北京市丰台区2017届高三上学期期末试题(附答案)

丰台区2016～2017学年度第一学期期末练习第一节单项填空（共15小题；每小题1分，共15分）21. My friend hasn’t answered my letter yet, and I _________ for a reply.A. waitedB. have waitedC. am waitingD. will wait22. Everyone tried to help the family _________ house had burned down in the fire.A. whyB. whoseC. whereD. which23. Don’t worry about the work. By the time you get back from your vacation, we _________ care of everything.A. will have takenB. takeC. have been takingD. are taking24. We must do _________ we can in order to save oil, as it is an irreplaceable natural resource.A. howeverB. whereverC. whoeverD. whatever25. I _________ snow before I moved to Canada last year.A. wasn’t seeingB. don’t seeC. had never seenD. would not see26. — Hello, this is Dan speaking.—Hi, Dan. It’s Milly. I’m calling _________ about your guitar lessons.A. askedB. to askC. askD. asking27. Take the mask with you _________ the air is bad.A. so thatB. as ifC. in caseD. even though28. Knocking loudly on the desktop, Mr. Brown made his anger _________.A. knowingB. to knowC. having knownD. known29. One advantage of having a car is _________ you don’t need to rely on public transportation.A. thatB. whetherC. whatD. why30. The coffee _________ when I walked into the kitchen.A. was being madeB. had madeC. has been madeD. was making31. “You _________ have a wrong number,” she said. “There is no one of that name here.”A. wouldB. needC. mustD. could32. Newly-built wooden cottages line the street, _________ the old town into a dreamland.A. turnB. turningC. to turnD. turned33. _________ you paid for the taxi fare, please let me pay for our dinner.A. SinceB. UntilC. UnlessD. Although34. If we _________ a ticket earlier, we would have watched the film.A. have bookedB. bookedC. bookD. had booked35. An elephant _________ is the earth’s largest land animal has few natural enemies other than human beings.A. whatB. whichC. whenD. where第二节完形填空（共20小题；每小题1.5分，共30分）What I RegretAt lunchtime, Jimmy, Patrick, Devon, and I began our regular routine of our lunches. I glanced across the busy cafeteria and saw the 36 student, Joel. He was holding his plate and waiting in lines.Patrick 37 him too. “Why’s the new kid dressed like the headmaster?” he asked. Devon and Jimmy laughed.“Joel’s cool. He’s in my English and history classes,” I said. However, I kept the 38 that Joel and I had become friends when we worked on a project together. We 39 that we were both enthusiastic readers––something I would never admit to Patrick, Jimmy, and Devon.I saw that Joel was 40 t oward us. “Don’t do it,” I thought, but in seconds he was at our table. My friends raised their eyebrows. Jimmy, Devon and Patrick piled their backpacks on the table and chairs so that there was no 41 left for another person to sit down. Patrick said, “I don’t think we have room.”This 42 situation froze the air. I could 43 Joel looking at me, but I stared at my 44 as if it contained precious pearls of wisdom instead of rice and beans. After a long, uncomfortable pause, Joel 45 . I 46 have spoken up for him, but I couldn’t walk away from my three friends, could I?Joel didn’t speak to me after that 47 . He was soon 48 around with another group of kids. A few months later, I saw an announcement about Joel being chosen to be president of the class book club. I was 49 for Joel’s achievements, but I realized I had made a big mistake 50 I said nothing at the lunch table that day. Why was I so 51 that my friends might find out that I like to read?As I stared at the announcement, I knew I needed to 52 to Joel––even if he did not want to become my friend again. I was certain that my three friends would not 53 . I was also certain that I 54 losing them as well. However, I knew that I would lose myself if I did nothing.As the dismissal bell rang, I gathered up my books, took (a) deep 55 , and went to find Joel.36. A. good B. new C. lucky D. top37. A. noticed B. helped C. examined D. called38. A. words B. ideas C. truth D. promise39. A. forgot B. argued C. discussed D. discovered40. A. nodding B. flying C. walking D. driving41. A. book B. food C. time D. space42. A. awkward B. dangerous C. pleasant D. comfortable43. A. taste B. smell C. hear D. feel44. A. face B. lunch C. backpack D. table45. A. left B. laughed C. started D. stopped46. A. need B. should C. would D. must47. A. greeting B. change C. meeting D. lesson48. A. turning B. looking C. showing D. hanging49. A. happy B. sorry C. thankful D. anxious50. A. if B. until C. when D. where51. A. confused B. surprised C. excited D. afraid52. A. adapt B. apologize C. smile D. refer53. A. refuse B. agree C. mind D. choose54. A. risked B. permitted C. tried D. suggested55. A. delight B. silence C. breath D. thought第三部分阅读理解（共两节40分）第一节：（共15小题；每小题2分，共30分）difficult to ride. And also, it makes a horrible sound. The sound is louder and more annoying than a roaring). However, it did not help. The wheel continues to56. Natasha bought her scooter ________.A. on a websiteB. at a supermarketC. in a second-hand storeD. from a scooter factory57. According to Natasha, the scooter _________.A. loses its front wheelB. makes a loud noiseC. has no handlebarsD. runs too slowly58.Natasha felt _________ about her purchase.A. nervousB. pleasedC. disappointedD. excited59. Natasha wrote this letter to _________.A. buy a new scooterB. get her money backC. advertise the scooterD. ask how to use the scooterBClimbing in the CloudsEdmund Percival Hillary was one of the greatest explorers of the twentieth century. He was born in Auckland, New Zealand, in 1919. He discovered an interest in mountain climbing while he was still in high school and began climbing New Zealand’s Southern Alps.Like his father, Hillary earned his living as a beekeeper. However, he continued to climb mountains. His goal was to climb Mt. Everest, which is the highest mountain in the world. By the early 1950s, several expeditions (探险队) had attempted to reach the summit of Everest, but all had failed. Then, in 1953, Hillary and a Nepalese climber named Tenzing Norgay became the first two people to reach the top of the world.Hillary’s spirit of explorati on was not satisfied. He joined an expedition to Antarctica and reached the South Pole in 1958. He also made an expedition up the Ganges River to its source in the Himalayas. Sir Edmund Hillary was a brave adventurer. He went where no man or woman had gone before.Although Hillary was best known as the young man who climbed to the summit of Mt. Everest in the 1950s, he continued his journeys to far-off places into his senior years. For instance, in his mid-sixites Hillary flew to the North Pole with Neil Armstrong, the first man on the moon. Moreover, Hillary authored many books. However, his most lasting gift, perhaps, was the Sir Edmund Hillary Himalayan Trust (信托基金). It raised millions of dollars and contributed to schools, hospitals and many other public improvements in the Sherpa villages of Nepal. In January 2008, Sir Edmund Hillary died at the age of 88.Despite being a great adventurer and known for the treasure he left, Sir Edmund Hillary always modestly referred to himself as a simple beekeeper from New Zealand.60. Hillary was interested in _________ when he was in high school.A. mountain-climbingB. bee-keepingC. money-raisingD. story-writing61.Hillary became well-known because _________.A. he reached both the South Pole and the North PoleB. he was the first to reach the top of Mt. EverestC. he lived in places where no humans had goneD. he made a lot of money as a beekeeper62. _________ is the right order of Hillary’s expeditions.a. He traveled to the source of the Ganges River.b. He climbed New Zealand’s Southern Alps.c. He reached the summit of Everest.d. He explored the North Pole.A.a-c-d-bB. b-d-c-aC. a-b-c-dD. b-c-a-d63. We can learn from the passage that Hillary is _________.A. outgoing and fearlessB. talented and honestC. determined and caringD. hardworking and carefulCThroughout childhood, kids are encouraged to take good care of their bodies by getting enough rest, exercising regularly, eating healthful foods, and drinking plenty of water. But recently children and teenagers have been warned to protect their skin. Skin cancer is on the rise among young people. Teens should make some basic lifestyle changes to help slow this trend.Melanoma, a skin cancer, is the second most common form of cancer for people aged 15 to 29. Unfortunately, the risk of developing it has increased in recent years. One of the most important causes of melanoma is UV radiation (辐射) damage. Scientists think that some of this damage is directly linked to the use of tanning beds (皮肤美黑床). Now they have found that these beds produce UV A radiation and UVB radiation, both of which are dangerous.Clearly, avoiding tanning beds is one way teens can protect their skin, but they must do more. They need to protect themselves from too much sun exposure as well. They must learn to stay out of the sun in summer. Doctors say that to avoid the harmful rays of the sun, young people should stay indoors between 10 a.m. and 2 p.m., when the rays are the strongest. When teens have to be outdoors during these hours, they should use sunscreen that provides protection from both UVA and UVB rays.Protection is the most effective weapon in the battle against melanoma, but paying close attention to the skin is also vital. Melanoma often begins as a mole (痣) on the skin. If it’s caught before it spreads below the skin’s surface, it’s highly curable. Therefore, teens should watch for both new moles and existing moles. If they see anything that looks unusual, they should visit a skin doctor right away.Teens who continue to bake in the sun to achieve that perfect tan should realize the potential consequences of their behavior. Is a sun-kissed look really worth the risk of melanoma? It’s not too late to change your habits and reduce your exposure to harmful UV rays. Take action now to protect your skin and avoid this deadly disease later.64. Teens are warned to protect their skin because _________.A. their lifestyles are not healthyB. skin helps slow the radiation damageC. skin cancer is growing among teenagersD. they spend longer time staying outdoors65. In Paragraph 2, the author mainly talks about _________ of melanoma.A. the causeB. the preventionC. the symptomD. the treatment66. _________ is the effective protection of skin.A. Using tanning bedsB. Eating more healthful foodsC. Visiting a skin doctor frequentlyD. Reducing exposure to strong UV raysDThe biggest criticism (批评) of social networking is that our young people are losing their offline friends to online friends. In fact there is a lot of research that shows these criticisms are generally unfounded. Research by Allen et al. found that people are not replacing offline friends with online companions but are using them to support their offline relationships. They also found that our online friendships actually allow us to have discussions with a much more diverse set of people than in the real world and improve our psychological happiness.However, there is one part of social networking that is deeply worrying. We find ourselves in a hyper-connected world where people access social media day and night, excited to make announcements about the tiniest details of their lives. Research is starting to show that this culture is negatively affecting not our friendships but our character.Professor Larry D. Rosen, in his book iDisorder, presents evidence that social networking is turning us into narcissists (自恋者). He says that young people who overuse social networking sites can become vain, aggressive, and show anti-social behavior in their offline lives. But perhaps an even more disturbing effect is that one of our most basic emotions seems to be disappearing––empathy. This is the emotion that bonds us together; it allows us to see the world from our friends’ points of view. Without it, we are far less able to connect and form meaningful adult relationships.Sherry Turkle, a professor of social sciences at MIT, suggests that people are no longer comfortable being alone. This is something confirmed by a study where 200 university students were asked to go without social media for 24 hours. Many admitted an addiction to their online social network; most complained that they felt cut off from family and friends. But being alone is a time, Turkle argues, when we self-reflect and get in touch with who we really are. It is only when we do this that we can make meaningful friendships with others. She believes, as is the title of her 2011 book, that we are simply “Alone Together.”These potential changes in our characters are rather disturbing. If nothing is done, our young people could well be in trouble. Therefore, suggestions about ways to encourage our young people to avoid the problems of social networking should be made, so they can develop the kinds of friendships that are required to grow into well-adjusted and happy adults.67. The underlined word “unfounded” in Paragraph 1 probably means _________.A. undoubtedB. falseC. acceptableD. illegal68. In this passage, the author mainly argues that _________.A. internet culture causes various problemsB. we are losing some most important emotionsC. online friendships do good to offline friendshipsD. social networking affects young people’s personalities69. By the underlined sentence in Paragraph 4, Turkle probably means _________.A. we rely on social network for connectionB. being alone is necessary for being togetherC. being alone makes us know ourselves betterD. we hardly communicate while being together70. From the passage, we can learn that _________.A. we are becoming unable to understand others wellB. young people will develop offline friendshipsC. young people can’t go without social mediaD. social media have more advantages第二节（共5小题；每小题2分，共10分）Is My Dog a Wolf?In the old days wolves and dogs shared the same ancestor. 71 . And wolves stayed wolves. Even though it has been thousands of years since dogs have been wild, many things a dog does by instinct (本能) a wolf also does.Why does my dog chew my stuff?I t’s not because he’s mad at you. The baby wolf chews on a deer bone for several reasons. There is some small nutritional value gained by chewing bones. 72 . But mostly, it is just fun and tastes good. Most of us don’t leave deer bones lying around the house, so table legs, shoes, and sticks probably seem like good bone replacements. Many dogs get scared or bored when they are left alone, and chewing on something can be comforting and entertaining to them.73 . So when he eats your homework, it really means he misses having you around.Why does my dog play with dirt?74 . Wolves dig holes to hide leftover food and bones, so they’ll have a nice snack for later. Some dig to catch small underground animals, which make tasty snacks. Or they dig to create a cool hole to lie in during the summer…or a warm snow cave in the winter. Adult wolves dig underground caves for their ba bies to provide shelter and safety. Dogs may dig for some of the same reasons, but one thing is for sure: newly dug dirt has all sorts of interesting smells which they are crazy about.Once you understand that dogs and wolves are similar, you can look at the ways they are different. In the wild, wolves live by wolf rules. Most of their days are spent caring for the young, resting, and hunting. 75 . Their willingness to do this is probably the biggest difference between the two species. That’s why dog s can become human’s friends while wolves never.A. Dogs, however, must live by people rules both inside and outside the home.B. If that “something” smells like you, it is all the more attractive.C. D igging is a survival tool for wolves, but it’s just fu n for dogs.D. Gradually, dogs changed to become their own species.E. Wolf and dog noses also do more than just smell.F. It is also the way wolves brush their teeth.G. How are they different?第四部分书面表达（共两节35分）第一节（15分）假设你是红星中学高三学生李华，你的英国朋友Jim在给你的邮件中提到他对中国传统节日很感兴趣，并请你介绍一个你喜欢的中国传统节日。

