复旦附中2017高三第一学期期中等级考考试

复旦附中高一期中数学卷2016.11一.填空题1.集合{1,2,3,,2015,2016}⋅⋅⋅的子集个数为2.已知全集U R =，集合{|1}A x x =≤，集合{|2}B x x =≥，则()U C A B =3.已知集合{|12}A x x =≤≤，集合{|}B x x a =≤，若A B ≠∅ ，则实数a 的取值范围是4.如果全集{,,,,,}U a b c d e f =，{,,,}A a b c d =，{}A B a = ，(){}U C A B f = ，则B =5.已知210a a >>，210b b >>，且12121a a b b +=+=，记1122A a b a b =+，1221B a b a b =+，12C =，则按A 、B 、C 从小到大的顺序排列是6.已知Rt ABC ∆的周长为定值2，则它的面积最大值为7.我们将b a -称为集合{|}M x a x b =≤≤的“长度”，若集合2{|}3M x m x m =≤≤+，{|0.5}N x n x n =-≤≤，且集合M 和集合N 都是集合{|01}x x ≤≤的子集，则集合M N 的“长度”的最小值是8.已知{|}A x x =>，{|(3)(3)0}B x x x x =-+>，则A B = 9.对于任意集合X 与Y ，定义：①{|X Y x x X -=∈且}x Y ∉，②()X Y X Y ∆=-()Y X -，已知2{|,}A y y x x R ==∈，{|22}B y y =-≤≤，则A B ∆=10.已知常数a 是正整数，集合1{|||,}2A x x a a x Z =-<+∈，{|||2,}B x x a x Z =<∈，则集合A B 中所有元素之和为11.非空集合G 关于运算*满足：①对任意,a b G ∈，都有a b G *∈；②存在e G ∈使对一切a G ∈都有a e e a a *=*=，则称G 是关于运算*的融洽集，现有下列集合及运算：①G 是非负整数集，*运算：实数的加法；②G 是偶数集，*运算：实数的乘法；③G 是所有二次三项式组成的集合，*运算：多项式的乘法；④{|,}G x x a a b Q ==+∈，*运算：实数的乘法；其中为融洽集的是12.集合{(,)|||,}A x y y a x x R ==∈，{(,)|,}B x y y x a x R ==+∈，已知集合A B 中有且仅有一个元素，则常数a 的取值范围是二.选择题13.已知集合{1,2,3,,2015,2016}A =⋅⋅⋅，集合{|31,}B x x k k Z ==+∈，则A B 中的最大元素是（）A.2014 B.2015 C.2016 D.以上答案都不对14.已知全集U A B = 中有m 个元素，()()U U C A C B 中有n 个元素，若A B 非空，则A B 的元素个数为（）A.mn B.n m - C.m n+ D.m n -15.命题“已知,x y R ∈，如果220x y +=，那么0x =且0y =”的逆否命题是（）A.已知,x y R ∈，如果220x y +≠，那么0x ≠且0y ≠B.已知,x y R ∈，如果220x y +≠，那么0x ≠或0y ≠C.已知,x y R ∈，如果0x ≠或0y ≠，那么220x y +≠D.已知,x y R ∈，如果0x ≠且0y ≠，那么220x y +≠16.对任意实数,,a b c ，给出下列命题：①“a b =”是“ac bc =”的充要条件；②“5a +是无理数”是“a 是无理数”的充要条件；③“ab >”是“22a b >”的充分条件；④“4a <”是“3a <”的必要条件；其中真命题的个数是（）A.1个 B.2个 C.3个 D.4个三.解答题17.已知集合{1,2,3}A =，2{|(1)0,}B x x a x a x R =-++=∈，若A B A = ，求实数a ；18.已知,,a b c R +∈，求证：3332222222()a b c ab a b bc b c ac a c ++≥+++++；19.设正有理数1a21211a a =++，求证：（1介于1a 与2a 之间；（2）2a 比1a ；20.已知对任意实数x ，不等式2(3)10mx m x --+>成立或不等式0mx >成立，求实数m 的取值范围；21.已知关于x 的不等式2(4129)(211)0kx k k x ---->，其中k R ∈；（1）试求不等式的解集A ；（2）对于不等式的解集A ，记B A Z = （其中Z 为整数集），若集合B 为有限集，求实数k 的取值范围，使得集合B 中元素个数最少，并用列举法表示集合B ；参考答案一.填空题1.201622.{|12}x x << 3.1a ≥ 4.{,}a e 5.B C A <<6.3-7.168.{|30}x x -<<9.[2,0)(2,)-+∞ 10.2a 11.①④12.[1,1]-二.选择题13.A14.D 15.C 16.B三.解答题17.1a =或2或3；18.略；19.略；20.0m >；21.（1）①当0k <，911{|3}442k A x x k =++<<；②当0k =，11{|}2A x x =<；③当01k <<或9k >，11{|2A x x =<或93}44k x k>++；④当19k ≤≤，9{|344k A x x k =<++或11}2x >；（2）0k <，{2,3,4,5}B =；。

2017-2018 上海市复旦附中高一上学期期中考试Grammar and Vocabulary: (18%)Section A (8%)Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.21. The discovery of gold in Australia led thousands to believe that a fortune_________.A, had been making B. was making C. was to be made D. would make 22. The president hopes that people will be better off when he quits than when he _________.A. has startedB. startsC. will startD. started23. Travellers to that area can carry disease to their own countries that have never experienced _________.A. themB. itC. themselvesD. itself24. No one can tell the exact number of U.S. pilots and fighter planes ________were lost in the Pearl Harbor air attack.A. whoB. whichC. thatD. what25. ____________, the climbers, who had already conquered many high mountains before, determined to reach the top of the mountain.A. However it was highB. How high it wasC. However high it wasD. However high was it26. They will not allow others to decide the future of their country, _________.A. which is to be knownB. as is to be knownC. as is known to allD. as what is known to all27. We have come to realize that the brain must “ forget” some pieces of information ________it can remember others.A. whenB. sinceC. so thatD. if28. They are our school’s volunteers _______to help elderly people cross the streets every day.A. whose task it isB. it is whose taskC. to whom is the taskD. whose task wasSection B (10%)Directions: Complete the following passage by using the words in the box. Each word can be only used once. Note that there is one word more than youneed.A. journeyingB. foundingC. educationalD. marvelous AB.viewAC. undoubtedly AD. thrill BC. existed BD. sights CD. surprisingly ABC. soilSept 27 is World Tourism Day. Of course, travel isn’t a new discovery. Imagine how Italian traveler Marco Polo must have felt when he found himself on Chinese ____29_____, seeing a way of life quite different from anything he’d seen before.And how ___30______ must it have been to listen to Zhang Qian when he returned to China from his journey through Central Asia and West Asia? His brain must have been packed with everything he’d seen and heard, leading to the ____31_____ of the Silk Road.Travel is one of the most exciting experiences a human being can have. Nowadays, more people are traveling than ever before. By train, plane and car, people all around the globe are ____32_____ to places that people didn’t even know ____33_____ a few centuries ago, or only knew from books.Some people have traveled all over the world, and travel is a way of life to them. They perhaps know what to expect before they travel. That’s why the best travel is when it’s for the first time. Imagine a person who has always wanted to travel to the United States. Of course, they’ve probably seen the Statue of Liberty a thousand times on the TV, and the White House, and all the other famous _______34__. But none of that would compare to the ___35______ of looking out of the cabin window as the plane lands, watching the cities and streets of the real America come into_____36____.Although travel is often just for fun, it’s also ____37_____. We may not know that we are getting an education, but we still are.We’re learning every day: new words in a new language, new people, and new ways of life. But this learning takes place in the school of the world, not the classroom. One of the lessons we learn is ____38_____ a moral one. As we get to know foreign places, we come to understand that there are many different ways to live, and that the way we live isn’t necessarily the best way. The British politician Benjamin Disraeli summed this up well when he said,“Travel teaches toleration.”Ⅲ.Reading Comprehension (40%)Section ADirections : For each blank in the following passages there are four words or phrases marked A,B,C and D. Fill in each blank with the word or phrases that best fits the context.( A )Leif Erickson reached North America around the year 1000, but the attempt to explore was started slowly. It would be five centuries __(39)__ other Europeans landed on that continent.Why were Europeans the ones to __(40)__ to the American? The Chinese and Arabs had the _(41)__ and technology to sail across the seas. __(42)__ of them tool regular voyages in the Indian Ocean and the Asian Pacific for trade. But exploration? By the mid-15th century China had followed the closed-door policy to __(43)__ itself from the rest of the world. The Arabs, with access to the minerals and spices (香料) of Africa and the Far East, saw no __(44)__ to journey into the unknown.Europe, ____(45)________ needed gold and silver; its mines could not meet the demand for coinage. Ottoman Turks blocked the routes across the land to Asia. Only the sea held the ___(46)_____of new wealth.With the return of Magellan’s ships in 1522 from its voyage around the world, the belief was __(47)__ that the oceans were interconnected, promising the age of discovery. The English, as well as the Spanish, Portuguese and French, __(48)__ themselves to finding the “river of the west” through North America to the east.39. A. after B. since C .before D .when40. A .push B .pull C .draw D .drive41. A .sources B .resources C .substances D .matters42. A .Neither B .Both C .Any D .None43. A .prevent B .protect C .isolate D .differ44. A .access B .admission C .application D .association45. A .as a matter of fact B . in other wordsC. for one thing D .on the other hand46. A .symbol B .impression C .promise D .reflection47. A .extended B .estimated C .attracted D .accepted48. A .contributed B .devoted C .referred D .connected( B )Those who keep their word become the most important members of an organization. People come to rely on and trust them. They can be____(49)____.___(50)______you make a promise , be sure to keep it. When you keep your promise, no matter how much ___(51)_______it takes, you will be rewarded.Whenever you say no, stand upon that as well. In a way, a no is also a promise. A good, _____(52)____no can be very important in building trust. Agreements are also important. Whenever you enter an agreement, live by it, ______(53)____you are not too happy with the deal after making the deal, you still live by it. In the long run, your integrity will _____(54)____.Victoria was the manager of a supermarket. She set out to do that____(55)_____. She was very careful, however, of not _____(56)_____. When she did, she moved mountains to make sure that she came through. After a while, the stone employee came to trust and respect her like no______(57)_____they had ever had. The teamwork became magical. People followed her example by living up to their word. She ____(58)______what she said, and people appreciated that.49. A. counted B. counted on C. depended D. numbered50.A. As far as B. Though C. Whenever D. However51.A. pain B. ache C. effort D. money52. A. loud B. clean C. sharp D. loose53. A. As B. As if C. Just as D. Even if54. A. set off B. show off C. pay off D. take off55. A. thoroughly B. entirely C. wholly D. totally56. A. lying B. overpromising C. underestimating D. overlooking57. A. manager B. employee C. supermarket D. others58. A. believed B. trusted C. meant D. promisedSection BDirections :Read the following passages. Each passage is followed byquestions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.