重庆市西南师大附中2010-2011学年高三第三次月考理科
2010届重庆八中高三第三次月考理综化学部分
2010届重庆八中高三第三次月考理科综合能力测试化学部分理科综合能力测试试题分选择题和综合题两部分。
可能用到的相对原子质量：H 1 ；N 14；Na 23；Cu 64; S 32；O 16； C 12；Ag 108第I卷(选择题)6. 下列叙述正确的是( )A •溶液是电中性的，胶体是带电的B. 雾是气溶胶，在阳光下可观察到丁达尔效应C. 强电解质一定为离子化合物，共价化合物一定为弱电解质D. 某物质A的水溶液导电能力与盐酸相同，则可证明A为强电解质7. N A表示阿伏加德罗常数，下列叙述中正确的是( )A . 24g镁原子的最外层电子数为N AB. CO和N2组成的28g混合气体中含有4N A个原子C. 将0. 1mol氯化铁溶于1L水中，所得溶液含有0. 1N A Fe'+1 _ -D. 一定条件下SO2 (g) + - O2 (g) 、' SO3 (g); △ H=-98 . 3kJ/mol，若反应2放出19. 66 kJ热量，则有0. 2N A SO2被氧化&下列各组离子在指定环境下一定能大量共存的是( )A .滴入甲基橙显红色的溶液中：K+、Fe3+、SO42-、NOJ+ + 2- 2-B. pH=0 的溶液中：Na、K、S、SO3C. 在水电离出的c (H +) =10-12mol 1溶液中：Na+、NH4+、HCO3-、SO42-+ 3+ 2D. 加入一小块钠后没有沉淀生成的溶液中：K、Al 、SO4-、AIO2-9. 下列有关实验操作的说法正确的是( )A .用25ml碱式滴定管量取20. 0ml KMnO 4溶液B .将固体加入容量瓶中溶解并稀释至刻度，配置成一定物质的量浓度的溶液C. 乙酸与乙醇的混合液可用分液漏斗进行分离D. 读取滴定管内液体的体积，俯视读数导致数值偏小10. 下列离子方程式书写正确的是( )2-A .硫化钠的水解：S + 2H2O ------------- H2S+ 2OHB. 实验室制Fe (OH) 3 胶体：Fe3* + 3出。
2010届重庆一中第一学期高三第三次月考文
7.2010届重庆一中第一学期高三第三次月考数学试卷（文科）满分150分。
考试时间120分钟。
注意事项:1•答题前，务必将自己的姓名、准考证号填写在答题卡规定的位置上2.答选择题时，必须使用2B铅笔将答题卡上对应题目的答案标号涂黑，如需改动,用橡皮擦干净后，再选涂其他答案标号。
3.答非选择题时，必须使用0.5毫米黑色签字笔，将答案书写在答题卡规定的位置上。
4•所有题目必须在答题卡上作答，试题卷上答题无效。
、选择题（共10小题，每小题5分，共50分。
请将唯一正确的选项选出来）已知集合A ={x||x -1 卜：2}, B ={x|0 ：： x :: 3}，则A B =A. {x | —1 ：： x :: 3} C. {x | -1 ：： x :: 2}A. a 釘或a -2B. 1^a < 2C.JT 1若sin( 厂6 3{x 10 ：： x ：： 3} {x | 2 ：： x ：： 3}2. F列函数中，在其定义域既是奇函数又是减函数的是3A . y —x y =|x-1|3. 已知平面向量 a = (-1,-2),b = (2,m),若a//b，则实数m=A . -1 C. -4已知等比数列{a n}中,a3 =4,a2 a6 =64，则a2 =函数y =3 sin x ■ cosx的一个单调减区间是JI 31[「2刁 B .[-二，0]函数2f(x)=x -2ax—3 在区间[1,2］上存在反函数的充要条件是r「 2 兀a则2cos2( ) -1 -7.1- 3 - B7- 9 -A -&设a,b € R +，则下列不等式不成立.的是( )1 lA . a b ------------ -2.2Jab1 1 —(a 2b)( )_322a b1=2，（n 2/ i 二na n ,则佝｝的前n 项和S n =n A .n +11 B .n +1io .已知向量 a =(1,cosR,b =(1,-cos"c = (2,1)，若不等式 a b_ t(2a b) 3c n"[O,#恒成立，贝U 实数t 的取值范围是11. 已知且sin 2 - -sin 〉.则tan 〉=。
贵州师大附中2010届高三第三次月数学试题(理科)答案
贵州师大附中2009——2010学年第一学期第三次月考高三数学 理科参考答案13、{1，7，9} 14、1315、15-16、①③④17、(I):(1)a<0,A=,∅∅ 解当时有A B=,{(2)0,-33}a A x a x a ≥=+≤≤+当时有,{81}B x x x =<->或.由∅ A B=,有3813a a -+≥-⎧⎨≥+⎩ 得112a a ≤⎧⎨≤-⎩ 与0a ≥,矛盾!故当∅ A B=时,a 的取值范围是(,0)-∞; (II)解:(1)a<0,A=,∅ 当时有A B=B ,{(2)0,-33}a A x a x a ≥=+≤≤+当时有,{-81}B x x x =<>或由 A B=B,必有A B ⊆,得38a +<-或31a -+>得11a <- (舍去)或2a <得02a ≤< 故当 A B=B 时, a 的取值范围是(,2)-∞.18、解：0)(,)1,1()(<'-x f x f 且内可导在 )1,1()(-∴在x f 上为减函数又当b a ,0)()(,0),1,1(=+=+-∈b f a f b a 时)()(),()(a f a f a f b f -=--=∴即)1,1()(-∴在x f 上为奇函数 )1()1(0)1()1(22m f m f m f m f -->-⇔>-+-∴2111111111)1()1(222<<∴⎪⎩⎪⎨⎧-<-<-<-<-<-⇔->-⇔m m m m m m f m f∴原不等式的解集为)2,1(19、解法一：(Ⅰ)由已知l 2⊥MN, l 2⊥l 1 , MN ∩l 1 =M, 可得l 2⊥平面ABN ． 由已知MN ⊥l 1 ，AM=MB=MN ，可知AN=NB 且AN ⊥NB ．又AN 为AC 在平面ABN 内的射影.∴AC ⊥NB（Ⅱ）∵Rt △CAN ≌Rt △CNB, ∴AC=BC,又已知∠ACB=60°，因此 △ABC 为正三角形．AB MNCl 2 l 1 H∵Rt △ANB ≌Rt △CNB ，∴NC=NA=NB ，因此N 在平面ABC 内的射影H 是正三角形ABC 的中心，连结BH,∠NBH 为NB 与平面ABC 所成的角． 在Rt △NHB 中,cos ∠NBH= HB NB = 33AB 22AB = 63 .解法二：如图,建立空间直角坐标系M －xyz.令MN=1，则有 A(－1, 0, 0)，B(1, 0, 0)，N(0, 1, 0)．(Ⅰ)∵MN 是 l 1、l 2的公垂线, l 1⊥l 2, ∴l 2⊥平面ABN. l 2平行于z 轴．故可设C(0,1,m).于是 AC →=(1,1,m), NB →=(1,－1,0)． ∴AC →·NB →=1+(－1)+0=0 ∴AC ⊥NB ． (Ⅱ)∵AC → =(1,1,m), BC →=(－1,1,m), ∴|AC →|=|BC →|, 又已知∠ACB=60°，∴△ABC 为正三角形，AC=BC=AB=2．在Rt △CNB 中，NB=2，可得NC=2,故C(0,1, 2)． 连结MC ，作NH ⊥MC 于H ，设H(0,λ, 2λ) (λ>0)．∴HN →=(0,1－λ,－2λ)， MC →=(0,1, 2)．HN →·MC →= 1－λ－2λ=0, ∴λ= 13，∴H(0, 13, 23)，可得HN →=(0,23, － 23)，连结BH,则BH →=(－1,13, 23)，∵HN →·BH →=0+29 － 29 =0，∴HN →⊥BH →, 又MC ∩BH=H ，∴HN ⊥平面ABC ，∠NBH 为NB 与平面ABC 所成的角.又BN →=(－1,1,0)， ∴cos ∠NBH= BH →·BN →|BH →|·|BN →| = 4323×2= 63．20、解：随机变量ξ的分布列是ξ的均值为111111233266E ξ=⨯+⨯+⨯=l附：ξ的分布列的一种求法，共有如下6种不同的可能情形，每种情形发生的概率都是1：⑥之下，A 直接感染了三个人．21、解：(Ⅰ)设{}n b 的公差为d ，则1132314=+=+=d d b b ，解得 3=d ， ∴数列{}n b 为25811852，，，，，，．(Ⅱ)12112112-+--+++++++=k k k k k c c c c c c S k k k k c c c c -+++=-+)(2121 ， 50134)13(42212-⨯+--=-k S k ， ∴当13=k 时，12-k S 取得最大值．12-k S 的最大值为626．22. 解：（Ⅰ）22222'(),1(1)(1)(1)a ax a f x ax x ax x +-=-=++++∵()f x 在x=1处取得极值，∴2'(1)0,120,f a a =+-= 即解得 1.a =（Ⅱ）222'(),(1)(1)ax a f x ax x +-=++ ∵0,0,x a ≥> ∴10.ax +>①当2a ≥时，在区间(0,)'()0,f x +∞>上，∴()f x 的单调增区间为(0,).+∞②当02a <<时，由'()0'()0f x x f x x >><<解得由解得∴()f x +∞的单调减区间为（0单调增区间为）.（Ⅲ）当2a ≥时，由（Ⅱ）①知，()(0)1;f x f =的最小值为当02a <<时，由（Ⅱ）②知，()f x 在x =(0)1,f f <=综上可知，若()f x 得最小值为1，则a 的取值范围是[2,)+∞．。
2011届重庆西南师大附中高三第一次月考201009
西南师大附中高2011级第一次月考理综化学部分测试题2010可能用到的相对原子质量：H 1 C 12 Q 16 Na 23 P31 Fe 56 Cu 64 Ag 108第I卷选择题(共126分)选择题(本题包括21小题，每小题6分，共126分。
每小题只有一个选项符合题意)1 .下列鉴别方法不可行的是A. 只用水就可以鉴别乙醇、溴乙烷与乙酸乙酯B. 用Ba(NQ)2溶液鉴别S&「、S©-和C®-C. 用氨水可鉴别Al3+和Ag +D. 用KMnCU酸性溶液鉴别苯和甲苯2 .下列说法正确的是A. 测定硫酸铜晶体中结晶水含量时，应先用称量纸称量一定质量的硫酸铜晶体，再将其转入到坩埚中加热B. NH+、Ag+、PQ3-、C「能在溶液中大量共存C. 1 L 1 mol • L的碳酸钠溶液吸收SQ的量大于1 L 1mol • L-1硫化钠溶液吸收SQ2的量D. 相同条件下，2 mol氢原子所具有的能量大于1 mol氢分子所具有的能量3. 下列热化学方程式或离子方程式中，正确的是A. 甲烷的燃烧热为890.3 kJ • mo「1，则甲烷燃烧的热化学方程式可表示为：—1CH t(g) + 2Q 2(g) = CQ 2(g) + 2H 20(g) ；△H = - 890.3kJ • molB. 500C、30MPa下，将0.5mol N2和1.5molH2置于密闭的容器中充分反应生成NH(g)，放热19.3kJ ,其热化学方程式为：催化剂38.6 kJ • molN2(g) 3H2(g)「5°°c、30MPa ’2NH3(g)；皿C. 氯化镁溶液与氨水反应：Mg2 ' 2QH --Mg(QH) 2D. 用FeCl3溶液腐蚀铜线路板：Cu + 2Fe3 += Ci i++ 2Fe4. 下列说法正确的是A. 测定中和热时，所用稀NaQH溶液和HCI的物质的量恰好相等，以减小实验误差B. NaHSQ固体受热变为熔融状态(未发生化学反应) ，需要克服的作用力有：离子键和共价键C. 在Fe(QH)3胶体中通电，一段时间后，阴极附近颜色加深D. 用蒸馏的方法分离淀粉溶液与C U(QH)2悬浊液的混合物5. 工业上用二氧化锰制备高锰酸钾可分两步进行。