丰台区2016~2017学年度第一学期期末练习 高三数学（理科）参考答案及评分参考2017．01 一、选择题共8小题，每小题5分，共40分．二、填空题共6小题，每小题5分，共30分．9．1i -+ 10．5311． 15 12．4 13．83π； 14．2；1111,,3432⎛⎤⎡⎫-- ⎪⎥⎢⎝⎦⎣⎭U 三、解答题共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.（本小题共13分）解：（Ⅰ）在△ADC 中，由余弦定理，得CD AC AD CD AC C ⋅-+=2cos 222 ……………….2分2123272322=⨯⨯-+=……………….4分因为0C <<π，所以3C π=. ……………….6分 （Ⅱ）因为3C π=，所以23sin =C . ……………….8分 在△ABC 中，由正弦定理，得CABB AC sin sin =， ……………….10分 即2213=AB ，所以边AB 的长为2213. ……………….13分16.（本小题共14分）证明：（Ⅰ）取PD 中点H ，连接GH ，HC ，因为ABCD 是正方形，所以AD ‖BC ，AD BC =.因为G,H 分别是PA ,PD 中点，所以GH ‖AD ,12GH AD =. 又因为EC ‖AD 且12EC AD =， 所以GH ‖EC ，GH EC =，所以四边形GHCE 是平行四边形, ………….3分 所以EG ‖HC .又因为EG Ë平面PDCQ ，HC Ì平面PDCQ所以EG ‖平面PDCQ ． ……………….5分 （Ⅱ）因为平面PDCQ ⊥平面ABCD ， 平面PDCQ I 平面ABCD CD =，PD DC ^，PD Ì平面PDCQ ，所以PD ^平面ABCD ． ……………….6分如图，以D 为原点，射线DA ，DC ，DP 分别为x ,y ,z 轴正方向，建立空间直角坐标系．设PD a =，则 ()()()00002201 P ,,a F ,,B ,,，，．………………7分因为PD ⊥底面ABCD ，所以平面ABCD 的一个法向量为(0,0,1)=m . ……………….8分 设平面PFB 的一个法向量为(,,)x y z =n ，()10PF ,,a u u u r =- ()120 FB ,,u u r =, 则0,=0.PF FB ⎧⋅=⎪⎨⋅⎪⎩uu u r uur n n即0+2=0x az x y -=⎧⎨⎩令x =1，得11,2z y a ==-，所以11(1,,)2a=-n ． ……………….10分由已知，二面角P BF C --所以得cos <,>||||⋅===m nm n m n ……………….11分 解得a =2,所以2PD =． ……………….13分因为PD 是四棱锥P ABCD -的高，所以其体积为182433P ABCD V -=⨯⨯=．……………….14分17．（本小题共14分）解：（Ⅰ）由题意知，四所中学报名参加数独比赛的学生总人数为100名， 抽取的样本容量与总体个数的比值为30310010=， 所以甲、乙、丙、丁四所中学各抽取的学生人数分别为9，12，6，3. ………………3分 （Ⅱ）设“从30名学生中随机抽取两名学生，这两名学生来自同一所中学”为事件A ，从30名学生中随机抽取两名学生的取法共有230435C =种， ………………5分 来自同一所中学的取法共有222291263120C C C C +++=． ………………7分所以1208()43529P A ==． 答：从30名学生中随机抽取两名学生来自同一所中学的概率为829． ………………8分 （Ⅲ）由（Ⅰ）知，30名学生中，来自甲、丙两所中学的学生人数分别为9，6．依题意得，X 的可能取值为0,1,2， ………………9分262151(0)7C P X C === ，119621518(1)35C C P X C === ，2921512(2)35C P X C ===． ……………12分 所以X 的分布列为：……………….14分18．（本小题共13分）解：（Ⅰ）因为()e e x x f x x '=+，所以(0)1f '=. ……………….2分因为()g x x a '=+，所以(0)g a '=. ……………….4分 因为()f x 与()g x 的图象在（0,0）处有相同的切线，所以(0)(0)f g ''=，所以1a =. …….5分（Ⅱ）由（Ⅰ）知, 21()2g x x x =+, 令21()()()e 2xh x f x bg x x bx bx =-=--，[1,2]x ∈，则()e e (1)(1)(e )xxxh x x b x x b '=+-+=+-． ……………….6分(1)当0b ≤时，[1,2]x ∀∈，()0h x '>，所以()h x 在上是增函数，故()h x 的最小值为3(1)=e 2h b -； ……………….7分 (2)当0b >时，由()=0h x '得，ln x b =， ……………….8分 ①若ln 1b ≤，即0e b <≤，则[1,2]x ∀∈，()0h x '>，所以()h x 在上是增函数， 故()h x 的最小值为3(1)=e 2h b -. ……………….9分 ②若1ln 2b <<，即2e e b <<，则(1,ln )x b ∀∈，()0h x '<，(ln 2)x b ∀∈，，()0h x '>，所以()h x 在(1,ln )b 上是减函数，在(ln 2)b ，上是增函数， 故()h x 的最小值为21(ln )=ln 2h b b b -； ……………….11分 ③若ln 2b ≥，即2e b ≥，则[1,2]x ∀∈，()0h x '<，所以()h x 在[1,2]上是减函数，故()h x 的最小值为2(2)=2e 4h b -. ……………….12分综上所述，当e b ≤时，()h x 的最小值为3(1)=e 2h b -， 当2e e b <<时，()h x 的最小值为21ln 2b b -， 当2e b ≥时，()h x 的最小值为22e 4b -. ……………….13分 19.（本小题共13分）解：（Ⅰ）把点(1,2)A 代入抛物线C 的方程22y px =，得42p =，解得2p =，所以抛物线C 的方程为24y x =. ……………….4分 （Ⅱ）因为2p =，所以直线2px =-为1x =-，焦点F 的坐标为(1,0) 设直线PQ 的方程为1x ty =+，211(,)4y P y ，222(,)4y Q y ， 则直线OP 的方程为14y x y =,直线OQ 的方程为24y x y =. ……………….5分由14,1,y x y x ⎧=⎪⎨⎪=-⎩得14(1,)S y --，同理得24(1,)T y --． ……………….7分所以14(2,)FS y =--uu r ，24(2,)FT y =--uu u r ，则12164FS FT y y ⋅=+uu r uu u r ． ……………….9分由21,4,x ty y x =+⎧⎨=⎩得2440y ty --=，所以124y y =-， ……………….11分则164(4)FS FT ⋅=+-uu r uu u r 440=-=． 所以，FS FT ⋅u u r u u u r的值是定值，且定值为0. ……………….13分20．（本小题共13分） 解：（Ⅰ）12462,,,,77777……………….4分（Ⅱ）存在满足题意的实数M , 且M 的最小值为1. 解法一：猜想10≤≤n c ，下面用数学归纳法进行证明. （1）当1n =时,101c ≤≤，结论成立.（2）假设当)(*N k k n ∈=时结论成立，即10≤≤k c ， 当1+=k n 时,022k c ≤≤ ,所以1121k c -≤-≤, 即0121k c ≤-≤,所以01121k c ≤--≤, 故01121k c ≤--≤. 又因为+1=112k k c c --, 所以+101k c ≤≤,所以1+=k n 时结论也成立.综上,由（1）,（2）知,10≤≤n c 成立 所以1M ≥,当112c =时,可得当2n ≥时, 1n c =,此时, M 的最小值为1 故M 的最小值为1.解法二：当2≥n 时，若存在2,3,4...,k =满足11k c -<,且1k c >. 显然1,21,01≠-k c ，则1211<<-k c 时，1221<-=-k k c c 与1>k c 矛盾； 2101<<-k c 时，121<=-k k c c 与1>k c 矛盾；所以01(2)n c n ≤≤≥ 所以1M ≥,当112c =时,可得当2n ≥时, 1n c =,此时, M 的最小值为1 故M 的最小值为1. ……………………10分（Ⅲ）2 ………………13分（若用其他方法解题，请酌情给分）。

