摘要:(1)设a.n∈N*.a≥2.证明:,

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1.C   2.A   3.B   4.D   5.C   6.B   7.D   8.C   9.B  10.A

  11.120°   12.3x+y-1=0   13.   14.10    15.100    16.(1),(4)

17.解:(1)设抛物线,将(2,2)代入,得p=1. …………4分

∴y2=2x为所求的抛物线的方程.………………………………………………………5分

(2)联立 消去y,得到. ………………………………7分

设AB的中点为,则

∴ 点到准线l的距离.…………………………………9分

,…………………………11分

,故以AB为直径的圆与准线l相切.…………………… 12分

(注:本题第(2)也可用抛物线的定义法证明)

18.解:(1)在△ACF中,,即.………………………………5分

.又,∴.…………………… 7分

(2)

. ……………………………14分

(注:用坐标法证明,同样给分)

19.

解法一:(1)连OM,作OH⊥SM于H.

∵SM为斜高,∴M为BC的中点,∴BC⊥OM.

∵BC⊥SM,∴BC⊥平面SMO.

又OH⊥SM,∴OH⊥平面SBC.……… 2分

由题意,得

设SM=x,

,解之,即.………………… 5分

(2)设面EBC∩SD=F,取AD中点N,连SN,设SN∩EF=Q.

∵AD∥BC,∴AD∥面BEFC.而面SAD∩面BEFC=EF,∴AD∥EF.

又AD⊥SN,AD⊥NM,AD⊥面SMN.

从而EF⊥面SMN,∴EF⊥QS,且EF⊥QM.

∴∠SQM为所求二面角的平面角,记为α.……… 7分

由平几知识,得

,∴

,即所求二面角为. ……………… 10分

(3)存在一点P,使得OP⊥平面EBC.取SD的中点F,连FC,可得梯形EFCB,

取AD的中点G,连SG,GM,得等腰三角形SGM,O为GM的中点,

设SG∩EF=H,则H是EF的中点.

连HM,则HM为平面EFCB与平面SGM的交线.

又∵BC⊥SO,BC⊥GM,∴平面EFCB⊥平面SGM. …………… 12分

在平面SGM中,过O作OQ⊥HM,由两平面垂直的性质,可知OQ⊥平面EFCB.

而OQ平面SOM,在平面SOM中,延长OQ必与SM相交于一点,

故存在一点P,使得OP⊥平面EBC. ……………………… 14分

 

∵底面边长为1,∴

.    ……………… 1分

平面SBC的一个法向量

∴y=2h,n=(0,2h,1).… 3分

=(0,1,0),由题意,得.解得

∴斜高. …………………………………………………… 5分

(2)n=(0,2h,1)=

由对称性,面SAD的一个法向量为n1. ………………………………6分

设平面EBC的一个法向量n2=(x,y,1),由

,得

 解得.………………… 8分

设所求的锐二面角为α,则

,∴.…………… 10分

(3)存在满足题意的点.证明如下:

. ………………………… 11分

,令与n2共线,则. ……………… 13分

.故存在P∈SM,使OP⊥面EBC.……………………… 14分

20. 解:(1)当n为奇数时,an≥a,于是,. ………………3分

         当n为偶数时,a-1≥1,且an≥a2,于是

=. …………6分

(2)∵,∴公比.……9分

. …………………………………………10分

(注:如用求和公式,漏掉q=1的讨论,扣1分)

 . ……………12分

.……15分21.解:(1)∵,∴,∴. 1分

,即,∴. …3分

①当,即时,上式不成立.………………………………………………4分

②当,即时,.由条件,得到

,解得. ……………………………………………5分

,解得.…………………………………………6分

 m的取值范围是. ………………………………………7分

(2)有一个实根.………………………………………………………………………………9分

,即

,则

. ………………………10分

 △>0,故有相异两实根

,∴ 显然

,∴,∴. …………12分

于是

                    

为三次函数的极小值点,故与x轴只有一个交点.

∴  方程只有一个实根.…………………………15分

Neatly putting an emphasis on his storytelling skill is how writer Mo Yan began his Nobel Lecture in Literature speech, “Storyteller”, on Friday (Saturday, Beijing time) in Stockholm.

For 40 minutes he talked about his mother’s   36  on him as a person and a writer, his literary inspirations, and how he   37  with the controversy(争论)that followed the announcement of his Nobel victory.

