江西省師大附中等重點學校高三聯(lián)考試卷(數(shù)學文)

1、二中高三數(shù)學（文科）聯(lián)考試卷參考公式： 錐體的體積13vsh ，其中 s是錐體的底面積，h是錐體的高 . 球的表面積公式24sr ，其中r為球的半徑 . 如果事件ab、互斥，那么()()()p abp ap b 第卷選擇題（共 50 分）一、選擇題（本大題共10 小題，每小題5 分，滿分50 分在每小題給出的四個選項中，只有一項是符合題目要求的. 請把答案涂在答題卡上）1已知復數(shù)11izi， z是 z的共軛復數(shù)，則z等于a4b2 c1 d122設(shè)12log 3a，0.313b，lnc，則a abcb acbc cabd bac3拋物線22yx的焦點坐標是a1(,0)2b( 1,0)c1(0,)

2、4d1(0,)84函數(shù)sincos(0)yaxbxab的一條對稱軸的方程為4x,則以( , )va b 為方向向量的直線的傾斜角為a 45b 60c120d 1355已知兩不共線向量(cos,sin)a，(cos,sin)b，則下列說法不正確的是a ()()ababb a 與 b的夾角等于c2ababd a與 b在 ab 方向上的投影相等6已知函數(shù)7(13 )10( )xa xf xa66xx,若數(shù)列na滿足*( )()naf n nn，且na是遞減數(shù)列，則實數(shù)a的取值范圍是a1(,1)3b1 1(,)3 2c1 5(,)3 6d5(,1)67下列說法中，正確的是a命題“若22ambm，則ab

3、”的逆命題是真命題b命題“xr，02xx”的否定是： “xr，02xx”c命題“p或q”為真命題，則命題“p”和命題“q”均為真命題d已知rx，則“1x”是“2x”的充分不必要條件7若一個底面是正三角形的三棱柱的正視圖如圖所示，其頂點都在一個球面上，則該球的表面積為a163b193c1912d438函數(shù)( )cosf xxx 的導函數(shù)( )fx 在區(qū)間 , 上的圖像大致是10如圖，有公共左頂點和公共左焦點f的橢圓與的長半軸的長分別為1a 和2a ，半焦距分別為1c 和2c . 則下列結(jié)論不正確的是a1122acacb1122acacc122 1a ca cd1 22 1a ca c第卷非選擇題

4、（共 100 分）二、填空題：本大題共5 小題，每小題5 分，共 25 分. 其中 15 題是選做題 , 請把答案填在答題卡的相應橫線上. 11按如下程序框圖運行，則輸出結(jié)果為_開始1i0siss22ii9i否s輸出結(jié)束是12. 甲乙兩人玩猜數(shù)字游戲，先由甲在心中任想一個數(shù)字，記為a，再由乙猜甲剛才所想的數(shù)字，把乙猜的數(shù)字記為b，且,1 ,2,3,4a b若 | 1ab，則稱甲乙“心有靈犀”現(xiàn)任意找兩人玩這個游戲，得出他們“心有靈犀”的概率為13某駕駛員喝了m 升酒后，血液中的酒精含量( )f x （毫克 /毫升）隨時間x（小時）變化的規(guī)律近似滿足表達式25, 01( )31( ) ,153x

5、xxf xx 酒后駕車與醉酒駕車的標準及相應的處罰規(guī)定：駕駛員血液中酒精含量不得超過0.02 毫克 /毫升此駕駛員至少要過小時后才能開車（不足1 小時部分算1 小時，結(jié)果精確到1 小時） 14把正整數(shù)排列成如圖甲的三角形數(shù)陣，然后擦去第偶數(shù)行中的奇數(shù)和第奇數(shù)行中的偶數(shù)，得到如圖乙的三角形數(shù)陣，再把圖乙中的數(shù)按從小到大的順序排成一列，得到一個數(shù)列na，若2011na，則n_15（不等式選講 ） 若不等式 |2|3|xxa 的解集為， 則實數(shù)a的取值范圍為. f 三、解答題（本大題共計6 小題，滿分75 分，解答應寫出文字說明，證明過程或演算步驟. ）（請在答題卡的指定區(qū)域內(nèi)作答，否則該題計為零分