( A )A few years ago, Paul Gerner began to gather a group of architects in Las Vegas to ask them what it would take to design a public school that used 50 percent less energy, cost much less to build and obviously improved student learning. “I think half of them fell off their chairs,” Gerner says.Gerner manages school facilities for Clark County, Nevada, a district roughly the size of Massachusetts. By 2018, 143,000 additional students will enter the already crowded public-education system. Gerner needs 73 new schools to house them. Four architecture teams have nearly finished designing primary school prototypes （原型）; they plan to construct their schools starting in 2009. The district will then assess how well the schools perform, and three winners will copy those designs in 50 to 70 new buildings.Green schools are appearing all over, but in Clark County, which stands out for its vastness(广阔), such aggressive targets are difficult because design requirements like more natural light for students go against the realities of a desert climate. “One of the biggest challenges is getting the right site orientation,” Mark McGinty, a director at SH Architecture, says. His firm recently completed a high school in Las Vegas. ”You have the same building, same set of windows, but if its orientation is incorrect and it faces the sun, it will be really expensive to cool.”Surprisingly, the man responsible for one of the most progressive green-design competitions has doubts about ideas of eco-friendly buildings. “I don’t believe in the new green religion,” Gerner says. “Some of the building technologies that you get are impractical. I’m interested in those that work.”But he wouldn’t mind if some green features inspire students. He says he hopes to set up green energy systems that allow them to learn about the process of harvesting wind and solar power. “You never know what’s going to start the interest of a child to study math and science,” he says.59. How did the architects react to Gerner’s design requirements?A .They lost balance in excitement.B .They showed strong disbelief.C .They expressed little interest.D .They burst into cheers.60. Which order of steps is followed in carrying out the project?A .Assessment — Prototype — Design — Construction.B .Assessment — Design — Prototype — Construction.C .Design — Assessment — Prototype — Construction.D .Design — Prototype — Assessment — Construction.61 What makes it difficult to build green schools in Clark County?A .The large size.B .Limited facilities.C .The desert climate.D .Poor natural resources.62. What does Gerner think of the ideas of green schools?A .They are questionable.B .They are out of date.C .They are advanced.D .They are practical.(B)Spring is in the air, as is romance. Perhaps you're even thinking of taking the plunge and making a honey trip with your significant other?Before you do, why not take a look at a list of the top three places in the world to propose(求婚)? With suggestions for traditionalists and private types, you just might find the perfect spot to pop the question.New YorkIf you pay attention to romantic comedies, New York is the place for romance. Ever since the Dutch first entered this harbor in 1624 it has become a historic landmark and a must visit dreamland. Every stretch of this island is packed full of fun that will keep everyone busy. Take a leaf out of sleepless in Seattle and head to the top of the Empire State Building at night, or how about run to your loved one on the streets of NYC this New Years even like in when harry Met Sally?ParisSweeping views? Check. Grand old stately home? Check. Luxurious spots to propose? check. pack your passports and say goodbye to your daily routine life-it's less than three hours to Paris from London by Eurostar. Famous for its breathtaking architecture, and many cultural attractions, France's capital is a must-see destination. While we're not suggesting you climb the Eiffel Tower for the big moment. There's a reason why this is the city of love, if you keep your proposal original. So gentleman, take your lady to the Louvre, turn your back on the Mona Lisa and declare she is more beautiful than thefamous work of art.Las VegasDo you want to bundle the proposal and wedding all-in-one? plead to. Las Vegas, get down on one knee, show your love and get married in less time than it takes to order 'honeymoon suit’ and if it doesn't work out. There's still plenty of entertain. Once the playground of the rich and famous, from Elvis Presley to Marilyn Monroe, Las Vegas now attracts millions of visitors by its bright lights and thrills each year. Whether you're to try your luck at the casinos (赌场), or watch a show, there's a wonder to explore in Las Vegas. 63. Which of the following city on the top-3 list would be the ideal place for film fans to propose?A. New YorkB. Paris.C. Las Vegas.D. None.64. Which place is recommended for a proposal in the passage?A. On the top of the Eiffel TowerB. In the Eurostar train from LondonC. Any luxurious spot in PairsD. In front of the Mona Lisa in the Louvre64. As a perfect place for propose, Las Vegas will provide you with all the following EXCEPT.A. a honeymoon suiteB. a package weddingC. a bundle of flowersD. various ways to entertain( C )Do you look happy? angry? Have you ever wondered how you know what another person’s mood is just by looking at his or her face? Studies have shown that one instantaneously (瞬间地) and subconsciously makes a determination of another person’s mood just by glancing at the position and appearance of both the eyebrows and mouth. But what if only the position of the eyebrows was varied , and not the mouth? Would you still be able to determine his or her mood or personality just by seeing the eyebrows?Observe the four faces shown below. Notice how each face has exactly the same shape. the same smile, and the same eyes. The only difference between each of the faces is the position of the eyebrows.Low, flat eyebrows that hang over the eyes indicate tiredness, while an eyebrow that is highest in the middle denotes sadness. Downward slanting eyebrows show anger, while highly arched eyebrows show happiness.Frequently, malposition of the eyebrows, such as eyebrow sagging(下垂) and upper eyelid fullness, can be overlooked when considering facial aging and expression. Furthermore, the heavy eyebrow skin pushed the eyelid down causing a tired appearance.To avoid eyebrow sagging, many people raise their eyebrows to remove the brow and eyelid skin from their visual space. These people eventually develop wrinkles in the forehead due to the constant movement of the muscles that raise the eyebrow. In addition, there are those who are sensitive to light and frequently’ squint(斜视) and squeeze’ their eyes. This effectively pulls the eyebrows down and leads to wrinkles between the eyebrows and at the corners of the eyes.Botox is an effective measure for fine lines of the forehead and lines between the eyebrows. Botox works by freezing the muscle movement for several months. For the purpose of creating a more pleasant appearance, the best corrective measure is brow-lift surgery.66. What can this passage be?A. An advertisementB. A magazine articleC. A business reportD. A scientific report67. A person’s eyebrows that hang over the eyes low and flat can cause a(n) _________appearance.A. sadB. tiredC. happyD. angry68. What is the purpose of the passage?A. To explain the fact that varied eye position can tell a person’s mood.B. To arouse people’s interest in the best way of removing wrinkles in the forehead and between the eyebrows.C. To explain what leads to wrinkles in the forehead and near the eyebrow.D. To enable people to know how to avoid developing fine lines on their faces.69. If the passage continues, what would the writer most likely discuss in the next paragraph?A. Facial agingB. Eye operationC. Brow life surgeryD. Face-lifts.