摘要:8. 空间四条直线a.b.c.d.满足a⊥b.b⊥c.c⊥d.d⊥a.则必有A.a⊥c B.b⊥d C.b∥d 或a∥c D.b∥d 且a∥c

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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

 

第二节 完形填空(共20小题;每小题1.5分,满分30分)

阅读下面短文,掌握其大意,然后从36—55各题所给的四个选项(A、B、C和D)中,选出可以填入空白处的最佳选项。

I was only eight years old when the Second World War ended, but I can still remember something about the   36   celebrations in the small town where I lived on the day when the war in Europe ended. We had not   37   much from the war where, though, like most children of my age, I often saw   38   houses in the streets and the very big   39   lorries(卡车) passing through. But both at home and at school I had become   40   to the phrases “before the war” and “when the war is over”. “Before the war”, obviously,   41   had been better, though I was too young to understand why,   42   there had been no bombs then, and people had eaten things like ice cream and bananas, which I had  43   heard of. When the war was over we would go back to London, but this meant very  44   to me. I did not remember what London was like.

What I remember now  45   V-Day(victory day) was the afternoon and the evening. Some boys and girls were collecting   46  and building an enormous bonfire(篝火). We stood and watched them for a time, and then I went home and   47   myself in with my key and waited for my parents to come back from work.

It was May and still broad   48  when my mother arrived, and my father came in about an hour later. After dinner I said I wanted to   49   the bonfire, so when it got dark my father took me to the end of the street. The bonfire was very   50  , and somehow people had collected some old clothes to   51   “Hitler” with the moustache(胡子) they had put on top of it. Just as we arrived, they set light to it. The flames   52   soon. Everyone was cheering and shouting.

I stood beside my father until the   53   started to go down, not knowing what to say. He said nothing, either. He had   54   in the First World War and remembered everything he had experienced. At last he said, “Well, that’s it, son. Let’s hope that this time it really will be the   55   one.”

36. A. war                           B. victory                        C. Christmas                      D. birthday

37. A. suffered                       B. learnt                              C. heard                              D. read

38. A. crowded                  B. rebuilt                        C. bombed                          D. enlarged

39. A. modern               B. old                                    C. railway                            D. army

40. A. used                          B. devoted                          C. engaged                         D. related

41. A. food                          B. things                         C. houses                                D. news  

42. A. except that        B. now that                         C. for fear that                       D. in order that

43. A. never                        B. hardly                         C. only                                  D. already

44. A. much                        B .little                                 C. great                               D. important

45. A. about                        B. on                                     C. for                                    D. during

46. A. money                 B. wood                               C. information              D. clothes

47. A. showed               B. allowed                           C. let                                     D. called

48. A. early                         B. daylight                           C. dark                                 D. warm

49. A. see                                B. light                                 C. find                                   D. put out

50. A. high                           B. hot                                   C. dangerous                D. far

51. A. draw                         B. paint                                C. write                                D. dress

52. A. disappeared      B. happened                       C. rose                                 D. came

53. A. sun                            B. moon                               C. fire                                   D. noise

54. A. fought                 B. worked                            C. grown                        D. changed

55. A. best                          B. worst                               C. first                                  D. last

 

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    阅读下面短文,从短文后各题所给的四个选项(A、B、C和D)中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑。

Growing up for me was a challenge. I started out at primary school and was always asked by my teacher to sit at the  36  of the class because I was a fool.

   I kept  37  things: I forgot nursery songs and spellings. I was the  38  of class jokes and I was all alone and  39 . I hated school, but my dad would hear none of it. He kept telling me I was a  40 , if I believed it.

   A  41  around came one day when I remembered the  42  of the word “Cognoscenti”; a word all the other “  43 students ” had forgotten how to spell  44  they spent their free time making fun of me. I wasn’t asked to spell,  45  I raised up my hand. So I stood up and went to the front of class,  46  23 pairs of eyes staring at me. My teacher grabbed her stick, ready to hit me if I’d  47_ . I wrote the letters, spelt the word and became an instant champion. Afterwards, I  48  and won, for my school, five Spelling Bee championships.

   Secondary school had its own share of challenges. I was a tall kid and wasn’t good at any  49 , except looking. I loved basketball and tennis.  50  I held a bat(球拍), I was laughed at by my opponent. He  51  six straight sets(盘,局) without sweat and there I was, sweating like I’d run a marathon, whereas I hadn’t even  52  a single point. My dad’s  53  kept playing in my ears “Stanley, you’re a champion if you believe it.”

