2009年全国高考理科数学试题及答案-宁夏卷
2009宁夏高考数学试题答案(理数)
工商管理专业学位外语考试模拟试题（1）2004.12一、语音题（每空1分，共10分）1、breach A. break B. theatre C. meadow D. least2、notice A. stomachs B. houses C. mouths D. reasonable3、opposite A. companion B. balloon C. stroll D. historic O:4、scatter A. laboratory B. separate C. gravity D. various5、twinkle A. windy B. drink C. footprint D. interesting6、shook A. shoot B. food C. shoe D. wood7、occasionally A. population B. Russian C. question D. television8、pressure A. directly B. oxygen C. absence D. camera9、float A. flower B. brown C. hometown D. bellows10、bulletin A. bury B. Prussian C. bullet D. punishment二、单选题（每空1.5分，共30分）11、Y ou are lucky since you've never ____anything in your life.A. lostB. gotC. stolenD. found12、W ould you please help me to ____up the present for the old gentleman?A. wrapB. tieC. coverD. send13、Since your supervisor has _____ the time for a talk, you must make sure that you will be there on time.A. predictedB. specifiedC. yieldedD. classified14、His _____ handwriting resulted from haste and carelessness rather than from the inability to form the letters correctly.A. unreadableB. beautifulC. carefulD. undecided15、My friend was full of _____ for the way in which I had so quickly learned to drive a car.A. prideB. surpriseC. admirationD. jealousy16、What time does my flight leave ____Tuesday?A. atB. inC. byD. on17、It has been a long time _____I saw you last time.A. sinceB. forC. beforeD. after18、What are you doing? I'm _____the bedroom for my wallet.A. lookingB. findingC. searchingD. searching for19、The little girl woke up screaming because she had had a_____.A. daydreamB. nightmareC. fantasyD. sweet dream20、The manager ___that the new employees go through professional training before they started working.A. persistedB. insistedC. resistedD. assisted21、She talked to him for a long time and ___him from doing that dangerous job.A. persuadedB. dissuadedC. overcameD. conquered22、The textile industry _____ greatly to the economy of Hong Kong.A. addsB. amountsC. contributesD. leads23、They decided to chase the cow away ______ it did more damage.A. unlessB. untilC. beforeD. what24、All _______ is a continuous supply of the basic necessities of life.A. what is neededB. for our needsC. the thing neededD. that is needed25、The manufacturers _____ carried out one of the Chairman's proposals, but they didn't.A. must haveB. couldn't haveC. ought to haveD. shouldn't have26、They are believed ____ in their experiment.A. to have already succeededB. to succeed alreadyC. to be succeededD. to be succeed27、Y ou ought not to ____ him the news that day.A. tellB. be tellingC. have toldD. had told28、I know you're planning to travel this summer, but do you know_____?A. how much cost it will beB. how much has it costC. how much will it costD. how much it will cost29、Y our little girl is becoming very rude. Y ou _____scold her.A. mayB. canC. oughtD. ought to30、Please listen to me. It's inappropriate for you to persist in ___ this.A. to doB. doC. doingD. having done三、词形变换（每空1分，共5分）31、(explode) Did you hear the terrible __explosion____last night?32、(disappoint) To his great __disappointment___, Mrs. White won't be able to join us in the party this weekend.33、(promote) He looks happy today. I guess he has got a_promotion_____.34、(economic)I am a college student now. My major is__economics___.35、(add)They need_additional__ help to get the work done as planed.