17.已知拋物線的頂點(diǎn)在原點(diǎn).焦點(diǎn)F在x軸的正半軸上.且過(guò)點(diǎn)P(2.2).過(guò)F的直線交拋物線于A(x1.y1).B(x2.y2)兩點(diǎn).(1)求拋物線的方程,(2)設(shè)直線l是拋物線的準(zhǔn)線.求證:以AB為直徑的圓與直線l相切. 查看更多

 

題目列表(包括答案和解析)

(本題12分)已知某種從太空帶回的植物種子每粒成功發(fā)芽的概率都為,某植物研究所分兩個(gè)小組分別獨(dú)立開(kāi)展該種子的發(fā)芽實(shí)驗(yàn),每次實(shí)驗(yàn)種一粒種子,假定某次實(shí)驗(yàn)種子發(fā)芽則稱(chēng)該次實(shí)驗(yàn)是成功的,如果種子沒(méi)有發(fā)芽,則稱(chēng)該次實(shí)驗(yàn)是失敗的.

(1) 第一小組做了三次實(shí)驗(yàn),求實(shí)驗(yàn)成功的平均次數(shù);

(2) 第二小組連續(xù)進(jìn)行實(shí)驗(yàn),求實(shí)驗(yàn)首次成功時(shí)所需的實(shí)驗(yàn)次數(shù)的期望;

(3)兩個(gè)小組分別進(jìn)行2次試驗(yàn),求至少有2次實(shí)驗(yàn)成功的概率.

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書(shū)面表達(dá) (滿(mǎn)分12分)

假設(shè)你學(xué)校的“英語(yǔ)愛(ài)好俱樂(lè)部”將對(duì)“良好飲食習(xí)慣”這一話題進(jìn)行討論。請(qǐng)根據(jù)下列提示,用英語(yǔ)寫(xiě)一篇發(fā)言稿。內(nèi)容要點(diǎn)應(yīng)包括:

部分同學(xué)的飲食習(xí)慣

良好的飲食習(xí)慣

個(gè)人看法

不愛(ài)吃早餐

愛(ài)吃零食

偏食

飲食過(guò)量

飲食多樣化

飲食定時(shí)定量

注意:

發(fā)言稿必須包括所有內(nèi)容要點(diǎn),可適當(dāng)發(fā)揮。

發(fā)言稿開(kāi)頭與結(jié)尾已為你寫(xiě)好,不計(jì)入總詞數(shù)。

詞數(shù)120左右。

參考詞匯: 挑食: be particular about food     零食:snack

friends

As we all know, we are what we eat. _______________________________________________________

                                      

_________________________________________________________________________________________

_________________________________________________________________________________________

That’s all. Thank you for listening.

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第四節(jié):書(shū)面表達(dá)(滿(mǎn)分12分)

       某期中學(xué)生報(bào)的“熱點(diǎn)話題”專(zhuān)欄討論的主題是“上大學(xué)是高中生的唯一選擇嗎?”你班同學(xué)就此話題進(jìn)行了熱烈討論。請(qǐng)根據(jù)以下內(nèi)容用英語(yǔ)給該專(zhuān)欄的編輯寫(xiě)一封信,介紹討論結(jié)果,并發(fā)表你的個(gè)人意見(jiàn)。

觀點(diǎn)

80%的學(xué)生認(rèn)為應(yīng)該上大學(xué)

20%的學(xué)生認(rèn)為不必上大學(xué)

原因

能夠增長(zhǎng)知識(shí)

提高自身的品質(zhì)

利于擇業(yè)…

大學(xué)的學(xué)費(fèi)昂貴

畢業(yè)后就業(yè)困難…

注意: 1. 信的開(kāi)頭已給出,但不計(jì)入總詞數(shù);

                  2. 詞數(shù):100左右。

Dear Editor,

       The students in our class had a discussion about whether the only way for senior high students to succeed is to go to college.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

                                                                              Yours sincerely,

                                                                     Li Hua

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單詞拼寫(xiě)(共 12小題;每小題 1 分,滿(mǎn)分12分)

1.His father is an a______ so he is always busy with designing buildings.

2.We s_____, although others died in the disaster.

3.There are many _____(古代的) buildings in Rome.

4.It’s ______(絕對(duì)的) impossible for them to finish the task in just one day’s time.

5.She is c_______ about her son’s future.

6.The room _____(測(cè)量) five meters across.

7.You’d better stop a_____ with Bill because he will never change his mind.

8.Teaching him Greek was a painful _____(過(guò)程).

9.The street was ____(擁擠的) with people and the traffic was held up.

10.The flat can a_____ a family of five.

11.Now, there is no library in our school, but it will be under _____ (建設(shè)) in a month.

12.S_____ in the center of the city, the shopping mall is full of people even on weekdays.