6、）16 （本小題滿分12 分）已知na是首項為19，公差為 - 2 的等差數(shù)列，ns為na的前n項和 . （ 1）求通項na及ns；（ 2）設(shè)nnba是首項為1，公比為3 的等比數(shù)列，求數(shù)列nb的通項公式及其前n項和nt.17 （本小題滿分12 分）為慶祝國慶，某中學團委組織了“歌頌祖國，愛我中華”知識競賽，從參加考試的學生中抽出 60 名學生，將其成績（成績均為整數(shù)）分成六段40,50) ，50,60) ， 90,100 后畫出如圖的部分頻率分布直方圖，觀察圖形的信息，回答下列問題：（ 1）求第四小組的頻率，并補全這個頻率分布直方圖；（ 2）估計這次考試的及格率（60 分及以上為及格）和平均

7、分；18 （本小題滿分12 分）已知函數(shù)223sin2 3sincos5cosfxxxxx （ 1）若5f，求tan的值；（ 2） 設(shè)abc 三內(nèi)角,a b c 所對邊分別為, , ,a b c 且2222222acbcabcac， 求( )f x 在 0,b 上的值域19 （本小題滿分12 分）如圖，ab為圓 o 的直徑， 點e、f在圓 o 上，abef，矩形 abcd 所在的平面和圓o所在的平面互相垂直，且2ab，1adef. （ 1）求證：af平面 cbf ；（ 2）設(shè) fc 的中點為m，求證： om 平面daf；（ 3）設(shè)平面 cbf 將幾何體 efabcd 分成的兩個錐體的體積分別為

8、fabcdv，fcbev，求fabcdv:fcbev20（本小題滿分13 分）已知函數(shù)( )lnf xxx . （ 1）求( )f x 的最小值；（ 2）若對所有1x都有( )1f xax，求實數(shù)a的取值范圍 . 21（本小題滿分14 分）已知雙曲線221xy的左、右頂點分別為12aa、，動直線:lykxm 與圓221xy相切，且與雙曲線左、右兩支的交點分別為111222(,),(,)p xyp xy. （ 1）求 k的取值范圍，并求21xx 的最小值；（ 2） 記直線11p a 的斜率為1k ， 直線22p a 的斜率為2k ，那么12kk 是定值嗎？證明你的結(jié)論. faecobdm高三聯(lián)考

9、數(shù)學（文科）參考答案一、選擇題題號1 2 3 4 5 6 7 8 9 10 答案c a d d b c b b a d 二、填空題11170 12. 5813414102815(,5三、解答題16解： （1）因為na是首項為,191a公差2d的等差數(shù)列，所以,212) 1(219nnan2(1)19( 2)202nn nsnnn6 分（ 2）由題意13,nnnba所以13,nnnba則1231(133)20.2nnnntsnn12 分17 解： （1）因為各組的頻率和等于1，故第四組的頻率：41(0.0250.01520.010.005)100.3f3 分直方圖如圖所示 6 分（2）依題意，及

10、格以上的分數(shù)所在的第三、四、五、六組的頻率之和為(0.0150.030.0250.005)100.75 ，9 分抽樣學生成績的合格率是75%利用組中值估算抽樣學生的平均分123456455565758595450.1550.15650.15750.3850.25950.0571ffffff則估計這次考試的平均分是71 分12 分18解：（1）由5f，得223sin2 3sincos5cos51cos21cos233sin 255223sin 2cos21，即3sin21cos222 3sincos2sinsin03或tan，tan0tan3或6 分（2）由2cos,2cos2acbcabcac

