摘要:点.AB=1.直线AD到平面SBC的距离等于.(1)求斜高SM的长,

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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

信息匹配(共5小题;每小题2分,满分10分)
请阅读下列应用文及相关信息,并按照要求匹配信息。请在答题卡56—60上将对应题号的相应字母涂黑。注意E涂AB,F涂CD。
首先,请阅读下面的售货广告:
A. HORNSBY Demolition Sale 21 Steward Avenue Saturday and Sunday 9am-12am Furniture, and even the kitchen sink, new outdoor lighting and a lot more to go
B. HUGE SALE PENNANT HILLS,2a Pomona Street, Saturday 7th October ,8am-2pm,furniture,househole goods, variety of items.
C. HUGE Garage Sale, PYMBLE 80 Bannockburn road, Corner Rushall Street Saturday 30th September only. 9.00am to 2.00pm Nothing sold before! Gymnasium equipment. Hi-fis, Fridges, Cycles, Book Furniture and much more! Don’t miss it!
D. Last Sale Moving Sunday 1st October form 7am. Great variety of goods ,twin bedroom suite other furniture and tools.11 Bellamy Avenue , Eastwood
E. MOVING SALE HORNSBY HTS. Claros Close. Saturday 7Th Oct .from .9am. H/Hold items, furniture, & o/door furniture, TV, garden tools & equip .Every thing must go .Bargain prices.
F.MOVING SALE MT.COLAH Sale Lounge, Dining and Bedroom Furniture, Electrical and Whitegoods . Ph:0405 770 699
请阅读下面购买者的信息,然后匹配他们可能购买的商品:
【小题1】 Ross ,a young man who has just found a job in a company. He rents a small apartment near the downtown and needs some bowls, plates and forks, ect.
【小题2】Joseph and his wife just moved into a new house with a big garden. Wild grass crawls all over the garden. They need some tools to make the garden tidy.
【小题3】 Roger, lives in a house 22 Bellamy Avenue, Eastwood. He needs a writing desk, a dining table, some chairs and a sofa.
【小题4】 Richard, a young man who likes sports and music. He would add something more to satisfy his interests at home.
【小题5】Mike, a private gymnasium owner. He has just increased several new tennis courts for his growing business. He is planning to open them at evening and needs the lighting.

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Weddings in the United States vary as much as the people do. There are church weddings with a great deal of fanfare(仪式上用的短曲); there are weddings on mountain-tops with guests barefooted (赤脚的); and there have been weddings on the ocean floor with oxygen tanks for the guests. But many weddings, no matter where or how they are performed, include certain traditional customs.
Before a couple is married, they become engaged. And then invitations are sent to those who live nearby, their close friends and their relatives who live far away. When everything is ready, then comes the most exciting moment.
The wedding itself usually lasts between 20 and 40 minutes. The wedding party enters the church while the wedding march is played. The bride carrying a bouquet (花束)enters last with her father who will "give her away ". The bridegroom enters the church from a side door. When the wedding party is gathered by the altar, the bride and bridegroom exchange vows (誓言). It is traditional to use the words "To have and to hold from this day forward, for better, for worse, for richer, for poorer, in sickness and in health, to love and to cherish, till death do us part ". Following the vows, the couple exchange rings. Wearing the wedding ring on the fourth finger of the left hand is an old custom.
After the ceremony there is often a party, called a "reception" which gives the wedding guests an opportunity to congratulate the new couple . The car in which the couple leaves the church is decorated with balloons, streamers and shaving cream. The words "Just Married" are painted on the trunk or back window. The bride and bridegroom run to the car under a shower of rice thrown by the wedding guests. When the couple drives away from the church, friends often chase them in cars, honking (鸣汽车喇叭)and drawing attention to them. And then the couple go on their honeymoon.
【小题1】This passage is written mainly to let us know something about _______ .

A.health and lifestyle B.science and technology
C.culture and customD.education and entertainment
【小题2】Why do the wedding guests throw a lot of rice at the bride and bridegroom when they run to the car ?
A.To wish them good luck . B.To make fun of them.
C.Not mentioned . D.To draw attention to them .
【小题3】Which of the following is TRUE of American weddings ?
A.They are always held in churches whoever they are .
B.The bride’s father is usually present to lead his daughter to the bridegroom and give her to him .
C.Only bridegrooms send rings to brides .
D.Brides needn’t make vows before bridegrooms .
【小题4】Which of the following is the correct order in which the following events happen ?
a. sending invitation           b. going on honeymoon
c. attending the wedding        d. giving a reception
e. getting engaged
A.e-b-c-d-aB.e-c-d-a-bC.b-c-d-a-eD.e-a-c-d-b

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CBC is a famous air company which has over twenty planes carrying passengers and goods, flying along 12 fixed lines all over the world. Its service is very good but some passengers are still not satisfied with it and that is why in 2004 and 2005 the company received letters of complaints from consumers or passengers who pointed out over a dozen kind of problems which are divided in groups in the following table. Those concerning passengers’ things carried on the plane are baggage problems. Customer service refers to service work which passengers are not satisfied with. Overselling of tickets is about the fact that more seats are sold and as a result the plane is too crowded to be safe. Refund problems appear when passengers fail to receive the money paid back to them because of what they have lost. Fares are problems concerning the price of tickets.  
Consumer Complaints Received By the CBC

Category
2004
2005
Flight problems
20.2%
22.1%
Baggage
18.3%
21.8%
Customer service
3.1%
11.3%
Over sales of seats
10.5%
11.8%
Refund problems
10.1%
8.1%
Fares
6.4%
6.0%
Reservation & Ticketing
5.8%
5.6%
Tours
3.3%
2.3%
Smoking
3.2%
2.9%
Advertising
1.2%
1.01%
Credit
1.0%
0.8%
Special passengers
0.9%
0.9%
Others
6.0%
5.3%
Total Number of Complaints
2,988
1,792
【小题1】 About how many complaints about Credit were received by the CBC in 2004?
A.28B.29C.30D.31
【小题2】By about what percentage did the total number of complaints decrease from 2004 to 2005?
A.40%B.60%C.75%D.100%
【小题3】If the circle graphs below show total consumer complaints for 2004, which graph shows a dark part that is about Flight problems and Refund problems together?

【小题4】Which of the following statements can be inferred from the table?
a. In 2004 and in 2005, complaints about Flight problems, Baggage, and Customer service
together took more than 40 percent of all consumer complaints received by the CBC Company.
b .The number of special passengers complaints was unchanged from 2004 to 2005.
c .From 2004 to 2005 the number of Flight problems complaints increased by more than 2 percent.
A.only aB.only bC.a and bD.a and c
【小题5】From the passage we can know that _______ .
A.customers are not satisfied with CBC
B.sometimes CBC sells more tickets than its plane’s fixed seats
C.CBC has more than twenty planes which fly to all the capital cities of the world
D.customers can only buy tickets with cash

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