( D )The past ages of man have all been carefully labeled by anthropologists. Descriptions like ‘Palaeolithic Man’, ‘Neolithic Man’, etc., neatly sum up whole periods. When the time comes for anthropologists to turn their attention to the twentieth century, they will surely choose the label ‘Legless Man’. Histories of the time will go something like this: ‘in the twentieth century, people forgot how to use their legs. Men and women moved about in cars, buses and trains from a very early age. There were lifts and escalators in all large buildings to prevent people from walking. This situation was forced upon earth dwellers of that time because of miles each day. But the surprising thing is that they didn’t use their legs even when they went on holiday. They built cable railways, ski-lifts and roads to the top of every huge mountain. All the beauty spots on earth were ruined by the presence of large car parks.’The future history books might also record that we were deprived of the use of our eyes. In our hurry to get from one place to another, we failed to see anything on the way. Air travel gives you a bird’s-eye view of the world—or even less if the wing of the aircraft happens to get in your way. When you travel by car or train a blurred (="not" clear) image of the countryside constantly smears the windows. Car drivers, in particular, are forever obsessed with the urge to go on and on: they never want to stop. Is it the lure of the great motorways, or what? And as for sea travel, it hardly deserves mention. It is perfectly summed up in the words of the old song: ‘I joined the navy to see the world, and what did I see? I saw the sea.’ The typical twentieth-century traveler is the man who always says ‘I’ve been there. ’You mention the remotest, most evocative (引起记忆的) place-names in the world like El Dorado, Kabul, Irkutsk and someone is bound to say ‘I’ve been there’—meaning, ‘I drove through it at 100 miles an hour on the way to somewhere else.’When you travel at high speeds, the present means nothing: you live mainly in the future because you spend most of your time looking forward to arriving at some other place. But actual arrival, when it is achieved, is meaningless.You want to move on again. By traveling like this, y ou suspend all experience; the present ceases to be a reality: you might just as well be dead. The traveler on foot, on the other hand, lives constantly in the present. For him traveling and arriving are one and the same thing: he arrives somewhere with every step he makes. He experiences the present moment with his eyes, his ears and the whole of his body. At the end of his journey he feels a delicious physical weariness. He knows that sound. Satisfying sleep will be his: the just reward of all true travellers.70. Anthropologists label nowadays’ men ‘Legless’ because _________.A. people forget how to use his legs.B. people prefer cars, buses and trains.C. lifts and escalators prevent people from walking.D. there are a lot of transportation devices.71.Why does the author say ‘we are deprived of the use of our eyes’?A. People won’t use their eyes.B. In traveling at high speeds, eyes become useless.C. People can’t see anything on his way of travel.D. People want to sleep during travelling.72. Travelling at high speed means _________.A. people’s focus on the futureB. a pleasureC. satisfying drivers’ great thrillD. a necessity of life73.What's the best title of the passage?A. More haste, less speedB. Modern means of transportation make the world a small placeC. Eyes open and mind broadenD. The only way to travel is on foot.( 以下各题请务必做在答卷纸上)Ⅰ. Grammar (8%)\One of the main points of traveling is to relax and take a break from your normal daily life. (1)__________the truth is, we’re not always free to do what we like when travelling to a foreign country, and a US tourist learned that the hard way.On Aug 12, the unnamed 41-year-old man was beaten by a passerby after he was seen giving Nazi salutes(纳粹礼) again and again on a street inDresden, Germany.Ever since the end of World WarⅡ, Germany has strict laws (2)_________(forbid) the Nazi salute, as well as other symbols of Nazism.In fact, most countries have their own taboos. If you plan to travel overseas, it’s best to get familiar with these taboos(3)______________you start touring local sites. Below, TEENS gives some examples.SingaporeYou can get (4) ________(fine) fore a lot things in Singapore, including feeding birds, spitting , urinating (小便)in public, smoking in public , not flushing a public toilet after you use it, and eating or drinking on buses or trains.JapanYou’re not supposed to wear your shoes in someone’s house, but you’re not supposed to take your shoes off (5)________the house either. Instead, there’s a small areas inside the door called a “ genkan” which is (6)__________your shoes should go. If you’re still not sure where that is , pay attention to what other people do and do the same.FranceFrench people don’t like (7)________when you talk about money. It’s OK if you say that you want to quit a job because you (8)___________(pay) little money, but you should never say the exact amount. Money is a “ dirty” topic in France.Ⅱ. Recitation (4%)In western cultures, (1)_______eye contact in conversation is necessary. As a matter of fact, a westerner might consider a lack of eye contact as a lack of interest. In Spain, Italy and Greece, where people stand close together talking to each other, eye contact is more frequent and lasts longer.In many Asian cultures, people avoid eye contact to show respect. It is done when talking with anyone in (2)__________or with anyone older.Habits like this can cause problems when people do not understand them. For example, an Asian person might close his or her eyes in (3) ___________ or look down while listening to a speaker. A Western speaker might thing the person is not interested.Eye contact is a (4) ___________ thing. A lack of eye contact may be considered impolite. But if you stare at others, it is also considered rude and should be avoided.Ⅲ. Translation (20%)1. 在炎热的夏日，将食物放在冰箱被认为是保藏食物最行之有效的方法。

复旦大学附属中学2017学年第一学期期中考试试卷高二数学 满分120分一、填空题（每题4分）1.计算矩阵乘积：则3001a b c d ⎛⎫⎛⎫= ⎪⎪⎝⎭⎝⎭__________2.若线性方程组的增广矩阵为3110m n -⎛⎫ ⎪-⎝⎭，解为12x y =⎧⎨=⎩，则m n -=__________ 3.平行于直线2350x y -+=，且过点()2,1的直线的点方向式方程为__________4.ABC ∆中，若90C ∠= ，2AC BC ==，则AB BC ⋅=__________5.已知1124(3)211201734n n n n n na n +++---=+-，则lim n n a →∞=__________ 6.已知直角坐标平面内的两个向量()2,1a =- ，()1,3b m m =-+，使得平面内的任意一个c 都可以唯一分解成(,)c a b R λμλμ=+∈，则m 的取值范围是__________ 7.若行列式124cos 50116θ中元素2的代数余子式的值为3，且[]0,2θπ∈，则θ=__________ 8.设0,0a b >>，若关于,x y 的方程组1010ax y x by +-=⎧⎨+-=⎩无解，则a b +的取值范围为__________9. 在ABC ∆中，()()(),1,2,,38,10A a a B a C ---，若ABC ∆的面积不超过2，则a 的取值范围是__________10.平面直角坐标平面系中，已知()()013,1,5,2P P ，且111()2n n n n P P P P n N *+-=-∈，当n →∞时，点n P 无限接近于点M ，则点M 的坐标为__________11.如图，八个边长为1的小正方形拼成一个24⨯的矩形，,,,A B D E 均为小正方形的顶点。

12. 在ABC ∆中，6AC =，7BC =，1cos 5A =，点O 是ABC ∆的内心，若OP xOA yOB =+ ，其中01,01x y ≤≤≤≤，则动点P 的轨迹所覆盖的面积为__________二、选择题（每题4分）13.下列命题正确的的是（ ）A. 若数列{}n a 、{}n b 的极限都存在，且(0)nn n na cb b =≠，则数列{}n c 的极限存在 B. 若数列{}n a 、{}n b 的极限都不存在，则数列{}n n a b +的极限也不存在 C. 若数列{}n n a b +、{}n n a b -的极限都存在，则数列{}n a 、{}n b 的极限也都存在 D.设12....n n S a a a =+++，若数列{}n a 的极限存在，则数列{}n S 的极限也存在14.设123,,e e e 为单位向量，且3121(0)2e e ke k =+>，若以向量12,e e 为邻边的三角形的面积为12，则k 的值为（ ）15.已知无穷等比数列{}n a 的公比为q ，前n 项和为n S ，且lim n n S S →∞=，下列条件中使得3()n S S n N *<∈恒成立的是（ ）A. 10a >，0.80.9q <<B. 10a <，0.90.8q -<<-C. 10a >，0.70.8q <<D. 10a <，0.80.7q -<<-16.设关于123,,x x x 的线性方程组2123123123000x x x x x x x x x λλλλ⎧++=⎪++=⎨⎪++=⎩的系数矩阵记为A ，且该方程组存在非零解。

2017学年复旦附中高一上期中2017.11一. 填空题1. 已知全集U =R ，{1,0,1,2}A =-，2{|}B x x x ==，则U A C B =2. 命题 “如果0a b +>，那么0a >且0b >”的否命题是 命题（填“真”或“假”）3. 已知集合2{|23}A y y x x ==--，2{|213}B y y x x ==-++，则AB = 4. 已知“12a x a ≤≤+”是“1232a x a -<<+”的充分不必要条件，则实数a 的取值范 围是5. 设{,}M a b =，则满足{,,}M N a b c ⊆的集合N 的个数为6.函数()f x 的定义域为[2,1]-，则a 的值为7. 已知函数()(1)23f x m x m =-+-，无论m 取什么实数，函数()f x 的图像始终过一个定点，该定点的坐标为8. 已知关于x 的方程2240x kx k k +++-=有两个实数根，且一根大于1，一根小于1，则实数k 的取值范围为9. 给出下列四个命题：① 若a b >，c d >，则a d b c ->-；② 若22a x a y >，则x y >；③ 若a b >，则11a b a >-；④ 若110a b<<，则2ab b <. 其中正确命题是 （填所有正确命题的序号）10. 若(,2)x ∈-∞，则2542x x x-+-的最小值为 11. 设函数()2f x x =-，若不等式|(3)||()|f x f x m +>+对任意实数x 恒成立，则m 的取值范围是12. 对于实数A 和正数B ，称满足不等式||x A B -<(,0)A B ∈>R 的实数x 的集合叫做A 的B 领域，已知t 为给定的正数，a 、b 为正数，若a b t +-的a b +领域是一个关于原点对称的区间，则22a b +的最小值为二. 选择题13. 设实数1a 、2a 、1b 、2b 均不为0，则“1122a b a b =成立”是“关于x 的不等式110a x b +> 与220a x b +>的解集相同”的（ ）条件A. 充分不必要B. 必要不充分C. 充要D. 既不充分也不必要14. 解析式为221y x =+，值域为{5,19}的函数有（ ）个A. 4B. 6C. 8D. 915. 设()f x 是定义在正整数集上的函数，且()f x 满足：“当2()f x x >成立时，总可以推出2(1)(1)f x x +>+成立”，给出以下四个命题：① 若(3)9f ≥，则(4)16f ≥； ② 若(3)10f =，则(5)25f >；③ 若(5)25f =，则(4)16f ≤； ④ 若2()(1)f x x ≥+，则2(1)f x x +≥.其中真命题的个数为（ ）个A. 1B. 2C. 3D. 416. 设a 、b 、c 为实数，2()()()f x x a x bx c =+++，2()(1)(1)g x ax cx bx =+++，记集合{|()0,}S x f x x ==∈R ，{|()0,}T x g x x ==∈R ，若||S 、||T 分别为集合S 、T 的元素个数，则下列结论不可能是（ ）A. ||1S =且||0T =B. ||1S =且||1T =C. ||2S =且||2T =D. ||2S =且||3T =三. 解答题17. 已知集合2{|(1)320}A x m x x =-+-=，是否存在这样的实数m ，使得集合A 有且仅有两个子集？若存在，求出所有的m 的值组成的集合M ；若不存在，请说明理由.18. 我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB 为多少时，可使总造价最低？最低价为多少？19. 已知a ∈R ，集合26{|0}1x x A x x --=≤+，集合{||2|1}B x x a a =+≤+. （1）求集合A 与集合B ；（2）若AB B =，求实数a 的取值范围.20. 已知函数2|1|()4x m f x x +-=-，0m >，满足(2)2f =-. （1）求实数m 的值；（2）在平面直角坐标系中，作出函数()f x 的图像，并且根据图像判断：若关于x 的方程()f x k =有两个不同实数解，求实数k 的取值范围（直接写结论）21. 已知M 是满足下列性质的所有函数()f x 组成的集合：对任何12,f x x D ∈（其中f D 为函数()f x 的定义域），均有1212|()()|||f x f x x x -≤-成立.（1）已知函数2()1f x x =+，11[,]22x ∈-，判断()f x 与集合M 的关系，并说明理由；（2）是否存在实数a ，使得()2a p x x =+，[1,)x ∈-+∞属于集合M ？若存在，求a 的取值 范围，若不存在，请说明理由；（3）对于实数a 、b ()a b <，用[,]a b M 表示集合M 中定义域为区间[,]a b 的函数的集合.定义：已知()h x 是定义在[,]p q 上的函数，如果存在常数0T >，对区间[,]p q 的任意划分：011n n p x x x x q -=<<⋅⋅⋅<<=，和式11|()()|ni i i h x h x T -=-≤∑恒成立，则称()h x 为[,]p q 上的“绝对差有界函数”，其中常数T 称为()h x 的“绝对差上界”，T 的最小值称为()h x 的“绝对差上确界”，符号121n i n i tt t t ==++⋅⋅⋅+∑；求证：集合[1009,1008]M -中的函数()h x 是“绝对差有界函数”，并求()h x 的“绝对差上确界”.参考答案一. 填空题1. {1,2}-2. 真3. [4,14]-4. 13a > 5. 8 6. 2 7. (2,1)- 8. (3,1)- 9. ①②④ 10. 2 11. 3m <- 12. 22t二. 选择题13. B 14. D 15. C 16. D三. 解答题 17. 1{1,}8M =.18. 15AB =时，总造价最低为132000元. 19.（1）(,2](1,3]A =-∞--，当1a >-，[31,1]B a a =---+，当1a =-，{2}B =，当1a <-，B =∅；（2）(,0)[3,)-∞+∞.20.（1）1m =；（2）(2,0)-.21.（1）()f x 属于集合M ；（2）[1,1]-；（3）略.。