重庆市南开中学2010-2011学年高三4月月考理科数学
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高2010级月考英语试题(2010.5.29)
西南师大附中高2010级适应性模拟训练英语试题第一节：单项填空：21．— Wow, so many new houses! I can’t believe that. It used to be a poor village.—Yes. _________ has changed here.A．Nothing B．Something C．Everything D．Anything22．—_________ potato salad is good.—I’m very glad you like it. I used _________ special cheese to make it.A．The; 不填B．The; a C．A; 不填D．A; the23．— Did you see a girl in white pass by just now?— No, sir. I _________ a newspaper.A．read B．was reading C．had read D．would read24．W hen you stud y the local map, you’ll find this town is _________.A．twice as a large town as that B．twice as larger a town as thatC．twice as larger as that one D．twice the size of that one25．T he soccer team has been doing well this season, so they _________ win the championship．A．should B．might C．would D．could26．T housands of Haitians cheered as the Chinese medical team arrived, many of ________ even cried with joy.A．those B．them C．whom D．who27．O ut there, in the midst of the snow, _________ in long, black clothes.A．a woman sat B．sat a womanC．sitting a woman was D．a woman was sitting28．A lways read the label _________ you wash your clothes.A．before B．unless C．since D．until29．_________ a written permission, he had to write another letter to the president of the university.A．Not giving B．Not having been givenC．Having not given D．Having not been given30．T he rise of oil prices made scientists search for new energy resources _________ oil.A．replace B．replacing C．to replace D．replaced31．S ince Liu Qian, a famous Taiwan magician, performed on CCTV, magic once again has _________ all over China.A．taken on B．taken down C．taken off D．taken out32．A fter driving for five hours, they arrived at _________ they thought was the place they had been dreaming of.A．what B．that C．which D．where33．H e turned down the request of his friend because it was _________ the limit of his power.A．beyond B．over C．off D．above34．W as it because she was ill _________ she didn’t go to attend the meeting?A．what B．which C．as D．that35．— How is everything, Jason?—_________.A．Not at all B．Very well, thank youC．I’m all right, thanks D．Not too bad第二节完形填空：Some years ago when I was in my first year in college, I heard Salome Bey sing for the first time. The moment was excitin g. Salome’s 36 filled the room and brought the theater to life. I was so 37 that I decided to write an article about her.I 38 Salome Bey, telling her I was from Essence magazine, and that I wanted to meet her to talk about her career. She 39 and told me to come to her studio next Tuesday. When I hung up, I was scared out of my mind. I 40 I was lying. I was not a writer at all and hadn’t even written a grocery list.I interviewed Salome Bey the next Tuesday. I sat there 41 , taking notes and asking questions that all began with, “Can you tell me…” I soon realized that 42 Salome Bey was one thing, but writing a story for a national magazine was just impossible. The 43 was almost unbearable. I struggled for days 44 draft after draft. Finally I put my manuscript (手稿) into a large envelope and dropped it into a mailbox.It didn’t take long. My manuscript 45 . How stupid of me! I thought. How could I 46 in a world of professional writers? Knowing I couldn’t 47 the rejection letter, I threw the unopened envelope into a drawer.Five years later, I was moving to California. While 48 my apartment, I came across the unopened envelope. This time I opened it and read the editor’s letter in 49 :Dear Ms Profit,Your story on Salome Bey is fantastic. Yet we need some 50 materials. Please add those and return the article immediately. We would like to 51 your story soon.Shocked, it took me a long time to 52 . Fear of rejection cost me dearly. I lost at least five hundred dollars and having my article appear in a major magazine. More importantly, I lost years of 53 writing. Today, I have become a full-time writer. Looking back on this 54 , I learned a very important lesson: You can’t 55 to doubt yourself.36．A．joy B．voice C．speech D．smile37．A．proud B．active C．satisfied D．moved38．A．visited B．emailed C．phoned D．interviewed 39．A．agreed B．refused C．hesitated D．paused40．A．replied B．discovered C．explained D．knew 41．A．seriously B．patiently C．nervously D．quietly 42．A．blaming B．fooling C．inviting D．urging 43．A．hardship B．failure C．comment D．pressure44．A．with B．by C．on D．in 45．A．disappeared B．returned C．spread D．improved 46．A．compare B．struggle C．survive D．compete 47．A．ignore B．deliver C．face D．receive 48．A．decorating B．repairing C．cleaning D．leaving 49．A．disbelief B．anxiety C．horror D．trouble 50．A．important B．related C．private D．