摘要:A.

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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

A. “Better road design and training hold the key to cycle safety”, the new Transport Secretary said today as he pledged to restore Britain’s safety record. Patrick McLoughlin told Conservative Party Conference that while cycling was enjoying a post-Olympics boom, the number of casualties among cyclists was also rising. “But the number of accidents has gone up too. That means it needs better design and better education too.” Mr McLoughlin said in his first speech as Transport Secretary. 
B.  Cycling in the UK will become safer through “sheer weight of numbers,” the founder of one of the world’s leading cycle brands has said as he backed The Times’s Cyclesafe campaign. Simon Mottram, founder and chief executive of Rapha, has added his support to 40 cross-party MPs who have signed a letter urging David Cameron to use his speech at the Conservative Party Conference to promote measures to make the streets safer for cyclists.
C.  Commuters who cycle to work face an increased danger as the casualty toll during peak hours rose by 10 percent last year. The rate at which cyclists were killed or seriously injured rose sharply last year, official figures showed yesterday.
D.  In future decades, Londoners will look back on the way cyclists jostled with buses and lorries on major roads as an absurd anachronism. Some risks are unavoidable. But other risks survive only because we are too slow to embrace bold solutions. That is the message from designers who are proposing an ambitious plan to create cycle lanes suspended above London’s busiest streets. London is one of the most dangerous places in the world for cycling. “SkyCycle” would remedy that problem by attaching dedicated cycle paths to existing railway viaducts.
E.  Money should be apportioned from the funding for major transport projects, such as the new Forth Crossing, to create a pot of cash for cycling, campaigners have told MSPs. Cycle groups have given warning that not enough money is being put into routes and promotion. They want the Scottish government to take a percentage of the funding allocated to key national projects and create an “active transport” fund to be distributed gradually.
F.  We’d like you to tell us why you love cycling by sending a photo of yourself, a family member or friend with their bike and a note about why it is so brilliant. To take part, instagram your photo with the hashtag #ilovemybike or email it to us at ilovemybike@thetimes.co.uk. We’ll post the best pictures here ilovemybike.tumblr.com.
请阅读以下信息,并为他们匹配合适的新闻内容。
【小题1】“Cycle lanes in the sky” answer to traffic danger
【小题2】More cyclists are seriously injured on Britain’s roads
【小题3】Share a picture of you and your bike and help us promote the fun and freedom of cycling
【小题4】“Weight of numbers” will bring safe cycling
【小题5】Transport Secretary calls for better road design and training to help cyclists

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A.DETECTIVES ABROAD
Read about the lives of real detectives. This monthly magazine brings you up-to-date true stories about real life of detectives as they chase criminals across continents. Find out how some of the most dangerous criminals in the world are caught by some of world’s finest detectives. Follow their routes on the free map which comes with every issue.
B. WORLD TRAVEL
This weekly magazine can bring the world to your home. Have you ever wondered what the Chinese eat for breakfast? Did you know that the Sahara Desert is getting bigger every year? This fascinating magazine, full of color photographs, is your window on the world.
C. ONLY 16
Every week well-known writers bring you the latest teenage love stories. Each magazine carries three full-length stories as well as cartoons and color pictures of your favorite film stars.
D. EUROPE NEWS
The weekly magazine keeps you in touch with what’s happening. Filled with facts and figures about almost everything you can think of, plus articles by our regular writers on the week’s most interesting news stories. Special back page sums up the news for the busy readers.
E. OLD SCHOOLHOUSE
The magazine is approximately 200 pages, full color, and packed with support and fun! Columns: Creation Answers with AiG’s Ken Ham, Resource Room for special needs home schooling with Christine Field, Diana Waring’s History column, our Finishing the Race (High School) department, and Show and Tell – where readers share their own detailed methods and curriculum choices.
F. CRIME AND CRIMINALS
These exciting short stories are written by well-known crime writers. Every magazine brings you the best in criminal thrillers, stories are so good that you won’t be able to put the magazine down. And every month we leave one crime unanswered so that you, that reader, can play detective.
请阅读以下读者的信息,然后匹配读者和适合他/她的杂志:
【小题1】Emi is a university student studying Italian and Politics. She doesn’t have much time to read anything very detailed but she is looking for something with plenty of news and information.
【小题2】Carrie is sixteen years old and loves spending time listening to pop music and lying on her   bed reading. She is always interested in finding out more about some of the stars in the world of pop and fashion.
【小题3】Bill travels a lot when he was younger. Now that he has stopped his work, he enjoys reading about foreign people, places and customs even if he has already visited that part of the world.
【小题4】 Leroy used to be a detective. He still takes an active interest in the work of the police, but these days he enjoys reading fictions after years spent chasing real criminals.
【小题5】Brigitte has a five-year-old daughter and after several talks with her husband, she is considering to educate their daughter at home. She would like a magazine to learn about this new trend.

