2013年广东理科高考卷真题及答案(不含语文部分).doc

2013年广东理科高考卷真题及答案（不含语文部分）数学部分参考公式:台体的体积公式,其中分别是台体的上、下底面积,表示台体的高.一、选择题:本大题共8小题,每小题5分,共40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设集合,则( )A . B C D【解析】D；易得,所以,故选D2定义域为的四个函数,中,奇函数的个数是( )A . B C D【解析】C；考查基本初等函数和奇函数的概念,是奇函数的为与,故选C3若复数满足,则在复平面内,对应的点的坐标是( )A . B C D【解析】C；对应的点的坐标是,故选C4已知离散型随机变量的分布列为正视图俯视图侧视图第5题图 则的数学期望 ( )A . B C D【解析】A；,故选A5某四棱台的三视图如图所示,则该四棱台的体积是 ( )A . B C D【解析】B；由三视图可知,该四棱台的上下底面边长分别为和的正方形,高为,故,故选B6设是两条不同的直线,是两个不同的平面,下列命题中正确的是( )A . 若,则 B若,则C若,则 D若,则【解析】D；ABC是典型错误命题,选D7已知中心在原点的双曲线的右焦点为,离心率等于,在双曲线的方程是 ( )A . B C D【解析】B；依题意,所以,从而,故选B8设整数,集合.令集合 若和都在中,则下列选项正确的是( )A . , B, C, D, 【解析】B；特殊值法,不妨令,则,故选B如果利用直接法:因为，所以，三个式子中恰有一个成立；，三个式子中恰有一个成立.配对后只有四种情况：第一种：成立，此时，于是，；第二种：成立，此时，于是，；第三种：成立，此时，于是，；第四种：成立，此时，于是，.综合上述四种情况，可得，.二、填空题：本题共7小题，考生作答6小题，每小题5分，共30分是否输入输出 结束开始第11题图n(一)必做题(913题)9不等式的解集为_【解析】；易得不等式的解集为.10若曲线在点处的切线平行于轴,则_.【解析】；求导得,依题意,所以.11执行如图所示的程序框图,若输入的值为,则输出的值为_.【解析】；第一次循环后:；第二次循环后:； 第三次循环后:；第四次循环后:；故输出.12. 在等差数列中,已知,则_.【解析】；依题意,所以. 或:xy441O13. 给定区域:,令点集是在上取得最大值或最小值的点,则中的点共确定_条不同的直线.【解析】；画出可行域如图所示,其中取得最小值时的整点为,取得最大值时的整点为,及共个整点.故可确定条不同的直线.（二）选做题（14、15题,考生只能从中选做一题,两题全答的,只计前一题的得分）14.(坐标系与参数方程选讲选做题)已知曲线的参数方程为(为参数),在点处的切线为,以坐标原点为极点,轴的正半轴为极轴建立极坐标系,则的极坐标方程为_.AEDCBO第15题图【解析】；曲线的普通方程为,其在点处的切线的方程为,对应的极坐标方程为,即.15. (几何证明选讲选做题)如图,是圆的直径,点在圆上,延长到使,过作圆的切线交于.若,则_.【解析】；依题意易知,所以,又,所以,从而.三、解答题:本大题共6小题,满分80分,解答须写出文字说明、证明过程或演算步骤.16（本小题满分12分）已知函数,.() 求的值； () 若,求【解析】()；() 因为,所以,所以,所以.17（本小题满分12分） 第17题图某车间共有名工人,随机抽取名,他们某日加工零件个数的茎叶图如图所示,其中茎为十位数,叶为个位数.() 根据茎叶图计算样本均值；() 日加工零件个数大于样本均值的工人为优秀工人.根据茎叶图推断该车间名工人中有几名优秀工人；() 从该车间名工人中,任取人,求恰有名优秀工人的概率.【解析】() 样本均值为； () 由()知样本中优秀工人占的比例为,故推断该车间名工人中有名优秀工人.() 设事件:从该车间名工人中,任取人,恰有名优秀工人,则.18（本小题满分14分）如图1,在等腰直角三角形中,分别是上的点,.COBDEACDOBE图1图2为的中点.将沿折起,得到如图2所示的四棱锥,其中.CDOBEH() 证明:平面；() 求二面角的平面角的余弦值.【解析】() 在图1中,易得连结,在中,由余弦定理可得由翻折不变性可知,所以,所以,理可证, 又,所以平面.() 传统法:过作交的延长线于,连结,因为平面,所以,所以为二面角的平面角.结合图1可知,为中点,故,从而CDOxE向量法图yzB所以,所以二面角的平面角的余弦值为.向量法:以点为原点,建立空间直角坐标系如图所示,则,所以,设为平面的法向量,则,即,解得,令,得由() 知,为平面的一个法向量,所以,即二面角的平面角的余弦值为.19（本小题满分14分）设数列的前项和为.已知,.() 求的值；() 求数列的通项公式；() 证明:对一切正整数,有.【解析】() 依题意,又,所以； () 当时, 两式相减得 整理得,即,又 故数列是首项为,公差为的等差数列,所以,所以. () 当时,；当时,； 当时,此时 综上,对一切正整数,有.20（本小题满分14分）已知抛物线的顶点为原点,其焦点到直线:的距离为.设为直线上的点,过点作抛物线的两条切线,其中为切点.() 求抛物线的方程；() 当点为直线上的定点时,求直线的方程；() 当点在直线上移动时,求的最小值.【解析】() 依题意,设抛物线的方程为,由结合,解得. 所以抛物线的方程为. () 抛物线的方程为,即,求导得设,(其中),则切线的斜率分别为,所以切线的方程为,即,即同理可得切线的方程为因为切线均过点,所以,所以为方程的两组解.所以直线的方程为.() 由抛物线定义可知,所以联立方程,消去整理得由一元二次方程根与系数的关系可得,所以又点在直线上,所以,所以所以当时, 取得最小值,且最小值为.21（本小题满分14分）设函数(其中). () 当时,求函数的单调区间；() 当时,求函数在上的最大值.【解析】() 当时, , 令,得, 当变化时,的变化如下表:极大值极小值 右表可知,函数的递减区间为,递增区间为,. (),令,得,令,则,所以在上递增,所以,从而,所以所以当时,；当时,；所以令,则,令,则所以在上递减,而所以存在使得,且当时,当时,所以在上单调递增,在上单调递减.因为,所以在上恒成立,当且仅当时取得“”.综上,函数在上的最大值.英语部分第一节 完型填空Number sense is not the ability to count. It is the ability to recognize a 1 in number. Human beings are born with this ability. 2 , Experiments show that many animas are, too. For example, many birds have good number sense. If a nest has four eggs and you remove one, the bird will not 3 . However, if you remove two, the bird 4 leaves. This means that the bird knows the 5 between two and three.Another interesting experiment showed a birds 6 number sense. A man was trying to take a photo of a crow(乌鸦) that had a nest in a tower, but the crow always left when she saw him coming. The bird did not 7 until the man left the tower. The man had an 8 . He took another man with him to the tower. One man left and the other stayed, but they did not 9 the bird. The crow stayed away until the second man left, too. The experiment was 10 with three men and then with four men. But the crow did not return to the nest until all the men were 11 . It was not until five men went into the tower and only four left that they were 12 able to fool the crow.How good is a humans number sense? Its not very good. For example, babies about fourteen months old almost always notice if something is taken away from a 13 group. But when the number goes beyond three or four, the children are 14 fooled.It seems that number sense is