北京市朝阳区2014届高三下学期第一次综合练习( 化学试题

2014届北京市朝阳区高三年纪第一次综合练习英语试卷 2014.3第二部分知识运用（共两节，45分）第一节单项填空21. In China, you _____ vote when you are 18.A. mustB. mightC. canD. would22. I’ve been away for only three years, _____I can hardly recognize my hometown.A. soB. orC. forD. yet23. This article is well written because special attention ______ to the choice of words.A. has paidB. has been paidC. has paidD. had been paid24. They always give the vacant seat to ____ comes first.A. anyoneB. whomC. whomeverD. whoever25. In some countries, friends kiss____ both checks when they say goodbye.A. onB. inC. atD. of26. It is hard to imagine ____ makes a top-level athlete.A. whichB. howC. thatD. what27. The movie Gravity won seven awards at the Oscar night, ____was beyond t he director’s wildest dream.A. whichB. thatC. whereD. what28. ---Did he get the job finally?---Though he ____ well before the gob interview, he failed to answer some important questions.A. Was preparingB. would prepareC. had preparedD. has prepared29. When ____ about one of the biggest concerns today, many citizens mentioned the sharp rise inhousing price.A. askingB. to askC. askedD. having asked30. _____time, the teacher had us do half of the exercises in class and complete the other half forour homework.A. To saveB. SaveC. SavingD. Having saved31. Remember me to your parents when you ____them.A. are callingB. callC. will callD. have called32. ---What’s that noise?---There’s a truck stopping outside. It’s someone ____ something.A. deliverB. to deliverC. deliveringD. delivered33. Quietness seems impossible _____ everyone takes their seats and begins to write.A. untilB. afterC. forD. once34. ---How long have you been here, Susan?---Only about five minutes. Alisa ____ here with me.A. walksB. walkedC. has walkedD. had walked35. I didn’t know your mobile phone number; otherwise I ____you the moment I got to Canada.A. would ringB. would have rungC. had rungD. rang第二节完型填空Wallet BackThis is a story about a learning experience that had a big effect on the way that I live my life. The ____36___in the story did not give me tests or even grade me on my work. I was taught by one of the most effective ___37___ of teaching, one that only people with lots of love can do.“My wallet! Where is it？” were my first words___38___ I found my wallet was missing. I ____39___ my memory for a few good seconds, then realized that I had left my precious wallet in the library’s public ___40___!Because the library was now __41__, I had to wait until the next morning to look for it. When I got there the next day, all I found was a clean restroom. This was the first time I could remember ever ___42___ to see a clean restroom. As I walked out, I looked at myself in the mirror and shook my head at the ___43____ fool in front of me.I politely ___44____ the librarian at the front desk and asked her if a wallet had been found in the restroom yesterday. “No.” That was that. I walked off with a sense of ____45____.I __46___ what I would do if I had found a wallet containing sixty dollars, a phone card and many other irreplaceable ___47____things. Finally, I ___48___ accepted the fact that my wallet was gone.A week later, I received a ___49____ in the mail. it was my wallet And most ___50____, nothing was missing！But there was a little yellow sheet of paper folded up in one of the wallet pockets that had not been there before. I slowly unfolded the paper, which ___51____something like this:When we continue to help around, we will live in a larger and more rewarding world.This person didn’t even leave a return address. So I couldn’t ___52___whoever it was. From that day on, I __53__ myself that I will follow this ___54___ and help others and make them as ___55__ as I was when I opened that parcel！