He told his audience that as a boy he told stories to cheer up his mother, and   38  that poverty and loneliness fueled his imagination as a writer after he grew up.   39 , authors such as William Faulkner and Gabriel Garcia Marquez   40  him, he said, especially their bold and unlimited writing style.

“A person should be   41  in daily life, but follow one’s instinct(本能)and take control when it   42  to literary creation.”

He said the soul of   43  all of his works is the boy in Transparent Carrot who has an almost superhuman ability to bear   44 . He added that he also tried to make his hometown of Gaomi in Shandong Province a microcosm(缩影)of China and even the   45 .

His greatest challenge, he said, was writing novels that deal with   46  realities.

“In writing about the dark aspects of society there is a(n)  47  that emotions and anger allow politics to limit literature.”

He said literature must be   48  on real life but go beyond it.

He also mentioned the   49  surrounding his selection as Nobel winner, saying he was showered with many flowers.   50  he was a target for “stone throwers”.

“At first I thought I was the   51  of the controversies, but over time I’ve come to realize that the real target was a person who had   52  to do with me.”

Mo   53  his lecture by saying he was made to feel like an actor in a play with all the attention he was   54 , but he had decided that the best way to communicate his thoughts was to   __55  writing.

1.                A.affection        B.influence       C.occasion  D.position

 

2.                A.agreed         B.fought          C.dealt D.did

 

3.                A.added          B.warned         C.reminded D.imagined

 

4.                A.However       B.Otherwise       C.Therefore D.Besides

 

5.                A.preserved      B.inspired        C.entertained   D.taught

 

6.                A.confident       B.certain         C.comfortable   D.modest

 

7.                A.goes           B.comes          C.turns D.gets

 

8.                A.nearly          B.hardly          C.scarcely  D.always

 

9.                A.danger         B.suffering        C.relieving  D.happiness

 

10.               A.city            B.village          C.world D.province

 

11.               A.social          B.economical      C.agricultural D.cultural

 

12.               A.encouragement  B.danger         C.advantage D.event

 

13.               A.insisted        B.spent          C.based D.passed

 

14.               A.contradiction    B.contest         C.contrary   D.controversy

 

15.               A.Meanwhile      B.Otherwise      C.However  D.Instead

 

16.               A.goal           B.intention       C.target D.purpose

 

17.               A.somebody      B.anything        C.nothing   D.anybody

 

18.               A.adopted        B.concluded      C.admitted  D.concerned

 

19.               A.throwing       B.accepting       C.offering   D.receiving

 

20.               A.carry on        B.take on         C.bring out  D.put out

 

 

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For the last couple of weeks, I had been stuck in front of my computer working on a project that was very important to me. My every waking hour was consumed by the project and although I imagined that I would feel happy after completing parts of the project, I was confused to find that instead, I was feeling rather depressed. I tried a range of methods to help cheer myself up. I had a relaxing bath, cooked a delicious meal to enjoy with my family and even watched a lighthearted movie, but to no avail. It was only when I turned to meditation(沉思)for a solution that the answer came to me: turn to nature!
The very next day, I grabbed my camera and a bottle of water and set off to spend a few hours walking in a nature reserve, even though it was pouring with rain. Within a couple of minutes I felt alive again. To be honest, I felt like a young school girl again and had to stop myself from hopping along the path singing, "I'm singing in the rain", a song I used to sing when I was a child. I think as adults we often try too hard to control our inner children and as a result we restrain(限制) our own spirits, which only leads to depression and stress.
Interestingly, it has been shown that people who spend 40 minutes walking in a nature reserve have a drop in their blood pressure levels, but this does not happen when they spend a similar amount of time walking in a busy city centre.
If you feel a little low in spirit and know that you have spent too much time indoors, relax completely, remove your shoes and let your inner child come out and play.
【小题1】The author felt depressed because she __________.