复旦附中高一期中数学卷一.填空题1.集合{1,2,3,,2015,2016}⋅⋅⋅的子集个数为________2.已知全集U =R ，集合{|1}A x x =≤，集合{|2}B x x =≥，则()U C A B =________3.已知集合{|12}A x x =≤≤，集合{|}B x x a =≤，若A B ⋂≠∅，则实数a 的取值范围是________4.如果全集{,,,,,}U a b c d e f =，{,,,}A a b c d =，{}A B a = ，(){}U C A B f = ，则B =________5.已知210a a >>，210b b >>，且12121a a b b +=+=，记1122A a b a b =+，1221B a b a b =+，12C =，则、、A B C按从小到大的顺序排列是________.6.已知Rt ABC ∆的周长为定值2，则它的面积最大值为__________.7.我们将b a -称为集合{|}M x a x b =≤≤的“长度”，若集合2{|}3M x m x m =≤≤+，{|0.5}N x n x n =-≤≤，且集合M 和集合N 都是集合{|01}x x ≤≤的子集，则集合M N ⋂的“长度”的最小值是________8.已知{}A x x =>，{|(3)(3)0}B x x x x =-+>，则A B = ________9.对任意两个集合X 与Y ，定义①{X Y x x X-=∈且}x Y ∉，②()()X Y X Y Y X∆=-- ，已知{}2,A y y x x R==∈，{}22B y y =-≤≤，则A B ∆=_________.10.已知常数a 是正整数，集合1{|||,}2A x x a a x Z =-<+∈，{|||2,}B x x a x Z =<∈，则集合A B ⋃中所有元素之和为________11.非空集合G 关于运算*满足：①对任意,a b G ∈，都有a b G *∈；②存在e G ∈使对一切a G ∈都有a e e a a *=*=，则称G 是关于运算*的融洽集，现有下列集合及运算：①G 是非负整数集，*运算：实数的加法；②G 是偶数集，*运算：实数的乘法；③G 是所有二次三项式组成的集合，*运算：多项式的乘法；④{|,}G x x a a b Q ==+∈，*运算：实数的乘法；其中为融洽集的是________12.集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，已知集合A B ⋂中有且仅有一个元素，则常数a 的取值范围是______________．二.选择题13.已知集合{1,2,3,,2015,2016}A =⋅⋅⋅，集合{|31,}B x x k k Z ==+∈，则A B ⋂中的最大元素是（）A.2014B.2015C.2016D.以上答案都不对14.已知全集U =A B ⋃中有m 个元素，()()U U A B ⋃痧中有n 个元素．若A B ⋂非空，则A B ⋂的元素个数为A.mnB.m n+ C.n m- D.m n-15.命题“已知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是（）A.已知,x y R ∈，若220x y +≠，则0x ≠且0y ≠B.已知,x y R ∈，若220x y +≠，则0x ≠或0y ≠C.已知,x y R ∈，若0x ≠且0y ≠，则220x y +≠D.已知,x y R ∈，若0x ≠或0y ≠，则22x y +≠16.对任意实数,,a b c ，给出下列命题：①“a b =”是“ac bc =”的充要条件；②“5a +是无理数”是“a 是无理数”的充要条件；③“a b >”是“22a b >”的充分条件；④“4a <”是“3a <”的必要条件；其中真命题的个数是（）A.1个B.2个C.3个D.4个三.解答题17.已知集合{1,2,3}A =，2{|(1)0,}B x x a x a x R =-++=∈，若A B A ⋃=，求实数a ；18.已知,,a b c R +∈，求证：3332222222()a b c ab a b bc b c ac a c ++≥+++++；19.设正有理数1a21211a a =++，求证：（11a 与2a 之间；（2）2a 比1a20.已知对任意实数x ，不等式2(3)10mx m x --+>成立或不等式0mx >成立，求实数m 的取值范围；21.已知关于x 的不等式2(4129)(211)0kx k k x ---->，其中R k ∈；（1）试求不等式的解集A ；（2）对于不等式的解集A ，记B A Z = （其中Z 为整数集），若集合B 为有限集，求实数k 的取值范围，使得集合B中元素个数最少，并用列举法表示集合B；复旦附中高一期中数学卷一.填空题1.集合{1,2,3,,2015,2016}⋅⋅⋅的子集个数为________【答案】20162【分析】若集合中有n 个元素,则该集合有2n 个子集,显然,集合中的元素有2016个,即2016n =,代入2n 中即可【详解】由题,集合中有2016个元素,所以该集合有20162个子集,故答案为:20162【点睛】本题考查集合的子集个数,属于基础题2.已知全集U =R ，集合{|1}A x x =≤，集合{|2}B x x =≥，则()U C A B = ________【答案】{|12}x x <<【分析】先求的A B ⋃,再求得补集即可【详解】由题,{|1A B x x ⋃=≤或}2x ≥,所以(){}U |12A B x x ⋃=<<ð,故答案为:{|12}x x <<【点睛】本题考查集合的并集、补集运算,属于基础题3.已知集合{|12}A x x =≤≤，集合{|}B x x a =≤，若A B ⋂≠∅，则实数a 的取值范围是________【答案】1a ≥【分析】由A B ⋂≠∅,画出数轴,表示出集合,即可求解【详解】因为A B ⋂≠∅,则画出数轴,并表示出集合,如下:可得1a ≥,故答案为:1a ≥【点睛】本题考查已知交集结果求参数范围,属于基础题4.如果全集{,,,,,}U a b c d e f =，{,,,}A a b c d =，{}A B a = ，(){}U C A B f = ，则B =________【答案】{,}a e 【分析】由题,用维恩图来表示集合,由图即可得到B 集合【详解】由题,将集合用维恩图表示,则{},B a e =,故答案为:{,}a e 【点睛】本题考查图示法处理集合问题,属于基础题5.已知210a a >>，210b b >>，且12121a a b b +=+=，记1122A a b a b =+，1221B a b a b =+，12C =，则、、A B C 按从小到大的顺序排列是________.【答案】B ＜C ＜A【分析】根据题设，取符合题设的特殊值即可快速判断，或者采用排序原理也可判断.【详解】方法一：212112120,0,1a a b b a a b b >>>>+=+= ，不妨令12121212,,,3333a ab b ====，11221221145224,999999A a b a bB a b a b =+=+==+=+=，1 4.529C == ，B C A \<<，故答案为：B ＜C ＜A .方法二：∵210a a >>，210b b >>，∴由排序原理可知：22112112a b a b a b a b +>+，∵12121,1a a b b +=+=，()()1212111221221a a b b a b a b a b a b ∴=++=+++()()()2211211222112a b a b a b a b a b a b =+++<+221112a b a b ∴+>，∴A ＞C ＞B ﹒故答案为：B ＜C ＜A .6.已知Rt ABC ∆的周长为定值2，则它的面积最大值为__________.【答案】3-.【分析】设出三角形的边长，根据周长和勾股定理列方程组，利用基本不等式求得ab 的最大值，进而求得三角形面积的最大值.【详解】设Rt ABC ∆三条边长分别为,,a b c ，其中c 为斜边长，所以2222a b c c a b++=⎧⎨=+⎩，2a b +=，2≥，2≤=-，所以6ab ≤-则三角形的面积132ABC S ab ∆=≤-.故答案为3-.【点睛】本小题主要考查利用基本不等式求三角形面积的最大值，考查直角三角形的性质，考查化归与转化的数学思想方法，属于中档题.7.我们将b a -称为集合{|}M x a x b =≤≤的“长度”，若集合2{|}3M x m x m =≤≤+，{|0.5}N x n x n =-≤≤，且集合M 和集合N 都是集合{|01}x x ≤≤的子集，则集合M N ⋂的“长度”的最小值是________【答案】16【分析】当集合M N ⋂的“长度”的最小值时,M 与N 应分别在区间[]0,1的左右两端,由此能求出M N ⋂的“长度”的最小值【详解】由题,M 的“长度”为23,N 的“长度”为12,当集合M N ⋂的“长度”的最小值时,M 与N 应分别在区间[]0,1的左右两端,故M N ⋂的“长度”的最小值是2111326+-=,故答案为:16【点睛】本题考查交集的“长度”的最小值的求法,考查新定义的合理运用8.已知{}A x x =>，{|(3)(3)0}B x x x x =-+>，则A B = ________【答案】{|30}-<<x x【分析】先分别求解集合中元素的所满足的不等式,再由交集的定义求解即可【详解】由题,因为20xx >-≥⎪⎩,解得1x <,则{}|1A x x =<,因为()()330x x x -+>,解得30x -<<或3x >,则{|30B x x =-<<或}3x >,所以{}|30A B x x ⋂=-<<,故答案为:{|30}-<<x x 【点睛】本题考查集合的交集运算,考查含根式的不等式的运算,考查解高次不等式9.对任意两个集合X 与Y ，定义①{X Y x x X -=∈且}x Y ∉，②()()X Y X Y Y X ∆=-- ，已知{}2,A y y x x R ==∈，{}22B y y =-≤≤，则A B ∆=_________.【答案】[)()2,02-+∞ ，【分析】由A ＝{y |y ＝x 2，x ∈R }＝{y |y ≥0}，B ＝{y |﹣2≤y ≤2}，先求出A ﹣B ＝{y |y ＞2}，B ﹣A ＝{y |﹣2≤y ＜0}，再求A △B 的值．【详解】∵A ＝{y |y ＝x 2，x ∈R }＝{y |y ≥0}，B ＝{y |﹣2≤y ≤2}，∴A ﹣B ＝{y |y ＞2}，B ﹣A ＝{y |﹣2≤y ＜0}，∴A △B ＝{y |y ＞2}∪{y |﹣2≤y ＜0}，故答案为[﹣2，0）∪（2，+∞）．【点睛】本题考查集合的交、并、补集的运算，解题时要认真审题，仔细解答，注意正确理解X ﹣Y ＝{x |x ∈X 且x ∉Y }、X △Y ＝（X ﹣Y ）∪（Y ﹣X ）．10.已知常数a 是正整数，集合1{|||,}2A x x a a x Z =-<+∈，{|||2,}B x x a x Z =<∈，则集合A B ⋃中所有元素之和为________【答案】2a【分析】分别求出集合A 、B 中的元素,再求出集合A 、B 的并集,即可求解【详解】由题,因为12x a a -<+,所以11222x a -<<+,则11|2,22A x x a x Z ⎧⎫=-<<+∈⎨⎬⎩⎭；因为2x a <,所以22a x a -<<,则{}|22,B x a x a x Z =-<<∈,因为常数a 是正整数,所以{}0,,,,2A a a = ,{}21,,0,,21B a a =-+- ,所以{}21,,0,,21,2A B a a a ⋃=-+- ,所以A B ⋃中所有元素之和是2a ,故答案为:2a【点睛】本题考查集合的并集,考查解含绝对值的不等式11.非空集合G 关于运算*满足：①对任意,a b G ∈，都有a b G *∈；②存在e G ∈使对一切a G ∈都有a e e a a *=*=，则称G 是关于运算*的融洽集，现有下列集合及运算：①G 是非负整数集，*运算：实数的加法；②G 是偶数集，*运算：实数的乘法；③G 是所有二次三项式组成的集合，*运算：多项式的乘法；④{|,}G x x a a b Q ==+∈，*运算：实数的乘法；其中为融洽集的是________【答案】①④【分析】逐一验证几个选项是否分别满足“融洽集”的两个条件,若两个条件都满足,是“融洽集”,有一个不满足,则不是“融洽集”【详解】①对于任意非负整数,a b ,则a b +仍为非负整数,即a b G +∈；取0e =,则00a a a +=+=,故①符合题意；②对于任意偶数,a b ,则ab 仍为偶数,即ab G ∈；但是不存在e G ∈,使对一切a G ∈都有ae ea a ==,故②不符合题意；③对于G 是所有二次三项式组成的集合,若,a b G ∈,ab 不再是二次三项式,故③不符合题意；④对于{|,}G x x a a b Q ==+∈,设1x a =+2x c =+,则()(122x x ac bd ad bc ⋅=+++,即12x x G ⋅∈；取1e =,则11a a a ⨯=⨯=,故④符合题意,故答案为:①④【点睛】本题考查对新定义“融洽集”的理解,考查理解分析能力12.集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，已知集合A B ⋂中有且仅有一个元素，则常数a 的取值范围是______________．【答案】[]1,1-【分析】将A B ⋂中有且仅有一个元素，转化为方程只有一个解，分情况讨论，确定参数范围.【详解】由集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，且A B ⋂中有且仅有一个元素，a x x a ∴=+只有1个解，若0x ≥，则ax x a =+，1a x a =-，若0x <，则ax x a -=+，1ax a =-+，所以0101a a a a ⎧≥⎪⎪-⎨⎪-≥⎪+⎩或0101aa a a ⎧≤⎪⎪-⎨⎪-≤⎪+⎩或101a a a =⎧⎪⎨-<⎪+⎩或011a a a ⎧≥⎪-⎨⎪=-⎩，解得11a -≤≤，故答案为：[]1,1-.二.选择题13.已知集合{1,2,3,,2015,2016}A =⋅⋅⋅，集合{|31,}B x x k k Z ==+∈，则A B ⋂中的最大元素是（）A.2014B.2015C.2016D.以上答案都不对【答案】A【分析】由题意可知集合B 表示整数的3倍且大1的数的集合,则找到集合A 中符合条件的最大元素即可【详解】由题,因为{|31,}B x x k k Z ==+∈,即为整数的3倍且大1的数的集合,则A B ⋂中的最大元素为2014,故选:A【点睛】本题考查集合的交集定义,属于基础题14.已知全集U =A B ⋃中有m 个元素，()()U U A B ⋃痧中有n 个元素．若A B ⋂非空，则A B ⋂的元素个数为A.mnB.m n+ C.n m- D.m n-【答案】D【详解】因为()()()U UUB A B A ⋃=⋂痧所以()()U UU A B A B ⋂=⋃⎡⎤⎣⎦痧，所以A B ⋂共有m n -个元素，故选D ．15.命题“已知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是（）A.已知,x y R ∈，若220x y +≠，则0x ≠且0y ≠B.已知,x y R ∈，若220x y +≠，则0x ≠或0y ≠C.已知,x y R ∈，若0x ≠且0y ≠，则220x y +≠D.已知,x y R ∈，若0x ≠或0y ≠，则22x y +≠【答案】D【分析】直接利用逆否命题的定义得到答案.【详解】己知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是：己知,x y R ∈，若0x ≠或0y ≠，则220x y +≠故选D【点睛】本题考查了命题的逆否命题，意在考查学生对于命题基础知识的掌握情况.16.对任意实数,,a b c ，给出下列命题：①“a b =”是“ac bc =”的充要条件；②“5a +是无理数”是“a 是无理数”的充要条件；③“a b >”是“22a b >”的充分条件；④“4a <”是“3a <”的必要条件；其中真命题的个数是（）A.1个B.2个C.3个D.4个【答案】B【分析】利用等式与不等式的性质逐一验证命题的真假即可【详解】①“a b =”⇒“ac bc =”,但当0c =时,“ac bc =”无法推出“a b =”,则“a b =”是“ac bc =”的充分不必要条件,故①是假命题；②“5a +是无理数”⇒“a 是无理数”,且“a 是无理数”⇒“5a +是无理数”,则“5a +是无理数”是“a 是无理数”的充要条件,故②是真命题；③当12a b =>-=时,2214a b =<=,即“a b >”无法推出“22a b >”,且当2241a b =>=时,21a b =-<=,即“22a b >”无法推出“a b >”,则“a b >”是“22a b >”的既不充分也不必要条件,故③是假命题；④因为{}|3a a <{}|4a a <,所以“4a <”是“3a <”的必要条件,故④是真命题；综上,真命题有2个,故选:B【点睛】本题考查命题的真假的判断,考查两命题的充分性和必要性的判断,考查等式与不等式的性质的应用三.解答题17.已知集合{1,2,3}A =，2{|(1)0,}B x x a x a x R =-++=∈，若A B A ⋃=，求实数a ；【答案】1a =或2或3【分析】由A B A ⋃=可得B A ⊆,分别讨论B =∅与B ≠∅的情况,进而求解即可【详解】由A B A ⋃=可得B A ⊆,若B =∅,则()2140a a ∆=+-<,解得a ∈∅；若B ≠∅,则()()10x a x --=,解得1x a =,21x =,①当1a =,则{}1B =,符合题意；②当2a =,则{}1,2B =,符合题意；③当3a =,则{}1,3B =,符合题意；综上,1a =或2或3【点睛】本题考查已知集合的包含关系求参数,考查分类讨论思想18.已知,,a b c R +∈，求证：3332222222()a b c ab a b bc b c ac a c ++≥+++++；【答案】证明见解析【分析】先对33+a b 与22a b ab +作差证明3322a b a b ab +≥+,同理证明3322a c a c ac +≥+,3322b c b c bc +≥+,再求和即可得证【详解】证明:()()()()()()()()233222222a b a b ab a a b b b a a b a b a b a b +-+=-+-=--=+-,因为,,a b c R +∈,所以0a b +>,()20a b -≥,所以()()33220a b a b ab +-+≥,即3322a b a b ab +≥+,同理,3322a c a c ac +≥+,3322b c b c bc +≥+,所以333333222222a b b c a c a b ab b c bc a c ac +++++≥+++++,即3332222222()a b c ab a b bc b c ac a c++≥+++++【点睛】本题考查作差法证明不等式,考查推理论证能力19.设正有理数1a21211a a =++，求证：（11a 与2a 之间；（2）2a 比1a【答案】（1）证明见解析（2）证明见解析【分析】（1）作差(12111a a a -=+,讨论1a2a （2）整理问题为21a a <-,进而求证即可【详解】证明:（1）(121112111a a a a --=+-++,因为若1a >,则10a >,又10<,则2a <；若1a <则10a <,又10-<,则2a >,介于1a 与2a 之间（2）12111121a a a a a a ----=--+,因为10a >20-<,10a>,所以210a a -<,所以21a a -<-所以2a 比1a 【点睛】本题考查不等式的证明,考查运算能力与分类讨论思想20.已知对任意实数x ，不等式2(3)10mx m x --+>成立或不等式0mx >成立，求实数m 的取值范围；【答案】19m <<【分析】①对任意实数x ,不等式2(3)10mx m x --+>成立,讨论0m =与0m ≠的情况,进而求解；②对任意实数x ,不等式0mx >成立,则m ∈∅,二者求并集即可【详解】解:①由题,对任意实数x ,不等式2(3)10mx m x --+>成立,当0m =时,不等式为310x -+>不成立,舍去；当0m ≠时,()20340m m m >⎧⎪⎨∆=--<⎪⎩,解得19m <<；②对任意实数x ,不等式0mx >成立,则m ∈∅,综上,19m <<【点睛】本题考查含参的一元二次不等式恒成立问题,考查分类讨论思想21.已知关于x 的不等式2(4129)(211)0kx k k x ---->，其中R k ∈；（1）试求不等式的解集A ；（2）对于不等式的解集A ，记B A Z = （其中Z 为整数集），若集合B 为有限集，求实数k 的取值范围，使得集合B 中元素个数最少，并用列举法表示集合B ；【答案】（1）答案见解析（2）[44k ∈--+，{2,3,4,5}B =【分析】（1）对k 进行分类讨论,分别讨论0k =,0k <,01k <<或9k >,19k ≤≤的情况,进而求解即可；（2）由（1）可知当0k <时,集合B 为有限集,利用对勾函数可知933442k k ++≤,当且仅当3k =-时等号成立,进而求解即可【详解】（1）当0k =,11{|}2A x x =<；当0k ≠时,令21291142k k k ++=,解得1k =或9k =,则当1k <或9k >时,9113442k k ++<,当19k <<时,9113442k k ++>,①当0k <,911{|3}442k A x x k =++<<；②当01k <<或9k >,11{|2A x x =<或93}44k x k >++；③当19k ≤≤,9{|344k A x x k =<++或11}2x >；（2）因为B A Z = （其中Z 为整数集）,由（1）,当0k ≥时,集合B 中的元素的个数无限；当0k <时,集合B 中的元素的个数有限,此时集合B 为有限集,因为0k <,所以9933333444422k k k k ⎛⎫++=---+≤-+= ⎪⎝⎭,当且仅当944k k -=-,即3k =-时等号成立,所以{2,3,4,5}B =且93144k k++≥，所以2890k k ++≤，所以[44k ∈--+【点睛】本题考查解含参的不等式,考查交集的定义的应用,考查分类讨论思想。

