摘要:12.垂直于直线x-3y=0且与曲线相切的直线方程为 ▲ .

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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

Marie Curie was a Polish-born physicist and chemist and one of the most famous scientists of her time. Together with her husband Pierre, she won the Nobel Prize in 1903, and another one in 1911.
Marie Sklodowska was born in Warsaw on 7 November 1867, the daughter of a teacher. In 1891, she went to Paris to study physics and maths at the Sorbonne where she met Pierre Curie, professor of the School of Physics. They married in 1895.
The Curies worked together studying radioactivity(放射性), building on the work of the German physicist Roentgen and the French physicist Becquerel. In July 1898, the Curies announced the discovery of polonium(钋). At the end of the year, they announced the discovery of another, radium(镭). The Curies, along with Becquerel, won the Nobel Prize for Physics in 1903.
Pierre’s life was cut short in 1906 when he was knocked down and killed by a carriage. Marie took over his teaching post, becoming the first woman to teach at the Sorbonne, and devoted (献身于) herself to continuing the work that they had begun together. She received a second Nobel Prize, for Chemistry, in 1911.
The Curies’ research was important in developing X-rays in surgery. During World WarⅠ, Marie helped fixed X-ray equipment, which she herself drove to the front lines. She helped train doctors for the International Red Cross.
Although she achieved much success, men scientists in France were still against Marie, and she never received any financial help from her work. By the late 1920s her health was beginning to become worse. She died on 4 July 1934 from her dangerous research. The Curies’ eldest daughter Irene was a scientist and winner of the Nobel Prize for Chemistry.
【小题1】All the following people contributed to Marie’s first Nobel Prize EXCEPT _____.

A.IreneB.PierreC.BecquerelD.Roentgen
【小题2】We can know from the text that Marie’s work______.
A.won her respect from men scientists
B.brought her some financial help
C.had a bad effect on her health
D.had no influence on her children
【小题3】Which is the right order of the following events?
①Marie became a teacher at the Sorbonne.
②Marie helped train doctors.
③The Curies discovered polonium.
④The Curies won the Nobel Prize for Physics.
⑤The Curies discovered radium.
A.①④⑤③②B.③⑤④①②C.⑤④①③②D.②③⑤①④
【小题4】Which of the following about Marie is NOT true?
A.She married at the age of 28.
B.Her parent was a teacher.
C.She was the first woman teacher at the Sorbonne.
D.She helped the International Red Cross fix X-ray equipment.

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C
(1)Mr. Brown(the motorist)
At about 9∶20 p.m. on October 14th, I was driving along Market Road in the direction of Midwick. I wanted to go to Sturham to collect my wife, who had been visiting some friends. I prepared to turn into Sturham Road, which was on my right. In the distance, I saw the lights of a car moving towards me but it was a long way from me. I put out my hand to show that I was going to turn right. Then I started to turn slowly towards Sturham Road. Suddenly there was a loud noise on the passenger’s (near) side of the car. I stopped the car and got out. A motorcycle had hit my car. The motorcyclist had been thrown over the car. He was injured, so I ran to a shop to phone for help.
(2)Mr. Smith (the injured motorcyclist)
On the evening of October 14th, I was going home along Market Road towards Newtown. I was riding my motorcycle. I was going slowly because some of the streetlights were out and the road was wet and slippery. Just before Sturham Road, a car suddenly drove right across my path. The driver did not flash his lights to give a warning. I could not turn in time, so I hit the side of the car. When I woke up, I was lying in a hospital in Market Road.
(3)Mr. Lee (another motorcyclist)
At about 9∶10p.m.on October 14th, I left my home in Midwick. Ten minutes later I was riding my motorcycle along Market Road. I was going to Newtown. There was a motorcycle about 40 metres in front of me. It was not going very quickly. The man on it was riding near the curb(路边) but I was near the center of the road. The motorcyclist in front of me tried to turn to his right but there was no time. He hit the car and was injured. There was no car going along in front of us or put by the road.
50.Which or these pictures exactly shows the scene of the accident?
X=the place where the motorcycle hit the car; N=Newtown; M=Midwick; S=Sturham. (Note that cars and motorcycles always keep to the left in England.)

51.Which of these statements about the accident is probably correct?
A.Mr. Brown wrongly supposed that the lights of the two motorcycles were those of a car.
B.The lights of the car moving towards Mr. Brown made him unable to see.
C.Mr. Brown knocked down a motorcyclist on purpose.
D.The accident was caused by the carelessness of the first motorcyclist.
52.It seems probable from the statements that Mr. Brown_______.
A.gave no signal to show that he was turning right
B.did not give any signal until he was actually turning
C.failed to give a proper signal at that time
D.flashed his light to show that he was going to turn
53.We would expect to find that Mr. Brown’s car was damaged on its______ side.
A.front     B.left     C.right     D.driver’s

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Marie Curie was a Polish-born physicist and chemist and one of the most famous scientists of her time. Together with her husband Pierre, she won the Nobel Prize in 1903, and another one in 1911.

Marie Sklodowska was born in Warsaw on 7 November 1867, the daughter of a teacher. In 1891, she went to Paris to study physics and maths at the Sorbonne where she met Pierre Curie, professor of the School of Physics. They married in 1895.

The Curies worked together studying radioactivity(放射性), building on the work of the German physicist Roentgen and the French physicist Becquerel. In July 1898, the Curies announced the discovery of polonium(钋). At the end of the year, they announced the discovery of another, radium(镭). The Curies, along with Becquerel, won the Nobel Prize for Physics in 1903.

Pierre’s life was cut short in 1906 when he was knocked down and killed by a carriage. Marie took over his teaching post, becoming the first woman to teach at the Sorbonne, and devoted (献身于) herself to continuing the work that they had begun together. She received a second Nobel Prize, for Chemistry, in 1911.

The Curies’ research was important in developing X-rays in surgery. During World WarⅠ, Marie helped fixed X-ray equipment, which she herself drove to the front lines. She helped train doctors for the International Red Cross.

Although she achieved much success, men scientists in France were still against Marie, and she never received any financial help from her work. By the late 1920s her health was beginning to become worse. She died on 4 July 1934 from her dangerous research. The Curies’ eldest daughter Irene was a scientist and winner of the Nobel Prize for Chemistry.

1.All the following people contributed to Marie’s first Nobel Prize EXCEPT _____.

A.Irene             B.Pierre            C.Becquerel         D.Roentgen

2.We can know from the text that Marie’s work______.

A.won her respect from men scientists

B.brought her some financial help

C.had a bad effect on her health

D.had no influence on her children

3.Which is the right order of the following events?

①Marie became a teacher at the Sorbonne.

②Marie helped train doctors.

③The Curies discovered polonium.

④The Curies won the Nobel Prize for Physics.

⑤The Curies discovered radium.

A.①④⑤③②       B.③⑤④①②        C.⑤④①③②        D.②③⑤①④

4.Which of the following about Marie is NOT true?

A.She married at the age of 28.

B.Her parent was a teacher.

C.She was the first woman teacher at the Sorbonne.

D.She helped the International Red Cross fix X-ray equipment.

 

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