reliable 51．A．broadcast B．create C．publish D．consider 52．A．recover B．prepare C．escape D．concentrate53．A．energetic B．endless C．typical D．enjoyable 54．A．experience B．success C．benefit D．accident 55．A．attempt B．afford C．expect D．pretend第三部分：阅读理解：AIt was a Sunday morning, and I was in a terrible mood. Two of my friends had gone to the movies the night before and hadn’t invited me. I was in my room thinking of ways to make them sorry when my father came in. “Want to go for a ride, today, Beck? It’s a beautiful day.”“No! Leave me alone!” Those were the last words I said to him that morning.My friends called and invited me to go to the mall with them a few hours later. I forgot to be mad at them and went. I came home to find a note on the table. My mother put it where I would be sure to see it. “Dad has had an accident. Please meet us at Highland Park Hospital”.When I reached the hospital, my mother came out and told me my father’s injuries we re extensive. “Your father told the driver to leave him alone and just call 911, thank God! If he had moved Daddy，there’s no telling what might have happened. A broken rib (肋骨) might have pierced (穿透) a lung….”My mother may have said more, but I didn’t h ear. I didn’t hear anything except those terrible words: Leave me alone. My dad said them to save himself from being hurt more. How much had I hurt him when I hurled those words at him earlier in the day?It was several days later that he was finally able to have a conversation. I held his hand gently, afraid of hurting him.“Daddy… I am so sorry….”“It’s okay, sweetheart. I’ll be okay.”“No, ”I said, “I mean about what I said to you that day. You know, that morning?”My father could no more tell a lie than he could fly. He looked at me and said, “Sweetheart,I don’t remember anything about that day, not before, during or after the accident. I remember kissing you goodnight the night before, though.” He managed a weak smile.My English teacher once told me that words have immeasurable power. They can hurt or they can heal. And we all have the power to choose our words. I intend to do that very carefully from now on.56．T he author was in a bad mood that morning because ________.A．his father had a terrible accidentB．he couldn’t drive to the mall with his friendsC．his friends hadn’t invited him to the cinemaD．his father didn’t allow him to go out with his friends57．W hy did the author say sorry to his father in the hospital?A．Because he didn’t go along with his father.B．Because he was rude to his father that morning.C．Because he failed to come earlier after the accident.D．Because he couldn’t look after his fathe r in the hospital.58．T he reason why the author’s father said he forgot everything about that day is that.A．he had a poor memory B．he didn’t want to forgive his sonC．he just wanted to comfort his son D．he lost his memory after the accident59．W hat lesson did Beck learn from the matter?A．Don’t treat your parents badly. B．Don’t hurt others with rude words.C．Don’t move the injured in an accident. D．Don’t be angry with friends at small things.BShort reader – submitted stories – for the woman you should think of today!—— Compiled by Amy Zerello Great Minds Reminded of MomAfter a long, exhausting day, a friend of mine, Allen, headed home. On the road, he passed an elderly woman who was standing by a car with a flat tire. If that were his mother, he thought, he would want someone to help her. With a tired sigh, he turned around and drove back.Just as he reached the stranded woman, a truck pulled up and a burly farmer got out. “Kind of remind s you of your mom, too?” the man asked as the two of them pitched in together to change the tire for the woman.—— Contributed by Katherine L. Houge Your Biggest FanWhile waiting in a bookstore for a guest author to sign her latest book, I leafed through some of the Civil War novels she had written. The woman in line behind me commented, “Those are the best books I’ve ever read. I couldn’t put them down.” Before I could reply, the author frowning, looked over and said, “Oh, come on, Mom!”—— Contributed by Marilyn Kopp Head of the HouseholdMy husband, Jeff, and I came across several problems while assembling our new computer system, so we called the help desk. The man on the phone started to talk to Jeff in computer jargon (行业术语), which confused us even more.“Sir,” my husband politely said, “please explain what I should do as if I were a four-year-old.”“Okay,” the computer technician replied. “Sweetie, could you please put your mommy on the phone?”—— Contributed by Lena Worth How does it feel to tickle your mom’s funny bone?Now send your own funny story to us! You could earn up to $ 300!60．W ho would the farmer be in the first joke?A．Another kind helper. B．The old lady’s son.C．Allen’s friend.D．A policeman.61．W hat was the gue st author’s mom trying to do in the second story?A．