36. A. leader B. writer C. teacher D. scholar37. A. aids B. systems C. materials D. methods38. A. once B. when C. before D. since39. A. searched B. improved C. developed D. recorded40. A. canteen B. lounge C. restroom D. showroom41. A. closed B. deserted C. crowded D. occupied42. A. hoping B. hating C. refusing D. preferring43. A. grateful B. curious C. forgetful D. nervous44. A. approached B. interviewed C. identified D. reminded45. A. safety B. forgiveness C. satisfaction D. disappointment46. A. described B. wondered C. discovered D. expressed47. A. personal B. strange C. surprising D. reasonable48. A. gladly B. naturally C. willingly D. painfully49. A. letter B. note C. package D. suitcase50. A. sincerely B. amazingly C. honestly D. obviously51. A. read B. printed C. explained D. wrote52. A. owe B. thank C. admire D. inspire53. A. supported B. suggested C. improved D. promised54. A. plan B. course C. regulation D. example55. A. shocked B. cautions C. delighted D. optimistic第三部分：阅读理解（共两节，40分）第一部分AJohnny the ExplorerJohnny was three when he ran away from home for the first time. Somebody left the garden gate open. Johnny wandered out, crossed some fields, and two hours later, and arrived in the next village. He was just able to give his name and address.By the time he was seven, Johnny used to vanish from home two to three times a year. Sometimes he covered quite long distances on foot. On other occasions he got on a bus or even a train, and simply sat there until someone asked for his ticket. Generally the police brought him home. "Why do you do it?" they used to ask. "You aren't unhappy at home, are you? .... ““Of course not," Johnny replied.” Then why?" "I just like seeing places," Johnny told them.Johnny continued to "see places" although everyone tried to stop him. His parents used to watch him closely, and so did his teachers; but sooner or later Johnny managed to slip away. As he grew older, his favorite trick was to hide on a long distance truck. Sometimes he used to travel hundreds of miles before anyone discovered him.It is hardly surprising that eventually Johnny managed to get on board a plane. He was twelve at the time. It was a cargo plane and, a few hours later, Johnny found himself in Cairo. How did he get on board? No one knows! According to Johnny himself, it was easy: he just went into the airport, walked along some corridors and got on board the nearest plane.In spite of all this, Johnny did well at school. He enjoyed maths and languages and, perhaps not surprisingly, he was especially good at geography. "What do you want to be when you grow up?" his teachers asked him. Johnny did not take long to answer that question. "An explorer!" he answered. "But it's difficult to become an explorer in this modem age." they tried to tell him, But it was no use: Johnny knew what he wanted!Just before he left school, Johnny saw a notice in one of the daily papers. An expedition was about to go to Brazil to travel up the Amazon River. There were vacancies for three young people "willing to work hard and with a sense of adventure". Johnny applied, and, two months later, he was on his way to Brazil.56. Johnny frequently left home because_________.A. he preferred to stay homeB. he enjoyed seeing new placesC. he couldn’t do well at schoolD. he didn’t get along well with his parents57. People around Johnny_______.A. tried