11、即cos1,cos2bbcac得cos1,sincos2sinsinbbcac則1cos2b即3b，8 分又223sin2 3sincos5cosfxxxxx3sin 2cos24xxfaecobdm2sin(2)46x10 分由03x ,，則1sin(2)126x剟，故5( )6f x剟，即值域是5,6 . 12 分19解（1）平面abcd平面abef,abcb, 平面abcd平面abef=ab，cb平面abef，af平面abef，cbaf,2 分又ab為圓o的直徑，bfaf，af平面cbf。4分（2）設(shè)df的中點為n，則mn/cd21，又ao/cd21，則mn/ao，mnao為平行四邊形，

12、/oman，又an平面daf，om平面daf，/om平面daf. 8 分(3) 過點f作abfg于g，平面abcd平面abef，fg平面abcd，fgfgsvabcdabcdf3231，cb平面abef，cbsvvbfebfeccbef31fgcbfgef612131，abcdfv1:4:cbefv12 分20、解： （1）( )f x的定義域為0( ，+ )，( )f x的導數(shù)( )1lnfxx. 2 分令( )0fx，解得1ex；令( )0fx，解得10ex. 從而( )f x在10e，單調(diào)遞減，在1e，+單調(diào)遞增 . 所以，當1ex時，( )f x取得最小值1e. 6 分（2） 解法一：

13、 令( )( )(1)g xf xax，則( )( )1lng xfxaax， 若1a，當1x時，( )1ln10gxaxa，故( )g x在(1)，+上為增函數(shù)，所以，1x時，( )(1)10g xga，即( )1f xax 若1a，方程( )0gx的根為10eax，此時，若0(1)xx，則( )0g x，故( )g x在該區(qū)間為減函數(shù). 所以0(1)xx，時，( )(1)10g xga，即( )1f xax，與題設(shè)( )1f xax相矛盾 . 綜上，滿足條件的a的取值范圍是(1，. 13 分解法二： 依題意，得( )1f xax在1)，上恒成立，即不等式1lnaxx對于1)x，恒成立. 8

14、 分令1( )lng xxx，則21111( )1g xxxxx. 10 分當1x時，因為11( )10g xxx，故( )g x是(1)，上的增函數(shù)，所以( )g x的最小值是(1)1g，所以a的取值范圍是(1，. 13 分21 解：（ 1）l與圓相切 ,211mk221mk 2分由221ykxmxy , 得222(1)2(1)0kxmkxm, 222222221221044(1)(1)4(1)80101km kkmmkmxxk , 21,k11k, 故k的取值范圍為( 1,1). 5 分由于21221121222222 222()4111mkxxxxxxx xkkk，201k當20k時，2

15、1xx取最小值2 2. 7 分（2）由已知可得12,a a的坐標分別為( 1,0),(1,0)，121212,11yykkxx，121212(1)(1)y ykkxx1212()()(1)(1)kxm kxmxx10 分2212121221()()1k x xmk xxmx xxx22222222121112 2111mmkkmkmkkmkk2222222222212 21m kkm km kmmk222222 2kmmk，由221mk，121(32 2)322kk為定值 . 14 分二中高三英語聯(lián)考試卷第卷（三部分，共115 分）第一部分聽力 （共兩節(jié) , 滿分 30 分）第一節(jié)（ 共 5

16、小題；每小題1.5 分, 滿分 7.5 分）聽下面5 段對話。每段對話后有一個小題, 從題中所給的a、b、c 三個選項中選出最佳選項 , 并標在試卷的相應位置。聽完每段對話后, 你都有10 秒鐘的時間來回答有關(guān)小題和閱讀下一小題。每段對話僅讀一遍。1. when did the speakers start? a. at 4:00. b. at 4:15. c. at 4:22. 2. what is jack now? a. a student. b. a teacher. c.a clerk. 3. what should carol have done according to the

17、man? a. met some friends. b. made a decision. c. met the woman. 4. who was the birthday party for? a. jade. b. lisa. c. lily. 5. what color of the right bottle s top is? a. red. b. brown. c. blue. 第二節(jié) （共 15 小題；每小題1.5 分, 滿分 22.5 分）聽下面5 段對話或獨白。每段對話或獨白后有幾個小題, 從題中所給的a、b、c 三個選項中選出最佳選項, 并標在試卷的相應位置。聽每段對話或獨

