第一节 岩石圈与地表形态【学习目标】1.说出地球的圈层结构，概括各圈层的主要特点。
2.掌握岩石圈的物质循环过程及变式图的判读3.掌握地质构造的成因、判断及其应用。
4.理解主要外力作用及形成的典型地貌 【重难点】1、岩石圈的物质循环过程及变式图的判读2、地质构造的成因、判断及其应用。
(第一课时)预习案一、地球内部圈层和岩石圈的结构 1．地球内部分层(1)依据：地震波的传播速度。
地震波分为：①_________ ②__________【见规律总结】地球内部圈层分为： 、 。
二、岩石圈的组成与物质循环2.地质作用⎩⎪⎨⎪⎧⑲外力作用⑳○213．循环意义(1)形成了地球上丰富的○22________________。
(2)改变了地表的形态，塑造了千姿百态的○23__________________________________。
(3)实现了地区之间、圈层之间的○24______________和○25______________，从而改变了地表的环境。
课中案探究点一地球内部圈层和岩石圈的结构【探究材料】最近，我国在渤海湾发现储量逾10亿吨的大油田。
该油田储量的探明是采用三维地震勘探技术的结果。
地震波分为纵波与横波，根据地震波传播原理，在通过含油层时，横波传播速度会发生明显变化。
1．材料中的地震波可分为几类？它们之间有何区别？2．地球物理学家根据对地震波传播速度的研究，将地球内部大致分为几个圈层？3．我们通常所说的岩石圈是否就是地壳？为什么？探究点二岩石圈的组成与物质循环【探究材料】晶晶和亮亮是两滴岩浆，他们生活在地球内部的“岩浆之家”。
一天，他们得到批准，与其他同伴一起到地球表面旅行。
他们飞快地奔向地表，半路上，晶晶觉得累了，于是就与亮亮约好，在地表会合。
亮亮没有停步，与其他同伴一起跳出地表，并沿着山坡往低地流动。
忽然，亮亮发现自己不能再动了，不禁问旁边的同伴这是怎么回事。
同伴笑着说：“别担心，只不过你已经不再是一滴岩浆罢了。
高中2014年高一第二学期化学期末试题答案摘要高中频道的编辑就为您准备了高中2014年高一第二学期化学期末试题答案一、选择题(每题1分，共10题，共10分)题号 1 2 3 4 5 6 7 8 9 10答案 B A C B B C C B B B二、选择题(每题2分，共40题，共80分)题号 11 12 13 14 15 16 17 18 19 20答案 C D A C C D A B A A题号 21 22 23 24 25 26 27 28 29 30答案 B B D C D A C B D B题号 31 32 33 34 35 36 37 38 39 40答案 D D A B C C D B D A题号 41 42 43 44 45 46 47 48 49 50答案 D C B B A B B A C A三、双选题(每题2分，选一个对的得1分，全对得2分，其它错误不得分，共10分)题号 51 52 53 54 55答案 BC BD CD AD AB四、双选题(每题4分，选一个对的得2分，全对得4分，其它错误不得分，共12分)题号 56 57 58答案 CD AB AD五、填空题(38分)(原题59题10分、61题11分，现调整为59题9分，61题12分)59. (9分)(1)羟基、羧基(2分)(2)CH3CHO(1分)(3)加成反应、取代(2分)(4)① CH2=CH2 + Cl2 rarr; CH2ClCH2Cl(2分)② HOCH2CH2OH +2CH3COOH CH3COOCH2CH2OO CCH+2H2O(2分)(缺条件与没有配平共扣1分)② 其他条件不变，升高反应温度，H2O2分解速率加快(或其他条件不变，使用合适的催化剂，H2O2分解速率加快等合理答案)(2分)。
(2)① (2分，缺条件未配平共扣1分)② 催化剂的聚集状态(或催化剂的表面积)(1分)61.(12分)(1)① 第三周期第ⅦA族(1分，只答周期或第ⅦA族不给分)② MnO2 + 2Cl- + 4H+ ==== Mn2++2H2O +Cl2uarr;(2分，缺条件未配平共扣1分)③ 吸收多余的Cl2(尾气处理)(1分);④ 不合理，没有事先证明干燥的氯气有无漂白性(2分);⑤ 不合理，制取的氯气中含HCl气体，其溶于水能与NaHCO3粉末反应产生气泡(2分)(2)淀粉碘化钾溶液(1分)(3)① Cu+4HNO3(浓)==Cu(NO3)2+2NO2uarr;+2H2O(2分，未配平扣1分)② 丁中气体的红棕色(颜色)变深(1分)62. (10分)(1)过滤(1分)、玻璃棒(1分)(2)不可行，因为用硝酸钡代替氯化钡会引入硝酸钾杂质(2分);(3) (2分);(4)(各1分)BaSO4 ;K2CO3KCl、KBr、K2CO3三种全才得分);蒸发浓缩、冷却结晶(或蒸发结晶)。
2014下学期高一英语期末试卷第二部分英语知识应用（共两题，满分45分）第一节单项填空（共15小题；每小题1分，满分15分）从A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。
21. What_____ pleasant surprise! I’ll tell Richard about it____ minute he comes home.A. a, theB. a, aC. a, /D. /, the22. The Anti-Japanese War _________ in 1937.A. broke downB. broke inC. broke outD. broke up23. --------Have you asked somebody to repair the machine?