摘要:(2)求证:对任意的α∈(0.).为定值.

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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

阅读下面的短文,然后按要求写一篇150词左右的英语短文。

What my mother does drives me crazy. She calls me at 10:30 pm every night to make sure I’ve arrived home safely. If I accidentally miss her call, she will keep calling all my friends and roommates until she "tracks me down".

As a 20-year-old lady in Beijing, sometimes I have to ask my friends to be quiet so that I can pick up my mother's phone call, telling her a white lie that I'm already at home.

    Recently I ran into a matchmaking meeting, which is held in a park and specifically designed for single white – collar workers in Beijing. The interesting part is that all of the attendees are single people’s parents, eager to look for a life partner for their children.

One mother told me that her 33-year-old son is busy with his career and has zero time to find a suitable girl for himself. So she goes to the matchmaking every week, trying to find her son a perfect bride.

She guaranteed that her future daughter-in-law doesn't need to worry about anything for she has prepared an apartment and a car for them, and if they can’t find a kindergarten near the apartment she has bought, she will buy them another one. Looking at hundreds of middle – aged parents standing in the cold outdoors in a freezing winter trying to build their children a perfect future, I suddenly understand my mother more.

 

【写作内容】

    1.以约30个词概括这段短文的内容;

    2.然后以约120个词就“父母的过分关爱”进行议论,内容包括;

(1)请举一个你或你周围的周学得到父母的过分关爱的事例;

(2)谈谈你对此事的看法。

【写作要求】

    1.在作文中可以使用亲身经历或虚构的故事,也可以参照阅读材料的内容,但不得直接引用原文中的句子。

    2.作文中不能出现真实姓名和学校名称。

【评分标准】

    概括准确,语言规范,内容合适,语篇连贯。

 

查看习题详情和答案>>

阅读下面的短文,然后按要求写一篇150词左右的英语短文。
What my mother does drives me crazy. She calls me at 10:30 pm every night to make sure I’ve arrived home safely. If I accidentally miss her call, she will keep calling all my friends and roommates until she "tracks me down".
As a 20-year-old lady in Beijing, sometimes I have to ask my friends to be quiet so that I can pick up my mother’s phone call, telling her a white lie that I’m already at home.
Recently I ran into a matchmaking meeting, which is held in a park and specifically designed for single white – collar workers in Beijing. The interesting part is that all of the attendees are single people’s parents, eager to look for a life partner for their children.
One mother told me that her 33-year-old son is busy with his career and has zero time to find a suitable girl for himself. So she goes to the matchmaking every week, trying to find her son a perfect bride.
She guaranteed that her future daughter-in-law doesn’t need to worry about anything for she has prepared an apartment and a car for them, and if they can’t find a kindergarten near the apartment she has bought, she will buy them another one. Looking at hundreds of middle – aged parents standing in the cold outdoors in a freezing winter trying to build their children a perfect future, I suddenly understand my mother more.
【写作内容】
1.以约30个词概括这段短文的内容;
2.然后以约120个词就“父母的过分关爱”进行议论,内容包括;
(1)请举一个你或你周围的周学得到父母的过分关爱的事例;
(2)谈谈你对此事的看法。
【写作要求】
1.在作文中可以使用亲身经历或虚构的故事,也可以参照阅读材料的内容,但不得直接引用原文中的句子。
2.作文中不能出现真实姓名和学校名称。
【评分标准】
概括准确,语言规范,内容合适,语篇连贯。

查看习题详情和答案>>

 

读写任务

阅读下面的短文,然后按照要求写一篇150词左右的英语短文。

Dear Patti

I’m writing to you for some advice on my studies. As you know, football is a very popular sport in the world and I am attracted to it and I have fallen in love with it, which makes me feel so crazy. I have spending lots of time doing many things related to it, like watching football matches, reading newspapers and magazines, and searching the Web for more information about football. As a result, it has certainly disturbed my normal study. Though I know to be a football fan is my hobby and my major adjective is to learn more knowledge in school, I can’t concentrate on my lessons and gradually I am tired of them. I am still a senior middle school student, and I’ll have my own business even when I grow up, so I am not likely to do a job in the field of football. But now I can’t stop myself from getting involved further with football. So I feel very depressed and want to know how to deal with the contradiction .