丰台区2016—2017学年度第一学期期末测试高三语文试卷答案2017.1一、本大题共8道小题，共24分。

1.D。

（3分）【解析】A.“改变和颠覆了人们现在的生活方式和理念”概括有误，原文为“它可能极大程度地改变甚至颠覆人们现在的生活方式和理念”。

B.原文为“微电子、大数据、云计算、移动互联网等信息技术的发展为机器人智能化程度的提高奠定了坚实基础”。

C.“人形机器人已经完全具备人类的交际能力”原文无据。

2.【参考示例】人机协作更密切、更安全。

（3分）【评分标准】“人机协作”，1分；“更密切”“更安全”各1分。

意思对即可。

3. C。

【解析】“工业高级自动化水平位居前列”概括有误。

原文为“中国的机器人化和工业高级自动化仍然任重道远”。

（3分）4.B。

【解析】“无需规划路径”原文无据。

（2分）5.B。

（3分）6.B。

【解析】此处的引号表示特定的称谓。

（2分）7.C。

【解析】“全向天线”应为“定向天线”。

（3分）8.（5分）○1都具有先进的传感器、相机等部件，对外部环境具有感觉能力。

○2都具有独立判断、记忆、推理和决策的能力，独立工作的能力。

○3都能适应外部环境或外部对象协调工作。

即能获取外部信息，并进行信息反馈，灵活调整工作状态。

○4都不断拓展人类应用或探测领域和范围。

如：制造行业、教育科研航空领域、月球探测等等。

○5都能胜任日趋复杂的工作，有成效。

如：完成装配工作、科研工作、月球探测工作等。

【评分标准】每个要点1分，共5分。

意思对即可。

二、本大题共6道小题，共24分。

9. C 【解析】间，（从）小路。

（3分）10. C【解析】A.均为连词，表原因，因为。

B.均为连词，第一个表承接，就；第二个表递进，并且。

C.第一个“之”为“代词，他（王亮）”，第二个“之”为“助词，表取独”。

D. 均为远指代词，那。

（3分）11. B 【解析】“进”“归”解释错误。

多次推荐选拔人才，成为士子们的归属（3分）12.（4分）①不久授予王亮晋陵太守，他任职清廉公正，有良好的政治措施。

丰台区2016〜2017学年度第一学期期末练习高三语文2017.01本试卷满分共150分。

考试时间150分钟。

注意事项：1. 答题前，考生务必先将答题卡上的学校、年级、班级、姓名、准考证号用黑色字迹签字笔填写清楚，并认真核对条形码上的准考证号、姓名，在答题卡的“条形码粘贴区”贴好条形码。