四、完形填空（每空1分，共20分）It was the night before the composition was due. As I looked at the list of topics (题目) , "The Art of Eating Spaghetti (意大利面条) " caught my eye. The word "spaghetti" brought back the 36 of an evening at Uncle Alien' s in Belleville 37 all of us were seated around the table and Aunt Pat 38 spaghetti for supper. Spaghetti was an exotic treat in 39 days. Never had I eaten spaghetti, and 40 of the grown-ups had enough experience to be 41 it. What laughing 42 we had about the 43 respectable method for moving spaghetti from plate to mouth. 44 , I wanted to write about that, but I wanted to 45 it down simply for my own 46 , not for Mr. Fleagle, my composition teacher. 47 , I would write something else.When I finished it the night was half gone and there was no 48 left to write a proper composition for Mr. Fleagle. There was no choice next morning but to 49 my work. Two days passed before Mr. Fleagle returned the 50 papers. He said, "Now, class, I want to read you a composition, "The Art of Eating Spaghetti'. "My words! He was reading my words out 51 to the whole class. 52 laughed, then the whole class was laughing with open-hearted enjoyment.I did my best not to show 53 , but what I was feeling was pure happiness, 54 my words had the power to make people 55 .36 A. memory B. thought C. knowledge D. experience37 A. when B. where C. since D. after38 A. cooked B. served C. got D. made39 A. their B. past C. last D. those40 A. none B. one C. earns D. neither41 A. careful about B. good at C. fond of D. interested in42 A. speeches B. lessons C. sayings D. arguments43 A. nearly B. naturally C. officially D. socially44 A. Especially B. Probably C. Suddenly D. Fortunately45 A. settle B. put C. bite D. let46 A. work B. story C. luck D. joy47 A. However B. Therefore C. As for him D. Except for that48 A. time B. excuse C. way D. idea49 A. give up B. continue C. hand in D. delay50 A. written B. graded C. collected D. calmly51 A. loud B. fast C. publicly D. calmly52 A. People B. Nobody C. Somebody D. I53 A. shock B. wonder C. worry D. pleasure54 A. if B. for C. while D. although55 A. excited B. satisfied C. think D. laugh五、阅读理解（每题1分，共20分）（一）Most great inventors in the capitalist society meet with much opposition to their inventions from the people who place their own interests before those of the people. Big monopolies try to buy inventions and turn them to their own profits. When they fail, they resort to other tricks. Inventors have to overcome thousands of difficulties put in their path before they can see their dreams realized.When George Stephenson was experimenting with the stream engine, there was much opposition from the Parliament, the newspaper, and landlords. They claimed that the noise and the smoke would kill cows, horses and sheep, that the engine would burst or that hot coals from it would set fire to their houses.So it was a very difficult matter for George Stephenson to persuade the people that trains could go on smooth rails, could pull carriages and wagons full of people and goods, and that there was no great danger of accidents.However, he was able to do it, and the first train driven by Stephenson himself showed that the newly invented steam engine was a complete success.56. The word "those" in