2017学年复旦附中第一学期期中考试试卷初一年级数学（满分100 时间：90分钟）一、选择题：（本大题共6题，每题2分，满分12分）1.下列代数式a xy x x x ,4,1,2,3732--中单项式的个数是 （ ） A.1个 B.2个 C.3个 D.4个2.下列运算正确的是( )A. 32)(aB.4223432y y =⎪⎭⎫ ⎝⎛- C.236a a a =÷ D.532a a a =⋅ 3.下列各式从左到右各式是因式分解的是（ ）A. 1)1)(1(2-=-+x x xB.6)5(652+-=+-x x x xC.22)1(12-=+-x x xD.)()(y x b y x a by bx ay ax +++=+++4.下列分式化简正确的是（ ） A. b a b a b a -=--3)(32 B.32322a a a a =- C.b a b ab a 31236142+=-- D.ba b a b a +=++122 5.数学老师上课出了一道因式分解的思考题，题意是1622++mx x 能在有理数的范围内因式分解，则整数m 的值有几个，小军和小华为此争论不休，请你判断整数m 的值有几个？（ ） A.4个 B.5个 C. 6个 D.8个6.从边长为a 的大正方形纸板中挖去一个边长为b 的小正方形后，将其裁成四个相同的等腰梯形（图甲），然后拼成一个平行四边形（图乙），那么通过计算两个图形的阴影部分的面积，可以验证成立的公式是（ ）A. 222)(b a b a -=-B.))((22b a b a b a +-=-C.2222)(b ab a b a +-=-D.b ab a b a ++=+2)(2二、填空题：（本大题共12题，每题3分，满分36分）7.“12减去y 的41的差”用代数式表示是： 8.将多项式153322---y y x xy 按字母y 升幂排列是： 9.使分式25-+x x 有意义的条件是： 10.计算：=÷-22332)453(y xy y 11.计算：=+--+-21212a a a a 12.若,3293211⨯=⨯⨯m 则=m13.如果,4,5==+ab b a 则=-b a14.要使)12)(3(22---x x x ax 的展开式中不含2x ，则=a 15.c b a ,,为三角形三边长，022=--+bc b ac a ，则该三角形的形状为16.现在规定一种运算ab b b a --=2*，期中ab 为有理数，=-m n m *)(17.李丽从家到学校的路程为S 米，无风时她以平均a 米/秒的速度骑行，便能按时到达；当风速为b 米/秒时，她若顶风按时到校，请用代数式表示她必须提前出发的时间是18.在图中取阴影等边三角形各边的中点,连成一个等边三角形,将其挖去,得到图;对图中的每个阴影等边三角形仿照先前的做法,得到图,如此继续.如果图的等边三角形面积为,则第个图形中所有阴影三角形面积的和为_________.三、简答题：（本大题共7小题，每小题4分，满分28分）19.计算：ax by axy b by ax 41)2(2)221(22÷⎥⎦⎤⎢⎣⎡-+- 20.计算：)52)(52(++-+-+z y x z y x21.解方程：2229)31)(13()12()3(4x x x x x +-+=+--22.因式分解：222222)53()35(n m n m +-+23.因式分解：72)(18)(222+---x x x x24.因式分解：ab b a 4)1)(1(22--- 25.先化简，再求值：11)1112(22+÷+-+-x x x x x ，期中.2-=x 四、解答题（本大题共5小题，第26-29题每题5分，第30题4分，满分24分）26.已知311=-y x ，求yxy x y xy x ---+2535的值。

2017-2018学年上海市复旦附中高一（上）期中数学试卷一.填空题1．（3分）已知全集U=Z，A={﹣1，0，1，2}，B={x|x2=x}0则A∩（C U B）=．2．（3分）命题“如果a+b＞0，那么a＞0且b＞0”的否命题是命题（填“真”或“假”）3．（3分）已知集合A={y|y=x2﹣2x﹣3}，集合B={y|y=﹣x2+2x+13}，则A∩B=．4．（3分）已知α：，β：1﹣2a＜x＜3a+2，若α是β的充分不必要条件，则实数a的取值范围是．5．（3分）设M={a，b}，则满足M∪N⊆{a，b，c}的集合N的个数为．6．（3分）函数f（x）=的定义域为[﹣2，1]，则a的值为．7．（3分）已知函数f（x）=（m﹣1）x+2m﹣3，无论m取什么实数，函数f（x）的图象始终过一个定点，该定点的坐标为．8．（3分）已知关于x的方程x2+kx+k2+k﹣4=0有两个实数根，且一根大于1，一根小于1，则实数k的取值范围为．9．（3分）给出下列四个命题：（1）若a＞b，c＞d，则a﹣d＞b﹣c；（2）若a2x＞a2y，则x＞y；（3）a＞b，则；（4）若，则ab＜b2．其中正确命题是．（填所有正确命题的序号）10．（3分）若x∈（﹣∞，2），则的最小值为．11．（3分）设函数f（x）=x﹣2，若不等式|f（x+3）|＞|f（x）|+m对任意实数x恒成立，则m的取值范围是．12．（3分）对于实数A和正数B，称满足不等式|x﹣A|＜B（A∈R，B＞0）的实数x的集合叫做A的B领域，已知t为给定的正数，a、b为正数，若a+b﹣t 的a+b领域是一个关于原点对称的区间，则a2+b2的最小值为．二.选择题13．（3分）设实数a1，a2，b1，b2均不为0，则“成立”是“关于x的不等式a1x+b1＞0与a2x+b2＞0的解集相同”的（）A．充分非必要条件B．必要非充分条件C．充要条件D．非充分非必要条件14．（3分）解析式为y=2x2+1，值域为{5，19}的函数有（）个．A．4B．6C．8D．915．（3分）设f（x）是定义在正整数集上的函数，且f（x）满足：“当f（x）＞x2成立时，总可以推出f（x+1）＞（x+1）2成立”．先给出以下四个命题：（1）若f（3）≥9，则f（4）≥16；（2）若f（3）=10，则f（5）＞25；（3）若f（5）=25，则f（4）≤16；（4）若f（x）≥（x+1）2，则f（x+1）≥x2．其中真命题的个数为（）A．1个B．2个C．3个D．4个16．（3分）设a，b，c为实数，f（x）=（x+a）（x2+bx+c），g（x）=（ax+1）（cx2+bx+1）记集合S={x|f（x）=0，x∈R}，T={x|g（x）=0，x∈R}．若|S|，|T|分别为集合S，T的元素个数，则下列结论不可能的是（）A．|S|=1且|T|=0B．|S|=1且|T|=1C．|S|=2且|T|=2D．|S|=2且|T|=3三.解答题17．已知集合A={x|（m﹣1）x2+3x﹣2=0}，是否存在这样的实数m，使得集合A 有且仅有两个子集？若存在，求出所有的m的值组成的集合M；若不存在，请说明理由．18．我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB为多少时，可使总造价最低？最低价为多少？19．已知集合A={ x|0}，集合B={x||x+2a|≤a+1，a∈R}．（1）求集合 A 及集合B；（2）若A∩B=B，求实数 a 的取值范围．20．已知函数，m＞0，满足f（2）=﹣2．（1）求实数m的值；（2）在平面直角坐标系中，作出函数f（x）的图象，并且根据图象判断：若关于x的方程f（x）=k有两个不同实数解，求实数k的取值范围（直接写结论）21．已知M是满足下列性质的所有函数f（x）组成的集合：对任何x1，x2∈D f （其中D f为函数f（x）的定义域），均有|f（x1）﹣f（x2）|≤|x1﹣x2|成立．（1）已知函数f（x）=x2+1，，判断f（x）与集合M的关系，并说明理由；（2）是否存在实数a，使得，x∈[﹣1，+∞）属于集合M？若存在，求a的取值范围，若不存在，请说明理由；表示集合M中定义域为区间[a，b]的函（3）对于实数a、b（a＜b），用M[a，b]数的集合．定义：已知h（x）是定义在[p，q]上的函数，如果存在常数T＞0，对区间[p，q]的任意划分：p=x0＜x1＜…＜x n﹣1＜x n=q，和式|h（x i）﹣h（x i=1）|≤T 恒成立，则称h（x）为[p，q]上的“绝对差有界函数”，其中常数T称为h（x）的“绝对差上界”，T的最小值称为h（x）的“绝对差上确界”，符号中的函数h（x）是“绝对差有[﹣1009，1008]界函数”，并求h（x）的“绝对差上确界”．2017-2018学年上海市复旦附中高一（上）期中数学试卷参考答案与试题解析一.填空题1．（3分）已知全集U=Z，A={﹣1，0，1，2}，B={x|x2=x}0则A∩（C U B）={﹣1，2} ．【解答】解：由集合B中的方程x2=x，解得x=0或1，∴B={0，1}，又全集U=Z，∴C U B={x|x≠0，且x≠1，x∈Z}，∴A∩（C U B）={﹣1，2}．故答案为：{﹣1，2}2．（3分）命题“如果a+b＞0，那么a＞0且b＞0”的否命题是真命题（填“真”或“假”）【解答】解：命题P：“如果a+b＞0，那么a＞0且b＞0．”则命题P的否命题是￢P：“如果a+b≤0，那么a≤0或b≤0．”且为真命题．故答案为：真．3．（3分）已知集合A={y|y=x2﹣2x﹣3}，集合B={y|y=﹣x2+2x+13}，则A∩B= [﹣4，14] ．【解答】解：由A中y=x2﹣2x﹣3=x2﹣2x+1﹣4=（x﹣1）2﹣4≥﹣4，得到A=[﹣4，+∞）；由B中y=﹣x2+2x+13=﹣（x﹣1）2+14≤14，得到B=（﹣∞，14]，则A∩B=[﹣4，14]，故答案为：[﹣4，14]4．（3分）已知α：，β：1﹣2a＜x＜3a+2，若α是β的充分不必要条件，则实数a的取值范围是（，+∞）．【解答】解：∵α：，β：1﹣2a＜x＜3a+2，若α是β的充分不必要条件，则，解得：a＞，故答案为：（，+∞）．5．（3分）设M={a，b}，则满足M∪N⊆{a，b，c}的集合N的个数为8．【解答】解：∵M={a，b}，满足M∪N⊆{a，b，c}，∴集合N是集合{a，b，c}的子集，∴满足M∪N⊆{a，b，c}的集合N的个数为23=8，故答案为：8．6．（3分）函数f（x）=的定义域为[﹣2，1]，则a的值为2．【解答】解：由二次根式的定义，得（1﹣a2）x2+3（1﹣a）x+6≥0的解集是[﹣2，1]，∴（1﹣a2）＜0，且﹣2和1是方程（1﹣a2）x2+3（1﹣a）x+6=0 的2个根；∴﹣2+1=①，﹣2×1=②；解得a=2．故答案为：2．7．（3分）已知函数f（x）=（m﹣1）x+2m﹣3，无论m取什么实数，函数f（x）的图象始终过一个定点，该定点的坐标为（﹣2，﹣1）．【解答】解：函数f（x）=（m﹣1）x+2m﹣3=m（x+2）﹣x﹣3，令x+2=0，求得x=﹣2，y=﹣1，故无论m取什么实数，函数f（x）的图象始终过一个定点，该定点的坐标为（﹣2，﹣1），故答案为：（﹣2，﹣1）．8．（3分）已知关于x的方程x2+kx+k2+k﹣4=0有两个实数根，且一根大于1，一根小于1，则实数k的取值范围为（﹣3，1）．【解答】解：关于x的方程x2+kx+k2+k﹣4=0有两个实数根，且一根大于1，一根小于1，构造函数f（x）=x2+kx+k2+k﹣4，∵一根大于1，一根小于1，∴f（1）＜0，∴1+k+k2+k﹣4＜0，∴﹣3＜k＜1．则k的取值范围是（﹣3，1）．故答案为：（﹣3，1）．9．（3分）给出下列四个命题：（1）若a＞b，c＞d，则a﹣d＞b﹣c；（2）若a2x＞a2y，则x＞y；（3）a＞b，则；（4）若，则ab＜b2．其中正确命题是（1）（2）（4）．（填所有正确命题的序号）【解答】解：（1）由c＞d，得﹣d＞﹣c，又a＞b，则a﹣d＞b﹣c．故（1）正确；（2）若a2x＞a2y，则a2≠0，则，∴x＞y．故（2）正确；（3）若a＞0＞b，则a﹣b＞a＞0，则．故（3）错误；（4）若，则b＜a＜0，∴ab＜b2 ．故（4）正确．故答案为：（1）（2）（4）．10．（3分）若x∈（﹣∞，2），则的最小值为2．【解答】解：y==，（x＜2）当且仅当x=1时取等号，则的最小值为2．故答案为：211．（3分）设函数f（x）=x﹣2，若不等式|f（x+3）|＞|f（x）|+m对任意实数x恒成立，则m的取值范围是（﹣∞，﹣3）．【解答】解：∵函数f（x）=x﹣2，不等式|f（x+3）|＞|f（x）|+m对任意实数x恒成立，∴|x+1|﹣|x﹣2|＞m，而|x+1|﹣|x﹣2|表示数轴上的x对应点到﹣1对应点的距离减去它到2对应点的距离，其最小值为﹣3，故有m＜﹣3，故答案为（﹣∞，﹣3）12．（3分）对于实数A和正数B，称满足不等式|x﹣A|＜B（A∈R，B＞0）的实数x的集合叫做A的B领域，已知t为给定的正数，a、b为正数，若a+b﹣t的a+b领域是一个关于原点对称的区间，则a2+b2的最小值为．【解答】解：因为：A的B邻域在数轴上表示以A为中心，B为半径的区域，∴|x﹣（a+b﹣t）|＜a+b⇒﹣t＜x＜2（a+b）﹣t，而邻域是一个关于原点对称的区间，所以可得a+b﹣t=0⇒a+b=t．又因为：a2+b2≥2ab⇒2（a2+b2）≥a2+2ab+b2=（a+b）2=t2．所以：a2+b2≥，当且仅当a=b时，上式取得最小值．故答案为：．二.选择题13．（3分）设实数a1，a2，b1，b2均不为0，则“成立”是“关于x的不等式a1x+b1＞0与a2x+b2＞0的解集相同”的（）A．充分非必要条件B．必要非充分条件C．充要条件D．非充分非必要条件【解答】解：若=m，（m≠0），则a1=ma2，b1=mb2，∴不等式a1x+b1＞0等价为m（a2x+b2）＞0，若m＞0，则m（a2x+b2）＞0，等价为a2x+b2＞0，此时两个不等式的解集相同，若m＜0，m（a2x+b2）＞0，等价为a2x+b2＜0，此时两个不等式的解集不相同．即充分性不成立．若关于x的不等式a1x+b1＞0与a2x+b2＞0的解集相同，即a1a2＞0，∵a1，a2，b1，b2均不为0，∴若a1，a2＞0，则不等式的解为x＞．x＞，则=，即成立，若a1，a2＜0，则不等式的解为x＜．x＜，则=，即成立，即必要性成立，故“成立”是“关于x的不等式a1x+b1＞0与a2x+b2＞0的解集相同”的必要不充分条件，故选：B．14．（3分）解析式为y=2x2+1，值域为{5，19}的函数有（）个．A．4B．6C．8D．9【解答】解：由2x2+1=5，可得x=，由2x2+1=19，可得x=±3，∴当x∈{，﹣3}时，函数y=2x2+1的值域为{5，19}；当x∈{﹣，3}时，函数y=2x2+1的值域为{5，19}；当x∈{﹣，﹣3，3}时，函数y=2x2+1的值域为{5，19}；当x∈{，﹣3}时，函数y=2x2+1的值域为{5，19}；当x∈{，3}时，函数y=2x2+1的值域为{5，19}；当x∈{，﹣3，3}时，函数y=2x2+1的值域为{5，19}；当x∈{﹣，，﹣3}时，函数y=2x2+1的值域为{5，19}；当x∈{﹣，，3}时，函数y=2x2+1的值域为{5，19}；当x∈{﹣，，﹣3，3}时，函数y=2x2+1的值域为{5，19}．∴解析式为y=2x2+1，值域为{5，19}的函数有9个．故选：D．15．（3分）设f（x）是定义在正整数集上的函数，且f（x）满足：“当f（x）＞x2成立时，总可以推出f（x+1）＞（x+1）2成立”．先给出以下四个命题：（1）若f（3）≥9，则f（4）≥16；（2）若f（3）=10，则f（5）＞25；（3）若f（5）=25，则f（4）≤16；（4）若f（x）≥（x+1）2，则f（x+1）≥x2．其中真命题的个数为（）A．1个B．2个C．3个D．4个【解答】解：由f（x）是定义在正整数集上的函数，且f（x）满足：“当f（x）＞x2成立时，总可以推出f（x+1）＞（x+1）2成立”．可得：（1）当x=3时，f（3）≥9，则f（4）≥16；（2）当x=3时，f（3）=10，则f（5）＞25；其逆否命题为：“当f（x+1）≤（x+1）2成立时，总可以推出f（x）≤x2成立”．（3）当x=5时，f（5）=25，则f（4）≤16；（4）若f（x）≥（x+1）2=x2+2x+1＞x2，则f（x+1）≥x2．故四个命题均正确，故选：D．16．（3分）设a，b，c为实数，f（x）=（x+a）（x2+bx+c），g（x）=（ax+1）（cx2+bx+1）记集合S={x|f（x）=0，x∈R}，T={x|g（x）=0，x∈R}．若|S|，|T|分别为集合S，T的元素个数，则下列结论不可能的是（）A．|S|=1且|T|=0B．|S|=1且|T|=1C．|S|=2且|T|=2D．|S|=2且|T|=3【解答】解：∵f（x）=（x+a）（x2+bx+c），S={x|f（x）=0，x∈R}，g（x）=（ax+1）（cx2+bx+1），T={x|g（x）=0，x∈R}．当a=0，b2﹣4c＜0，|S|=1，|T|=0；故A可能当a≠0，b2﹣4c＜0，|S|=1，|T|=1；故B可能当a=0，b2﹣4c=0，|S|=2，|T|=1；当a≠0，b2﹣4c=0，|S|=2，|T|=2；故C可能当a=0，b2﹣4c＞0，|S|=3，|T|=2；当a≠0，b2﹣4c＞0，|S|=3，|T|=3；综上，只有D不可能发生，故选：D．三.解答题17．已知集合A={x|（m﹣1）x2+3x﹣2=0}，是否存在这样的实数m，使得集合A 有且仅有两个子集？若存在，求出所有的m的值组成的集合M；若不存在，请说明理由．【解答】解：存在M={1，﹣}满足条件；理由如下：若集合A有且仅有两个子集，则A有且仅有一个元素，即方程（m﹣1）x2+3x﹣2=0只有一个根，则m﹣1=0，或，解得：m=1，或m=﹣，故M={1，﹣}．18．我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB为多少时，可使总造价最低？最低价为多少？【解答】解：设AB的长为x米，则宽BC为米，总造价y=400（2x+2•）•5+100••5+60×200=2000（2x+）+12000≥2000•2+12000=132000，当且仅当2x=，即x=15时，y取到最小值．故处理池的长AB设计为15米时，可使总造价y最低，最低造价为1322000元．