摘要:(2)等比数列{an}中..前n项的和为An.且A7.A9.A8成等差数列.设.数列{bn}前n项的和为Bn.证明:Bn<.

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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

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[1]One thing Britain is famous for is pubs, and no trip to the UK would be complete without a visit to one of the thousands of pubs across the country.

[2] Pubs play an important part in the social structure of the country. They are places where all ages and social classes mix to talk, do business, or just spend a couple of quiet hours before heading home in the evening.

[3] There are many different types of beer available in pubs. Traditional British beer is called bitter, or ale, and is usually served at room temperature. As a result, the British are famous for their ‘warm beer’ ! If you prefer a cold beer, ask for lager. This beer is a light yellow in color whereas bitter is usually a darker brown. All beers are served as pints (500ml) or haves (250ml). To order, you need to ask for a pint or half, and then name the beer. So, you could say “          ”.

[4]Wine, red or white, is normally available in all pubs, as are spirits such as whisky, gin or vodka.

[5]It is not, however, necessary to drink alcohol. Non-alcoholic drinks are called soft drinks. You can have juice, lemonade or cola, among others.

[6]If you visit a pub in a group, it is important to pay for your ‘round’. This means that you buy a drink for everyone in your group.  Not buying your round is a big social mistake! Remember that you need to order and pay for your drinks at the bar.

[7]So, follow these tips if you want to get the most out of visiting a pub, and, “cheers!”

1.What is the best title of the passage? (Please answer within 10 words.)

2.Which sentence in the passage can be replaced by the following one?

If you don’t buy a drink for everyone in your group, you are socially wrong.

3.Please fill in the blank in the third paragraph with proper words or phrases to complete the sentence. (Please answer within 1 words.)

4.If you are in a pub, what would you like to drink? Why? (Please answer within 20 words.)

5.Translate the underlined sentence in the second paragraph into Chinese.

 

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First it was jogging. Then aerobics(有氧运动). Not too long ago, Americans discovered race walking.
Now Americans are into a new fitness craze. They’re taking up bicycling. Over hills and down mountainsides and across quiet country roads, Americans are busily rolling along.
The number of adults who ride for fitness is around 17 million, an increase of 70 percent over four years ago. Twice as many women as men are coming to the sport. Americans are falling in love with biking because it has speed, the benefits of jogging and beautiful scenery.
Bicycling is a very appropriate sport, which is important to people who injured their knees while jogging or whose joints are aching from aerobics. And biking is a real awakening for people who have been into race walking in the past. Race walking is as dull as watching paint dry.
The most popular kind of bicycle for people who are new to the sport is the mountain bike, which has a fixed frame with wide tires and upright handles. Mountain bikes also have many gears(齿轮) to make it easier to climb hills. About 5 million Americans ride mountain bikes, compared with 200,000 who rode them only five years ago.
Costs range from about $130 for a bottom-of-the-line bicycle to more than $2,700 for an expensive bicycle.
Mountain biking has attracted some people who race down the sides of mountains like a bat out of hell. But most riders ride slowly and they rarely venture far from home.
The biking craze has brought an unexpected profit(盈利) to clothing and bicycle accessory(附属品)makers. Last year, bikers paid $630 million for biking clothes and accessories.
Bicycling seems likely to continue its fantastic growth.
53. Race walking is about as dull as watching paint dry because _______         
A. race walking is a slow-moving sport
B. the number of adults who ride for fitness has grown 70 percent in four years.
C. it has speed, the benefits of jogging and beautiful scenery.
D. Americans are taking up bicycling.
54. The bicycling craze has been a profit for _______.
A. people who want to ride like a bat out of hell
B. bicycle accessory makers
C. race walkers
D. twice as many women as men
55. What does the underlined word “bottom-of-the-line” mean?
A. poor       B. modern    C. old        D. cheapest
56. The main idea of the article is _______
A. riding a bicycle is one of the most dangerous sports in America
B. Americans are rolling along
C. bicycling is the latest fitness craze to hit America
D. most people in America want to own a hand-made bicycle that can cost more than 2,700

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The Chinese New Year is a great holiday to choose to celebrate Chinese culture with your child. Here are few fun ways to bring a bit of fun and   1   into your home through the festivities of the Chinese New Year.

1.Add a lucky red door. Red is a traditional color of   2  . It's an important part of the Chinese New Year to   3  on doing what one can to bring about good luck for the New Year. If you don't want to  4   the door red, how about wrapping it up like a present with red wrapping paper. If changing your front door's color is not workable, how about the door to your child's bedroom?

2.Eat. A huge part of most cultures is that of food and the Chinese New Year is not   5  , it's eating jiaozi at midnight on New Year's Eve, or longevity noodles on day seven of the festivities to    6  long life. The Chinese New Year celebrations mean many fancy meals that your child will   7  .

