摘要:9. 若a>0.b>0.a3+b3<2a2b.则的取值范围是

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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

Shakespeare's Birthplace and Exhibition of Shakespeare's World

ADMISSION:

Adult  £4.90

Child  £2.20

Family £12.0

 (2 adults+up to3 children)

    

OPENING TIMES:

20 Mar to 19 Oct

Mon to Sat: 9:00am to 5:00pm

Sun:9:30am to 5:00pm

20 Oct to 19Mar

Mon to Sat:9:30am to 4:00pm

Sun:10:00am to 4:00pm

Welcome to the world-famous house where William Shakespeare was born in 1564 and where

he grew up. The property(房产) remained in the ownership of Shakespeare’s family until 1806. The house has welcomed visitors travelling from all over the world, for over 250 years.

◆ Enter through the Visitors’ Centre and see the highly-praised exhibition Shakespeare’s World, a lively and full introduction to the life and work  of Shakespeare.

Stand in the rooms where Shakespeare grew up.

Discover examples of furniture and needlework from Shakespeare’s period.

Enjoy the traditional(传统的)English garden, planted with trees and flowers mentioned in the poet’s works.

◆ The Birthplace is within easy walking distance of all the car parks    shown on the map; nearest is Windsor Street(3 minutes’ walk).

◆ The House may present difficulties but the Visitors’ Centre, its  exhibition, and the garden are accessible(可进入的)to wheelchair users.

◆  The Shakespeare Coffee House (opposite the Birthplace).

How much is the admission for a family of two grown-ups and two children?

A. £9.80   B. £12.00  C. £14.20  D. £16.40

Where is the nearest parking place to Shakespeare’s Birthplace?

A. Behind the exhibition hall.    B. Opposite the Visitors’ Centre.

C. At Windsor Street.           D. Near the Coffee House.

A wheelchair user may need help to enter         .

A . the House     B the garden    C  the Visitor’s Centre    D. the exhibition hall

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  When you are at odds with someone close to you, the One-Minute Drill can show you how to express your feelings effectively – and how to listen more skillfully. All it requires is two individuals who are committed to improving their relationship.

  Set aside at least ten minutes, and then sit facing each other. Decide who will be the Talker and who will be the Listener. It makes no difference, because later you will change roles.

How to perform the One-Minute Drill

  For approximately 30 seconds, the Talker can say anything he or she wants. Your job will be to express your thoughts and feelings. You can discuss problems you've had a hard time talking about. Remember to limit yourself to about 30 seconds. When the Talker finishes, the Listener will summarize what the Talker just said, as well as how the Talker was feeling inside, as accurately as possible.

  The Talker now gives the Listener a grade between 0 and 100 per cent to indicate how accurate the summary was. If the rating is 95 per cent or more, you can change roles; the new Talker can continue with the same topic or move on to something entirely new.

  However, if the grade is below 95 per cent, the Talker should point out what the Listener missed or got wrong, and repeat the process until the overall rating is 95 per cent or more. Then you can change roles and repeat the exercise for as long as you both like.

How it works

  Thirty seconds of emotionally charged information is sufficiently challenging for anyone. Express your feelings in strong, clear, direct language, but as your partner will be listening attentively, you won't need to shout, exaggerate or put your partner down.

  The Listener should sit and listen respectfully without interrupting. Look into your partner's eyes, but avoid using negative body language. If you like, take a few notes.

  So the Talker might say: "When I come home from work, I feel tired and I need some quiet time. But you tell me I'm supposed to spend time with the kids. This makes me feel frustrated. I work hard and I'm exhausted at the end of the day. I feel like I deserve a little time to relax, not listen to more demands."

  In response, the Listener might summarize like this: "You just told me that you feel exhausted when you come home at night because you've been working hard all day. When I tell you I want you to spend time with the kids, you feel frustrated and ticked off because you're tired and you need time to relax. You see me as very demanding, and you're probably feeling like I don't appreciate you."

  The first time you attempt the One-Minute Drill, you may get a low score. Don't worry, because you'll get up to speed quickly. Once you've tried this exercise a few times, you'll find that you can nearly always get ratings of 95 per cent or better on the first or second try.