to stop him from slipping awayB. kept following him to get him backC. booked tickets for him if necessaryD. were closer about how he traveled abroad58. From the passage, we can learn that _______.A. Johnny worked for a daily paperB. Johnny lacked a sense of adventureC. Johnny went exploring along the Amazon RiverD. Johnny went to Brazil months after he finished school.BEditor Henry Slocum,I read your May 10th article in the local newspaper Honesdale Times about electronic books, or e-books, with great interest. You made several good points about the disadvantage of e-books. You may have overlooked, however, some of the ways in which they are superior to traditional books. Yes, e-books are expensive, but they are also convenient. In addition, duo to their environment-friendly nature, e-books have the potential to change our planets for the better.E-books, for anyone who is unfamiliar with the term, are about the same size and shape as regular books. They have a large screen in the middle, however, this screen shows the reader a page of the text that has been downloaded from a computer. Once the reader has finished reading the page on the e-book screen, he or she scrolls down to see a new page. The process continues until the entire book has been read.As you pointed out, Mr. Slocum, it’s great to lie on a warm, sandy beach with a book. You can do that just as easily with an e-book as you can with a traditional paper book. In fact, because e-books are so light, you can carry themselves. Say, for example, that you like to read on the bus. Which would you rather carry with you---a heavy 800-page novel, or an e-book that weighs only a few ounces?Another important advantage is offered by e-books as well. They are more environment-friendly than traditional books. At present, thousands of trees cut down each year to meet the publishing industry’s demand for paper. Books that don’t sell are eventually returned to the publisher and destroyed, This terrible waste could be avoided if everyone used e-books, which require no paper.Sincerely,David Eng59. What does Editor Henry Slocum think about e-books?A. InterestingB. ExpensiveC. ConvenientD. Environment-friendly60. What is mainly talked about in Paragraph 2?A. What an e-book isB. Why e-books are popularC. How e-books have developedD. Who are the readers of e-books61. In David’s letter, he thinks that_______A. E-books will come down in priceB. E-books come in various sizes and shapesC. E-books do little harm to the environmentD. E-books are no better than traditional books62. The main purpose of the letter is to ________A. explain how to read e-booksB. honor the person who invented e-booksC. scold publishers for wasting so much paperD. provide evidence that e-books are a good ideaCLosing weight comes with a lot of health benefits---including make your brain sharper.Yes, it turns out that overweight may damage cognitive functions such as memory and attention. There have been few studies of overweight and cognitive functioning, possibly because it is generally believed that it is not a primary risk cause for poor cognitive performance. Losing weight, therefore, may help improve these mental functions, according to a new research led by John Gunstad, assistant professor of psychology at Kent State University.Growing evidence suggests that being fat is linked to cognitive deficits(缺陷). So Gunstad and his team guessed that losing weight might improve mental function. For their study, they measured memory and attention in a group of 150 overweight participants, some