 

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完形填空 I :閱讀下面短文,掌握其大意,然后從各題所給的四個(gè)選項(xiàng)中,選出最佳選項(xiàng)。(共12個(gè)小題;每小題1分,滿(mǎn)分12分)
A businessman was on a business trip to Tokyo. One day he went to    29   some gifts for his employees (雇員) back in his country. He    30   a supermarket. A lady smiled and   welcomed him. He was very touched, and felt good .Because he was not able to    31    the warmth of her smile, he was watching her as he was    32  . She was giving the same    33    to all the people who walked into the supermarket.
The businessman started thinking if she hated doing the same thing. So he asked, “My dear lady, are you    34    of doing this job?” The lady smiled and said, “No, sir, I have    35   here for the last 10 years and I love my job.” The businessman was surprised and asked, “Why have you stayed here for ten years, and why do you like your job   36    much?” The lady said, “Because I am doing something good for my    37   .” The businessman found this interesting. He asked, “Why?” The lady said, “As most of our customers are    38   , they spend foreign currency here. So our country has a lot of money and becomes richer. People who are happy with our service will 39  _____ more often and spend more money in our country.”
Surprised by her    40   , the businessman thanked her. After returning to his own country he worked hard to introduce the same attitude (態(tài)度) to his workers, and today his company is one of the best companies in the world.
29. A. buy                         B. order         C. make                    D. pay
30. A. opened                    B. cleaned       C. entered                  D. checked 
31. A. require                  B. enjoy               C. hide                         D. forget  
32. A. traveling                   B. working             C. singing                            D. shopping
33. A. feeling                  B. smile         C. warmth                    D. watching 
34. A. fond                         B. tired          C. proud                             D. afraid
35. A. stood                         B. learned       C. worked                    D. lived 
36. A. so                         B. very          C. even                        D. enough
37. A. home                        B. country        C. supermarket           D. boss 
38. A. millionaires            B. managers      C. strangers              D. foreigners 
39. A. praise                        B. visit          C. talk                         D. save 
40. A. action                        B. service        C. attitude                    D. help 

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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)設(shè)拋物線,將(2,2)代入,得p=1. …………4分

∴y2=2x為所求的拋物線的方程.………………………………………………………5分

(2)聯(lián)立 消去y,得到. ………………………………7分

設(shè)AB的中點(diǎn)為,則

∴ 點(diǎn)到準(zhǔn)線l的距離.…………………………………9分

,…………………………11分

,故以AB為直徑的圓與準(zhǔn)線l相切.…………………… 12分

(注:本題第(2)也可用拋物線的定義法證明)

18.解:(1)在△ACF中,,即.………………………………5分

.又,∴.…………………… 7分

(2)

. ……………………………14分

(注:用坐標(biāo)法證明,同樣給分)

19.

解法一:(1)連OM,作OH⊥SM于H.

∵SM為斜高,∴M為BC的中點(diǎn),∴BC⊥OM.

∵BC⊥SM,∴BC⊥平面SMO.

又OH⊥SM,∴OH⊥平面SBC.……… 2分

由題意,得

設(shè)SM=x,

,解之,即.………………… 5分

(2)設(shè)面EBC∩SD=F,取AD中點(diǎn)N,連SN,設(shè)SN∩EF=Q.

∵AD∥BC,∴AD∥面BEFC.而面SAD∩面BEFC=EF,∴AD∥EF.

又AD⊥SN,AD⊥NM,AD⊥面SMN.

從而EF⊥面SMN,∴EF⊥QS,且EF⊥QM.

∴∠SQM為所求二面角的平面角,記為α.……… 7分

由平幾知識(shí),得

,∴

,即所求二面角為. ……………… 10分

(3)存在一點(diǎn)P,使得OP⊥平面EBC.取SD的中點(diǎn)F,連FC,可得梯形EFCB,

取AD的中點(diǎn)G,連SG,GM,得等腰三角形SGM,O為GM的中點(diǎn),

設(shè)SG∩EF=H,則H是EF的中點(diǎn).

連HM,則HM為平面EFCB與平面SGM的交線.

又∵BC⊥SO,BC⊥GM,∴平面EFCB⊥平面SGM. …………… 12分

在平面SGM中,過(guò)O作OQ⊥HM,由兩平面垂直的性質(zhì),可知OQ⊥平面EFCB.

而OQ平面SOM,在平面SOM中,延長(zhǎng)OQ必與SM相交于一點(diǎn),

故存在一點(diǎn)P,使得OP⊥平面EBC. ……………………… 14分

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∵底面邊長(zhǎng)為1,∴,

,

.    ……………… 1分

設(shè)

平面SBC的一個(gè)法向量,

,

,

∴y=2h,n=(0,2h,1).… 3分

=(0,1,0),由題意,得.解得

∴斜高. …………………………………………………… 5分

(2)n=(0,2h,1)=

由對(duì)稱(chēng)性,面SAD的一個(gè)法向量為n1. ………………………………6分

設(shè)平面EBC的一個(gè)法向量n2=(x,y,1),由

,,得

 解得.………………… 8分

設(shè)所求的銳二面角為α,則

,∴.…………… 10分

(3)存在滿(mǎn)足題意的點(diǎn).證明如下:

. ………………………… 11分

,令與n2共線,則. ……………… 13分

.故存在P∈SM,使OP⊥面EBC.……………………… 14分

20. 解:(1)當(dāng)n為奇數(shù)時(shí),an≥a,于是,. ………………3分

         當(dāng)n為偶數(shù)時(shí),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的討論,扣1分)

 . ……………12分

.……15分21.解:(1)∵,,∴,∴. 1分

,即,∴. …3分

①當(dāng),即時(shí),上式不成立.………………………………………………4分

②當(dāng),即時(shí),.由條件,得到

,解得. ……………………………………………5分

,解得.…………………………………………6分

 m的取值范圍是. ………………………………………7分

(2)有一個(gè)實(shí)根.………………………………………………………………………………9分

,即

,則

,. ………………………10分

 △>0,故有相異兩實(shí)根

,∴ 顯然,

,∴,∴. …………12分

于是

                    

為三次函數(shù)的極小值點(diǎn),故與x軸只有一個(gè)交點(diǎn).

∴  方程只有一個(gè)實(shí)根.…………………………15分


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