the first sentence refers toA. inventorsB. inventionsC. interestsD. monopolies57.Why do big monopolies buy inventions?A. They want to make a further research.B. They want to improve them.C. They want to make more money.D. They want to play tricks with inventors.58.Which of the following is not the very reason for the opposition to Stephenson's experiment?A. It would make terrible noise.B. It would give off heavy smoke.C. It would waste coal.D. It would set fire to houses.59. The word "dream" in the first paragraph refers to _____A. inventors' interests in inventionsB. inventors' plans for inventionsC. the profits inventors would makeD. the difficulties in their inventions.60. What is the main idea of this paragraph?A. Stephenson invented the stream engine.B. Big monopolies opposed to inventions.C. Inventors' difficulties in their invention.D. Oppositions to Stephenson the inventor.（二）As a young girl, Elizabeth Barrett (Browning英国作家勃朗宁) ruptured a blood vessel on the lungs which did not heal. The physician consigned her to a milder climate for the winter and she went Devonshire for restoration. Among the members of her family who accompanied her to those healing shores was her eldest brother.For a whole year they lived side by side in affectionate companionship, she all the while being greatly benefited by mild sea breezes of Torquay.One summer morning her brother went board a small sailboat with two friends for a trip of several hours around the coast. Just as the vessel came in sight of the window where Miss Barrett sat watching, the boat struck a sunken reef; and all who were in it went down and perished in the sea, before assistant could be rendered. None of the bodies were ever found although the whole village, full of sympathy, assembled in search. This was the tragedy which utterly prostrated for some years afterwards the health and soul of Elizabeth Barrett. Somehow she felt that she herself had in some measure been the cause of all this horror, and she suffered accordingly. Her whole being seemed shattered, and a year longer elapsed before, she was able to be more to London. This fatal event, which so saddened her youth gave also a still deeper devotional feeling to hue ofsorrow so apparent in many of her earlier pieces.61.What sort of climate did Elizabeth's doctor prescribe?A. Temperate.B. Tropical.C. Humid.D. Arid.62.How many people were drowned when the boat sank?A. OneB. TwoC. ThreeD. The article doesn't indicate63. How did the tragedy affect Elizabeth?A. It affected her physically but not emotionally.B. It affected her emotionally but not physically.C. It did not affect her in any way.D. It affected her both physically and emotionally.64. Whom did she blame for the accident?A. Her brother.B. Herself.C. No one.D. The villagers.65. The incident had _____ on her poetry.A. no influenceB. very little influenceC. a superficial influenceD. a strong influence（三）SYDNEY: As they sat sharing sweets beside a swimming pool in 1999 , Shane Gould and Jessicah Schipper were simply getting along well , chatting about sport , life and " anything else that came up . "Y et in Sydney next month , they will meet again by the pool , and for a short time the friends will race against each other in the 50-meter butterfly（蝶泳）in the Australian championships at Homebush Bay .Gould , now a 47-year-old mother of four , has announced she will be making a return to elite competition（顶级赛事）to swim the one event , having set a qualifying（合格的）time of 30.32 seconds in winning gold at last year's United States Masters championships . Her comeback comes 32 years after she won three golds at the Munich Olympics .Schipper , now a 17-year-old from Brisbane with a bright future of going to Athens for her first Olympics , yesterday recalled（回忆）her time with Gould five years ago ." I was at a national youth camp on the Gold Coast and Shane had come along to talk to us and watch us train , " Schipper explained . " It seemed as if we had long been good friends . I don't know why . W e just started talking and it went from there . "" She had a lot to share with all of us at that camp . She told us stories about what it was likeat big meets like the Olympics and what it's like to be on an Australian team . It was really interesting . "Next time , things will be more serious . " I will still be swimming in the 50m butterfly at the nationals , so there is a chance that I could actually be competing against Shane Gould , " said Schipper , who burst onto the scene at last year's national championships with second places in the 100m and 200m butterfly .66. What is the passage mainly about ?A. Stories happening in swimming competitions .B. Two women swimmers winning Olympic golds .C. Lessons learned from international swimming championships .D. Friendship and competition between two swimmers .67. Gould and Schipper are going to .A. talk about sport and lifeB. go back to elite competitionC. set a qualifying time and win goldD. take part in the same sports event68. Gould won her three Olympic golds when she was .A. 15B. 17C. 22D. 3069. The underlined word " it " in the fifth paragraph probably refers to .A. the OlympicsB. the youth campC. the friendshipD. the Australian team70. What Schipper said showed that she .A. was no longer Gould's friendB. had learned a lot from GouldC. was not interested in Gould's storiesD. would not like to compete against Gould（四）Giving BackFair W ayThe W estborough High School golf team had taken the official photos with the state prize. The other teams, disappointed, were on the bus heading home. And then W estborough instructor Greg Rota noticed something wrong with one of the score cards. A 9 had been recorded as a 7. They were not the state prize winner; W obum High had won. "No one would have known," saidW obum's instructor, Bob Doran. For Rota, it wasn't a difficult decision: "The prize wasn't ours to take."Coin Stars"College students are lazy, but they also want to help," says University of Pennsylvania graduate Dana Hork. So she made it easy, placing cups in rooms where students could leave their spare coins, and handing out cups to first-year students to keep in their rooms. Her " Change for Change" effort has collected $40,000 for charities 慈善机构) , which were decided upon by students.Never ForgottenA school in Massachusetts received a $ 9.5 million check from Jacques LeBermuth. But it took officials several days of digging to discover his connection to the school. Records showed the LeBermuth came from Belgium and studied in the school in the 1920s. When his family fell on hard times, he was offered free room and board. LeBermuth became a