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8. What will the classroom turn into?

A. A bedroom.    B. A dance hall.          C. A dining hall.

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7. What is the probable relationship between the two speakers?

A. Friends.      B. Teachers and students.      C. relatives.

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6. What does the woman think of the school?

A. Very good.      B. Just so-so.        C. Bad.

Conversation 4:

M: Mary, we are going to have a party on New Year’s Eve. I’m sure we’ll have a good time. Would you like to join us?

W: I’d like to. Where are you going to have it?

M: In our classroom. We are going to decorate it and turn it into a splendid ballroom.

W: Oh, it is great. I shall be very glad to spend my first New Year in China with you.

M: But we are going to ask everyone at the party to give a performance. Do sing us some English songs, please.

W: I will. My voice is not very pleasant to the ear, though.

M: I heard you sing once. Your voice was sweet and beautiful. I’m sure you’ll be the star of our New Year party.

W: Oh, thank you.

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5. What are the speakers?

A. Teachers.         B. Students.    C. Parents.

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4. What are they going there for?

A. To go outing.    B. To see Beijing Opera.      C. To learn Beijing Opera.

Conversation 3:

M: I think I was very lucky to enter this school. But it lies in the suburb.

W: Ah, this is a developing area. There will be a lot more people here in about five years' time. And there won't be many factories.

M: Yes. We can breathe fresh air every day. What do you think of the teachers here?

W: Very good and kind. They are helpful. I am making progress.

W: I hope I can get used to the life here soon.

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3. Where are they going at the weekend?

A. Beijing Theater.     B. Beihai Park.        C. ChaoYang Park.

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2. Whom did the man chat with?

A. People from America.     B. People who are watching a movie.   

C. People in different countries.

Conversation 2:

M: Susan, Please pass me a copy of Beijing Review.

W: Here you are.

M: I want to find what’s on this weekend.

W: Is there anything good on?

M: The Beijing Opera is showing on Saturday evening. Do you like Beijing Opera?

W: Oh, yes. Very much. When and where will it be?

M: At 7:30 in ChaoYang Park.

W: Let's go and see it, OK?

M: Good idea!

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19.(本小题满分13分)

已知数列的前项和为,对任意,点都在函数的图像上.

(1)求数列的通项公式;

(2)设,且数列是等差数列,求非零常数的值;

(3)设是数列的前项和,求使得对所有都成立的最小正整数

解析:(1)由已知,对所有,          ……(1分)

所以当时,

时,

因为也满足上式,所以数列的通项公式为(). ……(4分)

(2)由已知,                      ……(5分)

因为是等差数列,可设(为常数),        …(6分)

所以,于是

所以,   因为,所以.      ………(8分)

(注:用为定值也可解,可按学生解答步骤适当给分)

(3),            ……(10分)

所以

……(11分)

,得,因为,所以

所以,所求的最小正整数的值为.                 ……(13分)

20(本小题满分13分)

工厂生产某种产品,次品率p与日产量x(万件)间的关系为

.已知每生产1件合格产品盈利3元,每出现1件次品亏损1.5元.

(1)将日盈利额y(万元)表示为日产量(万件)的函数;

(2)为使日盈利额最大,日产量应为多少万件?(注:次品率=×100%)

(1)当时,

                     ……1分

           ……3分

日盈利额y(万元)与日产量x(万件)的函数关系为

                     …… 6分

(2)由(Ⅰ)知,当时,日盈利额为0.

时,

(舍去)               …… 8分

①当时,在区间上单调递增,

,此时;          ……10分

②当时,在(0,3)上,,在(3,6)上

,                      

综上,若,则当日产量为c万件时,日盈利额最大;

,则当日产量为3万件时,日盈利额最大            …… 13分

21(本小题满分13分)

如图:已知点,点P在y轴上,点Q在x轴的正半轴上,

点M在直线PQ上,且满足

(1)当点P在y轴上移动时,求点M的轨迹C;

(2)过点作直线m与轨迹C交于A、B两点,

若在x轴上存在一点,使得为等边三角形,求的值.

解析(1)设,由得:

  由得:,即

  由点Q在x轴的正半轴上,故

  即动点M的轨迹C是以为顶点,以为焦点的抛物线,除去原点;……(5分)

(2)设,代入得:

…………①

,则是方程①的两个实根,

,所以线段AB的中点为,……(8分)

线段AB的垂直平分线方程为

,得,               ……(10分)

因为为正三角形,则点E到直线AB的距离等于

所以,,解得: .     ……(13分)

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18.(本小题满分12分)

在三棱柱ABC-A1B1C1中,四边形A1ABB1是菱形,

四边形BCC1B1是矩形,且C1B1⊥AB.

(Ⅰ)求证:平面CA1B⊥平面A1AB B1

(Ⅱ)若C1B1=3,AB=4,∠ABB1=60O,求直线AC1与平面BCC1B1所成角的正弦值.

18(Ⅰ)证明 在三棱柱ABC-A1B1C1中,C1B1//CB,

∵C1B1⊥AB,∴CB⊥AB.

又四边形BCC1B1是矩形,CB⊥B1B,∴CB⊥平面A1AB B1

而CB平面CA1B ,故平面CA1B⊥平面A1A B B1

(Ⅱ)解 过A作AH⊥BB1于H,连C1H.

∵CB⊥平A1AB B1,CB平面BC C1B1

∴平面BCC1B1⊥平面A1AB B1

∴AH⊥平面BCC1B1

∴∠AC1H为AC1与平面BCC1B1所成的角.

  连结A1B交于A1B于O,由四边形A1ABB1是菱形,ABB1=60O

可知△ABB1为等边三角形, AB1=AB =4,而H为BB中点,于是AH=2                            

在Rt△C1B1A中,

AC1=,

在Rt△AH C1中,

故直线AC1与平面BCC1B1所成的角的正弦值为

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17.解:

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