19．已知集合A={ x|0}，集合B={x||x+2a|≤a+1，a∈R}．（1）求集合 A 及集合B；（2）若A∩B=B，求实数 a 的取值范围．【解答】解：（1）集合A={ x|≤0}={x|≤0}={x|x≤﹣2或﹣1＜x≤3}，集合B={x||x+2a|≤a+1，a∈R}，当a＜﹣1时，a+1＜0，此时B=∅；当a≥1时，a+1≥0，∴﹣a﹣1≤x+2a≤a+1，解得﹣3a﹣1≤x≤﹣a+1，∴B=[﹣3a﹣1，﹣a+1]；（2）A∩B=B，∴B⊆A，当a＜﹣1时，B=∅，满足B⊆A；当a≥﹣1时，B=[﹣3a﹣1，﹣a+1]，要使B⊆A，须或﹣a+1≤﹣2，解得﹣2≤a＜0或a≥3，即﹣1≤a＜0或a≥3，综上，实数a的取值范围是（﹣∞，0）∪[3，+∞）．20．已知函数，m＞0，满足f（2）=﹣2．（1）求实数m的值；（2）在平面直角坐标系中，作出函数f（x）的图象，并且根据图象判断：若关于x的方程f（x）=k有两个不同实数解，求实数k的取值范围（直接写结论）【解答】解：（1）由，且f（2）=﹣2，得，解得m=﹣3或m=1，∵m＞0，∴m=1；（2）由（1）知，f（x）==，当x≥0时，由f（x）=，得f′（x）=（x≠4），∴f（x）在[0，4），（4，+∞）上为减函数；当x＜0时，由f（x）=﹣，得f′（x）=，∴f（x）在（﹣∞，0）上为增函数．作出函数图象如图：由图可知，要使关于x的方程f（x）=k有两个不同实数解，则实数k的取值范围是（﹣2，0）．21．已知M是满足下列性质的所有函数f（x）组成的集合：对任何x1，x2∈D f （其中D f为函数f（x）的定义域），均有|f（x1）﹣f（x2）|≤|x1﹣x2|成立．（1）已知函数f（x）=x2+1，，判断f（x）与集合M的关系，并说明理由；（2）是否存在实数a，使得，x∈[﹣1，+∞）属于集合M？若存在，求a的取值范围，若不存在，请说明理由；（3）对于实数a、b（a＜b），用M表示集合M中定义域为区间[a，b]的函[a，b]数的集合．定义：已知h（x）是定义在[p，q]上的函数，如果存在常数T＞0，对区间[p，q]的任意划分：p=x0＜x1＜…＜x n﹣1＜x n=q，和式|h（x i）﹣h（x i=1）|≤T 恒成立，则称h（x）为[p，q]上的“绝对差有界函数”，其中常数T称为h（x）的“绝对差上界”，T的最小值称为h（x）的“绝对差上确界”，符号；求证：集合M中的函数h（x）是“绝对差有[﹣1009，1008]界函数”，并求h（x）的“绝对差上确界”．【解答】（1）解：f（x）属于集合M．事实上，任取x1，x2∈[﹣]，|f（x1）﹣f（x2）|=||=|x1+x2||x1﹣x2|，∵﹣≤x1≤，，∴﹣1≤x1+x2≤1，则0≤|x1+x2|≤1，∴|x1+x2||x1﹣x2|≤|x1﹣x2|，即|f（x1）﹣f（x2）|≤|x1﹣x2|成立，f（x）属于集合M；（2）解：若p（x）∈M，则|p（x1）﹣p（x2）|≤|x1﹣x2|对任意的x1、x2∈[﹣1，+∞）都成立．即|﹣|≤|x1﹣x2|，∴|a|≤|（x1+2）（x2+2）|，∵x1、x2∈[﹣1，+∞），∴|（x1+2）（x2+2）|≥1，∴|a|≤1，﹣1≤a≤1，∴当a∈[﹣1，1]时，p（x）∈M；当a∈（﹣∞，﹣1）∪（1，+∞）时，p（x）∉M；（3）证明：取p=﹣1009，q=1008，＜x n=1008，则对区间[﹣1009，1008]的任意划分：﹣1009=x0＜x1＜…＜x n﹣1和式|h（x i）﹣h（x i=1）|=|h（x1）﹣h（x0）|+|h（x2）﹣h（x1）|+…+|h（x n）﹣h（x n）|﹣1|=|x n﹣x0|=|1008﹣（﹣1009）|=2017=T．≤|x1﹣x0|+|x2﹣x1|+…+|x n﹣x n﹣1集合M中的函数h（x）是“绝对差有界函数”，h（x）的“绝对差上确[﹣1009，1008]界”T=2017．。

2017-2018学年上海市浦东复旦附中分校第一学期高二物理（等级考）期中测试卷一、单选题（1-8题每小题3分，9-12题每小题4分，共40分）1、下列哪些做法不属于防止静电危害的措施( D )A. 印染厂保持适当的湿度B. 油罐车运油时要装上一条拖地的金属链C. 在地毯中夹杂0.05mm∼0.07mm的不锈钢丝导电纤维D. 小汽车的顶部露出一根小金属杆2、关于元电荷,正确的说法是( D )A. 元电荷就是点电荷B. 1C电量叫元电荷C. 元电荷就是质子D. 元电荷目前被认为是自然界中电荷的最小单元3、关于电流强度的概念,下列叙述中正确的有( C )A. 通过导线截面的电量越多，电流强度越大B. 电子运动的速率越大，电流强度越大C. 单位时间内通过导体截面的电量越多，导体中的电流强度越大D. 电流的方向总是从电源正极流向负极4、把一个带正电的金属小球A跟同样的不带电的金属球B相碰,两球都带等量的正电荷,这从本质上看是因为( B )A. A球的正电荷移到B球上B. B球的负电荷移到A球上C. A球的负电荷移到B球上D. B球的正电荷移到A球上5、如图所示,Q是放在绝缘柄上的带正电的物体,把一个系在绝缘丝线上的带正电的小球,先后挂在图中的A. B两个位置,小球两次平衡时,丝线偏离竖直方向的夹角分别为θ1、θ2,则θ1和θ2的关系是( C )A. θ1>θ2B. θ1<θ2C. θ1=θ2D. 无法确定6、某静电场的电场线分布如图所示,图中P、Q两点的电场强度的大小分别为E P和E Q,电势分别为φP和φQ,则( A )A. E P>E Q，φP>φQB. E P>E Q，φP<φQC. E P<E Q，φP>φQD. E P<E Q，φP<φQ7、如图所示是一个电路的一部分,其中R1=10Ω,R2=4Ω,R3=4Ω,I1=0.3A,I2=0.5A,那么电流表测得的电流为( A )A. 0.25A，方向向右B. 0.15A，方向向左C. 0.75A，方向向左D. 0.35A，方向向右8、如图所示,a、b、c、d、e是五个相同的电阻,如果将电压逐渐升高,则最先烧坏的电阻应是( D )A. a和bB. cC. dD. e9、如图所示，A、B两点放有电量为+Q和+2Q的点电荷，A、B、C、D四点在同一直线上，且AC=CD=DB，将一正电荷从C点沿直线移到D点，则（B）A. 电场力一直做正功B. 电场力先做正功再做负功C. 电场力一直做负功D. 电场力先做负功再做正功10、如图所示,为使带正电小球平衡于图示位置,可在以小球为圆心的圆周上的相关区域固定另一电荷。

复旦大学附属中学2017-2018学年第一学期高三年级英语期中考试试卷第I卷（共103分）I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversation and the question will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. This afternoon. B. Tomorrow. C. Next week. D. Next month.2. A. She doesn‟t play tennis well. B. She likes other sports as well.C. She is an enthusiastic tennis player.D. She is a professional athlete.3. A. At a paint store. B. At an oil market.C. At a science museum.D. At a gallery.4. A. Work in the yard. B. Buy some wood.C. Go to the bookstore.D. Take a walk.5. A. A taxi driver. B. A passenger. C. A car cleaner. D. A mechanic.6. A. Call a repairman. B. Get out the paper stuck.C. Turn to her colleague for help.D. Restart the machine.7. A. There are not enough gardens. B. Parking areas are full before 10:00.C. Parking areas are closed after 10:00.D. All classes begin at 10:00.8. A. The presentation will begin at noon.B. She‟ll present her work to the man.C. She‟d like to invite the man for lunch.D. She suggests working on the presentation at 12:00.9. A. The dormitory hours. B. The problem with the rules.C. The door number of the dormitory.D. The time to open the dormitory.10. A. The chairs didn‟t need to be painted.B. He doesn‟t like the color of the chairs.C. The park could have avoided the problem.D. The woman should have been more careful.Section BDirections: In section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. Worried B. Surprised. C. Satisfied. D. Uninterested.12. A. It spoiled Juana‟s reputation. B. It copied her ideas without permission.C. It bought Juana‟s dishwashers.D. It wanted to share the dishwasher market.13. A. A successful business case. B. Juana‟s waterless laundry.C. A case against a global company.D. The worldwide dishwasher market.Questions 14 through 16 are based on the following passage.14. A. Footprints. B. Food. C. Living insects. D. Orange seeds.15. A. Don‟t touch animals under any circumstances.B. Don‟t take away any natural objects from the park.C. Don‟t leave litter in the park or throw any off the boat.D. Don‟t transport animals from one island to another.16. A. To protect the guide‟s interest. B. To improve the unique environment.C. To ensure a trouble-free visit.D. To get rid of illegal behaviors.Section CDirections: In section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. (本题做在答题纸上)Write onlyII. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Libraries are my world. I've been a patron all my life, and for the past nine years I (25) ______ (work) at multiple libraries and archives in and around Detroit. The library (26) ______ an institution has many roles, but as our country struggles through an economic crisis, I have watched the library where I work evolve into a career and business center, a community gathering place and a bastion for hope.In the spring of 2007 I got a library internship at the Southfield Public Library, just north of Detroit. Summers at SPL (27) ______ (be) usually slow, but that year, we experienced a library that hustled and bustled like science-fair project week, midterms or tax season. Yet patrons weren't looking for Mosby's Nursing Drug Reference or 1040 forms. They were coming for information on entrepreneurship and growing their small business.I interpreted people's interest in our business collection as the first step to (28) ______ (pursue) their dreams, but these patrons were not motivated by dreams. They were responding to reality, and they were looking for Plan B.Things worsened in 2008, and in 2009 the economic crisis continues to suffocate Michigan. Last year, we put up a display with a variety of job resources that we restocked every hour. Each night the library closed, the display was bare. (29) ______ we normally keep displays up for a week, we kept the job resources display up for months.Then there's the tightening credit market. People see the writing on the wall and they want to get educated. They can't afford a financial adviser, but checking books out is free. Some of (30) ______(popular) titles now are "Rich Dad, Poor Dad," "Think and Grow Rich," and "Suze Orman's 2009 Action Plan."The economic downturn affects us all. I have had to work long hours and don't get to see (31) ______ of my boyfriend or experience any kind of social life lately, but I am thankful to be in a position where I can help people overcome this struggle. In Michigan, we haven't lost hope. (32) ______ ______ ______ there are libraries here, there will always be hope.(B)It‟s estimated that 300 million people in China are studying, or (33) ______ (study), English. That‟s an impressive number and I can‟t think of any other country in the world where one quarter of the population is so dedicated to (34) ______ (learn) a second language. But some people are questioning whether this “craze” for studying English is worthwhile.Professor Zhang Shuhua of the Chinese Academy of Social Sciences says that too much emphasis is placed on learning English and that it is a waste of education resources as well as a threat to the study of Chinese. He says that having English as a compulsory course in university “has distracted much of students‟attention (35) ______ specialized subjects,”and that some students have been denied access to postgraduate education because they failed English. Others have admitted that studying so much English has made them (36) ______ (poor) Chinese speakers.Both of these criticisms are legitimate, but they beg the question of why so many Chinese still want to learn English. English, (37) ______ recognize, is the lingua franca of the modern world. It is the language of business and has become the language of international relations and culture. When people from different countries get together, they frequently speak in English rather than try to translate their native languages. It seems that everyone everywhere can speak at least some English.For China to be part of that international conversation, it is necessary that some level ofEnglish proficiency (38) ______ be achieved. But what, you may ask, about those who will never speak a word of English once they leave school? Well, for good or ill, they will still be surrounded by English. It is there in signs, in music, in movies and in the casual conversations they overhear of the increasing number of foreigners on the city streets. To know English is to be included in the rest of the world, (39) ______ ______ your world is limited to China.I agree with Professor Zhang on one point, (40) ______. English should not be a compulsory subject in university. For most, passing the CET is just the endless drudgery of memorizing word lists. There is little emphasis placed on communication. And if you can‟t communicate in English after years of study in primary school, middle school and high school, a few more years in university probably won‟t help.