2. 本次考试所有答题均在答题卡上完成。

选择题必须使用2B铅笔以正确填涂方式将各小题对应选项涂黑，如需改动，用橡皮擦涂干净后再选涂其它选项。

非选择题必须使用标准黑色字迹签字笔书写，要求字体工整、字迹清楚。

3. 请严格按照答题卡上题号在相应答题区内作答，超出答题区域书写的答案无效，在试题、草稿纸上答题无效。

4. 请保持答题卡卡面清洁，不要装订、不要折叠、不要破损。

一、本大题共8小题，共24分。

阅读下面的材料，完成 1 —8题。

材料一1962年美国正式投入使用第一台电子可编程序的工业机器人，标志着第一代机器人诞生，从此机器人开始进入人类生活领域。

有人认为机器人是引领全球经济变革的颠覆性技术，它可能极大程度地改变甚至颠覆人们现在的生活方式和理念。

如工业机器人造就了“黑灯工厂”，即不需开灯的全机器人工厂；医学上，达？芬奇机器人已经能帮助医生完成更高质量、低创伤的手术，且能进行远程操作；家庭生活中，多款家庭机器人已经能够帮助看家、与人聊天、陪小孩学习。

机器人正逐步实现智能化，以满足人类更高层次的需求。

微电子、大数据、云计算、移动互联网等信息技术的发展为机器人智能化程度的提高奠定了坚实基础。

通过摄像头、传感器感知外部环境变化，凭借强大的计算机处理能力和大数据、云计算技术获得超强的运算处理能力，甚至模拟人类解决问题的能力，机器人正从依赖嵌入程序或输入指令执行命令向自主学习、自主决策和自主作业的方向发展。

近年来，国际商业机器公司（IBM）、谷歌、微软、亚马逊等信息技术企业大举进入机器人产业，带来强大的信息网络技术，进一步推动了机器人的智能化。

DCBA丰台区2016—2017学年度第一学期期末练习高三数学（理科）2017.01 第一部分 （选择题 共40分）一、选择题共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项． 1．已知集合{(2)(1)0}A x x x =∈+-<Z ，{2,B =-1}-，那么AB 等于（A ）{2101}，，，-- （B ）{210}，，-- （C ）{21}，-- （D ）{1}- 2．已知0a b >>，则下列不等式一定成立的是 （A ）a b < （B ）11a b> （C ）11()()22a b > （D ）ln ln a b >3．如果平面向量(20)，=a ，(11)，=b ，那么下列结论中正确的是 （A ）=a b （B）⋅=a b （C ）()-⊥a b b （D ）//a b4．已知直线m ，n 和平面α，如果n α⊂，那么“m n ⊥”是“m α⊥”的（A ）充分而不必要条件 （B ）必要而不充分条件 （C ）充分必要条件 （D ）既不充分也不必要条件5．在等比数列}{n a 中，31=a ，123+=a a a +9，则456+a a a +等于（A ）9 （B ）72 （C ）9或72 （D ） 9或-72 6．如果函数()sin f x x x ωω=的两个相邻零点间的距离为2，那么(1)(2)(3)(9)f f f f ++++的值为（A ）1 （B ）-1 （C（D）7. 中国历法推测遵循以测为辅、以算为主的原则．例如《周髀算经》和《易经》里对二十四节气的晷(guǐ)影长的记录中，冬至和夏至的晷影长是实测得到的，其它节气的晷影长则是按照等差数列的规律计算得出的．下表为《周髀算经》对二十四节气晷影长的记录，其中4115.16寸表示115寸416分（1寸=10分）．已知《易经》中记录的冬至晷影长为130.0寸，夏至晷影长为14.8寸，那么《易经》中所记录的惊蛰的晷影长应为 （A ）72.4寸 （B ）81.4寸 （C ）82.0寸 （D ）91.6寸且()()()n A n B n A B +=，则|A B |等于 （A ）2017 （B ）2016 （C ）2015 （D ）2014第二部分 （非选择题 共110分）二、填空题共6小题，每小题5分，共30分． 9. i 是虚数单位，复数2i1i-= ． 10. 设椭圆C ：222+1(0)16x y a a =>的左、右焦点分别为1F ，2F ，点P 在椭圆C 上，如果12||+||10PF PF =，那么椭圆C 的离心率为 ．11．在261()x x-的展开式中，常数项是 （用数字作答）．12．若，x y 满足202200，，，x y x y y -≤⎧⎪+-≥⎨⎪≥⎩+ 则=2z x y -的最大值为 ． 13．如图，边长为2的正三角形ABC 放置在平面直角坐标系xOy 中，AC 在x 轴上，顶点B 与y 轴上的定点P 重合．将正三角形ABC 沿x 轴正方向滚动，即先以顶点C 为旋转中心顺时针旋转，当顶点B 落在x 轴上时，再以顶点B 为旋转中心顺时针旋转，如此继续．当△ABC 滚动到△111A B C 时，顶点B 运动轨迹的长度为 ；在滚动过程中，OB OP ⋅的最大值为 ．14．已知()f x 为偶函数，且0≥x 时，][)(x x x f -=（][x 表示不超过x 的最大整数）．设()()()g x f x kx k k =--∈R ，若1k =，则函数()g x 有____个零点；若函数()g x 三个不同的零点，则k 的取值范围是____．三、解答题共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.（本小题共13分）如图，在△ABC 中，D 是BC 上的点，3AC =，2CD =，AD =sin B =（Ⅰ）求角C 的大小；（Ⅱ）求边AB 的长. 16.（本小题共14分）如图所示的多面体中，面ABCD 是边长为2的正方形，平面PDCQ ⊥平面ABCD ，PD DC ，E F G ，，分别为棱，，BC AD PA 的中点. CBP GF DE Q A（Ⅰ）求证：EG ‖平面PDCQ ；（Ⅱ）已知二面角PBF CP ABCD 的体积． 17.（本小题共14分）数独游戏越来越受人们喜爱，今年某地区科技馆组织数独比赛，该区甲、乙、丙、丁四所学校的学生积极参赛，参赛学生的人数如右表所示。

丰台区2016 ~2017学年度第一学期期末练习高三化学可能用到的相对原子质量：H －1 C －12 N －14 O －16 S －32 Na －23 Cr －52 Cu －64 Cl —35.5第一部分（选择题 共42分）选择题（每题只有一个符合题意的选项，每题3分，共42分） 1．下列生活中常见的现象中，其反应原理不涉及氧化还原反应的是2A ．甘油和植物油都属于油脂 B ．柠檬有酸味，属于酸性食物C ．食品中的抗氧化剂不能起到防腐作用D ．残留有少量食盐水的铁锅易生锈，因为发生了电化学腐蚀 3．在生产、保存、运输和使用浓硫酸时，下列说法不正确．．．的是 A ．工业制取硫酸过程中生成的SO ２可循环使用 B ．常温下可选用铁制或铝制容器盛装C ．盛装容器的标签上应标注氧化剂和腐蚀品D ．使用时向其中直接加水可制得稀硫酸 4．下列有关性质的比较，不．能．用元素周期律解释的是 A ．酸性：H 2SO 4 ＞HClOB ．金属性：Na ＞MgC ．碱性：KOH ＞NaOHD ．热稳定性：HC1＞HBr 5．下列表示对应化学反应的离子方程式正确的是A ．向稀HNO 3中滴加Na 2SO 3溶液：SO 32－+2H ＋SO 2↑+H 2OB ．向Na 2SiO 3溶液中通入过量CO 2：SiO 32－+ CO 2+ H 2OH 2SiO 3↓+ CO 32－C ．向稀H 2SO 4中加入过量Ba(OH)2溶液：2H ++SO 42－+ Ba 2++2OH －BaSO 4↓+ 2H 2OD ．向AlCl 3溶液中加入过量的NH 3•H 2O ：Al 3++4NH 3•H 2OAlO 2－+4NH 4++2H 2O6．常温常压时烯烃与氢气混合不反应，高温时反应很慢，但在适当的催化剂存在时可氢气反应生成烷，一般认为加氢反应是在催化剂表面进行。

