8. What will the classroom turn into?
A. A bedroom. B. A dance hall. C. A dining hall.
7. What is the probable relationship between the two speakers?
A. Friends. B. Teachers and students. C. relatives.
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.
5. What are the speakers?
A. Teachers. B. Students. C. Parents.
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.
3. Where are they going at the weekend?
A. Beijing Theater. B. Beihai Park. C. ChaoYang Park.
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!
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,,
当时,,
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)
由,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
当,
……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.
当时,
,,
令得或(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;
若,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
设,,则是方程①的两个实根,
则,,所以线段AB的中点为,……(8分)
线段AB的垂直平分线方程为,
令,,得, ……(10分)
因为为正三角形,则点E到直线AB的距离等于,
又=,
所以,,解得:, . ……(13分)
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
17.解:
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