Who is the One-Minute Drill intended for?

A. Those who are to act some roles in a certain play for the first time in their life.

B. Those who are preparing for the interview in order to make a good first impression.

C. Those who have difficulty communicating with their colleagues or family members.

D. Those who have troubled relationships with their friends or family members and try to improve them.

Which of the following is NOT true?

A. In the One-Minute Drill, the Talker and the Listener change roles in the process.

B. The Talker should talk about his / her thoughts and feelings in a brief way.

C. The Listener should listen carefully, respectfully and later summarize accurately.

D. After the Talker finishes talking, the Listener is to give him / her a grade.

From the example given in “How it works,” we can guess that the talk might be between _____.

A. husband and wife   B. father and son   C. mother and daughter   D. sister and brother

What does the underlined part “ticked off” probably mean in this reading?

A. fast asleep                           B. very angry

C. burst into tears                   D. marked with a symbol

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Thousands of people began pouring into Pennsylvania from other states.They wanted to buy lottery tickets.The tickets cost only ﹩0.9 each.But that small spending could bring them a reward of ﹩90 million.That was the second largest lottery jackpot(积累奖金)in history.

More than 87 million tickets were bought for the Pennsylvania lottery drawing.Those who bought tickets had to choose seven numbers from 1 to 80.The chance of winning was one in 9.6 million.But that little chance certainly didn’t affect ticket sales.In the last few days before the drawing, tickets were selling at the unbelievable rate of 500 per second.

Experts say many people buy lottery tickets because they just want to have a piece of the action.Others say the lottery is a stock market for poor people.It allows them to dream about wealth they’ll probably never have.

But many people believe lotteries are no better than legalized(合法化的) gambling.Some critics note that most people who play are poor and may not be able to afford the tickets.There are also many addicts who take the game seriously.They may pour their life savings into lottery tickets.Some clubs have been formed to help them kick the habit.

Politicians like lotteries because they provide money that would otherwise have to come from new taxes.The profits from lotteries are usually used to pay for education or programs for senior citizens.But critics say this arrangement just allows states to legalize vice(恶习), under the name of social progress.No matter whether you regard state lotteries right or not, you cannot refuse to accept their extreme popularity with many Americans.

1.The main idea of the passage is that      

A.lotteries are of great benefit to everyone who buys them

B.playing a lottery is just like investing in the stock market

C.a lot of people buy lottery tickets, but lotteries cause disagreement

D.lotteries are just legalized vice

2.Which of the following is TRUE according to the passage?

A.Politicians like lotteries because they don’t have to pay extra tax.

B.The popularity of lotteries in America actually is social progress.

C.Some critics don’t like lotteries because many poor people waste their money on them.

D.People love the lottery because it is a stock market.

3.In just one hour in the last few days, the Pennsylvania lottery sold tickets totaling    

A.$1.62million    B.﹩90million     C.﹩9.6million  D.﹩87million

4.People who are addicted to playing lotteries should        

A.join a club                                                        B.kick the habitw.

C.win the Pennsylvania                                      D.save every cent

 

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阅读下列短文,从每题所给的四个选项(A、B、C和D)中,选出最佳选项,并在答题卡上将该项标号涂黑。

A

HIGHFIELD COMPREHENSIVE SCHOOL

SCHOOL REPORT

Form Teacher:  G. Baker            Pupil’s Name:  Simon Watkins

Term:         Summer 2010   Form:         Ⅳ B

Subject

Exam

Class work

Comments

English

59

61

Simon has reached a satisfactory standard but now needs to apply himself with more determination.

Mathematics

77

85

Sound work and progress throughout the year. Well done!

History

46

53

A disappointing exam result. He is unable to give attention to this subject for long.

Chemistry

78

85

His obvious ability in the subject was not fully reflected in his exam work, but I have high hopes for him nevertheless.

Physics

86

94

An excellent term’s performance. He goes from strength to strength. A born scientist, I feel.

Biology

57

60

This time next year he will be taking the “0” exam. He needs to concentrate on the work, not on class conversation.