反应过程的示意图如下：下列说法中正确的是A ．乙烯和H 2生成乙烷的反应是吸热反应B ．加入催化剂，可减小反应的热效应C ．催化剂能改变平衡转化率，不能改变化学平衡常数D ．催化加氢过程中金属氢化物的一个氢原子和双键碳原子先结合，得到中间体 7．下列反应的发生与沉淀溶解平衡或盐类水解平衡的移动无关．．的是 A ．硝酸银溶液与盐酸反应生成氯化银B ．镁条与氯化铵溶液反应生成氢气 C ．盐酸与碳酸钙反生成二氧化碳D ．硫酸铝溶液和小苏打溶液反应生成二氧化碳 8．工业上可以利用水煤气（H 2、CO ）合成二甲醚（CH 3OCH 3），同时生成CO 2。

丰台区2016～2017学年度第一学期期末练习第一节单项填空〔共15小题；每小题1分,共15分21. My friend hasn’t answered my letter yet, and I _________ for a reply.A. waitedB. have waitedC. am waitingD. will wait22. Everyone tried to help the family _________ house had burned down in the fire.A. whyB. whoseC. whereD. which23. Don’t worry about the work. By the time you get back from your vacation, we _________ care of everything.A. will have takenB. takeC. have been takingD. are taking24. We must do _________ we can in order to save oil, as it is an irreplaceable natural resource.A. howeverB. whereverC. whoeverD. whatever25. I _________ snow before I moved to Canada last year.A. wasn’t seeingB. don’t seeC. had never seenD. would not see26. — Hello, this is Dan speaking.—Hi, Dan. It’s Milly. I’m calling _________ about your guitar lessons.A. askedB. to askC. askD. asking27. Take the mask with you _________ the air is bad.A. so thatB. as ifC. in caseD. even though28. Knocking loudly on the desktop, Mr. Brown made his anger _________.A. knowingB. to knowC. having knownD. known29. One advantage of having a car is _________ you don’t need to rely on public transportation.A. thatB. whetherC. whatD. why30. The coffee _________ when I walked into the kitchen.A. was being madeB. had madeC. has been madeD. was making31. "You _________ have a wrong number," she said. "There is no one of that name here."A. wouldB. needC. mustD. could32. Newly-built wooden cottages line the street, _________ the old town into a dreamland.A. turnB. turningC. to turnD. turned33. _________ you paid for the taxi fare, please let me pay for our dinner.A. SinceB. UntilC. UnlessD. Although34. If we _________ a ticket earlier, we would have watched the film.A. have bookedB. bookedC. bookD. had booked35. An elephant _________ is the earth’s largest land animal has few natural enemies other than human beings.A. whatB. whichC. whenD. where第二节完形填空〔共20小题；每小题1.5分,共30分What I RegretAt lunchtime, Jimmy, Patrick, Devon, and I began our regular routine of our lunches. I glanced across the busy cafeteria and saw the 36 student, Joel. He was holding his plate and waiting in lines.Patrick 37 him too. "Why’s t he new kid dressed like the headmaster?" he asked. Devon and Jimmy laughed."Joel’s cool. He’s in my English and history classes," I said. However, I kept the 38 that Joel and I had become friends when we worked on a project together. We 39 that we were both enthusiastic readers––something I would never admit to Patrick, Jimmy, and Devon.I saw that Joel was 40 t oward us. "Don’t do it," I thought, but in seconds he was at our table. My friends raised their eyebrows. Jimmy, Devon and Patrick piled their backpacks on the table and chairs so that there was no 41 left for another person to sit down. Patrick said, "I don’t think we have room."This 42 situation froze the air. I could 43 Joel looking at me, but I stared at my 44 as if it contained precious pearls of wisdom instead of rice and beans. After a long, uncomfortable pause, Joel 45 . I 46 have spoken up for him, but I couldn’t walk away from my three friends, could I?Joel didn’t speak to me after that 47 . He was soon 48 around with another group of kids. A few months later, I saw an announcement about Joel being chosen to be president of the class book club.I was 49 for Joel’s achievements, but I realized I had made a big mistake 50 I said nothing at the lunch table that day. Why was I so 51 that my friends might find out that I like to read?As I stared at the announcement, I knew I needed to 52 to Joel––even if he did not want to become my friend again. I was certain that my three friends would not 53 . I was also certain that I 54 losing them as well. However, I knew that I would lose myself if I did nothing.As the dismissal bell rang, I gathered up my books, took <a> deep 55 , and went to find Joel.36. A. good B. new C. lucky D. top37. A. noticed B. helped C. examined D. called38. A. words B. ideas C. truth D. promise39. A. forgot B. argued C. discussed D. discovered40. A. nodding B. flying C. walking D. driving41. A. book B. food C. time D. space42. A. awkward B. dangerous C. pleasant D. comfortable43. A. taste B. smell C. hear D. feel44. A. face B. lunch C. backpack D. table45. A. left B. laughed C. started D. stopped46. A. need B. should C. would D. must47. A. greeting B. change C. meeting D. lesson48. A. turning B. looking C. showing D. hanging49. A. happy B. sorry C. thankful D. anxious50. A. if B. until C. when D. where51. A. confused B. surprised C. excited D. afraid52. A. adapt B. apologize C. smile D. refer53. A. refuse B. agree C. mind D. choose54. A. risked B. permitted C. tried D. suggested55. A. delight B. silence C. breath D. thought第三部分阅读理解〔共两节40分第一节：〔共15小题；每小题2分,共30分ATo Whom It May Concern:On August 27, 2016, I ordered a Skunk Scooter from your website. I was very excited when it arrived because I bought it with money I saved fromdoing odd jobs over summer. Unfortunately, I have experienced severalproblems with my Skunk Scooter.First of all, the front wheel shakes from side to side, making the scooter difficult to ride. And also, it makes a horrible sound. The sound is louder and more annoying thana roaring engine. My dad and I had to tighten the screws <螺丝>. However, it did not help. Thewheel continues to shake. The scooter is faulty and cannot be repaired.In addition, I cannot adjust the handlebars. According to your website, they can be easily raised to a height of thirty-six inches. This does not seem to be true. The handlebars are set at thirty inches, and they cannot be raised or lowered. It appears that the knob that is used to adjust the height is jammed into the handlebars, which makes it impossible to turn in either direction.Although you advertised the Skunk Scooter as "the quickest, slickest scooter on the planet,"56. Natasha bought her scooter ________.A. on a websiteB. at a supermarketC. in a second-hand storeD. from a scooter factory57. According to Natasha, the scooter _________.A. loses its front wheelB. makes a loud noiseC. has no handlebarsD. runs too slowly58.Natasha felt _________ about her purchase.A. nervousB. pleasedC. disappointedD. excited59. Natasha wrote this letter to _________.A. buy a new scooterB. get her money backC. advertise the scooterD. ask how to use the scooterBClimbing in the CloudsEdmund Percival Hillary was one of the greatest explorers of the twentieth century. He was born in Auckland, New Zealand, in 1919. He discovered an interest in mountain climbing while he was still in high school and began climbing New Z ealand’s Southern Alps.Like his father, Hillary earned his living as a beekeeper. However, he continued to climb mountains. His goal was to climb Mt. Everest, which is the highest mountain in the world. By the early 1950s, several expeditions <探险队> had attempted to reach the summit of Everest, but all had failed. Then, in 1953, Hillary and a Nepalese climber named Tenzing Norgay became the first two people to reach the top of the world.Hillary’s spirit of exploration was not satisfied. He joined a n expedition to Antarctica and reached the South Pole in 1958. He also made an expedition up the Ganges River to its source in the Himalayas. Sir Edmund Hillary was a brave adventurer. He went where no man or woman had gone before.Although Hillary was best known as the young man who climbed to the summit of Mt. Everest in the 1950s, he continued his journeys to far-off places into his senior years. For instance, in his mid-sixites Hillary flew to the North Pole with Neil Armstrong, the first man on the moon. Moreover, Hillary authored many books. However, his most lasting gift, perhaps, was the Sir Edmund Hillary Himalayan Trust <信托基金>. It raised millions of dollars and contributed to schools, hospitals and many other public improvements in theSherpa villages of Nepal. In January 2008, Sir Edmund Hillary died at the age of 88.Despite being a great adventurer and known for the treasure he left, Sir Edmund Hillary always modestly referred to himself as a simple beekeeper from New Zealand.60. Hillary was interested in _________ when he was in high school.A. mountain-climbingB. bee-keepingC. money-raisingD. story-writing61.Hillary became well-known because _________.A. he reached both the South Pole and the North PoleB. he was the first to reach the top of