of whom had some king of operation for weight loss and some did not. All of the volunteers completed mental skills tests to access their abilities if memory and attention at the beginning of the study, and again 12 weeks later. To begin with, about 24%of the patients showed damaged learning and 23%showed signs of poor memory when tested. At the end of the study, those who had lost weight after operation improved their scores into the average or above average for cognitive functions. Scores for the volunteer who didn’t lose weight dropped even further.The study helped, Gunstad to find out whether losing weight had any effect on mental function. Now that he’s been the positive effect that weight loss can have one memory and attention, he says he will next study those who choose to lose weight by the traditional way—eating healthier and getting more active. He expects that losing weight in this way will have a similarly positive effect on the brain. “If we can improve the condition with operation, then we can probably produce the same change with behavioral weight loss as well.” He says.63. There is less research on overweight and cognitive functions because researchers________.A. believe overweight only affects our bodyB. have focused on ways to sharpen people’s mindC. do not consider overweight a main cause for low cognitive abilityD. are clear about the relation between weight and mental functions64. The result of Gunstad’s study shows that_______A. losing weight has little effect on people’s memoryB. Losing weight can improve people’s mental functionsC. overweight people are likely to have psychology problemD. overweight people’s abilities of concentration differ greatly65. What is Gunstad planning to prove next in his research?A. Slim people are smarter than overweight peopleB. Healthy diet is better than exercise in losing weightC. Traditional ways of losing weight are better than operationD. Overweight people will get smarter by taking more exercise66. Which of the following is the best title for the text?A. Body Weight and HealthB. Losing Weight by OperationC. Ways to Improve Mental FunctionsD. Losing Weight to Sharpen Your MindDSeeing in StereoHave you wondered why you have two eyes and why they are set close together on the front of your face? The reasons are simple and important to the way you see the rest of your world.Your eyes are like two small cameras. A camera catches an image of an object and records it on film. Similarly, when you look at something, each eye takes in what it sees and sends this image to the back of the eyeball. Because your eyes are set close together, they view the world from about the same height but from slightly different angles. Working as a team, they eyes send the images to your brain, which puts them together into a single, centered image.Seeing in stereo means seeing with two eyes working together, which is called stereoscopic sight. This allows you to view the world in three dimensions, or 3-D. Seeing depth helps you to judge the distance between you and the objects you see and to adjust to the changing angle at which you see something as you move closer to or farther away from it. If images are coming from only one eye, however, only two of these dimensions—height and width---can be perceived.A world seen with one eye is thus two-dimensional, as in a photograph.Now consider why your two eyes are on the front of your face. Think of other animals with the same arrangement. They are all animal that hunt, like lions and wolves. Their eyes face directly in front of