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A.The great impact and progress in genetic engineering
B.Worries about privacy protection
C.Worries about medical use of genetic engineering
D.Genetic knowledge helps to predict diseases
E.Genetic knowledge may not be properly used
AB.The application of genetic engineering in the medical fields
 
【小题1】__________
Current research into the human gene system is helping us understand why people have predispositions(易患某病倾向)to certain diseases.Knowing our genetic makeup can help us to judge whether or not we may be stricken by particular illness, such as cancer.Even before birth, we are able to do genetic screenings to determine what a child's genetic disorder will be.Scientists have already isolated and identified the genes responsible for the more than 4,000 genetic diseases that affect human beings.
【小题2】__________
The implications of this knowledge are astonishing. In addition to predicting genetic predisposition towards diseases, gene therapies may provide new treatments or cures for serious diseases.Millions of people already use genetically engineered drugs to treat heart disease, cancer, AIDS, and strokes (中风). But with the research that is now being conducted, we may find cures to many more diseases.In the near future, genetic experimentation will also allow parents to select the traits of their children. Genetic traits that determine height, weight, eye and hair color will be able to be controlled, and many parents are excited about this potential.
【小题3】__________
Many people, however, are unwilling to accept the possibilities genetic research allowsFor example, one reason some women do not use the largest genetic testing for breast cancer is because they are afraid they will be discriminated against.Another problem is that many people do not want to discover their weakness.What if they learn that they have a disease for which there are no medical cures? How will such knowledge affect their lives? Do people really want to know what they will die of?
【小题4】__________
Many people believe that history has not always shown human decision-making to be bright when it comes to ethical(道德的)choices. Jeremy Rifkin is probably the most well known opponent of genetic engineering. He believes that humans are not responsible enough to experiment with genes and should not “play God” He asks, “Just because it can be done, does that mean it should be done?” He points out that our society will eventually look and act the same if parents select the traits of their children, and he questions the desirability of such a society.
【小题5】.__________
One of the fears expressed about genetic experimentation involves privacy. Already blood sample taken from patients in hospitals have been used for genetic research without the patients’ permission. Most people would agree that one’s health and genetic makeup are private concerns. But if insurance companies gain access to this information, it could have a large impact on insurance coverage or costs; if employers gain access to the information, it could have a large impact on hiring or promotion decisions. The possibilities for discrimination are obvious.

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A.American & British Classics
A classic is a literary work which has stood the test of time. Generations of readers have turned to classics to discover that which is ever-lasting. Through both the works themselves and the people they mirror, we may better be able to see ourselves.
B. Creative Writing
Creating Writing does not only provide us with an opportunity to express ourselves, but also holds our attention to word choice, paragraph development, and other skills useful in writing.
C. Technical Writing
It's a course which can help you to improve your communication skills in, for arid through technology.
D. Journalism
It's a course for seniors, in which we will cover how 10 gather, write and report the news. We will discuss how information is, or can be organized.
E. Non-fiction
The course is a study of non-fiction through reading many different types of non-fiction. The course will also be about the possible changes in journalistic reporting and the sharing of personal stories of various people on various topics such as travel and adventure.
请阅读以下学生的相关信息,然后匹配和他/她拟要选择的课程:
【小题1】______. Lucy .wants to become a famous reporter in the world. She is eager to have the course which can help her to realize her dream.
【小题2】_____. Sally's vocabulary is very large, but she can not organize what she write well, which makes her writing illogically. She wants to get some more skill of it.
【小题3】_____. Lily can not know how to communicate with others as a. writer. She needs to improve the skill of it badly.
【小题4】_______. Jenny wants to become a writer of biography. Therefore, she wants to choose a course connected with it.
【小题5】_______. Mary is interested in Mark Twain, especially his novels which arc full of humors. She really want to know some other writers who were born in the same country as Mark Twain was.

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A.American & British Classics
A. classic is a literary work which has stood the test of time. Generations of readers have turned to classics to discover that which is ever-lasting. Through both the works themselves and the people they mirror, we may better be able to see ourselves.
B. World Literature
World Literature examines the common people found in quality literature worldwide, in these worlds, we find not only what is unique to each culture but what is universal,
C. Creative Writing
Creating Writing does not only provide us with an opportunity to express ourselves, but also holds our attention to word choice, paragraph development, and other skills useful in writing.
D. Technical Writing
It's a course which can help you to improve your communication skills in, for arid through technology.
E. Journalism
It's a course for seniors, in which we will cover how 10 gather, write and report the news. We will discuss how information is, or can be organized.
F. Non-fiction
The course is a study of non-fiction through reading many different types of non-fiction. The course will also be about the possible changes in journalistic reporting and the sharing of personal stories of various people on various topics such as travel and adventure.
请阅读以下学生的相关信息,然后匹配和他/她拟要选择的课程:
【小题1】Lucy .wants to become a famous reporter in the world. She is eager to have the course which can help her to realize her dream.
【小题2】Sally's vocabulary is very large, but she can not organize what she write well, which makes her writing illogically. She wants to get some more skill of it.
【小题3】Lily can not know how to communicate with others as a. writer. She needs to improve the skill of it badly.
【小题4】Jenny wants to become a writer of biography. Therefore, she wants to choose a. course connected with it.
【小题5】Mary is interested in Mark Twain, especially his novels which arc full of humors. She really want to know some other writers who were born in the same country as Mark Twain was.

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