摘要:15.一排7个座位.让甲.乙.丙三人就坐.要求甲与乙之间至少有一个空位.且甲与丙之间也至少有一个空位.则不同的坐法有 ▲ 种.

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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

完成句子(共10小题;每小题2分,满分20分)

1.Langlang, ______________________ , has performed successfully on a lot of grand occasions . (gift)

朗朗,很有音乐天赋,曾经在很多大场合成功表演过。

2._________________ that the experiment ended in failure? We should try to find out the cause.(come)

实验怎么会失败呢? 我们应好好找找原因。

3.With about 2000 seats ______________, the concert hall can hold more than so many people. (sit)

有大约2000个座位,这个音乐厅可容纳更多的观众。

4.The young man has ______________________ of turning on the computer to read news at home and abroad as soon as he comes back from work. (get)

这个年轻人养成了下班就打开电脑看国内外新闻的习惯。

5.He pretended not ________________________ it. (hear)

他假装没听说过这件事。

6.______________________________ at home, the novelist went for a walk as a rest.(spend)

花了好几个小时在家写作,这位作家出去散步休息一下。

7.I’m sorry ,I can’t remember ______________ that the Qin dynasty united the currency of China. (it)

很抱歉,我不记得秦朝究竟是在何时统一中国货币的。

8.Have you ever been to Yuanmingyuan in Beijing?  Now it is in ruins, because it _______________ years ago and was not rebuilt. (burn)

你去过北京的圆明园吗?现在是一片废墟,因为多年前被烧毁了且没有重建。

9.I eventually persuaded my president to open a branch in the middle-sized city.As a result, I was there _________________________ our company。(behalf)

我最后终于说服了总裁在那个中等城市开分公司。结果,我就在那做我们公司的代表了。

10.Under no circumstances ______________________  the manager’s office except the manager himself. (access)

在任何情况下,除经理自己外,任何其他人都不能随意进入经理的办公室。

 

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短文阅读,根据所读内容在文后的空格里填上适当的单词或短语,并将答案转写到答题卡上。

注意每空一超过3个单词。

    The population of the United States is growing older and will continue to do so.

According to a report, 39 million Americans will be 65 or older by the year 2010, 51 million by 2020, and 65 million by 2030.

   The "graying" of the United States is mainly due to the fact that people in the U. S. living longer. As a matter of fact, the number of U.S. citizens 85 years old and older is growing six times as fast as the rest of the population. It is also largely due to the old-growing of the "baby boomers," the generation born after World War II. In 1957, over 4.3 million babies were born. More than 75 million Americans were born between 1946 and 1964, the largest generation in U.S. history. In less than twenty pears, millions of them will become elderly people.

   The "graying" of the U.S. will greatly affect the nation’s family and workforce. One likely development will be a gradual change in the family unit; it will move away from the nuclear family and towards a multigenerational family. The other likely development will be a change  the proportion (比例) of the nation’s workforce. In 1989 there were 3.5 workers for every person 65 and older; by the year 2030, they will only be 2 workers for every person 65 and older.

Title  1..            

Numbers of citizens 65 or older

2..    

By 2020

By 2030

39 million

51 million

65 million

3..               

4..                              

Baby boomers’ old growing

5..            

6.

7..                            

-- multigenerational family

8..            

9..     to citizens 65 or older

10.

By 2030

3.5:1

2:1

 

 

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