something we have in common with many animals in this world, and that our human 15 is not much better than a crows.1. A. rise B. pattern C. change D. trend2. A. Importantly B. Surprisingly C. Disappointedly D. Fortunately3. A. survive B. care C. hatch D. notice4. A. generally B. sincerely C. casually D. deliberately5. A. distance B. range C. difference D. interval6. A. amazing B. annoying C. satisfying D. disturbing7. A. relax B. recover C. react D. return8. A. appointment B. excuse C. idea D. explanation9. A. fool B. hurt C. catch D. kill10. A. reported B. repeated C. designed D. approved11. A. confused B. gone C. tired D. drunk12. A. gradually B. luckily C. strangely D. finally13. A. single B. small C. local D. new14. A. seldom B. temporarily C. merely D. often15. A. sight B. nature C. ability D. belief第二节 语法填空One day, Nick invited his friends to supper. He was cooking some delicious food in the kitchen. Suddenly, he 16 (find) that he had run out of salt. So Nick called to his son, “Go to the village and buy some salt, but pay a fair price for it: neither too much 17 too little.” His son looked surprised. “I can understand why shouldnt pay too much, Father, but if I can pay less, 18 not save a bit of money?”“That would be a very 19 (reason) thing to do in a big city, but it could destroy a small village like ours,” Nick said.Nicks guest, 20 had heard their conversation, asked why they should not buy salt more cheaply if they could. Nick replied, “The only reason a man would sell salt 21 a lower price would be because he was desperate for money. And anyone who took advantage of that situation would be showing a lack of respect 22 the sweat and struggle of the man who worked very hard to produce it.”“But such a small thing couldnt 23 (possible) destroy a village.”“In the beginning, there was only 24 very small amount of unfairness in the world, but everyone added a little, always 25 (think) that it was only small and not very important, and look where we have ended up today.”第三节 阅读理解AImagination and fantasy can play an important role in achieving the things we fear. Children know this very well. Fred Epstein, in his book I Make It to Five, tells a story he heard from one of his friends about Tom, a four-year-old boy with a cancer in his back bone. He came through several operations and a lot of pain by mastering his imagination.Tom loved to pretend, and he particularly loved to play superheroes. Dr. Epstein explained that it was actually a brilliant way for his young mind to handle the terrifying and painful life he led.The day before his third trip to the operating room, Tom was terribly afraid. “ Maybe I could go as Superman,” he whispered to his mom. Hearing this, the mother hesitated for while. She has avoided buying the expensive costume(戏装), but finally she agreed.The next day Tom appeared as the powerful Superman, showing off through the hospital halls and coolly waving his hand to the people greeting him along the way. And Tom, with the strength of his fantasy, successfully made it through the operation.The power of imagination need not be reserved for children only. We all have the power to use our fantasies to attempt things we never thought possible, to go through those things that seem impossible, and to achieve what we never believed we could. Just as Dr. Epstein puts it, “If you can dream it, you can do it.”It doesnt mean that you should dress as a superhero for your next job interview. But, next time you are tested in a way that seems impossible, imagine what it would take to overcome it. Become the person you need to become to win over your challenge and do it in your mind first. So, let your imagination run wild, and dare to dream.26. What do we know about Tom?A. He was seriously ill. B. He was a dishonest boy. C. He was crazy about magic. D. He was Dr. Epsteins patient.27. What can be inferred about Toms mother?A. She was a rich lady. B. She refused Toms request. C. She wanted Tom to be a superhero. D. She wanted to get