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.For writers in Western cultures, autumn is a difficult season to describe. On the one hand, it is the end of the summer, and therefore a little sad. The nights draw in, and when you wake in the morning, there‟s mist and it‟s co oler: Winter is around the ___41___. American writer Ernest Hemingway wrote in his book A Moveable Feast: “You expected to be sad in the fall. Part of you died each year when the leaves fell from the trees and their branches were ___42___against the wind a nd the cold, wintry light.”On the other hand, autumn has its good side. There are so many changes in nature at this time of year, such as the reds and browns that the leaves change to, and the ___43___ they fall from the trees. French writer Albert Camus even though autumn was a second spring: “Autumn is a second spring when every leaf is a flower.” It‟s a view you can also find in the most famous autumn poem in English literature, To Autumn by John Keats. In that poem Keats says that the autumn has its own songs, just like spring.Another autumn theme is wisdom. The arrival of the season is thought to be similar to a person becoming ___44___. Their summer peak may have been and gone, but old age has not yet come. At this time it‟s thought that people have ___45___ a thing or two about life. The great Irish poet W.B. Yeats takes up this theme in his poem The Wild Swans at Coole. Yeats puts together a picture for the reader out of the ___46___ of the changing seasons in Coole Park in the west of Ireland, a place he knew well. Seeing and counting 59 swans, he remembers first making the count 19 years ago. He ___47___ whether he can still love like the lover swans do.Of course, many other themes and subject matters can play a part in the literature of autumn. For example, it‟s the beginning of a new term of the school year. As you would expect, autumncan___48___ in writing for children and young people. But autumn writing usually ___49___ on the changes in nature that we see, which writers often use as a ___50___ for changes in human life.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.After the college-board examinations in June, Basil Duke Lee and five other boys from St. Regis School ___51___ the train for the West. Two got out at Pittsburgh, one slanted south toward St. Louis and two stayed in Chicago; from then on Basil was alone. It was the first time in his life that he had ever felt the need of tranquility, but now he took long breaths of it; for, though things had gone better toward the end, he had had a / an ___52___ year at school.He wore one of those extremely flat derbies (常礼帽) in vogue during the twelfth year of the century, and a blue business suit became a little too short for his constantly ___53___ body. Within he was by turns a disembodied (空洞的) spirit, almost ___54___ of his person and moving in a mist of impressions and emotions, and a fiercely competitive individual trying ___55___ to control the rush of events that were the steps in his own ___56___ from child to man. He believed that everything was a matter of ___57___ — the current principle of American education — and his fantastic ___58___ was continually leading him to expect too much. He wanted to be a great athlete, popular, brilliant and always happy. During this year at school, where he had been punished for his “freshness,” for fifteen years of thorough spoiling at hom e, he had grown uselessly introspective, and this ___59___ with that observation of others which is the beginning of wisdom. It was apparent that before he obtained much success in dealing with the world he would know that he‟d been in a fight.Fifteen is of all ages the most difficult to ___60___———to put one‟s fingers on and say, “That‟s the way I was.” And all one can know is that somewhere between thirteen, boyhood‟s___61___, and seventeen, when one is a sort of counterfeit young man, there is a time when youth ___62___ hourly between one world and another —— pushed ceaselessly forward into unprecedented experiences and ___63___ trying to struggle back to the days when nothing had to be ___64___ for. Fortunately none of our contemporaries remember much more than we do of how we behaved in those days; nevertheless the ___65___ is about to be drawn aside for an inspection of Basil‟s madness that summer.51. A. boarded B. missed C. jumped D.followed52. A. happy B. unhappy C.memorableD.favourable53. A. swelling B. bending C. lengthening D.strengthening54. A. aware B.fond C. critical D.unconscious55. A. randomly B. desperately C. particularly D.indifferently56. A. evolution B. revolution C. solutionD.introduction57. A. fact B. opinion C. course D. effort58. A. fashion B. ambition C. character D.treasure59. A. contacted B. associated C. interfered D.smashed60. A. digest B.describe C. deal D. locate61. A. majority B. minority C. senior D. junior62. A. floats B. varies C. fluctuates D. ranges63. A. successfully B. vainly C. wildly D. gently64. A. hunted B. provided C. compensated D. paid65. A.curtain B. adolescence C. portrait D. ceilingSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)There are people in Italy who can‟t stand soccer. Not all Canadians love hockey. A similar situation exists in America, where there are those individuals you may be one of them who yawn or even frown when somebody mentions baseball. Baseball to them means boring hours watching grown men in funny tight outfits standing around in a field staring away while very little of an ything happens. They tell you it‟s a game better suited to the 19th century, slow, quiet, gentlemanly. These are the same people you may be one of them who love football because there‟s the sport that glorifies “the hit”.By contrast, baseball seems abstract, cool, silent, still.On TV the game is fractured into a dozen perspectives, replays, close ups. The geometry of the game, however, is essential to understanding it. You will contemplate the game from one point as a painter does his subject; you may, of course, project yourself into the game. It is in this projection that the game affords so much space and time for involvement. The TV won‟t do it for you.Take, for example, the third baseman. You sit behind the third base dugout and you watch him watching home plate. His legs are apart, knees flexed. His arms hang loose. He does a lot of this. The skeptic still cannot think of any other sports so still, so passive. But watch what happens every time the pitcher throws: the third baseman goes up on his toes, flexes his arms or brings the glove to a point in front of him, takes a step right or left, backward or forward, perhaps he glances across the field to check his first baseman‟s position. Suppose the pitch is a ball. “Nothing happened,” you say. “I could have had my eyes closed.”The skeptic and the innocent must play the game. And this involvement in the stands is no more intellectual than listening to music is. Watch the third baseman. Smooth the dirt in front of you with one foot; smooth the pocket in your glove; watch the eyes of the batter, the speed of the bat, the sound of horsehide on wood. If football is a symphony of movement and theatre, baseball is chamber music, a spacious interlocking of notes, chores and responses.66. Those who don‟t like baseball may complain that ______.A. it is only to the taste of the oldB. it involves fewer players than footballC. it is not exciting enoughD. it is pretentious and looks funny67. The author admits that ______.A. baseball is too peaceful for the youngB. baseball may seem boring when watched on TVC. football is more attracting than baseballD. baseball is more interesting than football68. By stating …I could have had my eyes closed.