Believe it I did, because I wasn’t only good at tennis and basketball, I was an all-round athlete and  54  won both athletic and  55  scholarships to university.

36. A. front

B. back

C. side

D. corner

37. A. forgetting

B. leaving

C. repeating

D. using

38. A. cause

B. inventor

C. object

D. course

39. A. rootless

B. homeless

C. careless

D. friendless

40. A. champion

B. fool

C. character

D. failure

41. A. moment

B. possibility

C. turn

D. change

42. A. meaning

B. spelling

C. way

D. form

43. A. polite

B. dishonest

C. bright

D. absent-minded

44. A. once

B. while

C. when

D. because

45. A. even though

B. as though

C. in case

D. only if

46. A. for

B. as

C. with

D. before

47. A. hesitated

B. succeeded

C. lied

D. failed

48. A. presented

B. represented

C. requested

D. proposed

49. A. exercise

B. mathematics

C. sport

D. spelling

50. A. At first

B. First of all

C. The first time

D. For the first time

51. A. won

B. owned

C. missed

D. gained

52. A. reached

B. seized

C. caught

D. scored

53. A. message

B. information

C. sentences

D. words

54. A. even

B. still

C. almost

D. nearly

55. A. economic

B. historic

C. academic

D. financial

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第二节:完形填空(共20小题,每小题1.5分,满分30分)
阅读下面短文,掌握其大意,然后从36~55各题所给的四个选项(A、B、C和D)中,选出最佳选项,并在答题卡上将该项涂黑。
Throughout history,people have been the victims of pickpockets.Today,  36  is one of the most rapidly increasing  37 .Pickpockets are increasing   38  and developing better methods to Practice their skill.  39  one million Americans lose money to pickpockets every year.No one is really safe  40  a skilled pickpocket.His victims,or“marks” 41  they are rolled,can be rich or poor,young or old.  42 the 18th century,pickpockets   43  in England.Large crowds of people would gather to watch the hanging  44 was supposed to be a warning to other pickpockets.  45 ,in time the practice Was discontinued.
Police officials say that most   46  pickpockets come from South America. 47 these expert pickpockets  48   in special schools called Jingle Bell School.A pickpocket graduates from a J.B. 4 9 he is able to steal a wallet from a dressed dummy that has  50 inside its pockets!
Some of the  51  places of pickpockets are banks,airports,supermarkets,trains and bus stations.  52 a pickpocket will work with another pickpocket  53  his partner.  54  being the victim of a pickpocket,it is   55 to be very careful when in the midst of large gatherings of people.
36.A.pick pocketing           B.stealing pickpockets 
C.to pickpocket             D.to steal pickpockets
37.A.headaches           B.faults           C.mistakes                 D.crimes
38.A.by far                 B.at random    C.in number              D.out of order
39.A.Automatically     B.Obviously    C.Approximately       D.Subsequently
40.A.against               B.with            C.out of                    D.from
41.A.since                  B.as                C.so                          D.thus
42.A.At                      B.Since           C.From                     D.During
43.A.were hanged       B.would hang   C.were hung              D.must be hung
44.A.what                  B.of which      C.which                    D.among whom
43.A.Therefore           B.At once       C.Because                 D.However
46.A.attractive            B.convenient    C.efficient                 D.serious
47.A.Much of             B.A large amount of   
C.Many of                 D.A great number
48.A.are researched     B.specialize            C.are trained              D.major
49.A.where                 B.when                  C.although                D.however
50.A.money                B.jewelry               C.bells                      D.rings
51.A.favorite              B.liking                    C.favored                  D.be liked
52.A.Seldom               B.Once                  C.Often                     D.Forever
53.A.like                    B.being                  C.for                        D.as
54.A.To avoid             B.To neglect           C.Trying not              D.To forget
55.A.critical               B.fortunately          C.important               D.obvious

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第二部分:阅读理解(20小题, 每小题2分,满分40分)

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

A New Zealand fishermen caught what may prove to be a world-record-breaking colossal squid(鱿鱼).

In the cold, dark waters of the Antarctic hides a creature with eight arms, two super long tentacles(触须) and eyes as big as dinner plates. Sound like something out of a science fiction movie? Think again.

On February 21, New Zealand fishermen landed a colossal squid the length of a school bus. They had been fishing with long lines for Chilean sea bass in the waters off the coast of New Zealand when they caught the rare squid. With two hours of hard work, the crew skillfully pulled the creature into a net and dragged in aboard their ship.