trader, owned shares of AT&T and lived off the earnings until he died, at age 89.71. What did Greg Rota probably do in the end?A. Took photos of Doran.B. Had a meeting with Doran.C. Returned the prize to the organizer.D. Apologized to W obum High School.72. Greg Rota's decision shows that he was _______.A. honestB. politeC. carefulD. friendly73. The underlined word "Change" in the second paragraph means _______.A. ideaB. decisionC. cupsD. coins74. What did the school officials do after receiving the check from Mr. LeBermuth?A. They tried to find out why he gave them the money.B. They went to Belgium to pay their respects to him.C. They dug out the records that were buried underground.D. They decided to offer their students free room and board.75. Jacques LeBermuth gave the money to the school because _______.A. the school asked for itB. he had no need for that much moneyC. the school had helped him in the pastD. he wanted to be remembered by the students六、写作题（共15分）Directions: For this part, you are required to write a composition on the topic Is Competition a Good or Bad Thing? Y our composition should be based on the following outline. Y our composition should be no less than 120 words.Outline: 1. The seriousness of the present competition2. The advantages of competition3. The disadvantages of competitionCompetition is the method or practice of trying to do better than other people to win or become successful in a specific skill. As a camp, I believe competition is a way of nurturing one's ability and talent in such a way that the person is encouraged to excel more than other skilled person. In some cases and situation, competition may mean a struggle between two or more different competitors.In the workplace, competition has received some bad press in recent years. Greed and layoffs are the two most frequently touted sins of competition. These two sins, however, can always be minimized with new rules (if the appropriate governing bodies are willing to live up to this responsibility of making such new rules) such as increased taxes on the greedy and work replacement/ training/ length-of-workweek rules for employees.参考答案1、D.2、A.3、B.4、C.5、 B.6、 D.7、D.8、A.9、 D.10、C.11、A.12、A.13、 B.14、 A. 15、C.16、 D.17、A.18、C. 19、B.20 B.21、B.22、C.23、C. 24、 D.25、C.26、A.27、C.28、D.29、D. 30、C.31、explosion32、disappointment33、promotion34、economics35、additional36、A.37、A.38、B.39、B. 40、A41、B42、D43、D44、C45、B46、D47、C48、A49、C50、B51、A52、C53、D54、B55、D56、C57、C58、C59、B60、D61、A62、C63、D64、B65、D66、D67、D68、A69、C70、B71、C72、A73、D74、A75、C。
2009年宁夏高考试卷及解答
绝密 ★ 启封前2009年普通高等学校招生全国统一考试（宁夏卷）理科综合能力测试第Ⅰ卷二、选择题：本题共8小题，每小题6分，在每小题给出的四个选项中，有的只有一个选项正确，有的有多个选项正确，全部选对的得6分，选对但不全的得3分，有选错的得0分。
14. 在力学理论建立的过程中，有许多伟大的科学家做出了贡献。
关于科学家和他们的贡献，下列说法正确的是A. 伽利略发现了行星运动的规律B. 卡文迪许通过实验测出了引力常量C ．牛顿最早指出力不是维持物体运动的原因D ．笛卡尔对牛顿第一定律的建立做出了贡献答案BD 。
15. 地球和木星绕太阳运行的轨道都可以看作是圆形的。
已知木星的轨道半径约为地球轨道半径的5.2倍，则木星与地球绕太阳运行的线速度之比约为A. 0.19B. 0.44C. 2.3D. 5.2 答案B 。
16. 医生做某些特殊手术时，利用电磁血流计来监测通过动脉的血流速度。
电磁血流计由一对电极a 和b 以及磁极N 和S 构成，磁极间的磁场是均匀的。
使用时，两电极a 、b 均与血管壁接触，两触点的连线、磁场方向和血流速度方向两两垂直，如图所示。
由于血液中的正负离子随血流一起在磁场中运动，电极a 、b 之间会有微小电势差。
在达到平衡时，血管内部的电场可看作是匀强电场，血液中的离子所受的电场力和磁场力的合力为零。
在某次监测中，两触点的距离为3.0mm ，血管壁的厚度可忽略，两触点间的电势差为160µV ，磁感应强度的大小为0.040T 。
则血流速度的近似值和电极a 、b 的正负为A. 1.3m/s ，a 正、b 负B. 2.7m/s ， a 正、b 负C ．1.3m/s ，a 负、b 正 D. 2.7m/s ， a 负、b 正答案A 。
17. 质量为m 的物体静止在光滑水平面上，从t=0时刻开始受到水平力的作用。