them. This provided a field of sight about 180 degree wide, which is called binocular sight. On the other hand, animals that are hunted have eyes on the sides of the head, which provides nearly 360-degree field of sight. In order to stay alive, they need to see things coming from the sides and from behind. However, without stereoscopic sight, they have difficulty determining how far a danger is.With sight both stereoscopic and binocular, human share with animal hunters the ability to see from side to side and to accurately determine the distance. If you think it would be great to have another type of sight, perhaps with hundreds of tiny eyes like many insects do, think again! Each tiny insect eye sees only a tiny part. Besides, what if you needed glasses? Be glad for the eyesight that you have.67. According to the passage, an eye is like a camera because both_______A. can record imagesB. can imagine objectsC. provide centered imagesD. work at the same height68. Stereoscopic sight is a result of having_________.A. a three-hundred-sixty-degree field of sightB. hundreds of eyes, all seeing parts of an imageC. two eyes close to one another that work togetherD. one eye on either side of the head, each seeing a different image69. The underlined word “perceived” in paragraph 3means________.A. setB. takenC. seenD. understood70. The author implies that “seeing in stereo”________.A. is similar to the way camera workB. is an ability humans are fortunate to haveC. would be better for a wider field of sightD. helps people to have better sight than animals第二节Puppy FoodA puppy (young dog) is a precious addition to any family. The excitement of bringing home a little furry friend will always live in our memories. Like all of us, though, your puppy must have adequate nutrition right from the start to make cer tain that it’ll have a long and healthy life.____71____You might ask yourself what is the best for your new pet with all of the different varieties on the market in all of their attractive packaging. Some dry food produced especially for puppies is the best for the development of their teeth. _____72_____Contrary to the belief of many first time puppy owners, it is not always the best idea to purchase food that is too high in calcium, protein, and vitamin levels. _____73_____In addition, a high intake of calcium is associated with bone disease in large-breed dogs. If you have a small-breed puppy, you can buy that kind of food.It is not a good idea to feed the food you eat to your puppy frequently, as your puppy may become selective about food. ___74____Some people think that dog biscuits and other treats are fine, but they should not be a main part of puppy’s diet.Young puppies should be fed three times a day. Each puppy is unique, however, so feeding them twice a day is acceptable. After ten to twelve weeks of age, feed your puppy twice per day. Allow your puppy to cat as much as he would like in fifteen minutes. ____75____If you let your puppy eat too much or too often by keeping food accessible at all time, he may become overweight and have health problem as an adult. Like humans, your puppy will not enjoy the food any longer if it is there at all times.A.Pick up the dish with the remaining foodB.Proper food id a basic necessity for your puppiesC.Remember to give your puppy the food he would like to haveD.It can also cause an upset stomach due to an unbalanced dietE. A further benefit is that it is less expensive than the canned foodF.One example is that extra helpings of nutrients do harm to digestive organsG.It’s good to provide the extra nutrients a puppy n eeds until he grows larger.第四部分：书面表达（共两节，35分）第一节你的英国朋友Tim打算暑假来北京学习汉语，来信向你咨询你校国际版的汉语课程。

