期末数学卷(答案)

n n n ? 复旦附中 2017-2018 学年高一期末数学试卷 一. 填空题 1. 在等差数列{a n } 中,若a 4 = 0 , a 6 + a 7 = 10 ,则 a 7 = ?. 答案: 6 2. 在数列1、3、7、15、??? 中,按此规律,127 是该数列的第 项. 答案: 7 3. 已知数列{a } 的前 n 项和 S = n 2 -1,那么数列{a } 的通项公式为 . ?0, n = 1 答案: ? 2n -1, n ≥ 2 4. 若在等比数列{a n } 中, a 1 ? a 2 ?? ??? a 9 = 512 ,则 a 5 = ?. 答案: 2 5. 方程(3cos x -1)(cos x + 1 3 sin x ) = 0 的解集是 . π 答案:{x | x = ±arccos + 2k π , x = - + k π , k ∈ Z } 3 6 6. 若数列{a } 满足 a = 13 , a - a = n ,则 a n 的最小值为 . n 1 答案: 23 5 n +1 n n 7. 若数列{a } 是等差数列,则数列b = a n +1 + ? ?? + a n +m (m ∈ N * ) 也为等差数列,类比上述性质,相应地,若正项 n n m 数列{c n } 是等比数列,则数列d n = ?也是等比数列 m c n +1 ? c n +2 ?? ??? c n +m 8. 观察下列式子:1+ 1 ≥ 3 ,1+ 1 + 1 + 1 > 2 ,1+ 1 + 1 + ? ?? + 1 > 5 ,…,你可归纳出的不等式是 . 2 2 2 3 4 2 3 8 2 答案:1+ 1 + 1 + ?? ? + 1 ≥ 2 3 2n n + 2 2 9. 在我国古代数学著作《孙子算经》中,卷下第二十六题是:今有物,不知其数,三三数之剩二,五五数之剩三, 七七数之剩二,问物几何?满足题意的答案可以用数列表示,该数列的通项公式可以表示为 a n = ?. 答案:105n + 23 10. 对于下列数排成的数阵: -1 4 -9 16 -25 36 -49 64 -81 100 ??? ??? ??? 它的第10 行所有数的和为 . 答案: -505 11. 对于数列{a } 满足:a = 1,a - a ∈{a , a ,?? ?, a } (n ∈ N * ) ,其前 n 项和为 S ,记满足条件的所有数列{a } n 1 n +1 n 1 2 n n n

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