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題目列表(包括答案和解析)

touch

[  ]
A.

B.

C.

D.

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rely

[  ]
A.

B.

C.

D.

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loss

[  ]
A.

B.

C.

D.

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agriculrure

[  ]
A.

B.

C.

D.

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B.閱讀理解:(30分)
Now we can see a man and his wife at the breakfast table. They are not speaking to each other.
They haven’t spoken to each other at the breakfast table for years. The husband is reading his newspaper. We can’t see his face. The wife looks very worried as she gets a cup of tea ready for him. Today she is using a new kind of tea for the first time. The husband picks up his cup. He isn’t interested. He tastes his tea. Suddenly he puts down his newspaper. Something is different! Can it be the tea? He takes another taste. It’s wonderful. He smiles. He looks at his wife and says in surprise, “Doris, when did you cut your hair?” Doris is pleased. She answers, “Two months ago.” Doris asks, “Herbie, when did your hair begin to become white?” He answers, “A long time ago.” Doris says, “We have been together for many years, but we never cared about each other.” Now they aren’t worried any longer. Breakfast is different. Has a new kind of tea changed their lives?
36. This story happens______________________.
A. before breakfast                     B. after breakfast
C. at home                            D. in a teahouse
37. In the passage, we can see ________________________.
A. Doris is drinking tea                 B. Herbie likes the new kind of tea
C. Doris is reading a newspaper           D. Herbie is very young and good-looking
38. Herbie and Doris lived ______________ before this day.
A. a wonderful                        B. an unhappy
C. an enjoyable                        D. a friendly
39. Which of the following statements is true?
A. They are good friends.                B. They have just got married.
C. They like to talk about their hair.       D. They are no longer young.
40. From the passage, we think it may be ______________.
A. a radio programme                   B.  a short film
C. a computer game                     D.  a beautiful painting

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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)設(shè)拋物線,將(2,2)代入,得p=1. …………4分

∴y2=2x為所求的拋物線的方程.………………………………………………………5分

(2)聯(lián)立 消去y,得到. ………………………………7分

設(shè)AB的中點(diǎn)為,則

∴ 點(diǎn)到準(zhǔn)線l的距離.…………………………………9分

,…………………………11分

,故以AB為直徑的圓與準(zhǔn)線l相切.…………………… 12分

(注:本題第(2)也可用拋物線的定義法證明)

18.解:(1)在△ACF中,,即.………………………………5分

.又,∴.…………………… 7分

(2)

. ……………………………14分

(注:用坐標(biāo)法證明,同樣給分)

19.

解法一:(1)連OM,作OH⊥SM于H.

∵SM為斜高,∴M為BC的中點(diǎn),∴BC⊥OM.

∵BC⊥SM,∴BC⊥平面SMO.

又OH⊥SM,∴OH⊥平面SBC.……… 2分

由題意,得

設(shè)SM=x,

,解之,即.………………… 5分

(2)設(shè)面EBC∩SD=F,取AD中點(diǎn)N,連SN,設(shè)SN∩EF=Q.

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

又AD⊥SN,AD⊥NM,AD⊥面SMN.

從而EF⊥面SMN,∴EF⊥QS,且EF⊥QM.

∴∠SQM為所求二面角的平面角,記為α.……… 7分

由平幾知識,得

,∴

,即所求二面角為. ……………… 10分

(3)存在一點(diǎn)P,使得OP⊥平面EBC.取SD的中點(diǎn)F,連FC,可得梯形EFCB,

取AD的中點(diǎn)G,連SG,GM,得等腰三角形SGM,O為GM的中點(diǎn),

設(shè)SG∩EF=H,則H是EF的中點(diǎn).

連HM,則HM為平面EFCB與平面SGM的交線.

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

在平面SGM中,過O作OQ⊥HM,由兩平面垂直的性質(zhì),可知OQ⊥平面EFCB.

而OQ平面SOM,在平面SOM中,延長OQ必與SM相交于一點(diǎn),

故存在一點(diǎn)P,使得OP⊥平面EBC. ……………………… 14分

 

∵底面邊長為1,∴

,

.    ……………… 1分

設(shè),

平面SBC的一個法向量

,

,

∴y=2h,n=(0,2h,1).… 3分

=(0,1,0),由題意,得.解得

∴斜高. …………………………………………………… 5分

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

由對稱性,面SAD的一個法向量為n1. ………………………………6分

設(shè)平面EBC的一個法向量n2=(x,y,1),由

,,得

 解得.………………… 8分

設(shè)所求的銳二面角為α,則

,∴.…………… 10分

(3)存在滿足題意的點(diǎn).證明如下:

. ………………………… 11分

,令與n2共線,則. ……………… 13分

.故存在P∈SM,使OP⊥面EBC.……………………… 14分

20. 解:(1)當(dāng)n為奇數(shù)時,an≥a,于是,. ………………3分

         當(dāng)n為偶數(shù)時,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的討論,扣1分)

 . ……………12分

.……15分21.解:(1)∵,,∴,∴. 1分

,即,∴. …3分

①當(dāng),即時,上式不成立.………………………………………………4分

②當(dāng),即時,.由條件,得到

,解得. ……………………………………………5分

,解得.…………………………………………6分

 m的取值范圍是. ………………………………………7分

(2)有一個實(shí)根.………………………………………………………………………………9分

,即

,則

,. ………………………10分

 △>0,故有相異兩實(shí)根

,∴ 顯然,,

,∴,∴. …………12分

于是

                    

為三次函數(shù)的極小值點(diǎn),故與x軸只有一個交點(diǎn).

∴  方程只有一個實(shí)根.…………………………15分


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