北京市朝阳区高中示范校2014-2015学年度第一学期高二化学选修4综合测试卷 3（试卷满分为100分，考试时间为100分钟）第Ⅰ卷（选择题共50分）可能用到的相对原子质量：H:1 N:14 O:16 Na:23 S:32 Cl:35.5 Zn：65 Cu:64选择题（每小题只有一个选项符合题意，每小题2分，共50分）1．下列物质中属于强电解质的是A．NH3·H2O B．H2O C．CH3COOH D．醋酸铵2．有关化学反应的说法中，正确的是A．自发反应都是放热反应B．自发反应都是熵增大的反应C．能自发进行的吸热反应一定是熵增大的反应D．非自发反应在任何条件下都不能实现3．下列与化学反应能量变化相关的叙述正确的是A．生成物能量一定低于反应物总能量B．放热反应的反应速率总是大于吸热反应的反应速率C．应用盖斯定律，可计算某些难以直接测量的反应焓变D．同温同压下，H2(g) + Cl2(g) = 2 HCl(g)在光照和点燃条件下的ΔH不同4．“嫦娥奔月”是一个充满浪漫主义的中国神话故事。

2007年10月24日我国“嫦娥一号”探月卫星由长三甲火箭送入预定的轨道。

长三甲火箭第三级推进剂采用低温液氧/液氢。

已知在298K时，2g氢气与氧气完全反应生成液态水放热285.8kJ，则此反应的热化学方程式为A．2H2(g)+O2(g) === 2H2O(l) △H=－285.8KJ·mol－1B．2H2(g)+O2(g) === 2H2O(l) △H=+285.8KJ·mol－1C．H2(g)+O2(g) === H2O(l) △H=－285.8KJ·mol－1D．H2(g)+ O2(g) === H2O(g) △H=－285.8KJ·mol－1５．工业上制备纯硅反应的热化学方程式如下：SiCl4(g)+2H2(g)=Si(s)+4HCl(g)；ΔH = + Q kJ/m ol(Q＞0)某温度、压强下，将一定量反应物通入密闭容器进行以上反应（此条件下为可逆反应），下列叙述正确的是A．反应过程中，若增大压强能提高SiCl4的转化率B．若反应开始时SiCl4为1 mol，则达平衡时，吸收热量为Q kJC．反应至4 min时，若HCl浓度为0.12 mol/L，则H2的反应速率为0.03 mol/(L·min) D．当反应吸收热量为0.025Q kJ时，生成的HCl通入100 mL 1 mol/L的NaOH溶液恰好反应６．下列电离方程式中书写正确的是A．NaHSO4 Na++H++SO42- B．NaHCO3 Na++H++CO32-C．HClO = H++ClO- D．H2S H++HS-；HS- H++S2-７．合成氨所需氢气可由煤和水反应制得，其中一步反应为CO(g)+H2O(g) 错误！未找到引用源。

北京市朝阳区示范性高中校2014—2015学年度第一学期高一化学期中复习练习卷 3可能用到的相对原子质量：H ～1 C～12 O～16Na～23Cl～35.5K～39 S～32 N～14 Mg～24 Zn～65第一卷选择题(每题2分,共50分)一、选择题（每小题只有一个正确答案）1．胶体区别于其他分散系的本质特征是（）A．胶体的分散质能通过滤纸空隙，而浊液的分散质不能B．产生丁达尔现象C．分散质粒子直径在1nm～100nm之间D．胶体在一定条件下能稳定存在2．以下过滤操作中，不正确的是（）A．蒸发时用玻璃棒不断搅动B．过滤时，玻璃棒与三层滤纸的一边接触C．分液时，先将上层液体倒出D．将浓硫酸慢慢注入盛有水的烧杯中进行稀释3. 关于用CCl4萃取碘水的说法中不正确的是（）A.碘在CCl4中的溶解度大于在水中的溶解度B.萃取后水层颜色变浅C.萃取后CCl4溶液层为紫红色D.萃取后水层颜色变红且在下层4.过滤后的食盐水仍含有可溶性的CaCl2、MgCl2、Na2SO4 等杂质，通过如下几个实验步骤，可制得纯净的食盐水：①加入稍过量的Na2CO3溶液；②加入稍过量的NaOH溶液；③加入稍过量的BaCl2 溶液；④滴入稀盐酸至无气泡产生；⑤过滤,正确的操作顺序是（）A．③②①⑤④ B．①②③⑤④C．②③①④⑤ D．③⑤②①④5.下列电离方程式错误的是（）A．NaHCO3 = Na+ + H+ + CO32－B．NaHSO4 = Na ++ H+ + SO42－C．H2SO4 = 2H+ + SO42－D．KClO3 = K+ + ClO3－6.实验室有三瓶失去标签的试剂，分别是Na2CO3、NaCl、AgNO3，实验员选择了一种试剂就把它们区别开来了，这种试剂是( )A．盐酸B．氢氧化钠溶液C．氯化钡溶液D．硝酸7.下列各物质中含氢原子数最多的是（）A．1mol NH4C1 B．1.5mol NH4NO3C．1.204×1024 CO(NH2)2D．1mol NH3·H2O8.在物质分类中，前者包括后者的是（）A．氧化物、化合物B．化合物、电解质C．溶液、胶体D．溶液、分散系9.设N A 表示阿伏加德罗常数，下列叙述中不正确的是（ ） A. 常温常压下，11.2L 氧气所含的原子数为N AB .1.8g 的NH 4＋离子中含有的电子数为N AC .常温常压下，48gO 3含有的氧原子数为3N AD .2.4g 金属镁变为镁离子时失去的电子数为0.2N A10.与50 mL 0.1 mol· L -1 Na 2CO 3溶液中Na +的物质的量浓度相同的溶液（ ） A. 50mL 0.2mol·L -1 的 NaCl 溶液 B. 100mL 0.1mol·L -1的 NaCl 溶液 C. 25mL 0.2mol·L -1 的 Na 2SO 4 溶液 D. 10mL 0.5mol·L -1 的 Na 2CO 3 溶液11．将5mol/L 的Mg （NO 3）2溶液a mL 稀释至b mL ，稀释后溶液中NO 3－的物质的量浓度为（ ） A ．b a 5mol/L B ．b a 10mol/L C ．a b 5mol/L D ．ba mol/L12.已知1.505×1023个X 气体分子的质量为8g ，则X 气体的摩尔质量是( ) A ．16g B ．32g C ．64g /mol D ．32g /mol13．下列物质能导电的是( )A ．硫酸铜晶体B ．CO 2C ．熔融状态下的氯化钾D ．无水乙醇14.将饱和FeCl 3溶液分别滴入下列液体中，能形成胶体的是（ ） A. 冷水 B. 沸水 C. NaOH 溶液 D. NaCl 溶液15．下列关于电解质的判断中，正确的观点是（ ） A ．在熔融状态下能导电的物质 B ．在水溶液中能导电的物质C ．在水溶液中或熔融状态下能导电的化合物D ．在熔融和溶液的状态下都能导电的化合物16.下列反应的离子方程式书写正确的是( ) A.氯化铜溶液与铁粉反应：Cu 2++Fe=Fe 2++Cu B.稀 H 2SO 4与铁粉反应：2Fe+6H +=2Fe 3++3H 2↑C.氢氧化钡溶液与稀 H 2SO 4 反应：Ba 2++SO 42-=BaSO 4↓D.碳酸钙与盐酸反应：CO 32-+2H +=H 2O+CO 2↑17.能用H ＋＋OH －＝H 2O 来表示的化学反应是( )A. 氢氧化镁和稀盐酸反应B. Ba(OH)2溶液滴入稀硫酸中C. 澄清石灰水和稀硝酸反应D. 二氧化碳通入澄清石灰水中18.有四位同学分别对四种溶液中所含的离子进行检测，所得结果如下，其中所得结果错误的是( ) A ．K +、Na +、Cl -、NO 3- B ．OH -、CO 32-、Cl -、K + C ．Ba 2+、Na +、OH -、NO 3- D ．Cu 2+、NO 3-、OH -、Cl -19．将标准状况下，将VL A 气体（摩尔质量为Mg/mol ）溶于0.1L 水中，所得溶液密度为ρg/cm 3，则此溶液的物质的量浓度（mol/L ）为（ ）A ．)2240(+MV V ρ B ．)2240(1000+MV V ρC ．ρ)1.0(4.22+V MVD ．100VρM （MV+2240）20．某位同学配制一定物质的量浓度的NaOH 溶液时，造成所配溶液浓度偏高的原因是（ ） A ．所用NaOH 已经潮解 B ．向容量瓶中加水未到刻度线 C ．有少量NaOH 溶液残留在烧杯里D ．用带游码的托盘天平称2.4gNaOH 时误用了“左码右物”方法21.浓度为0.50 mol ·L -1的某金属阳离子M n+的溶液10.00 mL ，恰好与0.40 mol ·L -1的NaOH 溶液12.50 mL 完全反应，生成沉淀，则n 等于( ) A.1 B.2 C.3 D.422.欲配制100ml 1.0 mol/L Na 2SO 4溶液，正确的方法是（ ） ① 将14.2 g Na 2SO 4 溶于100ml 水中② 将32.2g Na 2SO 4·10H 2O 溶于少量水中，再用水稀释至100 ml ③ 将20 ml 5.0 mol/L Na 2SO 4溶液用水稀释至100 ml A ．①② B ．②③ C ．①③ D ．①②③23.在无土栽培中，需配制一定量含50 mol NH 4Cl; 6 mol KCl 和24 mol K 2SO 4的营养液。