3.Create a lantern. Sara Naumann, the Guide to China Travel, shares a bit about the legend of the Lantern Festival or Yuanxiao, which occurs on the   8  day of the Chinese New Year festivities. It's a   9  that includes an emperor, a young woman who misses her family, and tricking the God of Fire. Your kids should love this story. After   10  it with them, or while reading the story, enjoy making your own paper lantern to display.

4.Give lucky money. The Guide to Mandarin Language shares that another very popular   11  during the Chinese New Year is that of the gift of red envelopes with   12  in them. These gifts are given to children and usually follow a bit of superstition(迷信) in that the money needs to be given in even amounts and never contain   13  numbers, such as four. Therefore, four dollars is not a good gift. The envelopes are also decorated with lucky symbols and New Year   14  .

5.Give a small gift. The giving of simple gifts is also an appropriate way to   15  the Chinese New Year. What better gift than that of a children's book about the Chinese New Year or the Chinese Culture.

6.Make some noise. Just like in America, the Chinese use   16  in ringing in their New Year. In the Chinese culture it began as a way to   17   away any demons(鬼) that threaten to bring a profitable and lucky New Year, but today it's also about excitement and   18  . Consider setting off a few firecrackers of your own, if allowed in your area. If not, make a cute firework picture with a bit of glitter and glue. A pretend firecracker is another great craft that could also be considered a festive way to decorate your New Year table.

7.Sing Happy Birthday to your dog. The second day of the Chinese New Year is   19  the birthday of all dogs. Why not   20  your child to throw Fido a birthday celebration? Perhaps an extra ride in the car or new chew toy is in order? I know my dog would appreciate a few extra belly rubs too.

(    ) 1. A. tradition           B. culture             C. civilization       D. habit

(    ) 2. A. wealth              B. disaster             C. belief                      D. luck

(    ) 3. A. focus                      B. accuse              C. adapt               D. mind

(    ) 4. A. boil                 B. paint               C. wash               D. purchase

(    ) 5. A. same               B. similar             C. common           D. different

(    ) 6. A. come about       B. take about        C. bring about       D. get out

(    ) 7. A. bore                 B. destroy             C. enjoy                      D. absorb

(    ) 8. A. last                  B. first                 C. second              D. next

(    ) 9. A. play                 B. story               C. novel                      D. history

(    ) 10. A. sharing           B. listening           C. reading             D. making

(    ) 11. A. invention               B. story               C. race                 D. tradition

(    ) 12. A. food                      B. clothes             C. money              D. jewels

(    ) 13. A. unclear           B. unlucky            C. unfair                   D. uncertain

(    ) 14. A. wishes            B. signs               C. presents            D. happiness

(    ) 15. A. spend             B. envy               C. buy                  D. celebrate

(    ) 16. A. firecrackers     B. songs                      C. dances              D. goods

(    ) 17. A. take                      B. scare               C. get                   D. burn

(    ) 18. A. fun               B. relax               C. sleep               D. travel

(    ) 19. A. fixed                  B. named              C. considered               D. marked

(    ) 20. A. order              B. accompany       C. tease               D. Allow

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                            B

  What is language for? Some people seem to think it's for practicing grammar rules and learning lists of words—the longer the lists,the better. That's wrong. Language is for the exchange(交流)of ideas and information. It's meaningless knowing all about a language if you can't use it freely. Many students I have met know hundreds of grammar rules, but they can't speak correctly or fluently. They are afraid of making mistakes. One shouldn't be afraid of making mistakes when speaking a foreign language. Native speakers make mistakes and break rules, too. Bernard saw once wrote, "Foreigners often speak English too correctly." But the mistakes that native speakers make are different from those that Chinese students make. They're English mistakes in the English language. And if enough native speakers break a rule, it is no longer a rule. What used to be wrong becomes right. People not only make history, they make language. But a people can only make its own language. It can't make another people's language. So Chinese students of English should pay attention to grammar, but they shouldn't overdo(做过头)it. They should put communication first. 

1.Language is used to ________.

A. express oneself           B. practice grammar rules

B. talk with foreigners only    D. learn lists of words

2.Generally, when an American or an Englishman speaks English, he ________.

A. never makes mistakes           B. often makes mistakes

C. can't avoid making mistakes      D. always makes mistakes

3."Foreigners often speak English too correctly. "This sentence means that ________.

A. foreigners speak correct English

B. foreigners speak incorrect English

C. foreigners speak English according to the grammar rules

D. foreigners never make mistakes when they speak English

4.If too many native speakers break a rule, ________.

A. what they use will become right  B. they are against the law

C. they should say sorry to others  D. they will become heroes

5.When we speak a foreign language, we should ________.

A. speak in Chinese way       B. speak by the rules

C. speak to native speakers   D. not be afraid of making mistakes

 

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