18、白前, 你將有時間閱讀各個小題, 每小題 5 秒鐘；聽完后, 各小題將給出5 秒鐘的作答時間。每段對話或獨白讀兩遍。聽第 6 段材料 , 回答第 6 至 7 題。6. what are the speakers mainly talking about? a. scenery. b. basketball game. c. weather. 7. why have they decided to go inside? a. they feel rather cold outside. b. they try to avoid the sunshine. c. they want to watc

19、h a tv program. 聽第 7 段材料 , 回答第 8 至 9 題。8. what is the man now? a. a reporter. b. a teacher. c. a singer. 9. why does the man talk to the woman? a. to ask for help. b. to seek comfort. c. to have an interview. 聽第 8 段材料 , 回答第 10 至 12 題。10. what do we know about beaufort from the conversation? a. he wa

20、s a sport player. b. he was a nobleman. c. he was very smart. 11. what did beaufort do? a. he invented badminton. b. he traveled the whole europe. c. he made a kind of sport popular. 12. where did the name “ badminton ” come from?a. an estate（莊園） . b. a duke. c. a town. 聽第 9 段材料 , 回答第 13 至 16 題。13.

21、when will the performance start? a. at 1:00 pm. b. at 2:00 pm. c. at 3:00 pm. 14. what are they visiting? a. a club. b. a museum. c. an ancient machine. 15. what does the woman think about the ancient chinese woman who did needle work? a. decent. b. beautiful. c. surprised. 16. what are they going t

22、o do finally? a. look at practicing singing. b. look around the theater. c. leave for home. 聽第 10 段材料 , 回答第 17 至 20 題。17. what is the main reason for more people to shop online according to the report? a. to avoid crowded stores. b. to buy gifts at lower prices. c. to push business into the black. 1

23、8. what day is called black friday? a. the monday before thanksgiving. b. the day before thanksgiving. c. the day after thanksgiving. 19. how much was online spending during the holiday season last year? a.20%. b. 25%. c. 30%. 20. what is the report mainly about? a. the development of the internet.

24、b. the spending of the holiday season. c. the change of people s shopping habit. 第二部分英語知識運用（共兩節(jié) , 滿分 45 分）第一節(jié)語法和詞匯 （共 15 小題；每小題1 分, 滿分 15 分）從 a、b、c、d 四個選項中 , 選出可以填入空白處的最佳選項。21. as _ mountains beyond our village are becoming greener and greener, they have become_ home to a large amount of wild life.

25、a. the; / b. the; a c. /; / d. the; the 22. the third summit of the group of 20 (g20) _ in pittsburgh, pennsylvania on the evening of september 24, 2009. a. took off b. kicked off c. put off d. set off 23._, the driver looked at the vast desert without knowing if he could get across safely. a. tired

26、ly and sadly b. tired and sad c. tired and sadly d. tiredly and sad 24. it was foolish of you to take a taxi _you could easily walk there in five minutes. a. though b. as long as c. so that d. when 25. in your _, i would say that reading a lot is one of the best ways to learn a foreign language unde

27、r the _ that you are not living in an english speaking country. a. situation; case b. condition; case c. situation; condition d. condition; situation 26. have you got accustomed to your new job? well, yes. it s not as good as i expected, _. a. though b. but c. too d. either 27. it was too cold yeste

28、rday morning, and i couldn t get my car _. why didn t you try _ the battery with some hot water? a. started; to fill b. to run; filling c. going; fill d. starting; filling 28. though alice is busy, music has always been _ her work. a. as much a part of her life as b. as a part of her life much as c.

29、 as much as a part of her life d. so much a part of her life as 29. thinking you know in fact you don t is a terrible mistake. a. that; that b. that; what c. what; what d. what; that 30. _all over the hills and around the lake are wild flowers of different kinds. a. to grow b. growing c. grown d. gr

30、ow 31. if not _ from work, i will spend some time _ in my study every evening. a. being tired; locking b. tiring; locked c. tired; locked d. to be tired; being locked 32. when shall we restart our business? not until we our plan. a. will finish b. are finishing c. are to finish d. have finished 33.