Scientists evaluate that the animal weighs about a half ton and is about 40 feet long. That would make this colossal squid the biggest on record.

First identified in 1925 after two tentacles were found in a whale’s stomach, the colossal squid has long been a mystery. The animals are not easy to observe because they can go down to ocean depths of 6,500 feet. What scientists do know from studying the bodies of a half dozen colossal squids is that they are fierce hunters.

The recently captured colossal squid has been frozen to keep it for scientific study. It will be transported to New Zealand’s national museum, Te Papa, in the capital city of Wellington. Experts believe it to be the first adult male ever caught undamaged. Scientists hope to learn more about the colossal squid’s diet, behavior and reproductive(繁殖)patterns.

“Scientists will be very interested in this amazing creature, ”said New Zealand Fisheries Minister Jim Anderson. “It adds immeasurably to our understanding of the marine environment. ”

1. Why is it usually difficult for experts to observe the squid?

A. Because it moves too fast                       B. Because it is too large.

C. Because it is dangerous.                      D. Because it can go down to deep ocean.

2. What can be inferred from the passage?

A. The squid is from a science fiction story 

B. The fishermen often meet colossal squids

C. Scientists know much about the colossal squid. 

D. The fishermen had some difficulty catching the large squid.

3. What’s the purpose of catching such a huge squid?

A. To make it into food  B. To set a world record 

C. To do research on it  D. To display it for visitors

4. What would be the best title for the passage?

A. The biggest squid ever found                      B. Scientific research on squid

C. The lifestyle of the colossal squid         D. How the fishermen caught the squid

 

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阅读下面短文,从短文后各题所给的四个选项A、B、C和D中,选出最佳选项。

On Sunday morning, January 29, the call woke me up. It was the president of ABC News. “Lee, Bob has been __41__ in Iraq,” he said, choosing his words __42__. “He’s alive but he may have taken shrapnel (炮弹碎片) to the brain.”

When I saw Bob in the hospital, nothing could have __43__ me. He was unconscious. His __44__ was swollen to the size of a rugby ball and a piece of his skull was missing. All sorts of __45__ were coming out of his body. His left eye looked like a dead fish. I tried to __46__ myself that he didn’t look that bad, that this was the __47__ and that he’d only get better from here.

There were many months of treatment __48__. Every morning I would head over to the hospital and check on Bob. In the __49__ that a mother uses with her baby I would __50__ to him. I let him know about the kids. I told him stories about us and some of our best __51__ together. I brought music and had home movies for Bob to hear.

One day when I pushed open the door as usual, I __52__. Bob was sitting up in bed, a huge smile on his face. He saw me and __53__ his hands in the air. “Hey, sweetie,” he said, “where have you been?” I tried to speak but no words came out. This was so much more than I’d wanted and prayed for, __54__ I couldn’t really believe it. My husband was __55__ and he was calling me. Half of me wanted to shout in __56__ and gratitude and half of me wanted to __57__ everything, how I’d been there day after day for months. I __58__ to him.

Bob was __59__. He had the best medical treatment possible and the finest doctors. But the most important thing __60__ to be the love that held us close.

1.                A.hidden         B.caught          C.disturbed D.wounded

 

2.                A.seriously        B.carefully        C.actively   D.freely

 

3.                A.pleased        B.damaged        C.prepared D.choked

 

4.                A.arm            B.head           C.leg  D.hand

 

5.                A.tools           B.clothes         C.weapons D.tubes

 

6.                A.convince        B.accept          C.suggest   D.imagine

 

7.                A.best           B.worst           C.least     D.most

 

8.                A.then           B.ever           C.before   D.ahead

 

9.                A.name          B.sound          C.voice D.air

 

10.               A.talk            B.shout          C.point D.refer

 

11.               A.dreams         B.memories       C.thoughts   D.secrets

 

12.               A.froze          B.cried           C.failed     D.left

 

13.               A.held           B.found          C.lifted D.seized

 

14.               A.that           B.but            C.which     D.and

 

15.               A.off            B.up             C.down     D.back

 

16.               A.anger          B.relief          C.faith D.detail

 

17.               A.forget          B.follow          C.explain    D.check

 

18.               A.waved         B.walked         C.moved    D.ran

 

19.               A.fortunate       B.patient         C.generous D.powerful

 

20.               A.turned up       B.turned out      C.took up    D.took out

 

 

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