Push hard to get her daughter’s signature.B．Promote her daughter’s books by pretending to be a fan.C．Show her pride in her daughter’s achievement.D．Persuade Marilyn Kopp to buy her daughter’s book.62．T he computer technician on the phone in the third story .A．actually could find no way to solve Jeff’s problemsB．laughed at Jeff about his poor knowledge of computer jargonC．wanted to talk to Lena instead of her husband very muchD．believed that Jeff’s mom would know more computer jargon63．T he passage is most possibly found .A．in a storybook B．in a commercial ad C．in a magazine D．in a student’s textbookCIf you’re a male and you’re reading this, congratulations! You’re a surv ivor. According to statistics, you’re more than twice as likely to die of skin cancer than a woman, and nine times more likely to die ofAIDS. Assuming you make it to the end of your natural term, about 78 years for men in Australia, you’ll die on average five years before a woman.There’re many reasons for this — typically, men take more risks than women and are more likely to drink and smoke but perhaps more importantly, men don’t go to the doctor.“Men aren’t seeing doctors as often as they should,” sa ys Dr. Gullotta. “This is particularly so for the over 40s, when diseases tend to strike. According to a recent survey, 95％of women aged between 15 and early 40s see a doctor once a year, compared to 70％of men in the same age group.“A lot of men think they’re unbeatable,” Gullotta says. “They only come in when a friend drops dead on the golf course and they think, Geez, if it could happen to him …”Then there’s the ostrich (鸵鸟) approach. “Some men are scared of what might be there and would rather not kn ow,” says Dr. Ross Cartmill.“Most men get their cars serviced more regularly than they service their bodies,” Cartmill says. He believes most diseases that commonly affect men could be addressed by preventive check-ups. “Prevention is cheaper in the long run than having to treat the diseases. Besides, the final cost is far greater, it’s called premature death.”64．W hy does the author congratulate male readers at the beginning of the passage?A．They can live longer than they expected.B．They are sure to enjoy a longer and happier life.C．They have lived long enough to read this article.D．They are more likely to survive serious diseases now.65．W hich of the author’s statements is the most important reason that men die five years earlier on average than women according to the passage?A．Men drink and smoke much more than women.B．Men don’t seek medical care as often as women.C．Men are more likely to suffer from deadly diseases.D．Men aren’t as cautious as women in face of danger.66．W hich of the following best completes the underlined sentence “Geez, if it could happen to him…”（in Para 4）?A．it could happen to me, too. B．it would be a big misfortune.C．I should avoid playing golf. D．I should consider myself lucky.67．W hat does Dr. Ross Cartmill mean by “the ostrich approach” (in Para5) ?A．A careless attitude towards one’s health conditions.B．A new treatment for certain psychological problems.C．Refusal to get medical treatment for fear of the pain involved.D．Unwillingness to find out about one’s disease because of fear.DWith alarming regularity, we read about oil tankers having accidents near land and the terrible consequences of the oil spills (泄漏) on people, nature, and the environment.Millions of dollars have been used in developing special chemicals to help dismiss the spills and to clean up the animals, beaches, and land spoiled by the oil. Unfortunately, when many of these chemicals are used, more damage is caused to the environment, especially to lives in the sea.Of all of today’s environmental disasters, an oil spill may actually be one of the least serious. Although oil is poisonous, it is a natural material. In the end, it breaks down naturally. There are, of course, long-term effects, but it is usually more serious in the short term.Nature by itself works better than chemical materials, but when there is a spill we demand that governments act immediately with as much hi-tech knowledge as possible. In 1967 the tanker Torrey Canyon sank off the Scilly Isles near the coast of England and spilled 120,000 tones of oil into the ocean. If you go there today, you will find it hard to see any sign that it ever happened.Governments seem to accept the risk of transporting millions of tons of oil by ship every day so that we can fill up our cars and drive around and cause even more environmental damage. Interestingly, the biggest companies in the world produce cars, and the next biggest supply the gasoline to make them run.We should be thinking more about reducing our dependency on oil. Governments should be encouraging research into new technologies, such as cars run by solar power (太阳能), electricity, hydrogen, and so on. Much of this research has, in the past, been held back by the oil, gas, and coal.If the world’s millions of cars were 10% more efficient (高效的) and the industry could easily produce cars at least twice as efficient? We would need many fewer tankers crossing the oceans each year. If this happened, the risks of oil spills would be reduced, and the air we breathe would be cleanerand fresher, too.68．