Mt. EverestC. he lived in places where no humans had goneD. he made a lot of money as a beekeeper62. _________ is the right order of Hillary’s expeditions.a. He traveled to the source of the Ganges River.b. He climbed New Zealand’s Southern A lps.c. He reached the summit of Everest.d. He explored the North Pole.A.a-c-d-bB. b-d-c-aC. a-b-c-dD. b-c-a-d63. We can learn from the passage that Hillary is _________.A. outgoing and fearlessB. talented and honestC. determined and caringD. hardworking and carefulCThroughout childhood, kids are encouraged to take good care of their bodies by getting enough rest, exercising regularly, eating healthful foods, and drinking plenty of water. But recently children and teenagers have been warned to protect their skin. Skin cancer is on the rise among young people. Teens should make some basic lifestyle changes to help slow this trend.Melanoma, a skin cancer, is the second most common form of cancer for people aged 15 to 29. Unfortunately, the risk of developing it has increased in recent years. One of the most important causes of melanoma is UV radiation <辐射> damage. Scientists think that some of this damage is directly linked to the use of tanning beds <皮肤美黑床>. Now they have found that these beds produce UVA radiation and UVB radiation, both of which are dangerous.Clearly, avoiding tanning beds is one way teens can protect their skin, but they must do more. They need to protect themselves from too much sun exposure as well. They must learn to stay out of the sun in summer. Doctors say that to avoid the harmful rays of the sun, young people should stay indoors between 10 a.m. and 2 p.m., when the rays are the strongest. When teens have to be outdoors during these hours, they should use sunscreen that provides protection from both UVA and UVB rays.Protection is the most effective weapon in the battle against melanoma, but paying close attention to the skin is also vital. Melanoma often begins as a mole <痣> on the skin. If it’s caught before it spreads below the skin’s surface, it’s highly curable. Therefore, teens should watch for both new moles and existingmoles. If they see anything that looks unusual, they should visit a skin doctor right away.Teens who continue to bake in the sun to achieve that perfect tan should realize the potential consequences of their behavior. Is a sun-kissed look really worth the risk of melanoma? It’s not too late to change your habits and reduce your exposure to harmful UV rays. Take action now to protect your skin and avoid this deadly disease later.64. Teens are warned to protect their skin because _________.A. their lifestyles are not healthyB. skin helps slow the radiation damageC. skin cancer is growing among teenagersD. they spend longer time staying outdoors65. In Paragraph 2, the author mainly talks about _________ of melanoma.A. the causeB. the preventionC. the symptomD. the treatment66. _________ is the effective protection of skin.A. Using tanning bedsB. Eating more healthful foodsC. Visiting a skin doctor frequentlyD. Reducing exposure to strong UV raysDThe biggest criticism <批评> of social networking is that our young people are losing their offline friends to online friends. In fact there is a lot of research that shows these criticisms are generally unfounded. Research by Allen et al. found that people are not replacing offline friends with online companions but are using them to support their offline relationships. They also found that our online friendships actually allow us to have discussions with a much more diverse set of people than in the real world and improve our psychological happiness.However, there is one part of social networking that is deeply worrying. We find ourselves in a hyper-connected world where people access social media day and night, excited to make announcements about the tiniest details of their lives. Research is starting to show that this culture is negatively affecting not our friendships but our character.Professor Larry D. Rosen, in his book iDisorder, presents evidence that social networking is turning us into narcissists <自恋者>. He says that young people who overuse social networking sites can become vain, aggressive, and show anti-social behavior in their offline lives. But perhaps an even more disturbing effect is that one of our most basic emotions seems to be disappearing––empathy. This is the emotion that bonds us together; it allows us to see the world from our friends’ points of view. Without it, we are far less able to connect and form meaningful adult relationships.Sherry Turkle, a professor of social sciences at MIT, suggests that people are no longer comfortablebeing alone. This is something confirmed by a study where 200 university students were asked to go without social media for 24 hours. Many admitted an addiction to their online social network; most complained that they felt cut off from family and friends. But being alone is a time, Turkle argues, when we self-reflect and get in touch with who we really are. It is only when we do this that we can make meaningful friendships with others. She believes, as is the title of her 2011 book, that we are simply "Alone Together."These potential changes in our characters are rather disturbing. If nothing is done, our young people could well be in trouble. Therefore, suggestions about ways to encourage our young people to avoid the problems of social networking should be made, so they can develop the kinds of friendships that are required to grow into well-adjusted and happy adults.67. The underlined word "unfounded" in Paragraph 1 probably means _________.A. undoubtedB. falseC. acceptableD. illegal68. In this passage, the author mainly argues that _________.A. internet culture causes various problemsB. we are losing some most important emotionsC. online friendships do good to offline friendshipsD. social networking affects young people’s personalities69. By the underlined sentence in Paragraph 4, Turkle probably means _________.A. we rely on social network for connectionB. being alone is necessary for being togetherC. being alone makes us know ourselves betterD. we hardly communicate while being together70. From the passage, we can learn that _________.A. we are becoming unable to understand others wellB. young people will develop offline friendshipsC. young people can’t go without social mediaD. social media have more advantages第二节〔共5小题；每小题2分,共10分Is My Dog a Wolf?In the old days wolves and dogs shared the same ancestor. 71 . And wolves stayed wolves. Even though it has been thousands of years since dogs have been wild, many things a dog does by instinct <本能> a wolf also does.Why does my dog chew my stuff?I t’s not because he’s mad at you. The baby wolf chews on a deer bone for s everal reasons. There is some small nutritional value gained by chewing bones. 72 . But mostly, it is just fun and tastes good. Most of us don’t leave deer bones lying around the house, so table legs, shoes, and sticks probably seem like good bone replacements. Many dogs get scared or bored when they are left alone, and chewing on something canbe comforting and entertaining to them. 73 . So when he eats your homework, it really means he misses having you around.Why does my dog play with dirt?74 . Wolves dig holes to hide leftover food and bones, so they’ll have a nice snack for later. Some dig to catch small underground animals, which make tasty snacks. Or they dig to create a cool hole to lie in during the summer…or a warm snow cave i n the winter. Adult wolves dig underground caves for their babies to provide shelter and safety. Dogs may dig for some of the same reasons, but one thing is for sure: newly dug dirt has all sorts of interesting smells which they are crazy about.Once you understand that dogs and wolves are similar, you can look at the ways they aredifferent.In the wild, wolves live by wolf rules. Most of their days are spent caring for the young, resting, and hunting.75. Their willingness to do this is probably the biggest difference between the two species. That’s why dogs can become human’s friends while wolves never.A. Dogs, however, must live by people rules both inside and outside the home.B. If that "something" smells like you, it is all the more attractive.C. Dig ging is a survival tool for wolves, but it’s just fun for dogs.D. Gradually, dogs changed to become their own species.E. Wolf and dog noses also do more than just smell.F. It is also the way wolves brush their teeth.G. How are they different?第四部分书面表达〔共两节35分第一节〔15分假设你是红星中学高三学生李华,你的英国朋友Jim 在给你的邮件中提到他对中国传统节日很感兴趣,并请你介绍一个你喜欢的中国传统节日。