力的大小F与时间t 的关系如图所示，力的方向保持不变，则A ．03t 时刻的瞬时功率为mt F 0205B ．03t 时刻的瞬时功率为mt F 02015 C ．在0=t 到03t 这段时间内，水平力的平均功率为mt F 423020 D. 在0=t 到03t 这段时间内，水平力的平均功率为mt F 625020 答案BD 。
2009宁夏高考数学试题答案(理数)
小班下学期美术教学进度表2012.2附页：（一）小刺猬背果果本活动是让孩子学习用半圆加线条来画刺猬，同时可以激发孩子用圆加线等画出各种果子。
在本学期中开始让孩子有目的地先勾线，再涂色。
目标：学习用半圆画出不同形状的刺猬；学习用水笔先勾图。
准备：范画、水笔、蜡笔、纸。
过程：1、出示范画，介绍内容，引导观察。
（1）、画上有谁？它在干什么？小刺猬的身体是什么形状的？身体上又有什么？有什么用？（2）、介绍内容：小刺猬来到树林，看到树上有很多果果，可是它不会爬树。
正在这时，风姑娘帮助它把果子吹下来了，小刺猬想把果子背回家，就在地上打滚，把果子插在刺上，手里又捧了几个果子回家了。
（3）、小刺猬背果子时，肚子是直直的还是平平的？弯弯的背在肚子上面还是旁边？果子是怎么背上去的？什么地方还可以拿果子？2、教师示范用水笔勾线的方法画刺猬。
3、幼儿创作，教师指导。
提示幼儿画平的和直立的半圆形，可变换方向；在刺上插果子；多画些刺猬和果子。
4、引导评价（二）我和妈妈拍照妈妈是孩子最爱的人，他们对妈妈有很深的感情，在三八节之时，让孩子来画画自己和妈妈，进行爱妈妈的教育是非常好的，本次活动中可以让孩子学习用两个图形连接与线条的组合来画出人，对小班下学期的孩子是适合的。
目标：初步学习用两个图形连接与线条组合画人。
准备：水笔与蜡笔，幼儿与妈妈的合影数张，以贴好花边的纸像架。
过程：1、欣赏与讨论。
出示小朋友与妈妈的合影，引导观察：这是谁和妈妈的照片？照片上谁是宝宝？谁是妈妈？哪个大？哪个小？妈妈梳着怎样的头发？穿着什么衣服？宝宝呢？他们在哪里拍的照片？2、操作与思考（1）、请幼儿尝试画人，边画边提问：照片上的人头是什么形状？妈妈的身体是什么形状？再请幼儿画手和脚。
谁会画妈妈的头发、眼睛、鼻子、嘴巴？教师引导孩子想一想妈妈的头发是长的还是短的，及眼睛、嘴巴的大小等。
（2）、教师在孩子画的旁边画另一个人，边画边请幼儿说出特征。
3、幼儿作画，教师指导。
2009年高考数学(宁夏)理(word版含答案)
锥体体积公式 V=
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其中 x 为样本平均数 柱体体积公式 V=Sh 其中 S 为底面面积，h 为高
其中 S 为底面面积，h 为高 球的表面积、体积公式
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NA NB NC 0 ，且 9．已知点 O，N，P 在 △ ABC 所在平面内，且 OA OB OC ，
，则点 O，N，P 依次是 △ ABC 的（ PA ·PB PB· PC PC PA · A．重心、外心、垂心 B．重心、外心、内心 C．外心、重心、垂心 D．外心、重心、内心 （注：三角形的三条高线交于一点，此点为三角 形的垂心） 10 ． 如 果 执 行 右 边 的 程 序 框 图 ， 输 入 x 2，h 0 . ，那么输出的各个数的和等于 5 （ ） A．3 B． 3.5 C． 4 D．4.5 11．一个棱锥的三视图如图，则该棱锥的全面积 （单位：cm2）为（ ） A．48+12 2 C．36+12 2 3 4 6 6 B．48+24 2 D．36+24 2 3 4 ）
2009 年普通高等学校招生全国统一考试（宁夏卷） 理 科 数 学
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分．其中第Ⅱ卷第（22）~（24） 题为选考题， 其它题为必考题． 考生作答时， 将答案答在答题卡上， 在本试卷上答题无效． 考 试结束后，将本试卷和答题卡一并交回． 注意事项： 1．答题前，考生务必先将自己的姓名、准考证号填写在答题卡上，认真核对条形码上的姓 名、准考证号，并将条形码粘贴在答题卡的指定位置上． 2．选择题答案使用 2B 铅笔填涂，如需改动，用橡皮擦干净后，再选涂其它答案标号；非 选择题答案使用 0.5 毫米的黑色中性（签字）笔或碳素笔书写，字体工整、笔迹清楚． 3．请按照题号在各题的答题区域（黑色线框）内作答，超出答题区域书写的答案无效． 4．保持卡面清洁，不折叠，不破损． 5．做选考题时，考生按照题目要求作答，并用 2B 铅笔在答题卡上把所选题目对应的题号 涂黑． 参考公式： 样本数据 x1，x2， „，xn 的标准差 s=
2009宁夏高考数学试题答案(理数)
二. 在相同观测条件下观测A、B两个角度，设对 观测4测回的权为1，则对 观测7个测回的权为多少？（10分）
三. 在图一所示测角网中，A、B、C为已知点，P为待定点，为同精度观测角值。
若按条件平差法对该网进行平差：
(1).有多少个条件方程？各类条件方程各有多少
个？
(2).试列出全部条件方程（非线性条件方程不必
一、填空题（本题共20个空格，每个空格1.5分，共30分）
1、引起观测误差的主要原因有 （1） 、 （2） 、 （3） 三个方面的因素，我们称这些因素为 （4） 。
2、根据对观测结果的影响性质，观测误差分为 （5） 、 （6） 、 （7） 三类，观测误差通过由于 （8） 引起的闭合差反映出来。
· 武汉大学2005年－2006学年第二学期“数
· 武汉大学2006年－2007学年第二学期“数
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6、观测值的权阵为，的方差为3，则的方差为 （16） 、的权为 （17） 。
7、某点的方差阵为，则的点位方差为 （18） 、误差曲线的最大值为 （19） 、误差椭圆的短半轴的方位角为 （20） 。
二、简答题（本题共2小题，每题5分，共10分）
1、简述观测值的精度与精确度含义及指标。在什么情况下二者相同？
图三
，，为同精度观测值，其中。若按坐标平差法对该网进行平差，试列出观测角的误差方程
(设，、以dm为单位)。(10分)
六、有水准网如图四所示，网中A、B为已知点，C、D为待定点， 为高差观测值，设各线路等长。已知平差后算得 ，试求平差后C、D两点间高差 的权及中误差。（10分）
2009宁夏高考数学试题答案(理数)
2009年普通高等学校招生全国统一考试（宁夏卷）数学（理工农医类）参考答案一、选择题（每小题5分，共60分）（1）B（2）D（3）B（4）B（5A（6）B（7）D（8）B（9）A（10）C（11）C（12）C（13）10131（14）3（15）4（16）9（17）解:在△ABC中，∠DAC=30°, ∠ADC=60°－∠DAC=30,所以CD=AC=0.1 又∠BCD=180°－60°－60°=60°， 故CB 是△CAD 底边AD 的中垂线，所以BD=BA,在△ABC 中，,AB C sin CB C A sin ∠=∠A AB 即AB=,2062315sin ACsin60+= 因此，BD=。
km 33.020623≈+ 故B ，D 的距离约为0.33km.（18）解：取CD 的中点G ，连接MG ，NG 。
设正方形ABCD ，DCEF 的边长为2， 则MG ⊥CD ，MG=2，NG=2.因为平面ABCD ⊥平面DCED ， 所以MG ⊥平面DCEF ，可得∠MNG 是MN 与平面DCEF 所成的角。