W hat could be the best title of the passage?A．Oil spills pollution. B．What oil pollution is.C．Oil tanker accidents. D．How to reduce oil pollution.69．H ow does the author support the idea that oil spills are not as serious as people believe?A．By giving a description. B．By making an argument.C．By giving an example. D．By making a comparison.70．W hat does the underlined word “risk” in Paragraph 5 refer to?A．Transportation depending more on oil.B．Poisonous oil breaking down naturally.C．Millions of tons of oil spilling into the sea.D．More environmental damage being caused.71．W hich suggestion, is made for reducing oil tank accidents according to the passage?A．We should build safer tankers in the near future.B．We should develop new technologies to cut oil use.C．Tankers should not be allowed to sail near the coastlines.D．Countries should build more oil pipelines under the sea.EOur brains work in complex and strange ways. There are some people who can calculate the day of the week for any given date in 40,000 years, but who cannot add two plus two. Others can perform complex classical piano pieces after hearing them once, but they cannot read or write. Dr. J. Langdon Down first described this condition in 1887. He called these people idiot savants. An idiot savant is a person who has significant mental impairment (损伤), such as in autism or retardation. At the same time, the person also exhibits some extraordinary skills, which are unusual for most people. The skills of the savant may vary from being exceptionally gifted in music or in mathematics, or having a photographic memory.One of the first descriptions of a human who could calculate quickly was written in 1789 by Dr．Benjamin Rush, an American doctor. His patient, Thomas Fuller, was brought to Virginia as a slave in 1724. It took Thomas only 90 seconds to work out that a man who has lived 70 years, 17 days, and 12 hours has lived 2,210,500,800 seconds. Despite this ability, he died in 1790 without ever learning to read or write.Another idiot savant slave became famous as a pianist in the 1860s. Blind Tom had a vocabulary ofonly 100 words, but he played 5,000 musical pieces beautifully.In the excellent movie Rain Man, made in 1988 and available on video cassette, Dustin Hoffman plays an idiot savant who amazes his brother played by Tom Cruise, with his ability to perform complex calculations very rapidly.Today we more clearly recognize that the idiot savant is special because of brain impairment. Yet not all brain impairment leads to savant skills. Some studies have shown that people who have purposeful interruption of the left side of the brain can develop idiot savant skills. However few people wish to participate in such experiments. There are many excellent reasons for not undergoing unnecessary experimentation on one’s brain. The term idiot savant is outdated and inappropriate. Virtually all savants have a high degree of intelligence and are thus not idiots.72．W hat does the passage mainly talk about?A．Idiot savants have areas of outstanding abilities.B．Human Beings have complicated thinking process.C．The brains of the idiot savants are partly impaired.D．The reasons why people have wonderful skills vary.73．W hich of the following can be done by Rain Man?A．He can play wonderful pieces of classical music.B．He can guess out exactly the length of a man’s life.C．He can memorize the contents of the pictures fast.D．He can count matches dropped on the floor quickly.74．W hat can you infer from the passage?A．Idiot savants have real talents for art and math.B．Dr. Down is the first person who found idiot savants.C．Few people wish to risk becoming savants by brain operations.D．Intentional left brain impairments will surely lead to idiot savants.75．W hich of the following shows the structure of the passage?A．B．C．D．第一节：短文改错：My father and I are taking a camping trip at July 76．__________________ and August. We will travel for about two month and 77．__________________will tour United States and parts of Canada. We have 78．__________________decided to camp because it does not cost as many as 79．__________________vacationing in hotels, but we had to plan carefully. I 80．__________________think the car that we are going to drive it is very small, 81．__________________we decide to take only one small suitcase for both of us 82．__________________and as few camping things as possibly. We will take some 83．__________________medicine with us to preventing insects from hurting us, and 84．__________________also some food for picnics. I’m sure that they will have fun. 85．__________________第二节：书面表达（满分25分）假如你是高三学生程鹏。