（第6题图）北京市朝阳区高三年级第一次综合练习数学学科测试（理工类）2014．3（考试时间120分钟 满分150分）本试卷分为选择题（共40分）和非选择题（共110分）两部分第一部分（选择题 共40分）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，选出符合题目要求的一项． （1）复数i(2+i)z =在复平面内对应的点位于（A ）第一象限 （B ）第二象限 （C ）第三象限 （D ）第四象限 （2）已知集合1{|(1}2xA x =<，集合{|lg 0}B x x =>，则AB =（A ）{|0}x x > （B ）{|1}x x > （C ） {|1}{|0}x x x x >< （D ） ∅ （3）已知平面向量a ，b 满足2==a b ，(2)()=2⋅--a +b a b ，则a 与b 的夹角为（A ）6π （B ） 3π（C ）32π （D ） 65π（4）如图，设区域{(,)01,01}D x y x y =≤≤≤≤，向区域D 内随机投一点，且投入到区域内任一点都是等可能的，则点落 入到阴影区域3{(,)01,0}M x y x y x =≤≤≤≤的概率为（A ）14（B ）13（C ） 25 （D ） 27（5）在ABC △中，π4A =，BC =“AC ”是“π3B =”的（A ）充分不必要条件 （B ）必要不充分条件 （C ）充要条件 （D ）既不充分也不必要条件 （6）执行如图所示的程序框图,输出的S 值为（A ）2 （B ）2- （C ）4 （D ）4-（7）已知函数2sin ()1xf x x =+．下列命题： ①函数()f x 的图象关于原点对称； ②函数()f x 是周期函数； ③当2x π=时,函数()f x 取最大值；④函数()f x 的图象与函数1y x=的图象没有公共点，其中正确命题的序号是（A ） ①③ （B ）②③ （C ） ①④ （D ）②④（8）直线y x m =+与圆2216xy +=交于不同的两点M ，N ，且3MN O M O N ≥+，其中O 是坐标原点，则实数m 的取值范围是 （A ）(2,22⎡-⎣ （B ）(22,4⎡--⎣（C） [2,2]- （D ） [-第二部分（非选择题 共110分）二、填空题：本大题共6小题，每小题5分，共30分．把答案填在答题卡上． （9）在各项均为正数的等比数列{}n a 中，12a =，2312a a +=，则该数列的前4项和为 ．（10）在极坐标系中，A 为曲线2cos ρθ=上的点，B 为曲线cos 4ρθ=上的点，则线段AB 长度的最小值是 ．（11）某三棱锥的三视图如图所示，则这个三棱锥的体积为 ；表面积为 ．（12）双曲线2221(0)y x b b-=>的一个焦点到其渐近线的距离是2，则b = ；此双曲线的离心率为 ．（13）有标号分别为1,2,3的红色卡片3张，标号分别为1,2,3的蓝色卡片3张，现将全部的6张卡片放在2行3列的格内 （如图）．若颜色相同的卡片在同一行，则不同的放法种数为 ．（用数字作答）正视图俯视图（14）如图，在四棱锥S ABCD -中，SB ⊥底面ABCD ．底面ABCD 为梯形，AB AD ⊥，AB ∥CD ,1,3AB AD ==，2CD =．若点E 是线段AD 上的动点，则满足90SEC ∠=︒的点E 的个数是 ．三、解答题：本大题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程． （15）（本小题满分13分）已知函数22()2sin()cos sin cos f x x x x x =π-⋅+-，x ∈R ． （Ⅰ）求()2f π的值及函数()f x 的最小正周期； （Ⅱ）求函数()f x 在[]0,π上的单调减区间．（16）（本小题满分13分）某单位从一所学校招收某类特殊人才．对20位已经选拔入围的学生进行运动协调能力和逻辑思维能力的测试，其测试结果如下表：例如，只知道从这20位参加测试的学生中随机抽取一位，抽到运动协调能力或逻辑思维能力优秀的学生的概率为25． （I ）求a ，b 的值；（II ）从参加测试的20位学生中任意抽取2位，求其中至少有一位运动协调能力或逻辑思维能力优秀的学生的概率；（III ）从参加测试的20位学生中任意抽取2位，设运动协调能力或逻辑思维能力优秀的学生人数为ξ，求随机变量ξ的分布列及其数学期望E ξ．BCDESA（17）（本小题满分14分）如图，四棱锥P ABCD -的底面为正方形，侧面PAD ⊥底面ABCD ．PAD △为等腰直角三角形，且PA AD ⊥． E ，F 分别为底边AB 和侧棱PC 的中点．（Ⅰ）求证：EF ∥平面PAD ； （Ⅱ）求证：EF ⊥平面PCD ； （Ⅲ）求二面角E PD C --的余弦值．（18）（本小题满分13分）已知函数21()ln 2f x ax x =-，a ∈R ． （Ⅰ）求函数()f x 的单调区间；（Ⅱ）若函数()f x 在区间[1,e]的最小值为1，求a 的值．（19）（本小题满分14分）已知椭圆2222:1(0)x y C a b a b +=>>经过点（Ⅰ）求椭圆C 的方程；（Ⅱ）直线(1)(0)y k x k =-≠与椭圆C 交于,A B 两点，点M 是椭圆C 的右顶点．直线AM 与直线BM 分别与y 轴交于点,P Q ，试问以线段PQ 为直径的圆是否过x 轴上的定点？若是，求出定点坐标；若不是，说明理由．（20）（本小题满分13分）从1,2,3,,n 中这n 个数中取m （,m n *∈N ，3m n ≤≤）个数组成递增等差数列，所有可能的递增等差数列的个数记为(,)f n m ．（Ⅰ）当5,3n m ==时，写出所有可能的递增等差数列及(5,3)f 的值； （Ⅱ）求(100,10)f ；（Ⅲ）求证：()(1)(,)2(1)n m n f n m m -+>-．A E BCDPF北京市朝阳区高三年级第一次综合练习数学答案（理工类） 2014.3三、解答题15. （本小题满分13分） 解： ()f x =sin 2cos 2x x -)4x π=-.（Ⅰ）())12242f πππ=⋅-==.显然，函数()f x 的最小正周期为π. …………… 8分 （Ⅱ）令ππ3π2π22π242k x k +-+≤≤得 37ππππ88k x k ++≤≤，k ∈Z .又因为[]0,πx ∈，所以3π7π,88x ⎡⎤∈⎢⎥⎣⎦. 函数()f x 在[]0,π上的单调减区间为3π7π,88⎡⎤⎢⎥⎣⎦． …………… 13分 16. （本小题满分13分）解：（I ）设事件A ：从20位学生中随机抽取一位，抽到运动协调能力或逻辑思维能力优秀的学生．由题意可知，运动协调能力或逻辑思维能力优秀的学生共有(6)a +人． 则62()205a P A +==． 解得 2a =．所以4b =． …………… 4分（II ）设事件B ：从20人中任意抽取2人，至少有一位运动协调能力或逻辑思维能力优秀的学生．由题意可知，至少有一项能力测试优秀的学生共有8人．则21222062()1()195C P B P B C =-=-=． …………… 7分（III ）ξ的可能取值为0，1，2．20位学生中运动协调能力或逻辑思维能力优秀的学生人数为8人．所以21222033(0)95C P C ξ===，1112822048(1)95C C P C ξ===，2822014(2)95C P C ξ===．