‟ the author means (4th paragraph last sentence):A. The third baseman would rather sleep than play the game.B. Even if the third baseman closed his eyes a moment ago, it could make no difference to theresult.C. The third baseman is so good at baseball that he could finish the game with eyes closed allthe time and do his work well.D. The consequence was too bad he could not bear to see it.69. We can safely conclude that the author ______.A. likes footballB. hates footballC. hates baseballD. likes baseball(B)Some of the world‟s most signifi cant problems never hit headlines. One example comes from agriculture. Food riots and hunger make news. But the trend lying behind these matters is rarely talked about. This is the decline in the growth in yields of some of the world‟s major crops. A new study by the University of Minnesota and McGill University in Montreal looks at where, and how far, this decline is occurring.The authors take a vast number of data points for the four most important crops: rice, wheat corn and soybeans. They find that on between 24% and 39% of all harvested areas, the improvement in yields that took place before the 1980s slowed down in the 1990s and 2000s.There are two worrying features of the slowdown. One is that it has been particularly sharp in the world‟s most p opulous countries, India and China. Their ability to feed themselves has been an important source of relative stability both within the countries and on world food markets. That self-sufficiency cannot be taken for granted if yields continue to slow down or reverse.Second, yield growth has been lower in wheat and rice than in corn and soya beans. This is problematic because wheat and rice are more important as foods, accounting for around half of all calories consumed. Corn and soybeans are more important as feed grains. The authors note that “we have preferentially focused our crop improvement efforts on feeding animals and cars rather than on crops that feed people and are the basis of food security in much of the world.”The report qualifies the more optimistic findings of another new paper which suggests that the world will not have to dig up a lot more land for farming in order to feed 9 billion people in 2050, as the Food and Agriculture Organization has argued.Instead, it says, thanks to slowing population growth, land currently ploughed up for crops might be able to revert to forest or wilderness. This could happen. The trouble is that the forecast assumes continued improvements in yields, which may not actually happen.70. What does the author try to draw attention to?A. Food riots and hunger in the world.B. News headlines in the leading media.C. The decline of the grain yield growth.D. The food supply in populous countries.71. Why does the author mention India and China in particular?A. Their self-sufficiency is vital to the stability of world food markets.B. Their food yields have begun to decrease sharply in recent years.C. Their big populations are causing worldwide concerns.D. Their food self-sufficiency has been taken for granted.72. What does the new study by the two universities say about recent crop improvement efforts?A. They fail to produce the same remarkable results as before the 1980s.B. They contribute a lot to the improvement of human food production.C. They play a major role in guaranteeing the food security of the world.D. They focus more on the increase of animal feed than human food grains.73. What does the Food and Agriculture Organization say about world food production in the coming decades?A. The growing population will greatly increase the pressure on world food supplies.B. The optimistic prediction about food production should be viewed with caution.C. The slowdown of the growth in yields of major food crops will be reversed.D. The world will be able to feed its population without increasing farmland.(C)Among the more colorful characters of Leadville‟s golden age were H.A.W. Tabor and his second wife, Elizabeth McCourt, better known as “Baby Doe”. Their history is fast becoming one of the legends of the Old West. Horace Austin Warner Tabor was a school teacher in Vermont. With his first wife and two children he left Vermont by covered wagon in 1855 to homestead in Kansas. Perhaps he did not find farming to his liking, or perhaps he was tempted by rumors of fortunes to be made in Colorado mines. At any rate, a few years later he moved west to the small Colorado mining camp known as California Gulch, which he later renamed Leadville when he became its leading citizen. “Great deposits of lead are sure to be found here.” he said.As it turned out, it was silver, not lead, that was to make Leadville‟s fortune and wealth. Tabor knew little about mining himself, so he opened a general store, which sold everything from boots to salt, flour, and tobacco. It was his custom to “grubstake” prospective miners, in other words, to supply them with food and supplies, or “grub”, while they looked for ore, in return for which he would get a share in the mine if one was discovered. He did this for a number of years, but no one that he aided ever found anything of value.Finally one day in the year 1878, so the story goes, two miners came in and asked for “grub”. Tabor had decided to quit supplying it because he had lost too much money that way. These werepersistent, howe ver, and Tabor was too busy to argue with them. “Oh help yourself. One more time won‟t make any difference,” He said and went on selling shoes and hats to other customers.The two miners took $17 worth of supplies, in return for which they gave Tabor a one-third interest in their findings. They picked a barren place on the mountain side and began to dig. After nine days they struck a rich vein of silver. Tabor bought the shares of the other two men, and sothe mine belonged to him alone. This mine, known as the “Pittsburgh Mine,” made 1 300 000 for Tabor in return for his $17 investment.Later Tabor bought the Matchless Mine on another barren hillside just outside the town for $117 000. This turned out to be even more fabulous than the Pittsburgh, yielding $35 000 worth of silver per day at one time. Leadville grew. Tabor became its first mayor, and later became lieutenant governor of the state.74. Leadville got its name for the following reasons EXCEPT ______.A. because Tabor became its leading citizenB. because great deposits of lead is expected to be found thereC. because it could bring good fortune to TaborD. because Tabor renamed it so75. The word “grubstake” in paragraph 2 means ______.A. to supply miners with food and suppliesB. to open a general storeC. to do one‟s contribution to the development of the mineD. to supply miners with food and supplies and in return get a share in the mine, if one wasdiscovered76. Tabor made his first fortune ______.A. by supplying two prospective miners and getting in return a one-third interest in the findingsB. because he was persuaded by the two miners to quit supplyingC. by buying the shares of the otherD. as a land speculator77. The underlying reason for Tabor‟s life career is ______.A. purely accidentalB.based on the analysis of miner‟s being very poor and their possibility of discoveringprofitable mining siteC. through the help from his second wifeD. he planned well and accomplished targets step by stepSection CDirections: Read the passage carefully. Then answer the questions or complete the statements inthe fewest possible words.When the Internet powerhouse Yahoo wanted to teach ethics to its employees, it faced a challenge familiar to multinational companies.Yahoo employs nearly 14,000 people at 25 sites worldwide. They would feel bored at sitting down in front of a dated video in which actors with 1980s haircuts tell them what to do. So it hired a company called The Network to design a game. In the game, the truck where Yahoo wasfounded traveled the world, turning into a boat and a helicopter along the way as it visited some of Yahoo's foreign offices. Participants play in game show-like scenarios that quiz them about conflicts of interest and doing business fairly. And employees note: Yahoo is tracking how well they do.Such activities draw more enthusiastic participation and teach more effectively than traditional methods. They are described as alternative-reality games (ARGs), involving both interactive and real-world elements. Besides teaching employees, ARGs have also been used in many areas for a number of different purposes.From a marketing perspective, a number of very successful ARGs have been written as a way to build product awareness. A very popular ARG called I Love Bees was produced to market the 2004 video game Halo 2. At its height, I Love Bees received between two to three million unique visitors over the course of three months.ARGs are more than just a fun way to learn. They have also been used to solve real world problems. An ARG called World Without Oil was created to obtain collective input from players about dealing with the world's dependency on oil. World without Oil simulates the first 32 days of a global oil crisis and anybody could play by creating a personal story that recorded the imagined reality of their life in the crisis. World Without Oil's success on a small budget has opened the door for similar games to engage mainstream Internet users with climate change, education reform, governmental policy and other timely, vital issues.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78.What challenge did yahoo face in teaching ethics to its employees?79.In the game designed for yahoo, participants had to answer questions about ________.80.What are the three major functions of ARG mentioned in the passage?81.The success of World Without Oil suggests that ARGs can ________.第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.没有人不希望和平。