2009届重庆西南师大附中高三第三次月考理综化学部分
2009届重庆市西南师大附中高三第三次月考理科综合试卷化学部分6、近期《美国化学学会志》报道，中国科学家以CO2为碳源，金属钠为还原剂，在470℃、80MPa下合成金刚石，具有深远意义。
下列说法正确的是（）A．反应过程中反应物被破坏的化学键有：极性键、非极性键和金属键B．金刚石是碳的一种同位素C．反应过程中钠与表现氧化性的CO2的物质的量之比为4∶1D．反应物和产物中，只有两种晶体类型7、N A表示阿伏加德罗常数，下列说法正确的是（）A．标准状况下，22.4 L 水所具有的水分子数为N AB．1 L 1mol/L CH3COOH溶液中CH3COOH分子和CH3COO－离子数目之和为N AC．pH = 1的H2SO4溶液，H＋的数目为0.2N AD．含1 mol FeCl3的溶液经过水解完全转化为Fe(OH)3胶体，所具有的Fe(OH)3胶体微粒个数为N A8、下列离子方程式的书写不正确的是（）A．NaAlO2溶液与NaHCO3溶液混合：AlO2－+ HCO3－+ H2O = Al(OH)3↓+ CO2↑B．NaHSO3溶液与足量Ca(OH)2溶液反应：HSO3－+ Ca2＋+ OH－= CaSO3↓+ H2OC．100 mL 1 mol/L FeBr2溶液中通入标准状况下2.24 L Cl2充分反应：2Fe2＋+ 2Br－+ 2Cl2 = 2Fe3＋+ Br2 + 4Cl－D．Na2S溶液显碱性：S2－+ H2O HS－+ OH－9、下列有关实验的描述正确的是（）A．中和热的实验中，将稀NaOH溶液倒入稀盐酸中立即读取混合后的温度，以防止热量散失B．酸、碱中和滴定实验中，锥形瓶应该先用待测液润洗C．中和滴定实验过程中眼睛应注视滴定管液面的高度D．一定物质的量浓度的NaOH溶液配制过程中如果定容时俯视刻度线，将会使配制的溶液浓度偏高10、原子半径依次增大的三种短周期主族元素：X、Y、Z，其中X、Y同主族，Y、Z同周期，X和Z的单质都与冷水剧烈反应。
重庆市西南师大附中10—11下学期高三数学(理)第六次月考考试试卷
西南师大附中高2011级第六次月考数学试题(理) 2011年3月本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分．共150分，考试时间120分钟．注意事项：1．答题前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上． 2．选择题每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，不能答在试题上． 3．填空题的答案和解答题的解答过程直接写在答题卡Ⅱ上． 4．考试结束，监考人将本试题和答题卡一并收回．第Ⅰ卷(选择题，共50分)一、选择题：本大题共10小题，每题5分，共50分．在每小题给出的四个选项中，只有一项是符合题目要求的． 1．正项等比数列{a n }中，3813lg lg lg 6a a a ++=，则115a a 的值为( )A ．100 B ．10000C ．1000D ．102．二项式9的展开式中有理项共有( ) A ．1项B ．2项C ．3项D ．4项3．已知点P (x ，y )在不等式组2010220x y x y -≤⎧⎪-≤⎨⎪+-≥⎩表示的平面区域上运动，则z x y =-的取值范围是( )A ．[21]--，B ．[21]-，C ．[12]-，D ．[12]，4．已知三条不重合的直线m 、n 、l ，两个不重合的平面αβ、，有下列命题： ①若////m n n m αα⊂，，则 ②若////l m l m αβαβ⊥⊥，且，则 ③若//////m n m n ααββαβ⊂⊂，，，，则 ④若m n n m n αβαββα⊥=⊂⊥⊥，，，，则其中正确的命题个数是( ) A ．1 B ．2 C ．3 D ．45．25人排成5×5的方阵，从中选出3人，要求任意2人既不同行也不同列，则不同的选法有( )A ．60种B ．100种C ．300种D ．600种6．设()()f x g x 与是定义在同一区间[]a b ，上的两个函数，若对任意[]x a b ∈，，都有|()()|1f x g x -≤成立，则称()()f x g x 和在[]a b ，上是“密切函数”，区间[]a b ，称为“密切区间”．若2()34()23f x x x g x x =-+=-与在[]a b ，上是“密切函数”，则其“密切区间”可以是( ) A ．[14]， B ．[24]，C ．[34]，D ．[23]，7．已知△ABC 中，I 为内心，AC ＝2，BC ＝3，AB ＝4，且AI xAB yAC =+，则x ＋y 的值为( ) A ．13B ．49C ．23 D ．598．在平面直角坐标系中，定义11()n n nn n n x y x n N y y x ++=-⎧∈⎨=+⎩为点()n n n P x y ，到点111()n n n P x y +++，的一个变换——“附中变换”．已知1222111(01)()()()n n n n n n P P x y P x y P x y +++，，，，，，，，是经过“附中变换”得到的一列点，设1||n n n a P P +=，数列{a n }的前n 项和为S n ，那么S 10的值为( ) A．31(2B．31(2C．1)D．1)9．已知()f x 是定义在R 上的函数，(1)10f =，且对于任意x R ∈都有(20)()20f x f x +≥+，(1)()1f x f x +≤+，若()()1g x f x x =+-，则(10)g =( ) A ．20B ．10C ．1D ．010．抛物线24y x =的焦点为F ，点A 、B 在抛物线上，且23AFB π∠=，弦AB 的中点M在准线l 上的射影为'M ，则|'|||MM AB 的最大值为( )ABCD第Ⅱ卷(非选择题，共100分)二、填空题：本大题共5小题，每题5分，共25分．各题答案必须填写在答题卡Ⅱ上(只填结果，不要过程)11．为了了解某市今年准备报考体育专业的学生的体重情况，将所得的数据整理后，画出了频率分布直方图(如右图)，已知图中从左到右的前3个小组的频率之比为1∶2∶3，第2小组的频数为12，则抽取的学生人数是__________． 12．已知α为第三象限角，3cos2tan(2)54παα=-+=，则________．13．如图所示，在正三棱锥S —ABC 中，M 、N 分别是棱SC 、BC 的中点，且MN ⊥AM，若侧棱SA =S —ABC 的外接球的表面积是_____________． 14．已知正数a 、b 、c 满足1113451a b c a b b c c a++=+++++，则的最小值是_____________．15．①由“若()()a b c R ab c a bc ∈=，，，则”类比“若a b c ，，为三个向量，则()()a b c a b c =”；②设圆220x y Dx Ey F ++++=与坐标轴的4个交点分别为A (x 1，0)、B (x 2，0)、C (0，y 1)、D (0，y 2)，则12120x x y y -=；③在平面内“三角形的两边之和大于第三边”类比在空间中“四面体的任意三个面的面积之和大于第四个面的面积”； ④在实数列{}n a 中，已知a 1＝0，21321|||1||||1||||1|n n a a a a a a -=-=-=-，，…,，则1234a a a a +++的最大值为2．上述四个推理中，得出的结论正确的是_____________(写出所有正确结论的序号)． 三、解答题：本题共6小题，共75分．各题解答必须答在答题卡Ⅱ上(必须写出必要的文字说明、演算步骤或推理过程)． 16．(本小题满分13分)已知函数22()sin )cos()cos 44f x x x x x ππ=++--(1)求函数()f x 的最小正周期和单调递减区间；(2)求函数()f x 在25[]1236ππ-，上的最大值和最小值，并指出此时相应的x 的值．17．(本小题满分13分) 西师附中“低碳生活”研究小组同学利用寒假在三个小区进行了一次生活习惯是否符合低碳观念的调查，若生活习惯符合低碳观念的称为“低碳族”，否则称为“非低碳族”，这两族人数占各自小区总人数的比例如下：(1)从A B C 三个社区中各选一人，求恰好有2人是低碳族的概率；(2)在B 小区中随机选择20户，从中抽取的3户中“非低碳族”数量为X ，求X 的分布列和EX ．18．(本小题满分13分)P —ABC 中，E为BC 中点，F 为PC 的中点． (1)求证：平面PAE ⊥平面ABC ； (2)求二面角P —AE —F 的大小．19．(本小题满分12分)已知函数||()2x m f x -=和函数()||28g x x x m m =-+-．(1)若m ＝2，求函数()g x 的单调区间；(2)若方程||()2m f x =在[4)x ∈-+∞，恒有唯一解，求实数m 的取值范围； (3)若对任意1(4]x ∈-∞，，均存在2[4)x ∈∞，+，使得12()()f x g x =成立，求实数m 的取值范围．20．(本小题满分12分)已知一条曲线C 在y 轴右边，C 上每一点到点F (1，0)的距离减去它到y 轴距离的差都是1． (1)求曲线C 的方程；(2)是否存在正数m ，对于过点M (m ，0)且与曲线C 有两个交点A 、B 的任一直线，都有0FA FB <？若存在，求出m 的取值范围；若不存在，请说明理由．21．(本小题满分12分)若函数()f x 对任意()()()(1)2p q R f p q f p f q f ∈+==，，都有，且 ． (1)若数列{a n }满足*()()n a f n n N =∈，求a n ；(2)若数列{b n }满足*21318()n n n n b b b a n N ++--=∈，且b 1＝b 2＝1，求b n ；(3)令*12(3)2[]3520n n n n n c b n N -=++∈，，证明：122311111231112n n c c c n nc c c +----<+++<---． 西南师大附中高2011级第六次月考数学试题参考答案(理)2011年3月一、选择题：本大题共10小题，每题5分，共50分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．B 2．B 3．C 4．B 5．D 6．D 7．C 8．C 9．B 10．B 二、填空题：本大题共5小题，每题5分，共25分．11．48 12．17- 13．36π 14．6+15．②③④三、解答题：本题共6小题，共75分． 16．解：(1)22()sin )cos()cos 44f x x x x x ππ=++--2()cos24x x π=+-2cos2x x =-2sin(2)6x π=-∴22T ππ== 4分由3222()262k x k k z πππππ+≤-≤+∈，得5()36k x k k z ππππ+≤≤+∈ ∴单调递减区间为5[]()36k k k z ππππ++∈，7分(2)由(1)知()2sin(2)6f x x π=- ∵25[]1236x ππ∈-， ∴112[]639x πππ-∈-，∴当min 2()6312x x f x πππ-=-=-=，即时，当max 2()2623x x f x πππ-===，即时， 13分17．