Sincerely yours,

Li Hua

【写作内容】

假设你是李华的笔友Patti,请根据他信中所诉说的苦恼回信。以下是回信的内容(信的开头和结尾已经为你写好)

以约30个词概括李华的苦恼;

以约120个词发表你的看法,并包括如下要点:

(1)你认为李华应该如何处理好他的学习和业余爱好的关系,并说明你的理由。

(2)表达你对他的希望。

【写作要求】

1.可以使用实例或其他论述的方法支持你的论点,也可以参照阅读材料的内容,但不得直接引用原文中的句子;

2.信中不能出现真实姓名和学校名称。

Dear Li Hua,

Thank you for your letter. From your letter, I’ve known something about your situation.                                                                              

                                                                                                                                             

Yours

Patti

 

 

查看习题详情和答案>>

阅读下面的短文,然后按照要求写一篇150词左右的英语短文。

Dear Patti,

I’m writing to you for some advice on my studies. As you know, football is a very popular sport in the world and I am attracted to it and I have fallen in love with it, which makes me feel so crazy. I have spending lots of time doing many things related to it, like watching football matches, reading newspapers and magazines, and searching the Web for more information about football. As a result, it has certainly disturbed my normal study. Though I know to be a football fan is my hobby and my major adjective is to learn more knowledge in school, I can’t concentrate on my lessons and gradually I am tired of them. I am still a senior two middle school student, and I’ll have my own business even when I grow up, so I am not likely to do a job in the field of football. But now I can’t stop myself from getting involved further with football. So I feel very depressed and want to know how to deal with the contradiction (矛盾. between my studies and boobies.)

Sincerely yours,

Li Ming

【写作内容】

假设你是李明的笔友Patti,请根据他信中所诉说的苦恼回信。以下是回信的内容(信的开头和结尾已经为你写好)

以约30个词概括李明的苦恼;

以约120个词发表你的看法,并包括如下要点:

(1)你认为李明应该如何处理好他的学习和业余爱好的关系,并说明你的理由。

(2)表达你对他的希望。

【写作要求】

1.可以使用实例或其他论述的方法支持你的论点,也可以参照阅读材料的内容,但不得直接引用原文中的句子;

2.信中不能出现真实姓名和学校名称。

Dear Li Ming,

Thank you for your letter. From your letter, I’ve known something about your situation.                                                                                

                                                                                                                                                                    

                                                                                                                                                                

                                                                                                                                                                                     

                                                                                                                                                                

                                                                                

                                                                             

                                                                               

                                                                            

                                                                                                                                            

                                                                                                                                                                                

                                                                                                                                                                

                                                                                 

                                                                             

                                                                               

                                                                            

                                                                   

                                                                            

                                                                              

Yours

Patti

查看习题详情和答案>>

第二节:读写任务(共1小题,满分25分)

阅读下面的短文,然后按照要求写一篇150词左右的英语短文。

For many years, scientists have warned that smoking tobacco is bad for health. Yet people around the world continue to smoke. The World Health Organization estimates that more than four million people die each year from the effects of smoking. That number is increasing.

Scientists have identified more than forty chemicals in tobacco smoke that cause cancer in humans and animals. Nicotine (尼古丁) is the major poison in cigarettes that gives pleasure to smokers. The American Cancer Society says nicotine can kill a person when taken in large amounts. It does this by stopping the muscles used for breathing. Also, studies have found that nicotine can be as harmful as alcohol or the illegal drugs. So experts say it is better never to start smoking and become dependent on nicotine than it is to smoke with the idea of stopping later.

Smoking tobacco is the leading cause of lung disease. Smoking also has been linked to heart disease, stroke and many kinds of cancer. American government health experts say smoking affects not only the smoker. Tobacco smoke also affects the health of people who do not smoke. Smokers may harm the health of family members and people at work. Tobacco smoke causes an estimated 3,000 non-smoking Americans to die of lung cancer each year.

Therefore, it can be seen that smoking begins to cause damage immediately. All cigarettes can damage the body. And there is no safe way to smoke.

[写作内容]

假设你是Adam,你叔叔是一个烟瘾很大的人。在看了有关吸烟危害的文章后,想给叔叔写一封信劝其戒烟。以下是信的内容(信的开头和结尾已经为你写好):

1.以约30个词概括香烟对身体健康的伤害;

2.以约120个词表达你对叔叔的劝告,并包括如下要点:

(1) 对叔叔提出戒烟的具体建议;

(2) 指出叔叔戒烟对家人的益处;

(3) 期望叔叔能够成功地戒烟。

[写作要求]

1.作文可以参照阅读材料的内容但不得直接引用原文中的句子;

2.信中不能出现真实姓名和学校名称。

[评分标准]           概括准确,语言规范,内容合适,篇章连贯。

 

查看习题详情和答案>>

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