Tom through the pain.28. When Tom went for the third operation, he_.A. pretended to be painful B. acted like a superhero C. appeared in poor spirits D. argued with his mother29. In the last paragraph, you are advised_.A. to go through some difficult tests B. to wake up from your wild dreams C. to become a powerful person in your mind D. to wear expensive clothes for job interviews30. What is the purpose of the passage?A. To tell us an interesting story. B. To help us make right decisions. C. To advise us to care about children. D. To encourage us to use our imagination.B.Some people think that success is only for those with talent or those who grow up in the right family, and others believe that success mostly comes down to luck. Im not going to say luck, talent, and circumstances dont come into play because they do. Some people are born into the right family while others are born with great intelligence, and thats just the reality of how life is.However, to succeed in life, one first needs to set a goal and then gradually make it more practical. And, in addition to that, in order to get really good at something, one needs to spend at least 10,000 hours studying and practicing. To become great at certain things, itll require even more time, time that most people wont put in.This is a big reason why many successful people advise you to do something you love. If you dont enjoy what you do, it is going to feel like unbearable pain and will likely make you quit well before you ever become good at it.When you see people exhibiting some great skills or having achieved great success, you know that they have put in a huge part of their life to get there at a huge cost. Its sometimes easy to think they got lucky or they were born with some rare talent, but thinking that way does you no good, and theres a huge chance that youre wrong anyway.Whatever you do, if you want to become great at it, you need to work day in and day out, almost to the point of addiction, and over a long period of time. If youre not willing to put in the time and work, dont expect to receive any rewards. Consistent, hard work wont guarantee you the level of success you may want, but it will guarantee that you will become rally good at whatever it is you put all that work into.31. Paragraph 1 mainly talks about_.A. the reasons for success B. the meaning of success C. the standards of success D. the importance of success32. Paragraph 2, the underlined word that refers to_.A. being good at something B. setting a practical goal C. putting in more time D. succeeding in life33. Successful people suggest doing what one loves because_.A. work makes one feel pain B. one tends to enjoy his work C. one gives up his work easily D. it takes a lot of time to succeed34. What can be infer from Paragraph 4?A. Successful people like to show their great skills. B. People sometimes succeed without luck or talent. C. People need to achieve success at the cost of life. D. It helps to think that luck or talent leads to success.35. What is the main theme of the passage?A. Having a goal is vital to success. B. Being good is different from being great. C. One cannot succeed without time and practice. D. Luck, talent and family help to achieve success.C.One day, when I was working as a psychologist in England, an adolescent boy showed up in my office. It was David. He kept waling up and down restlessly, his face pale, and his hands shaking slightly. His head teacher had referred him to me. “This boy has lost his family,” he wrote. “He is understandably very sad and refuses to talk to others, and Im very worried about him. Can I help?”I looked at David and showed him to a chair. How could I help him? There are problems psychology doesnt have the answer to, and which no wards can describe. Sometimes the best thing one can do is to 0listen openly and sympathetically.The first two times we met, David didnt say a word. He sat there, only looking up to look at the childrens drawings on the wall behind me. I suggested we play a game of chess. He nodded. After that he played chess with me every Wednesday afternoon-in complete silence and without looking at me. Its not easy to cheat in chess, but I admit I made sure David won once or twice.Usually, he arrived earlier than agreed, took the chess board and pieces from the shelf and began setting them up before I even got a chance to sit down. It seemed as if he enjoyed my company. But why did he never look at me?