解：(1)记这3人中恰好有2人是低碳族为事件A1411121427()25325325315P A =⨯⨯+⨯⨯+⨯⨯=4分 (2)在B 小区中随机选择20户中，“非低碳族”有4户，3416320()(0123)k k C C P X k k C -===，，，，10分2888101230.6571995285EX =⨯+⨯+⨯+⨯= 13分18．法一：(1)由题BC ⊥AE ，BC ⊥DE ，∴BC ⊥平面PAE ，∴平面PAE ⊥平面ABC …5分 (2)由(1)知，所求二面角大小与二面角F —AE —C 大小互余．取AB 中点M ，连CM 与AE 交于O ，则O 为△ABC 的中心，取CO 的中点N ，连结FN ，则FN ⊥面ABC ，作NH ⊥AE 于H ，则H 为OE 中点，连结FH ，∠FHN 即为F —AE —C 的平面角．易求得11213222323FN PO ==-== 9分12NH CE ==∴tanFN FHN NH ∠=12分∴所求角为2π-13分 法二：将正四面体置于正方体内，如图所示，则P (0，0，0)，A (1，0，1)，B (0，1，1)，C (1，1，0)，E (12，1，12)，F (12，12，0) (1)设平面PAE 的一个法向量为1(1)n y z =，，，则由11100110022z n PA y z n PE +=⎧⎧=⎪⎪⎨⎨++==⎪⎪⎩⎩有∴1(101)n =-，， 同理可求平面ABC 的一个法向量为2(111)n =，， ∵121010n n =+-= ∴12n n ⊥ ∴平面PAE ⊥平面ABC5分(2)设平面AEF 的一个法向量为(1)n k r =，，， 则由11(1)(1)001122(1)11330(1)(1)022k r nAE n nAF k r ⎧--=⎪⎧=⎪⎪⇒=-⎨⎨=⎪⎪⎩--=⎪⎩，，，，有，，，，，，9分由(1)知平面PAE 的一个法向量为1(11)n =，0，-1114cos ||||112n n n n n n <>===， 12分∴所求二面角为13分法三：也可如右图建系，则) A0，)B0，(00)C，，(00P，，下略．19．解：(1)m＝2时，2224(2)()24(2)x x xg xx x x⎧--≥⎪=⎨-+-<⎪⎩，函数()g x的单调增区间为(1)(2)-∞+∞，，，，单调减区间为(1，2)．2分(2)由||()2[4)mf x x=∈-+∞在，恒有唯一解，得||||x m m-=在[4)x∈-+∞，恒有唯一解；当x－m＝m时，得x＝2m，则2m＝0或2m＜－4，即m＜－2或m＝0．综上，m的取值范围是m＜－2或m＝0．6分(3)2()()()2()x mm xx mf x f xx m--⎧≥⎪=⎨<⎪⎩，则的值域应是()g x的值域的子集．①当48m≤≤时，()f x在(4]-∞，上单调递减，故4()(4)2mf x f-≥=，()g x在[4，m]上单调递减，[)m+∞，上单调递增，故()()28g x g m m≥=-，所以4228m m-≥-，解得456m m≤≤≥或．②当m＞8时，()f x在(4]-∞，上单调递减，故4()(4)2mf x f-≥=，()g x在[4，2m]单调递增，[2m，m]上单调递减，[)m+∞，上单调递增，(4)624()28g m g m m=->=-，故()()28g x g m m≥=-，所以4228m m-≥-，解得456m m≤≤≥或．③0＜m＜4时，()f x在(]m-∞，上单调递减，[m，4]上单调递增，故()()1f x f m≥=．()g x在[4)+∞，上单调递增，故()(4)82g x g m≥=-，所以782142m m-≤≤<，即．④0m≤时，()f x在(]m-∞，上单调递减，[m，4]上单调递增，故()()1f x f m≥=．()g x在[4)+∞，上单调递增，故7()(4)828212g x g m m m ≥=--≤≥，所以，即(舍去)． 综上，m 的取值范围是7[5][6)2+∞，，．12分20．解：(1)设P (x ，y )是曲线C 上任意一点．那么P (x ，y )1(0)x x =>，化简得24(0)y x x =>．2分(2)经过点M (m ，0) (m ＞ 0)的直线l 与曲线C 的交点为A (x 1，y 1)，B (x 2，y 2)，设直线l 的方程为x ty m =+，由24x ty my x =+⎧⎪⎨=⎪⎩2440y ty m --=得，216()0t m ∆=+>于是121244y y ty y m +=⎧⎪⎨=-⎪⎩ ① 4分又1122(1)(1)FA x y FB x y =-=-，，，，12120(1)(1)0FA FB x x y y <⇔--+< ②6分又24y x =，于是不等式②等价于22222212121212121212()1()10[()2]104444164y y y y yy y y y yy y y y +-++<⇔+-+-+<③ 由①式，不等式③等价于22614m m t -+< ④ 10分对于任意实数t ，24t 的最小值为0，所以不等式④对一切t 成立等于价于261033m m m -+<-<+即，由此可见，存在正数m ，对于过点M (m ，0)且与曲线C 有两个交点A 、B 的任一直线，都有0FA FB <，且m 的取值范围是(33-+． 12分21．解：(1)由已知，21()(1)(1)2(1)2(2)2(1)2n n f n f n f f n f n f -=-=-=-=== 2分(2)由(1)知：213182n n n n b b b ++=++设212123(2)18(2)n n n n n n b k b k a k ++++-=-+-(k 为常数)，展开比较系数知120k =- 则212111123(2)18(2)202020n n n n n n b b b +++++=+++ 令211231820n n n n n n d b d d d ++=+=+，则 即21136(3)n n n n d d d d ++++=+，而12116105d d ==， ∴1219{3}32n n d d d d +++=是以为首项，6为公比的等比数列∴119336624n n n n d d -++=⨯=⨯，即111163(6)1212n n n n d d -+-⨯=--⨯∴11113{6}612125n n d d --=是以为首项，－3为公比的等比数列 ∴ 113(3)6(3)1255n n n n d ---=-=-∴6(3)125n n n d -=- ∴6(3)212520n n nn b -=--． 7分(3)由题2nn c =，∴1112121112122(2)2k k k k k k c c ++---==<---∴ 122311111111112222n n c c c nc c c +---+++<+++=--- 又1111211111111(1)12122(21)23222232k k k k k k kk c k n c +++--==-=-≥-=---+-，， ∴1223111(1)111111122(1)1111232322312n n n n c c c n n n c c c +----+++≥-=-->----- ∴原命题得证． 12分。
届重庆市西南师大附中高三第三次月考(理)
2009届重庆市西南师大附中高三第三次月考数学试卷（理）本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分．共150分，考试时间120分钟．第Ⅰ卷 （选择题 共50分）一、选择题：本大题共10小题，每题5分，共50分．在每小题给出的四个选项中，只有一项是符合题目要求的．1.已知向量(82)(1)a b x ==，，，，若//a b ，则x 的值为（ ） A ．14 B ．14- C ．4 D ．– 42.两圆32cos 3cos 42sin 3sin x x y y θθθθ=-+=⎧⎧⎨⎨=+=⎩⎩与的位置关系是（ ） A ．内切 B ．外切 C ．相离 D ．内含3.“a = 3”是“直线210ax y --=与直线640x y c -+=平行”的（ ）条件A ．充要B ．充分而不必要C ．必要而不充分D ．既不充分也不必要 4.已知直线l 1：122y x =+，l 2过点P （– 3，1），且l 1到l 2的角为45︒，则l 2的方程为（ ） A ．3100x y ++=B ．3100x y -+=C ．20x y ++=D ．30x y += 5.已知23()1x f x x +=-，函数()y g x =的图象与函数1(1)y f x -=+的图象关于直线y x =对称，则(11)g 等于（ ）A ．32B ．52C ．2711D ．2396.已知点P （x ，y ）是直线kx + y + 4 = 0（k > 0）上一动点，P A 、PB 是圆C ：2220x y y +-=的两条切线，A 、B 是切点，若四边形P ACB 的最小面积是2，则k 的值为（ ）A ．3BC ．D ．27.已知4a b ab +=，a 、b 均为正数，则使a b m +>恒成立的m 的取值范围是（ ）A ．m < 9B ．9m ≤C ．m < 8D ．8m ≤8.已知{}n a 为等差数列，若11101a a <-，且它的前n 项和n S 有最大值，那么当n S 取得最小正值时，n =（ ）A ．11B ．20C ．19D ．219.已知O 是△ABC 内一点，230OA OB OC ++=，则△AOC 与△BOC 的面积的比值为（ ）A ．32B ．53C ．2D ．310.把数列{21n +}依次按第一个括号一个数，第二个括号两个数，第三个括号三个数，第四个括号四个数，第五个括号一个数，第六个括号两个数，…循环分别为（3），（5，7），（9，11，13），（15，17，19，21），（23），（25，27），（29，31，33），（35，37，39，41），（43） （45，47）…则第104个括号内各数之和为（ ）A ．2036B ．2048C ．2060D ．2072第II 卷 （共100分）二、填空题：本大题共6小题，每题4分，共24分．11.若cos 2sin 4απα=⎛⎫- ⎪⎝⎭，则cos sin αα+的值为____________． 12.等差数列{}n a 的前n 项和为n S ，若31815618S S S =--=，，则18S =____________．13.如图，某地一天从6时到14时的温度变化曲线近似满足函数sin()(02)y A x B ωϕϕπ=++≤<，则温度变化曲线的函数解析式为____________．14.已知函数2|1|(0)()1(0)x x f x x x -+≤⎧=⎨->⎩．那么不等式()0f x <的解集为_______________． 15.x 、y 满足约束条件：225040y x y x y ≥⎧⎪+-≥⎨⎪+-≤⎩，则|5|z x y =+-的最小值是______________．16对于函数f ( x ) = x | x | + px + q ，现给出四个命题：① q = 0时，f ( x )为奇函数② y = f ( x )的图象关于（0，q ）对称③ p = 0，q > 0时，方程f ( x ) = 0有且只有一个实数根④方程f ( x ) = 0至多有两个实数根其中正确命题的序号为_____________________．