一、本大题共8小题,共24分。

阅读下面的材料,完成1～8题。

材料一从20世纪中期开始,伴随着世界各国经济的快速发展而出现的城市问题日益加剧，包括环境污染、资源匱乏、人口膨胀、交通堵塞等；全球化更加剧了城市间的资本、资源和创造力的竞争,如何解决城市发展中的问题,实现可持续发展,成为城市建设规划的重要命题。

2008年,IBM公司在《智慧地球:下一代领导人议程》的主题报告中,首先提出“智慧地球”的理念,希冀把新一代信息技术充分运用在人们所面对的各行各业中,2010年IBM又提出了“智慧城市”的愿景,希望为世界和中国的城市发展贡献自己的力量。

IBM经过研究认为,城市由关系到城市主要功能的不同类型的组织(人)、业务(政务)、交通、通讯、水和能源六个核心系统组成。

这些系统不是零散的,而是以一种协作的方式相互衔接；而城市本身,则是由这些系统所组成的宏观系统,在过去的城市发展过程中，由于科技力量的不足,这些系统之间的关系无法为城市发展提供整合的信息支持。

而以物联网”和“云计算”为标志的信息技术的突破性发展,将信息技术与城市发展推向一个崭新的智能互联时代；利用遍布全市的各类硬件感知设备和智能化系统,随时随地实现对城市全面感知和监测,通过传感设备智能识别及立体感知城市的位置、人口、环境、状态等信息的变化,对感知到的信息进行数据提取、融合、分析和处理,并能与交通、医疗、安全等具体的业务流程进行智能化集成，从而能及时主动作出响应,保诬城市各个关键系统高效地运行。

所以,21世纪的“智慧城市”,能够充分运用信息和通信技术手段感测、分析、整合城市运行核心系统的各项关键信息,从而对包括民生、环保公共安全、城市服务、工商业活动在内的各种需求作出智能响应,为人类创造更美好的城市生活。

此后这一理念被世界各国接纳,并作为应对金融海啸刺激经济增长的策略。

1.根据材料一,下列选项中,属于智慧城市建设条件的一项是(2分)A.越来越严重的城市问题B.城市间竞争日益加剧C.信息技术的突破性发展D.波及全球的金融危机2.根据材料一,下列有关智慧城市的表述,不正确的一项是(3分)A.智慧城市是由六个核心系统构成,并智能互联、相互协作的宏观系统。

丰台区2016〜2017学年度第一学期期末练习高三英语（本试卷满分共150分。

考试时间120分钟）第一部分听力理解（共三节30分）潼2017.0 1第一节（共5小题；每小题1.5分，共7.5分）®听下面5段对话。

每段对话后有一道小题，从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你将有10秒钟的时间來回答有关小题和阅读下一小题。

每段对话你将听一遍。

潼1.When will the man have English classes?A. On Tuesdays.B. On Thursdays.2.What does the man like best?A. Food.B. Games.3・ What is the woman doing?A. Washing a car・B. Buying a car・4. What's wrong with the man? C. On Saturdays.C. Music.C・ Repairing a car.A. He has bad eyesight.B. He has a headache. C・ He feelsdizzy.5. What's the relationship between the speakers?A. Teacher and student.B. Husband and wife. C・ Brother andsister.第二节（共10小题；每小题1.5分，共15分）听下面4段对话或独白。

每段对话或独白后有几道小题，从每题所给的A、B、C三个选项中选出最佳选项°听每段对话或独白前，你将有5秒钟的时间阅读每小题。

听完后，每小题将给出5 秒钟的作答时间。

每段对话或独白你将听两遍。

潼听下面一段独白，回答第6至7两道小题。

6.Who is the speaker?A. A shop keeper・B. A postman・C・ A waiter.7.Which table is probably talked about?A. B. C.16页）听下面一段对话，回答第8至9两道小题。