“Perhaps he simply needs someone to share his pain with,” I thought. “Perhaps he senses that I respect his suffering.” Some months later, when we were playing chess, he looked up at me suddenly.“Its your turn,” he said.After that day, David started talking. He got friends in school and joined a bicycle club. He wrote to me a few times, about his biking with some friends, and about his plan to get into university. Now he had really started to live his own life.Maybe I gave David something. But I also learned that one-without any words-can reach out to another person. All it takes is a hug, a shoulder to cry on, a friendly touch, and an ear that listens.36. When he first met the author, David_.A. felt a little excited B. walked energetically C. looked a little nervous D. showed up with his teacher37. As a psychologist, the author _.A. was ready to listen to David B. was skeptical about psychology C. was able to describe Davids problem D. was sure of handling Davids problem38. David enjoyed being with the author because he_.A. wanted to ask the author for advice B. needed to share sorrow with the author C. liked the childrens drawing in the office D. beat the author many times in the chess game39. What can be inferred about David?A. He recovered after months of treatment. B. He liked biking before he lost his family.C. He went into university soon after starting to talk. D. He got friends in school before he met the author.40. What made David change?A. His teachers help. B. The authors friendship. C. His exchange of letters with the author.D. The authors silent communication with him.D.While Jennifer was at home taking an online exam for her business law class, a monitor(监控器) a few hundred miles away was watching her every move.Using a web camera equipped in Jennifers Los Angeles apartment, the monitor in Phoenix tracked how frequently her eyes moved from the computer screen and listened for the secret sounds of a possible helper in the room. Her Internet access was locked-remotely-to prevent Internet searches, and her typing style was analyzed to make sure she was who she said she was; Did she enter her student number at the same speed as she had in the past? Or was she slowing down?In the battle against cheating, this is the cutting edge and a key to encourage honestly in the booming field of on line education. The technology gives trust to the entire system, to the institution and to online education in general. Only with solid measures against cheating, experts say, can Internet universities show that their exams and diplomas are valid-that students havent searched the Internet to get the right answers.Although online classes have existed for more than a decade, the concern over cheating become sharper in the last year with the growth of “open online courses.” Private colleges, public universities and corporations are jumping into the online education field, spending millions of dollars to attract potential students, while also taking steps to help guarantee honesty at a distance.Aside from the web cameras, a number of other high-tech methods are becoming increasingly popular. Among them are programs that check students identities using personas information, such as the telephone numbers they once used.Other programs can produce unique exams by drawing on a large list of questions and can recognize possible cheaters by analyzing whether difficult test questions are answered at he same speed as easy ones. As in many university classes, term papers are scanned against some large Int