A.couldn't consume her waking hour
B.had not seen a film for a long time.
C.had not finished her work on time
D.had worked on a hard job for too long
【小题2】The author walked in a nature reserve in the rain in order to__________.
A.take photosB.find a solution to the project
C.hop along the pathD.cheer herself up
【小题3】The underlined part "to no avail" in Paragraph 1 probably means " __________.".
A.unsuccessfulB.unrelatedC.uninterestingD.unexpected
【小题4】In the author's opinion, __________.
A.a bath can make people relaxed
B.depression is usually caused by hard work
C.walking in a busy city centre harms people's health
D.adults should express their inner feelings freely
【小题5】The last paragraph mainly serves as a(n) __________.
A.explanationB.suggestionC.introductionD.reminder

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It was a cold evening and my daughter and I were walking up Broadway.I didn’t notice a guy sitting inside a cardboard box.But Nora did.She wasn’t even four, but she  36  at my coat and said, “That man’s cold, Daddy,  37  we take him home?”

I don’t remember my reply.But I do remember a sudden  38  feeling inside me.I had always been delighted at how much my daughter noticed in her  39 , whether it was  40  in flight or children playing.But now she was noticing  41  and beggary.

A few days later, I saw an article in the newspaper about volunteers who picked up a food package from a nearby school on a Sunday morning and  42  it to an elderly person.It was quick and easy.I  43  us up.Nora was  44  about it.She could understand the importance of food, so she could easily see how  45  our job was.When Sunday came, she was ready, but I had to  46  myself to leave the house to fetch the food package.On the way to the school, I fought an urge to turn  47 .The Sunday paper and coffee were waiting for me at home.Why do this?  48 , we phoned the elderly person we’d been appointed.She  49  us right over.

The building was in a bad state.Facing us was a silver-haired woman in an old dress.She took the package and asked us to come in.Nora ran inside.I unwillingly followed. 50  inside, I saw that the apartment belonged to someone poor.Our hostess showed us some photos.Nora played and when it came time to say good-bye, we three hugged, I walked home in tears.

Professionals call such a(n) 51  a “volunteer opportunity”.They are opportunities, and I’ve come to see.Where else but as volunteers do you have the opportunity to do something  52 that’s good for others as well as for yourself? Nora and I regularly serve meals to needy people and  53  clothes for the homeless.Yet, as I’ve  54  her grow over these past four years, I still wonder ------ which of us has  55  more?

1.                A.pulled          B.glanced         C.pointed   D.aimed

 

2.                A.would          B.need           C.can  D.must

 

3.                A.general         B.heavy          C.funny    D.simple

 

4.                A.area           B.part            C.eyesight  D.world

 

5.                A.insects         B.animals         C.plants    D.birds

 

6.                A.coldness        B.suffering        C.illness    D.ignorance

 

7.                A.delivered       B.returned        C.devoted  D.posted

 

8.                A.held           B.hurried         C.lined D.signed

 

9.                A.casual          B.sorry           C.astonished D.excited

 

10.               A.valuable        B.creative        C.shocking   D.simple

 

11.               A.push           B.stop           C.allow D.warn

 

12.               A.away          B.back           C.up   D.out

 

13.               A.Therefore      B.Obviously       C.Still   D.Also

 

14.               A.called          B.promised       C.invited    D.helped

 

15.               A.Although       B.Though         C.Because   D.Once

 

16.               A.visit           B.stay           C.adventure D.challenge

 

17.               A.fair            B.famous         C.difficult   D.enjoyable

 

18.               A.wear          B.make          C.order D.collect

 

19.               A.let            B.watched        C.made D.noticed

 

20.               A.increased       B.tried           C.benefited  D.seized

 

 

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The Museum: The Charles Dickens Museum in London is the world's most important collection of material relating to the great Victorian novelist and social commentator.The only surviving London home of Dickens (from 1837 until 1839) was opened as a museum in 1925 and is still welcoming visitors from all over the world.On four floors, visitors can see paintings, rare editions, manuscripts, original furniture and many items relating to the life of one of the most popular and beloved personalities of the Victorian age.       

Opening Hours

◇ The Museum is open from Mondays to Saturdays 10:00-17:00; Sundays 11:00-17:00.

◇ Last admission is 30 minutes before closing time.

Special opening times can be arranged for groups, who may wish to book a private view

Admission Charges: Adults: £5.00; Students: £4:00; Seniors: £4.00; Children: £3.00; Families:£14.00( 2 adults & up to five children)

Group Rates: For a group of 10 or more, a special group rate of £4.00 each applies.