三、解答题：本题共6小题，共76分，解答应写出文字说明、证明过程或演算步骤．17.(本小题满分12分) 已知2)(),cos 2,(sin ),cos ,cos 35(b b a x f x x b x x a +===记函数(1) 求函数f ( x )的最小正周期；(2) 当62x ππ≤≤时，求函数f ( x )的值域．18.(本小题满分12分) 已知2(1)()(0)2x p x p f x p x p+++=>+ （1）若p > 1时，解关于x 的不等式()0f x ≥；（2）若()2f x >对24x ≤≤时恒成立，求p 的范围．19.(本小题满分12分) 数列{a n }中，a 1 = 1，当2n ≥时，其前n 项和满足21()2n n n S a S =- （1）求S n 的表达式；（2）设21n n S b n =+，数列{b n }的前n 项和为T n ，求T n ． 20.(本小题满分14分) 已知圆C 经过P （4，– 2），Q （– 1，3）两点，且在y 轴上截得的线段长为，半径小于5．（1）求直线PQ 与圆C 的方程．（2）若直线l ∥PQ ，且l 与圆C 交于点A 、B ，90AOB ∠=︒，求直线l 的方程．21.(本小题满分12分) 已知函数1()|1|(0)f x x x=->， . （1）当0 < a < b ，且f ( a ) = f ( b )时，求证：ab >1；（2）若存在实数a ，b （a < b ），使得函数()y f x =的定义域为 [a ，b ]时，值域为[]ma mb ，(0m ≠)，求m 的取值范围．22.(本小题满分14分) 数轴上有一列点P 1，P 2，P 3，…，P n ，…，已知当2n ≥时，点P n 是把线段P n – 1 P n +1作n 等分的分点中最靠近P n+1的点，设线段P 1P 2，P 2P 3，…，P n P n + 1的长度分别为a 1，a 2，a 3，…，a n ，其中a 1 = 1．（1）写出a 2，a 3和a n （2n ≥，*n N ∈）的表达式；（2）证明a 1 + a 2 + a 3 +…+a n < 3（*n N ∈）；（3）设点M n ( n ，a n )（n > 2，*n N ∈），在这些点中是否存在两个点同时在函数2(0)(1)k y k x =>-的图像上，如果存在，请求出点的坐标；如果不存在，请说明理由．。
2010届西南师大附中高三第四次月考理综物理部分
2010届西南师大附中高三第四次月考理科综合测试卷物理部分第I 卷选择题选择题（每小题只有一个选项符合题意。
）14.下列与能量或分子运动有关的说法中，正确的是（）A •常温、常压下，一定质量的理想气体在等温变化过程中，若吸热•则一定对外做功B .温度越高的物体，分子的平均动能越大，内能也越大C •热机工作过程中，若没有摩擦，则它可以将吸收的热量全部转化为机械能D •布朗运动是悬浮在液体中的固体分子的无规则运动15•如图所示，物体 P 放在粗糙水平面上，左边用一根轻弹簧与竖直墙相连，物体静止时弹簧的长度小于原长.若再用一个从 0开始逐渐增大的水平力 F 向右拉P ,直到拉动， 那么在P 被拉动之前的过程中，弹簧对 P 的弹力T 的大小和地面对 P 的摩擦力f 的大小的变化情况是（）C . T 保持不变，f 先减小后增大D . T 先不变后增大，f 先增大后减小16.从同一地点同时开始沿同一方向做直线运动的两个物体I 、H 的速度图象如图所示。
在0-to 时间内，下列说法中正确的是（）A .i 、n 两个物体所受的合外力都在不断减小B .I 物体所受的合外力不断增大，n 物体所受的合外力不断减小C .I 物体的位移不断增大，n 物体的位移不断减小D .I 、n 两个物体的平均速度大小都是（w+V 2）/217•—列简谐横波某时刻的波形如图（甲）所示，该时刻开始计时，波上像如图（乙）所示，则（）A . T 始终增大，f 始终减小B. T 保持不变，f 始终增大A 质点的振动图A .这列波沿x轴正方向传播B .再过0.5 s, A质点通过的路程是20 cmC .再过2.6 s，P质点的加速度正在增大D •从该时刻起，质点P将比质点Q晚回到平衡位置18. 2008年9月25日我国成功发射了神舟七号”载人飞船.在飞船绕地球做匀速圆周运动的过程中，下列说法正确的是（）A .若知道飞船运动的轨道半径和周期，再利用万有引力常量，就可以算出飞船质量B .若宇航员从船舱中慢慢“走”出并离开飞船，飞船因质量减小，所受万有引力减小，则飞船速率减小C. 若飞船执行完任务仅在地球万有引力作用下返回地球，在进入大气层之前的过程中，飞船的动能逐渐增大，重力势能逐渐减小，机械能保持不变D .若有两个这样的飞船在同一轨道上，相隔一段距离一前一后沿同一方向绕行，只要后一飞船向后喷出气体，则两飞船一定能实现对接19•图中虚线a、b、c代表电场中的三条等势线，相邻两等势线之间的电势差相等，实线为一带正电的粒子仅在电场力作用下通过该区域时的运动轨迹，P、Q是这条轨迹上的两点，则以下说法中错误的是（）A. P点的电势较高B .带电粒子通过P点时动能较大C.带电粒子通过P点时的电势能较大D .带电粒子通过P点时的加速度较大20.如下图所示，在光滑的水平面上，小车内一被压缩弹簧的两边与物块m和n相靠，m和n的质量之比为1 : 2,它们与小车间的动摩擦因数相等.释放弹簧后物块在极短的时间内与弹簧分开，分别向左、右运动，两物块相对小车静止下来时，都未与车壁相碰，则（）A . m先相对小车静止下来B. n先相对小车静止下来C .小车始终静止在水平面上D .小车向右加速到一定速度后匀速运动21•将一长木板静止放在光滑的水平面上，如甲图所示，一个小铅块（可视为质点）以水平初速度v0由木板左端向右滑动，到达右端时恰能与木板相对静止.铅块运动中所受的摩擦力始终不变.现将木板分成A和B相同的两块，并紧挨着放在原水平面上，让小铅块仍以初速度V。
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重庆市西南师大附中2010-2011学年高三第三次月
考（期中）
数学（理）试题
2010年11月
（满分：150分时间：120分钟）
一、选择题（每小题5分，共50分）
1．已知集合
，
，则
（）
A．
B．
C．
D．{ 1 }
2．设向量
，
，则“x = 2”是
的（）
A．充分但不必要条件 B．必要但不充分条件
C．充要条件 D．既不充分也不必要条件3．若
，则下列结论不正确的是（）
A．
B．
C．
D．
4．公差不为0的等差数列
中，
，数列
是等比数列，且
，则
（）A．2 B．4 C．8 D．16 5．不等式
对任意实数x恒成立，则实数a的取值范围为（）A．
B．
C．[ 1，2 ] D．
6．已知向量
与
的夹角为30°，且
，
，设
，
，则向量
在
方向上的投影为（）
A．1 B．–1 C．
D．
7．已知函数
，
，
，
，其中以4为最小值的函数个数是（）
A．0 B．1 C．2 D．3
8．将函数
的图象按向量
平移后所得的图象关于点（
，0）中心对称，则向量
的坐标可能为（）
A．（
，0） B．（
，0） C．（
，0） D．（
，0）
9．在
中，三边a、b、c成等比数列，角B所对的边为b，则
的最小值为（）
A．
B．– 1 C．
D．1
10．已知以T = 4为周期的函数
，其中m > 0，若方程
恰有5个实数解，则m的取值范围为（）A．（
，
） B．（
，
） C．（
，
） D．（
，
）
二、填空题（每小题5分，共25分）
11．已知点P（4，– 9）与Q（– 2，3），则直线PQ与y轴的交点分有向线段
所成的比为________________．
12．
，
，则
的值为________________．
13．在等差数列
中，
为其前n项和，若
且A、B、C三点共线，则
_________________．
14．已知函数
（a > 0，且
）的图象恒过定点A，若点A在直线
上，其中
，则
的最小值为_________________．
15．若O为
内一点，
且
，则
________________．
三、解答题（共75分）
16．已知
，
，且
，
，
(1) 求
，
；
(2) 求（
）与
的夹角．
17．
设函数
，且关于x的不等式
的解集为
，
(1) 求b的值；
(2) 解关于x的不等式
（
）．
18．已知向量
=（
，
），
=（
，
），设
，
(1) 求
的最小正周期及单调递增区间；
(2) 若
，求
的值域；
(3) 若
的图象按
=（t，0）作长度最短的平移后，其图象关于原点对称，求
的坐标．
19．已知函数
的定义域是（0，
），当x > 1时，
>0，且
，
(1) 证明：
在定义域上是增函数；
(2) 若
，解不等式
．
20．
重庆市某棚户区改造建筑用地平面示意图如图所示．经规划调研确定，棚改规划建筑用地区域是半径为R的圆面．该圆面的内接四边形ABCD是原棚户建筑用地，测量可知边界AB = AD = 4万米，BC = 6万米，CD = 2万米，
(1) 请计算原棚户区建筑用地ABCD的面积及圆面的半径R的值；
(2) 因地理条件的限制，边界AD、DC不能变更，而边界AB、BC可以调整，为了提高棚户区改造建筑用地的利用率，请在圆弧ABC上设计一点P，使得棚户区改造的新建筑用地APCD的面积最大，并求最大值．
21．设数列
的前n项和为
，对任意的正整数n，都有
成立，记
（
），
(1) 求数列
的通项公式；
(2) 记
（
），设数列
的前n和为
，求证：对任意正整数n，都有
．
西南师大附中高2011级第三次月考
数学试题参考答案(理)
一、选择题（每小题5分，共50分）
1．B 2．A 3．D 4．D 5．A 6．B 7．A 8．C 9．C 10．B
二、填空题（每小题5分，共25分）
11．2 12．
13．1005 14．8 15．4
三、解答题（共75分）
16．解：(1)
7分
(2) 设
的夹角为
∴
13分
17．解：(1) 由
∴
，
∵
的解集为
∴
6分
(2)
①当
，原不等式无解
②当
时，原不等式的解集为
③当当
时，原不等式的解集为
13分
18．解：
4分
(1) 最小正周期为：
（
）
（
∴ 单调递增区间为[
，
]（
） 7分
(2) ∵
∴
∴
∴
10分
(3)
（
）
∴
的对称中心坐标为（
，0）（
∵
的图象按
的长度最短的平移
∴
13分
19．(1) 证：设
且
，则
∴
∴
∴
在（0，
）上是增函数 5分
(2) 解：令
，y = 1得，
令x = 2，
得，
令x = y = 2得，
∴
，
∵
12分
20．解：(1)
，由余弦定理得：
∴
∵
∴
，
S四边形ABCD =
（万平方米）
∴
由正弦定理得：
（万米）
（万米） 6分
(2) S四边形APCD =
，又
设AP = x，CP = y，则
由余弦定理得：
∴
，当且仅当x = y时取“＝”
∴ S四边形APCD =
（万平方米）
∴ 作AC的垂直平分线与圆弧ABC的交点即为点P，最大面积为
万平方米 12分
21．解：(1)
当n = 1时，
∴
当
时，
，
∴ 数列
成等比数列，其首项
，公比
∴
∴
（
） 5分
(2) 由(1)知
∴
又
，
∴
当n = 1时，
当
时，
12分。