丰台区2016—2017学年度第一学期期末练习高三数学（理科）2017.01 第一部分 （选择题 共40分）一、选择题共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项． 1．已知集合{(2)(1)0}A x x x =∈+-<Z ，{2,B =-1}-，那么A B U 等于（A ）{2101}，，，-- （B ）{210}，，-- （C ）{21}，-- （D ）{1}-2．已知0a b >>，则下列不等式一定成立的是（A ）a b <（B ）11a b> （C ）11()()22ab>（D ）ln ln a b >3．如果平面向量(20)，=a ，(11)，=b ，那么下列结论中正确的是 （A ）=a b （B）⋅=a b （C ）()-⊥a b b（D ）//a b4．已知直线m ，n 和平面α，如果n α⊂，那么“m n ⊥”是“m α⊥”的（A ）充分而不必要条件 （B ）必要而不充分条件 （C ）充分必要条件（D ）既不充分也不必要条件5．在等比数列}{n a 中，31=a ，123+=a a a +9，则456+a a a +等于（A ）9（B ）72（C ）9或72（D ） 9或-726．如果函数()sin f x x x ωω=的两个相邻零点间的距离为2，那么(1)(2)(3)(9)f f f f ++++L 的值为 （A ）1（B ）-1（C（D）7.中国历法推测遵循以测为辅、以算为主的原则．例如《周髀算经》和《易经》里对二十四节气的晷(guǐ)影长的记录中，冬至和夏至的晷影长是实测得到的，其它节气的晷影长则是按照等差数列的规律计算得出的．下表为《周髀算经》对二十四节气晷影长的记录，其中4115.16寸表示115寸416分（1寸=10分）．已知《易经》中记录的冬至晷影长为130.0寸，夏至晷影长为14.8寸，那么《易经》中所记录的惊蛰的晷影长应为（A ）72.4寸 （B ）81.4寸 （C ）82.0寸 （D ）91.6寸8.对于任何集合S ，用|S |表示集合S 中的元素个数，用()n S 表示集合S 的子集个数. 若集合A ，B 满足条件：|A|=2017，且()()()n A n B n A B +=U ，则|A B |I 等于（A ）2017（B ）2016（C ）2015（D ）2014第二部分 （非选择题 共110分）二、填空题共6小题，每小题5分，共30分． 9. i 是虚数单位，复数2i1i-= ． 10. 设椭圆C ：222+1(0)16x y a a =>的左、右焦点分别为1F ，2F ，点P 在椭圆C 上，如果12||+||10PF PF =，那么椭圆C 的离心率为 ．11．在261()x x-的展开式中，常数项是 （用数字作答）．12．若，x y 满足202200，，，x y x y y -≤⎧⎪+-≥⎨⎪≥⎩+则=2z x y -的最大值为 ．13．如图，边长为2的正三角形ABC 放置在平面直角坐标系xOy 中，AC 在x 轴上，顶点B 与y 轴上的定点P重合．将正三角形ABC 沿x 轴正方向滚动，即先以顶点C 为旋转中心顺时针旋转，当顶点B 落在x 轴上时，再以顶点B 为旋转中心顺时针旋转，如此继续．当△ABC 滚动到△111A B C 时，顶点B 运动轨迹的长度为 ；在滚动过程中，OB OP ⋅uu u r uu u r的最大值为 ．14．已知()f x 为偶函数，且0≥x 时，][)(x x x f -=（][x 表示不超过x 的最大整数）．设()()()g x f x kx k k =--∈R ，若1k =，则函数()g x 有____个零点；若函数()g x 三个不同的零点，则k 的取值范围是____．DCBA三、解答题共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.（本小题共13分）如图，在△ABC 中，D 是BC 上的点，3AC =，2CD =，AD =sin B . （Ⅰ）求角C 的大小； （Ⅱ）求边AB 的长.16.（本小题共14分）如图所示的多面体中，面ABCD 是边长为2的正方形，平面PDCQ ⊥平面ABCD ，PD DC ^，E F G ，，分别为棱，，BC AD PA 的中点.（Ⅰ）求证：EG ‖平面PDCQ ； （Ⅱ）已知二面角P BF C --求四棱锥P ABCD -的体积．17.（本小题共14分）数独游戏越来越受人们喜爱，今年某地区科技馆组织数独比赛，该区甲、乙、丙、丁四所学校的学生积极参赛，参赛学生的人数如下表所示：为了解参赛学生的数独水平，该科技馆采用分层抽样的方法从这四所中学的参赛学生中抽取30名参加问卷调查．（Ⅰ）问甲、乙、丙、丁四所中学各抽取多少名学生？（Ⅱ）从参加问卷调查的30名学生中随机抽取2名，求这2名学生来自同一所中学的概率；（Ⅲ）在参加问卷调查的30名学生中，从来自甲、丙两所中学的学生中随机抽取2名，用X 表示抽得甲中学的学生人数，求X 的分布列．CBPGF DE QA18.（本小题共13分）已知函数()e x f x x =与函数21()2g x x ax =+的图象在点(00)，处有相同的切线. （Ⅰ）求a 的值；（Ⅱ）设()()()()h x f x bg x b =-∈R ，求函数()h x 在[12]，上的最小值.19.（本小题共13分）已知抛物线C ：22(0)y px p =>的焦点为F ，且经过点(12)，A ，过点F 的直线与抛物线C 交于P ，Q 两点.（Ⅰ）求抛物线C 的方程；（Ⅱ）O 为坐标原点，直线OP ，OQ 与直线2px =-分别交于S ，T 两点，试判断FS FT ⋅uu r uu u r 是否为定值？若是，求出这个定值；若不是，请说明理由.20.（本小题共13分）已知无穷数列{}n c 满足1112n n c c +=--. （Ⅰ）若117c =，写出数列{}n c 的前4项； （Ⅱ）对于任意101c ≤≤，是否存在实数M ，使数列{}n c 中的所有项均不大于M ？若存在，求M 的最小值；若不存在，请说明理由；（Ⅲ）当1c 为有理数，且10c ≥时，若数列{}n c 自某项后是周期数列，写出1c 的最大值.（直接写出结果，无需证明）丰台区2016~2017学年度第一学期期末练习高三数学（理科）参考答案及评分参考2017．01 一、选择题共二、填空题共6小题，每小题5分，共30分．9．1i -+ 10．5311． 15 12．4 13．83π； 14．2；1111,,3432⎛⎤⎡⎫-- ⎪⎥⎢⎝⎦⎣⎭U 三、解答题共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.（本小题共13分）解：（Ⅰ）在△ADC 中，由余弦定理，得CD AC AD CD AC C ⋅-+=2cos 222 ……………….2分2123272322=⨯⨯-+=……………….4分因为0C <<π，所以3C π=. ……………….6分 （Ⅱ）因为3C π=，所以23sin =C . ……………….8分 在△ABC 中，由正弦定理，得CABB AC sin sin =， ……………….10分 即2213=AB ，所以边AB 的长为2213. ……………….13分 16.（本小题共14分）证明：（Ⅰ）取PD 中点H ，连接GH ，HC ，因为ABCD 是正方形，所以AD ‖BC ，AD BC =. 因为G,H 分别是PA ,PD 中点，所以GH ‖AD ,12GH AD =. 又因为EC ‖AD 且12EC AD =， 所以GH ‖EC ，GH EC =，所以四边形GHCE 是平行四边形, ………….3分 所以EG ‖HC .又因为EG Ë平面PDCQ ，HC Ì平面PDCQ所以EG ‖平面PDCQ ． ……………….5分 （Ⅱ）因为平面PDCQ ⊥平面ABCD ， 平面PDCQ I 平面ABCD CD =， P D D C ^，PD Ì平面PDCQ ，所以PD ^平面ABCD ． ……………….6分 如图，以D 为原点，射线DA ，DC ，DP 分别为x ,y ,z 轴正方向，建立空间直角坐标系．设PD a =，则 ()()()00002201 P ,,a F ,,B ,,，，．………………7分因为PD ⊥底面ABCD ，所以平面ABCD 的一个法向量为(0,0,1)=m . ……………….8分设平面PFB 的一个法向量为(,,)x y z =n ，()10 PF ,,a u u u r =- ()120 FB ,,u u r=,则0,=0.PF FB ⎧⋅=⎪⎨⋅⎪⎩uu u ruur n n即0+2=0x az x y -=⎧⎨⎩令x =1，得11,2z y a ==-，所以11(1,,)2a=-n ． ……………….10分由已知，二面角P BF C --所以得cos <,>||||⋅===m nm n m n ……………….11分 解得a =2,所以2PD =． ……………….13分因为PD 是四棱锥P ABCD -的高，所以其体积为182433P ABCD V -=⨯⨯=． ……………….14分17．（本小题共14分） 解：（Ⅰ）由题意知，四所中学报名参加数独比赛的学生总人数为100名， 抽取的样本容量与总体个数的比值为30310010=， 所以甲、乙、丙、丁四所中学各抽取的学生人数分别为9，12，6，3. ………………3分（Ⅱ）设“从30名学生中随机抽取两名学生，这两名学生来自同一所中学”为事件A ，从30名学生中随机抽取两名学生的取法共有230435C =种， ………………5分来自同一所中学的取法共有222291263120C C C C +++=． ………………7分所以1208()43529P A ==． 答：从30名学生中随机抽取两名学生来自同一所中学的概率为829． ………………8分 （Ⅲ）由（Ⅰ）知，30名学生中，来自甲、丙两所中学的学生人数分别为9，6．依题意得，X 的可能取值为0,1,2， ………………9分262151(0)7C P X C === ，119621518(1)35C C P X C === ，2921512(2)35C P X C ===． ……………12分 所以……………….14分18．（本小题共13分）解：（Ⅰ）因为()e e x x f x x '=+，所以(0)1f '=. ……………….2分因为()g x x a '=+，所以(0)g a '=. ……………….4分 因为()f x 与()g x 的图象在（0,0）处有相同的切线，所以(0)(0)f g ''=，所以1a =. …….5分（Ⅱ）由（Ⅰ）知, 21()2g x x x =+, 令21()()()e 2xh x f x bg x x bx bx =-=--，[1,2]x ∈，则()e e (1)(1)(e )x x x h x x b x x b '=+-+=+-． ……………….6分(1)当0b ≤时，[1,2]x ∀∈，()0h x '>，所以()h x 在[1,2]上是增函数，故()h x 的最小值为3(1)=e 2h b -； ……………….7分 (2)当0b >时，由()=0h x '得，ln x b =， ……………….8分①若ln 1b ≤，即0e b <≤，则[1,2]x ∀∈，()0h x '>，所以()h x 在[1,2]上是增函数，故()h x 的最小值为3(1)=e 2h b -. ……………….9分 ②若1ln 2b <<，即2e e b <<，则(1,ln )x b ∀∈，()0h x '<，(ln 2)x b ∀∈，，()0h x '>， 所以()h x 在(1,ln )b 上是减函数，在(ln 2)b ，上是增函数， 故()h x 的最小值为21(ln )=ln 2h b b b -； ……………….11分 ③若ln 2b ≥，即2e b ≥，则[1,2]x ∀∈，()0h x '<，所以()h x 在[1,2]上是减函数，故()h x 的最小值为2(2)=2e 4h b -. ……………….12分 综上所述，当e b ≤时，()h x 的最小值为3(1)=e 2h b -， 当2e e b <<时，()h x 的最小值为21ln 2b b -， 当2e b ≥时，()h x 的最小值为22e 4b -. ……………….13分19.（本小题共13分）解：（Ⅰ）把点(1,2)A 代入抛物线C 的方程22y px =，得42p =，解得2p =，所以抛物线C 的方程为24y x =. ……………….4分（Ⅱ）因为2p =，所以直线2px =-为1x =-，焦点F 的坐标为(1,0) 设直线PQ 的方程为1x ty =+，211(,)4y P y ，222(,)4y Q y ， 则直线OP 的方程为14y x y =,直线OQ 的方程为24y x y =. ……………….5分 由14,1,y x y x ⎧=⎪⎨⎪=-⎩得14(1,)S y --，同理得24(1,)T y --． ……………….7分 所以14(2,)FS y =--uu r ，24(2,)FT y =--uu u r ，则12164FS FT y y ⋅=+uu r uu u r ． ……………….9分由21,4,x ty y x =+⎧⎨=⎩得2440y ty --=，所以124y y =-， ……………….11分 则164(4)FS FT ⋅=+-uu r uu u r 440=-=． 所以，FS FT ⋅u u r u u u r的值是定值，且定值为0. ……………….13分20．（本小题共13分） 解：（Ⅰ）12462,,,,77777……………….4分 （Ⅱ）存在满足题意的实数M , 且M 的最小值为1.解法一：猜想10≤≤n c ，下面用数学归纳法进行证明. （1）当1n =时,101c ≤≤，结论成立.（2）假设当)(*N k k n ∈=时结论成立，即10≤≤k c ， 当1+=k n 时,022k c ≤≤ ,所以1121k c -≤-≤, 即0121k c ≤-≤,所以01121k c ≤--≤, 故01121k c ≤--≤. 又因为+1=112k k c c --, 所以+101k c ≤≤,所以1+=k n 时结论也成立.综上,由（1）,（2）知,10≤≤n c 成立 所以1M ≥,当112c =时,可得当2n ≥时, 1n c =,此时, M 的最小值为1 故M 的最小值为1.解法二：当2≥n 时，若存在2,3,4...,k =满足11k c -<,且1k c >. 显然1,21,01≠-k c ，则1211<<-k c 时，1221<-=-k k c c 与1>k c 矛盾； 2101<<-k c 时，121<=-k k c c 与1>k c 矛盾；所以01(2)n c n ≤≤≥ 所以1M ≥,当112c =时,可得当2n ≥时, 1n c =,此时, M 的最小值为1 故M 的最小值为1. ……………………10分（Ⅲ）2 ………………13分（若用其他方法解题，请酌情给分）。