所以ξ的分布列为所以，0E ξ=⨯33951+⨯48952+⨯1495764955==． …………… 13分17. （本小题满分14分）（Ⅰ）证明：取PD 的中点G ，连接FG ，AG .因为F ，G 分别是PC ，PD 的中点， 所以FG 是△PCD 的中位线. 所以FG ∥CD ，且12FG CD =． 又因为E 是AB 的中点，且底面ABCD 为正方形，所以1122AE AB CD ==，且AE ∥CD . 所以AE ∥FG ，且AE FG =． 所以四边形AEFG 是平行四边形． 所以EF ∥AG ．又EF ⊄平面PAD ，AG ⊂平面PAD ，AE BCDPFG所以EF平面PAD ． ……………4分（Ⅱ）证明： 因为平面PAD ⊥平面ABCD ，PA AD ⊥，且平面PAD 平面ABCD AD =， 所以PA ⊥平面ABCD ． 所以PA AB ⊥，PA AD ⊥．又因为ABCD 为正方形，所以AB AD ⊥， 所以,,AB AD AP 两两垂直.以点A 为原点，分别以, , AB AD AP 为, , x y z 轴， 建立空间直角坐标系（如图）． 由题意易知AB AD AP ==， 设2AB AD AP ===，则(0,0,0)A ，(2,0,0)B ，(2,2,0)C ，(0,2,0)D ，(0,0,2)P ,(1,0,0)E ,(1,1,1)F ．因为(0,11)EF =，，(022)PD =-，，，(200)CD =-，，， 且(0,11)(0,2,2)0EF PD ⋅=⋅-=，，(0,11)(2,00)0EF CD ⋅=⋅-=，，所以EF PD ⊥，EF CD ⊥．又因为PD ，CD 相交于D ，所以EF ⊥平面PCD ． …………… 9分 （Ⅲ）易得(102)EP =-，，，(0,22)PD =-,．设平面EPD 的法向量为(, , )x y z =n ，则0,0.EP PD ⎧⋅=⎪⎨⋅=⎪⎩n n 所以 20,220. x z y z -+=⎧⎨-=⎩即2,. x z y z =⎧⎨=⎩令1z =，则(2,1,1)=n ．由（Ⅱ）可知平面PCD 的法向量是(0,11)EF =，， 所以cos ,2EF EF EF⋅〈〉===⋅n n n .由图可知，二面角E PD C --的大小为锐角，所以二面角E PD C --的余弦值为3． ……………14分 18. （本小题满分13分）解：函数()f x 的定义域是(0,)+∞， 1()f x ax x '=-21ax x-=．（Ⅰ）（1）当0a =时，1()0f x x'=-<，故函数()f x 在(0,)+∞上单调递减． （2）当0a <时，()0f x '<恒成立，所以函数()f x 在(0,)+∞上单调递减．（3）当0a >时，令()0f x '=，又因为0x >，解得x =①当x ∈时，()0f x '<，所以函数()f x 在单调递减．②当)x ∈+∞时，()0f x '>，所以函数()f x 在)+∞单调递增． 综上所述，当0a ≤时，函数()f x 的单调减区间是(0,)+∞，当0a >时，函数()f x 的单调减区间是，单调增区间为)+∞．…7分 （Ⅱ）（1）当0a ≤时，由（Ⅰ）可知，()f x 在[1,e]上单调递减，所以()f x 的最小值为21(e)e 112f a =-=，解得240ea =>，舍去． （2）当0a >时，由（Ⅰ）可知，①1，即1a ≥时，函数()f x 在[1,e]上单调递增， 所以函数()f x 的最小值为1(1)12f a ==，解得2a =．②当1e <<，即211e a <<时，函数()f x 在上单调递减，在上单调递增，所以函数()f x 的最小值为11ln 122f a =+=，解得e a =，舍去．③e ，即210e a <≤时，函数()f x 在[1,e]上单调递减，所以函数()f x 的最小值为21(e)e 112f a =-=，得24ea =，舍去． 综上所述，2a =． ……………13分19. （本小题满分14分）解：（Ⅰ）由题意得22=21314c a a b ⎧⎪⎪⎨⎪+=⎪⎩，解得=2a ，1b =． 所以椭圆C 的方程是2214x y +=． …………… 4分 （Ⅱ）以线段PQ 为直径的圆过x 轴上的定点.由22(1)14y k x x y =-⎧⎪⎨+=⎪⎩得2222(14)8440k x k x k +-+-=． 设1122(,),(,)A x y B x y ，则有2122814k x x k +=+，21224414k x x k -=+．又因为点M 是椭圆C 的右顶点，所以点(2,0)M ．由题意可知直线AM 的方程为11(2)2y y x x =--，故点112(0,)2y P x --． 直线BM 的方程为22(2)2y y x x =--，故点222(0,)2y Q x --． 若以线段PQ 为直径的圆过x 轴上的定点0(,0)N x ，则等价于0PN QN ⋅=恒成立．又因为1012(,)2y PN x x =-，2022(,)2y QN x x =-， 所以221212001212224022(2)(2)y y y y PN QN x x x x x x ⋅=+⋅=+=----恒成立． 又因为121212(2)(2)2()4x x x x x x --=-++2222448241414k k k k -=-+++ 22414k k=+， 212121212(1)(1)[()1]y y k x k x k x x x x =--=-++22222448(1)1414k k k k k -=-+++22314k k-=+， 所以222212000212212414304(2)(2)14k y y k x x x k x x k -++=+=-=--+．解得0x =．故以线段PQ 为直径的圆过x轴上的定点(． …………… 14分 20. （本小题满分13分） 解：（Ⅰ）符合要求的递增等差数列为1，2，3；2，3，4；3，4，5；1，3，5，共4个.所以(5,3)4f =. …………… 3分 （Ⅱ）设满足条件的一个等差数列首项为1a ，公差为d ，d *∈N .1019a a d =+，10110011199a a d --==≤，d 的可能取值为1,2,,11．对于给定的d ，11091009a a d d =--≤， 当1a 分别取1,2,3,,1009d -时，可得递增等差数列1009d -个（如：1d =时，191a ≤，当1a 分别取1,2,3,,91时，可得递增等差数列91个：1,2,3,,11；2,3,4,,12；；91,92,93,,100，其它同理）.所以当d 取1,2,,11时，可得符合要求的等差数列的个数为：(100,10)100119(1211)1100966506f =⋅-⋅+++=-⋅=．…………… 8分（Ⅲ）设等差数列首项为1a ，公差为d ，1(1)m a a m d =+-，1111m a a n d m m --=--≤，记11n m --的整数部分是t ，则11111n n t m m ---<--≤，即111n m n t m m --<--≤． d 的可能取值为1,2,,t ，对于给定的d ，1(1)(1)m a a m d n m d =----≤，当1a 分别取1,2,3,,(1)n m d --时，可得递增等差数列(1)n m d --个.所以当d 取1,2,,t 时，得符合要求的等差数列的个数2(1)121(,)(1)222t t m n m f n m nt m t t +--+=--⋅=-+ 22121(21)()22(1)8(1)m n m n m t m m --+-+=--+-- 易证21112(1)1n m n m n m m m --+-<---≤． 又因为211||12(1)2(1)n m n m m m m m --++-=---，2113||2(1)12(1)n m n m m m m -+---=---， 所以21211||||12(1)2(1)1n m n m n m n m m m m --+-+-->-----． 所以(1)(,)(1)2t t f n m nt m +=--⋅ (1)()(1)11(1)122(1)n m n m n m n m n m m n m m m --+--+-->⋅--⋅=--． 即()(1)(,)2(1)n m n f n m m -+>-． …………… 13分。