因为MN=6，所以sin ∠MNG=36为MN 与平面DCEF 所成角的正弦值 （19）解：（Ⅰ）依题意X 的分列为（Ⅱ）设A 1表示事件“第一次击中目标时，击中第i 部分”，i=1，2.B 1表示事件“第二次击中目标时，击中第i 部分”，i=1，2. 依题意知P （A 1）=P(B 1)=0.1，P （A 2）=P(B 2)=0.3，11111122A A B A B A B A B =⋃⋃⋃,所求的概率为11111122()()()()P A P A B P A B P A B P A B =+++（）11111122()()())()()()P A B P A P B P A P B P A P B +++（ 0.10.90.90.10.10.10.30.30.28⨯+⨯+⨯+⨯=（20）解：（Ⅰ）由题意，c=1,可设椭圆方程为2219114b b+=+，解得23b =，234b =-（舍去） 所以椭圆方程为22143x y +=。
09年全国高考理科数学试题及答案
2009年全国高考理科数学试题及答案2009年普通高等学校招生全国统一考试数学第Ⅰ卷本试卷共12小题，每小题5分，共60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。
参考公式：如果事件A，B互斥，那么球的表面积公式S?4πR 其中R表示球的半径2P(A?B)?P(A)?P(B) 如果事件A，B相互独立，那么球的体积公式V?43πR 3P(AB)?P(A)P(B) 一、选择题：其中R表示球的半径21. 设集合S?x|x?5,T?x|x?4x?21?0,则S????T? Ａ.?x|?7?x??5?Ｂ.?x|3?x?5? Ｃ.?x|?5?x?3?Ｄ.?x|?7?x?5? ?a?log2x(当x?2时)?２.已知函数f(x)??x2?4在点x?2处连续，则常数a的值是(当x?2时）??x?2Ａ.２Ｂ.３Ｃ.４Ｄ.５(1?2i)2３.复数的值是3?4iＡ.－１Ｂ.１Ｃ.－iＤ.i 4.已知函数f(x)?sin(x??2)(x?R)，下面结论错误的是．． A.函数f(x)的最小正周期为2? B.函数f(x)在区间?0,???上是增函数??2?1 C.函数f(x)的图像关于直线x?0对称D.函数f(x)是奇函数 5.如图，已知六棱锥P?ABCDEF的底面是正六边形，PA?平面ABC,PA?2AB，则下列结论正确的是 A. PB?AD B. 平面PAB?平面PBC C. 直线BC∥平面PAE D. 直线PD与平面ABC所称的角为45 6.已知a,b,c,d为实数，且c?d。
则“a?b”是“a?c?b?d”的 A. 充分而不必要条件 B. 必要而不充分条件C．充要条件 D. 既不充分也不必要条件?x2y2?2?1(b?0)的左右焦点分别为F1,F2，其一条渐近线方程为y?x，7. 已知双曲线2b点P(3,y0)在该双曲线上，则PF1?PF2= A. -12 B. -2C. 0D. 4 8. 如图，在半径为3的球面上有A,B,C三点，?ABC?90,BA?BC，?球心O到平面ABC的距离是32，则B、C两点的球面距离是2A.?4? B.?C.? 3329. 已知直线l1:4x?3y?6?0和直线l2:x??1，抛物线y?4x 上一动点P到直线l1和直线l2的距离之和的最小值是 C. 1137D. 51610. 某企业生产甲、乙两种产品，已知生产每吨甲产品要用A原料3吨、B原料2吨；生产每吨乙产品要用A原料1吨、B原料3吨。
da2009年高考数学(宁夏)理
由已知可得 ，可得 ．
所以 平分 ．
23．解：（Ⅰ） ： ， ： ．
为圆心是 ，半径是1的圆．
为中心是坐标原点，焦点在 轴上，长半轴长是8，短半轴长是3的椭圆．
（Ⅱ）当 时， 、 ，故 ．
为直线 ， 到 的距离 ．
从而当 时， 取得最小值 ．
24．解：（Ⅰ） ．
（Ⅱ）依题意， 满足
解不等式组，其解集为 ．所以 ．
15．14016．10
三、解答题
17．解：方案一：①需要测量的数据有： 点到 ， 点的俯角 ； 点到 ， 的俯角 ； 的距离 （如图所示）．
②第一步：计算 ．由正弦定理 ；
第二步：计算 ．由正弦定理 ；
第三步：计算 ．由余弦定理 ．
方案二：①需要测量的数据有：
点到 点的俯角 ； 点到 ， 的俯角 ； 的距离 （如图所示）．
②第一步：计算 ．由正弦定理 ；
第二步：计算 ．由正弦定理 ；
第三步：计算 ．由余弦定理 ．
18．解：（Ⅰ）甲、乙被抽到的概率均为 ，且事件“甲工人被抽到”与事件“乙工人被抽到”相互独立，故甲、乙两工人都被抽到的概率为 ．
（Ⅱ）（ⅰ）由题意知 类工人中ຫໍສະໝຸດ 抽查25名， 类工人中应抽查75名．
故 ，得 ， ，得 ．
（Ⅱ）
．
由条件得 ，即 ，
故 ．从而 ．
因为 ，
所以 ．
将右边展开，与左边比较系数得， ．
故 ．
又 ，即 ．
由此可得 ．
于是 ．
22．解：（Ⅰ）在 中，因为 ，
所以 ．
因为 是角平分线，
所以 ，故 ．
于是 ．
因为 ，
所以 四点共圆．
（Ⅱ）连结 ，则 为 的平分线，得 ．
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2009年普通高等学校招生全国统一考试（宁夏卷）数学（理工农医类）一、选择题（每小题5分，共60分）（1）已知集合M={x|－3<x ≤5},N={x|－5<x<5},则M ∩N=(A) {x|－5＜x ＜5} (B) {x|－3＜x ＜5} (C) {x|－5＜x ≤5} (D) {x|－3＜x ≤5}【解析】直接利用交集性质求解,或者画出数轴求解. 【答案】B（2）已知复数12z i =-，那么1z=（A + （B （C ）1255i + （D ）1255i - 【解析】211121212(12)(12)12i i i i i z --===++-+＝1255i - 【答案】D（3）平面向量a 与b 的夹角为060，(2,0)a =，1b = 则2a b +=（A (B) (C) 4 (D)12 【解析】由已知|a|＝2,|a ＋2b|2＝a 2＋4a ·b ＋4b 2＝4＋4×2×1×cos60°＋4＝12∴2a b +=【答案】B（4）已知圆C 与直线x －y=0 及x －y －4=0都相切，圆心在直线x+y=0上，则圆C 的方程为（A ）22(1)(1)2x y ++-= (B) 22(1)(1)2x y -++= (C) 22(1)(1)2x y -+-= (D) 22(1)(1)2x y +++=【解析】圆心在x ＋y ＝0上,排除C 、D,再结合图象,或者验证A 、B 中圆心到两直线的距离等于半径2即可. 【答案】B（5）从5名男医生、4名女医生中选3名医生组成一个医疗小分队，要求其中男、女医生都有，则不同的组队方案共有（A ）70种 （B ） 80种 （C ） 100种 （D ）140种【解析】直接法：一男两女,有C 51C 42＝5×6＝30种,两男一女,有C 52C 41＝10×4＝40种,共计70种间接法：任意选取C 93＝84种,其中都是男医生有C 53＝10种,都是女医生有C 41＝4种,于是符合条件的有84－10－4＝70种. 【答案】A（6）设等比数列{ n a }的前n 项和为n S ，若63S S =3 ，则96S S = （A ） 2 （B ）73 （C ） 83（D ）3 【解析】设公比为q ,则36333(1)S q S S S +=＝1＋q 3＝3 ⇒ q 3＝2 于是36936112471123S q q S q ++++===++【答案】B （7）曲线y=2xx -在点（1，－1）处的切线方程为 （A ）y=x －2 (B) y=－3x+2 (C)y=2x －3 (D)y=－2x+1 【解析】y ’＝2222(2)(2)x x x x ---=--,当x ＝1时切线斜率为k ＝－2 【答案】D(8)已知函数()f x =Acos(x ωϕ+)的图象如图所示，2()23f π=-，则(0)f = （A ）23-(B) 23 (C)－ 12 (D) 12【解析】由图象可得最小正周期为2π3于是f(0)＝f(2π3),注意到2π3与π2关于7π12对称 所以f(2π3)＝－f(π2)＝23【答案】B（9）已知偶函数()f x 在区间[0,)+∞单调增加，则满足(21)f x -＜1()3f 的x 取值范围是（A ）（13，23） (B) ［13，23） (C)（12，23） (D) ［12，23） 【解析】由于f(x)是偶函数,故f(x)＝f(|x|)∴得f(|2x －1|)＜f(13),再根据f(x)的单调性 得|2x －1|＜13 解得13＜x ＜23【答案】A（10）某店一个月的收入和支出总共记录了 N 个数据1a ，2a ，。