31、you know what? tom wants to be harry potter after he graduates from school. are you kidding? he will never _ a person like him. a. change b. turn c. make d. get 34. karl louise has just won the 100-meter race. _! he never won it before. a. congratulations b. what a good news c. what a good surprise

32、d. how exciting the race is 35. i d rather you did some housework when you are free ,but you . a. didn t b. shouldn t c. weren t d. don t 第二節(jié) .完形填空：（共 20 小題 , 每小題 1.5 分, 滿分 30 分）閱讀下面短文, 掌握其大意 , 然后從 41 到 60 各題所給的四個選項選出最佳答案。it was a cold winter s night when i stopped for gas on my way home from work.

33、i was tired and had a slight 36 . i worked in a 37 doctor s office and this was one of those days when the unexpected happened, making the schedule run 38 than usual. it seemed i was going to be late 39 home and my husband, being the 40 person, would be ready to pronounce me late once again. maybe 4

34、1 i hurried, i could still make it home. i was heading inside to 42 for my gas when i noticed an older couple at the counter. i heard them asking for 43 to the local hospital. it was the same hospital that i had just 44 a few minutes ago. the young man at the counter was trying to be 45 in explainin

35、g how to get there, with two other people making 46 . one of them was 47 trying to give them a whole different route back. it was then that i walked over to the couple and said, “ would you like to follow me to the 48 ?”a look of 49 crossed the woman s face. “ i m going right by there,” i said , whi

36、ch wasn t a(an) 50 since i had just made up my mind to do 51 that. i got in my car and began the journey back. i was trying to watch to be sure they were right 52 me. it took only fifteen minutes to get there as rush hour traffic was beginning to 53 . i felt better than i had all day and my headache

37、 was nearly gone. later, as i arrived home, my husband 54 , “ so you aren t ever late any more.” i said, “ sometimes it s 55 to be late.”36. a. break b. fever c. cold d. headache 37. a. foreign b. common c. busy d. noisy 38. a. earlier b. later c. easier d. simpler 39. a. getting b. cooking c. calli

38、ng d. working 40. a. tough b. punctual c. generous d. careful 41. a. as b. since c. while d. if 42. a. pay b. change c. wait d. search 43. a. opinions b. trouble c. directions d. money 44. a. reached b. visited c. called d. left 45. a. skilled b. helpful c. experienced d. active 46. a. comments b. p

39、romises c. jokes d. offers 47. a. only b. still c. even d. ever 48. a. station b. office c. hospital d. hotel 49. a. panic b. relief c. sadness d. peace 50. a. duty b. fact c. reason d. lie 51. a. partly b. properly c. exactly d. perfectly 52. a. across b. before c. beside d. behind 53. a. go up b.

40、die down c. speed up d. turn down 54. a. teased b. shouted c. burst d. laughed 55. a. possible b. special c. good d. safe 第三部分閱讀理解 ： （共 20 小題 , 每小題 2 分, 滿分 40 分）閱讀下列短文, 從每題所給的四個選項a、b、c、d 中選出最佳選項。a based on sue monk kidd s best selling novel, the secret life of bees is a movie of hope and faith for e

41、ven the unloved and oppressed. just as in the book, young lily s thoughts sound and read like poetry, from the first moment when her room fills with bees. the movie tells the story of the young white girl who runs away from her cruel father. lily convinces rosaleen, the black housekeeper to escape w

42、ith her, after rosaleen is beaten when she attempts to vote. when lily asks rosaleen why she risked her life standing up to the angry men who wanted to kill her, she hears “ giving in to them would be just another way of dying”.that s lily s story, too. she finally stands up to her father. they come

43、 to tiburon, a town whose name is written on a label from a jar belonging to her mother before her death. in tiburon, there is no place where rosaleen can eat or stay, despite the fact that president johnson just sighed the civil rights act in 1964. (it s still just a piece of paper, rosaleen says.)

