摘要:C. D.

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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


C
"Reduce, reuse and recycle, this familiar environmentalist slogan tells us how to reduce the amount of rubbish that ends up in landfills and waterways.
The concept is being used to deal with one possibly dangerous form of waste –--- electronic junk (电子垃圾), such as old computers, cell-phones, and televisions. But this process for managing e-waste may be used in an unscrupulous(不择手段的) way more often than not used, a recent report suggests.
“A lot of these materials are being sent to developing nations under the excuse of reuse –--- to bridge the digital divide,” said Richard Gutierrez, a policy researcher.
One of the problems is that no one proves whether these old machines work before they hit the seaways. Because of this, the report says, e-waste is a growing problem in Lagos, Nigeria, and elsewhere in the developing world. Much of the waste ends up being thrown away along rivers and roads. Often it’s picked apart by poor people, who may face dangerous exposure to poisonous chemicals in the equipment.
Businessmen also pay workers a little money to get back materials such as gold and copper. This low-tech recovery process could expose workers and the local environment to many dangerous materials used to build electronics. According to Gutierrez, this shadow economy exists because the excuse of recycling and reusing electronics gives businessmen “a green passport” to ship waste around the globe. “Developing nations must take upon some of the responsibility themselves,” Gutierrez said. But, he added, “A greater portion of this responsibility should fall on the exporting state.”
China, for example, has become a dumping(倾倒,堆放) place for large amounts of e-waste. The nation is beginning to take action to stop the flow of dangerous materials across its borders. The Chinese government, after many years of denial(否认), is finally beginning to take the lead.
70.What does the fourth paragraph mainly discuss?
A. Old computers and TVs still work before they are sent abroad.
B. Poor people break up e-waste to collect some valuable materials.
C. A lot of e-waste is dumped in developing countries.
D. The problem of e-waste is growing in developing countries.
71.From what Gutierrez said we can learn that ________.
A. exporting countries should mainly be responsible for this problem.
B. neither rich nor poor countries should be blamed for this problem
C. developing countries should be responsible for this problem
D. poor countries should be blamed for this problem
72.It can be inferred from the last paragraph that _______.
A. China has hidden a large amount of e-waste in many secret places
B. China has greatly changed the idea about the problem of e-waste
C. China has prevented poisonous materials from entering China for a long time
D. China is falling behind other countries in dealing with e-waste
73.The passage mainly tells us that _______.
A. developing countries are facing serious environmental problems
B. e-waste is a growing problem in developed countries
C. e-waste is sent to developing countries under the excuse of reuse
D. developing countries are making full use of e-waste

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