Children will still be admitted for £3.00 each,

Access: We are constantly working to improve access to the Museum and its collection.Our current projects involve the fitting of a wheelchair ramp for better access, a customer care kit and an audio tour for visitors with impaired (受损的) vision.Our Handling Sessions are also suitable for the visually impaired.The Museum has developed an online virtual tour through the Museum.Click here to visit all the rooms in the Museum online.

Hire the Museum: The Museum can be hired for private functions, performances soirees(社交晚会)  and many other social occasions.

Find Us: The Museum may be reached by using the following buses: 7, 17, 19, 38, 45,46, 55, 243.And by these underground services: Piccadilly Line; Central Line.For a map, please click here.The British Museum and the Foundling Museum are within walking distance.

1.The passage is probably from a(n)          .

A.book   B.website   C.newspaper        D.announcement

2.Compared to going there separately, if a family with two adults and five children go to the Museum together they will save

A.£25.00   B.£14.00   C.£ 9:00       D.£11.00

3.In the Charles Dickens Museum, people can not find          .

A.paintings                B.rare editions     C.manuscripts    D.cars

4.According to the passage, which of the following statements is TRUE?

A.The Museum is not very far from the British Museum.

B.In any case people cannot visit the Museum after 17:00.

C.Visitors with poor vision cannot enjoy the Museum.

D.Anyone cannot hire the Museum for other users.

5.The passage is written to         .

A.persuade readers to visit London.

B.inform readers about the history of the Charles Dickens Museum.

C.offer readers some information about the Charles Dickens Museum.

D.tell readers how to make use of the Charles Dickens Museum.

 

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He drove after drinking alcohol, having a severe accident and had to get his arms removed.Since then, he has had to __31__ on his younger brother, who became his shadow, never leaving him alone for years. Except for writing with his toes, he was totally unable to do __32__ else. As the two brothers grew up together, they had their own problems and would often __33__. Finally, his younger brother went away and lived __34__, leaving him heartbroken and at a loss what to do.
__35__, a misfortune befell(降临)a girl. One night she was preparing dinner when the kerosene light on the stove was overturned, __36__ in a fire which took her hands away. Having decidedly __37__ her sister’s willingness to help her, she determined to be thoroughly __38__. At school, she always studied hard.Most of all she learned to be self-reliant. “I am lucky. Though my __39__ are broken, my heart can still fly.” she wrote in her blog.
One day, the young man and the girl were both invited to a(n)__40__ programme. The boy told the television hostess about his __41__ future, whereas the girl was full of __42__ for her life. They were both asked to write something on a piece of paper with their __43__. The boy: My younger brother’s arms are my arms. The girl: Broken wings, flying heart.
They had both gone through the same ordeal(痛苦经历), but their different __44__   determined the nature of their lives. As seems the case, __45__ disasters can strike our life at any time. How you handle the __46__ when faced with it is the true __47__  of your character. If you choose to __48__ or escape from the ordeal, it will follow you wherever you go. But if you decide to be strong, the __49__ will turn out to be a fortune on which new __50__will arise.

【小题1】
A.liveB.standC.relyD.assist

1,3,5

 
【小题2】
A.somethingB.everythingC.nothingD.anything

【小题3】
A.quarrelB.shareC.supportD.dislike
【小题4】
A.happilyB.lonelyC.separatelyD.disappointedly
【小题5】
A.UnfortunatelyB.UnexpectedlyC.SimilarlyD.Naturally
【小题6】
A.leadingB.bringingC.causingD.resulting
【小题7】
A.turned toB.turned downC.turned offD.turned against
【小题8】
A.aloneB.freeC.independentD.successful
【小题9】
A.armsB.wingsC.dreamsD.promises
【小题10】
A.interviewB.radioC.sportsD.health
【小题11】
A.hopefulB.uncertainC.brightD.miserable
【小题12】
A.calmnessB.enthusiasmC.patienceD.excitement
【小题13】
A.handsB.strengthC.toesD.mouths
【小题14】
A.charactersB.desiresC.opinionsD.attitudes
【小题15】
A.unexpectedB.passiveC.roughD.serious
【小题16】
A.emergencyB.misfortuneC.difficultyD.accident
【小题17】
A.testB.reflectionC.displayD.problem
【小题18】
A.ignoreB.resistC.complainD.suffer
【小题19】
A.problemB.resultC.failureD.hardship
【小题20】
A.solutionsB.waysC.rewardsD.hopes

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