N a ，其中收入记为 正数，支出记为负数。
该店用下边的程序框图计算月总收入S 和月净盈利V ，那么在图中空白的判断框和处理框中，应分别填入下列四个选项中的 （A ）A>0,V=S －T (B) A<0,V=S －T (C) A>0, V=S+T （D ）A<0, V=S+T【解析】月总收入为S,因此A ＞0时归入S,判断框内填A ＞0 支出T 为负数,因此月盈利V ＝S ＋T 【答案】C（11）正六棱锥P －ABCDEF 中，G 为PB 的中点，则三棱锥D －GAC 与三棱锥P －GAC 体积之比为（A ）1：1 (B) 1：2 (C) 2：1 (D) 3：2【解析】由于G 是PB 的中点,故P －GAC 的体积等于B －GAC 的体积 在底面正六边形ABCDER 中 BH ＝ABtan30°AB 而BD故DH ＝2BH于是V D －GAC ＝2V B －GAC ＝2V P －GAC 【答案】C（12）若1x 满足2x+2x=5, 2x 满足2x+22log (x －1)=5, 1x +2x ＝（A ）52 (B)3 (C) 72(D)4 【解析】由题意11225x x += ①22222log (1)5x x +-= ② 所以11252x x =-,121log (52)x x =-即21212log (52)x x =-令2x 1＝7－2t,代入上式得7－2t ＝2log 2(2t －2)＝2＋2log 2(t －1) ∴5－2t ＝2log 2(t －1)与②式比较得t ＝x 2 于是2x 1＝7－2x 2 【答案】C（13）某企业有3个分厂生产同一种电子产品，第一、二、三分厂的产量之比为1：2：1，用分层抽样方法（每个分厂的产品为一层）从3个分厂生产的电子产品中共取100件作使用寿命的测试，由所得的测试结果算得从第一、二、三分厂取出的产品的使用寿命的平均值分别为980h ，1020h ，1032h ，则抽取的100件产品的使用寿命的平均值为 h. 【解析】9801+10202+103214x ⨯⨯⨯=＝1013【答案】1013（14）等差数列{}n a 的前n 项和为n S ，且53655,S S -=则4a = 【解析】∵S n ＝na 1＋12n(n －1)d ∴S 5＝5a 1＋10d,S 3＝3a 1＋3d∴6S 5－5S 3＝30a 1＋60d －(15a 1＋15d)＝15a 1＋45d ＝15(a 1＋3d)＝15a 4 【答案】31（15）设某几何体的三视图如下（尺寸的长度单位为m ）。
则该几何体的体积为 3m【解析】这是一个三棱锥,高为2,底面三角形一边为4,这边上的高为3, 体积等于16×2×4×3＝4【答案】4（16）以知F 是双曲线221412x y -=的左焦点，(1,4),A P 是双曲线右支上的动点，则PF PA +的最小值为 。
【解析】注意到P 点在双曲线的两只之间,且双曲线右焦点为F ’(4,0), 于是由双曲线性质|PF|－|PF ’|＝2a ＝4 而|PA|＋|PF ’|≥|AF ’|＝5两式相加得|PF|＋|PA|≥9,当且仅当A 、P 、F ’三点共线时等号成立. 【答案】9（17）（本小题满分12分）如图，A,B,C,D 都在同一个与水平面垂直的平面内，B ，D 为两岛上的两座灯塔的塔顶。
测量船于水面A 处测得B 点和D 点的仰角分别为075，030，于水面C 处测得B 点和D 点的仰角均为060，AC=0.1km 。
试探究图中B ，D 间距离与另外哪两点间距离相等，然后求B ，D 的距离（计算结果精确到0.01km ，≈1.414≈2.449）在△ABC 中，∠DAC=30°, ∠ADC=60°－∠DAC=30, 所以CD=AC=0.1 又∠BCD=180°－60°－60°=60°， 故CB 是△CAD 底边AD 的中垂线，所以BD=BA ， ……5分在△ABC 中，,ABC sin CBCA sin ∠=∠A AB即AB=,2062315sin ACsin60+=因此，BD=。
km 33.020623≈+ 故B ，D 的距离约为0.33km 。
……12分（18）（本小题满分12分）如图，已知两个正方行ABCD 和DCEF 不在同一平面内，M ，N 分别为AB ，DF 的中点。
（I ）若平面ABCD ⊥平面DCEF ，求直线MN 与平面DCEF 所成角的正值弦； （II ）用反证法证明：直线ME 与 BN 是两条异面直线。
（18）（I ）解法一：取CD 的中点G ，连接MG ，NG 。
设正方形ABCD ，DCEF 的边长为2， 则M G ⊥CD ，MG=2，NG=2.因为平面ABCD ⊥平面DCED ， 所以MG ⊥平面DCEF ，可得∠MNG 是MN 与平面DCEF 所成的角。
因为MN=6，所以sin ∠MNG=36为MN 与平面DCEF 所成角的正弦值 ……6分设正方形ABCD ，DCEF 的边长为2，以D 为坐标原点，分别以射线DC ，DF ，DA 为x,y,z 轴正半轴建立空间直角坐标系如图.则M （1,0,2）,N(0,1,0),可得MN =(－1,1,2). 又DA =（0，0，2）为平面DCEF 的法向量，可得cos(,)3||||MN DA MN DA MN DA ⋅==-所以MN 与平面DCEF 所成角的正弦值为cos36=· ……6分(Ⅱ)假设直线ME 与BN 共面， ……8分 则A B ⊂平面MBEN ，且平面MBEN 与平面DCEF 交于EN 由已知，两正方形不共面，故AB ⊄平面DCEF 。
又AB//CD ，所以AB//平面DCEF 。
面EN 为平面MBEN 与平面DCEF 的交线， 所以AB//EN 。
又AB//CD//EF ，所以EN//EF ，这与E N ∩EF=E 矛盾，故假设不成立。
所以ME 与BN 不共面，它们是异面直线. ……12分（19）（本小题满分12分）某人向一目射击4次，每次击中目标的概率为。
该目标分为3个不同的部分，第一、二、三部分面积之比为1：3：6。
击中目标时，击中任何一部分的概率与其面积成正比。
（Ⅰ）设X 表示目标被击中的次数，求X 的分布列；（Ⅱ）若目标被击中2次，A 表示事件“第一部分至少被击中1次或第二部分被击中2次”，求P （A ） （19）解：（Ⅰ）依题意X 的分列为13………………6分（Ⅱ）设A 1表示事件“第一次击中目标时，击中第i 部分”，i=1，2. B 1表示事件“第二次击中目标时，击中第i 部分”，i=1，2. 依题意知P （A 1）=P(B 1)=0.1，P （A 2）=P(B 2)=0.3，11111122A A B A B A B A B =⋃⋃⋃,所求的概率为11111122()()()()P A P A B P A B P A B P A B =+++（）11111122()()())()()()P A B P A P B P A P B P A P B +++（ 0.10.90.90.10.10.10.30⨯+⨯+⨯+⨯= ………12分（20）（本小题满分12分）已知，椭圆C 过点A 3(1,)2，两个焦点为（－1，0），（1，0）。