44、 so lily goes in to buy food for them, and sees the jar on sale. when lily finds out it s made right there in a farmhouse, they go there and ask for help. the goodhearted august who runs a successful company, offers them the honey house to live in. from august, lily learns honey business and a life

45、lesson from the bees. she sees a world where intelligence, independence and culture are honored and rewarded. she watches rosaleen begin to understand that the dream of freedom from oppression she gave up when she was beaten is now possible for her. it is august who helps lily see that love is all a

46、round her and all the others. 56. the story of the lily is mainly developed by _. a. time b. space c. examples d. comparison 57. which is true according to the passage? a. the movie is adapted from a novel. b. lily s father treats rosaleen cruelly. c. lily s mother writes the label for her. d. in fa

47、ct, lily s mother is august. 58. what does rosaleen really want to get? a. better pay and honey business. b. equal rights and freedom. c. the right to be voted as president d. enough food and houses. 59. we can conclude that the story of lily happened_. a. in modern america b. in the 1960 s in north

48、 america c. when the black owned equal rights in america. d. before the independence of america. 60. the passage is written to _. a. advertise a book b. explain the secret of bees life c. introduce a movie d. tell about american politics b eating a diet high in processed food (加工食品 ) increases the r

49、isk of depression, research suggests. what s more, people who ate plenty of vegetables, fruit and fish actually had a lower risk of depression, the university college london team found. data on diet among 3,500 middle-aged civil servants (公務員 ) were compared with their emotional state five years lat

50、er, a british journal reported. they split the participants into two types of diet those who ate a diet largely based on whole food, which includes lots of fruit, vegetables and fish, and those who ate a mainly processed food diet, such as sweetened desserts, fried food, processed meat, refined grai

51、ns and high-fat dairy products. after accounting for factors such as gender, age, education, physical activity, smoking habits and chronic (慢性的 ) diseases, they found a significant difference in the future depression risk with the different diets. those who ate the most wholefood had a 26% lower ris

52、k of future depression than those who ate the least wholefood. by contrast, people with a diet high in processed food had a 58% higher risk of depression than those who ate a diet low in processed foods. study author dr. archana singh- manoux pointed out there was a chance the finding could be expla

53、ined by a lifestyle factor they had not accounted for. there was a paper showing a mediterranean diet was associated with a lower risk of depression, but the problem with that is if you live in britain, the likelihood (可能性 ) of you eating a mediterranean diet is not very high. dr. andrew mcculloch,

54、chief executive of the mental health foundation, said, this study adds to an existing body of solid research that shows the strong links between what we eat and our mental health. he added people s diets were becoming increasingly unhealthy. the uk population is consuming less nutritious, fresh prod

55、uce and more saturated (含飽和脂肪酸的) fats and sugars. 61. the text is mainly about _. a. the increasingly unhealthy diet of the uk population b. the link between processed food and depression c. the relationship between physical and mental health d. a healthy diet largely based on wholefood 62. what do

56、we know about the participants? a. they are of different ages from young to old. b. they have been eating a less healthy diet these years. c. most of them prefer wholefood to processed food. d. those who ate wholefood generally were happier in the long term. 63. what can we learn from what dr. archa

57、na singh manoux said? a. it is difficult for most british people to have a mediterranean diet. b. the mediterranean diet is the most healthy in the world. c. many studies have been done on the mediterranean diet before. d. the mediterranean diet is not good for depression. 64. dr. andrew mcculloch a

58、grees that _. a. our diets are closely related to our mental health b. the present study needs more facts and other information c. the uk population will become ill in the near future d. more saturated fats and sugars should be taken in 65. why might the author have written this text? a. to tell peo

59、ple what a healthy diet actually is. b. to prove people s diets are increasingly unhealthy. c. to encourage people to cut down on processed food. d. to introduce some experts on the research team. c speechthe act of uttering sounds to convey meaningis a kind of human action. like any other constantl

60、y repeated action, speaking has to be learned, but once it is learned, it becomes a generally unconscious and apparently automatic process. as far as we can determine, human beings do not need to be forced to speak； most babies seem to possess a sort of instinctive drive to produce speech like noise