French

41

46

Clearly he didn’t bother to revise. His general attitude is far too casual.

Physical

Education

/

31

Weak. It’s time he exercised his body more and his voice less. He should try to work with a team.

FORM TEACHER’S REMARKS                  HEADMASTER

Basically satisfactory work and progress              I shall be keeping an eye on his

though he will now have realized, I hope, that          progress in his weaker subjects

in certain subject areas he needs to make speedy        though his success in the sciences is

improvement.                                   most pleasing.

According to the comments of the Physical Education teacher, Simon    .

    A.is too talkative in the class

    B.likes to work with his classmates

    C.doesn’t exercise his body at the right time

    D.becomes weak because he doesn’t exercise at all

Which of Simon’s subjects will attract the headmaster’s attention in future?

    A. Biology and Maths.   B.History and French.

    C. English and Chemistry.   D. Physics and Physical Education.

Which of the following statements best describes Simon?

    A. He has made great progress in language classes.

    B. His potential has been fully reflected in science classes.

    C. His grade in maths makes him a born scientist.

    D. He needs to improve his attitude on certain subjects.

Based on the school report, which of the following statements is true?

A. Simon didn’t bother his teacher to revise French.

B. Basically, Simon did a good job in science.

C. Simon is a determined learner in English.

D. Simon is able to pay attention to history for long.

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Ad.1  April fool’s party

On Friday, April 1, Inner Affair goes back to the days of funk! Classic Tunes from the 70’s and 80’s by DJs Den & Sion.9 pm till late.

Tickets:Free entrance for those in costume, otherwise 50 yuan(US $6)

Time/date:9pm, April 1

Place:Inner Affair, 1/F Qiankun Dasha, 6 Sanlitun xiliujie, Chaoang District

Tel:8454-0321

Ad.2  Language in use

Enjoy free in-house coffee, tea and beer as well as music and dancing.Practice your Chinese, make friends and have fun.

Time/date:7 to 9 pm, March 25

Place:Language In Use Club, 2/F, Science Fortune Centre, 8 Xueqing Lu, north of Xueyuan Lu, Haidian District.

Ad.3  The “worst ” party

Organized by 0-zone productions, the party is set to be “the worst ever,” with the lamest music from the 60s, 70s and 80s.Special prizes will be awarded to the worst dressed or for bad fashion sense.

Tickets:Free entrance

Time/date:9 pm, April 1

Place:Pula Pula, Tianze Lu, Oriental Seven Colors Plaza, Chaoyang District

Ad.4  La Nuit Francaise

Again on the 2nd Thursday of the month La Nuit Francaise will be held at Le Rendezvous.The monthly event is an opportunity for all French people and everyone interested in France of speaking French to gather together.

The evening features three glasses of wine and canapés for participants and a special exhibition.

Time/date:7 to 10pm, April 14

Place:Le Rendez-vous, 3 Gongti Beilu, across from the Pacific Century Plaza Chaoyang

Ad.5  Marco V

Dutch DJ Marco V drops by Banana for a gig which is supported by Hong Kong’s DJ Spark.

Marco V has been around for many years, as an inventive, style-blending deejay and successful and devoted producer.His spinning is energetic, crowd-pleasing and never sees an empty dance floor.He was ranked No 15 in this year’s international DJ MAG DJ Top 100.

Tickets:40 yuan (US $ 4.80) in advance, 50 yuan(US$6) at the door, both include a free drink.

Which of the following is NOT True of Ad.1and Ad.3 ?

A.The two parties will be held on the same day.

B.The two parties will be held at the same time.

C.The entrance fees of the two parties will not be charged.

D.Some old music will be played at the parties.

Which of the following is intended for the Chinese learners?

A.Marco V                              B.La Nuit Francaise

C.Language in use                      D.The “worst” party

Which of the following events takes place every month?

A.Marco V                              B.La Nuit Francaise

C.The “worst” party                      D.Language in use

We can infer that _____.

A.Marco V is a newly-established band

B.La Nuit Francaise may be French words

C.The “worst” party will attract a lot of college students

D.You will enjoy free drink at April fool’s party

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