--------Oh, sorry, I forgot it. I _________for an engineer at once.A. am going to sendB. would sendC. have sentD. will send24. It was ________ that the PLA men got to the earth-strike area.A. midnightB. at midnightC. untilD. for midnight25. We’re looking forward to _______a chance to watch the opening ceremony of the London 2012Olympic Games.A. giveB. be givenC. givingD. being given26. Seeing the happy _________of children playing in the park, I’m full of joy and confidence in thefuture of our country.A. sightB. sceneC. viewD. sign27. “ We can’t go out in this weather,” said Bob,______ at the desk.A. seatingB. seatedC. sat D sit28. ----Excuse me, sir,_______________----I’d like a cup of coffee and two pieces of bread.A. what do you want?B. may I have your order?C. this table is reserved.D. I would like to serve you.29. — Have you thought of a topic for your speech yet?—No, I______ a lot about it, but I haven’t decided.A. will thinkB. have been thinkingC. had thoughtD. was thinking30. I would _____ it if you come to my grandma’s birthday party and say “Hello” to her.A. associateB. appreciateC. impressD. congratulate31. The Tower of London is _____ the Church tower.A. twice high thanB. two times as high asC. twice higher asD. three times the height of32. ——Did you see a girl in white pass by just now?——No, Sir. I______ a newspaper.A. readB. had readC. would readD. was reading33. It’s always difficult being in a foreign country, ______if you don’t speak the language.A. extremelyB. naturallyC. basicallyD. especially34. ——Why didn't you tell him about the meeting?——He rushed out of the house______ I could say a word.A. afterB. beforeC. sinceD. when35. ——Nice to meet you, Mike. ?——Everything is OK. Thanks.A. What are you doingB. Where have you beenC. How is it goingD. What's wrong with you第二节完形填空（共20题；每小题1.5分，满分30分）Telling the truth is a very good habit. If you 36 speak the truth, you can save yourself from a lot of 37 ! Here is a story of a man who did a lot of 38 things, but his promise to tell the truth 39 him.Once a man came to a prophet（预言家）and said, “Oh, prophet, I have many bad 40. Which one of them should I 41 first？” The prophet said：“Give up telling 42 first and always speak the truth.” The man promised to do so and went home.At night the man was about to go out to steal. Before setting out, he thought for a moment about the 43 he made with the prophet. “44 tomorrow the prophet asks me where I have been, what shall I say？Shall I say that I went out 45？No, I cannot say that. But nor can I lie. If I tell the truth, 46 will start hating me and call me a thief. I would be 47 for stealing.”So the man 48 not to steal that night, and gave up this bad habit. Next day, he 49 drinking wine. When he was about to do so, he said to himself, “What shall I say to the prophet if he asks me wha t I did during the day？I cannot tell a lie, and if I speak the truth people will 50 me, because a Muslim（穆斯林）is not 51 to drink wine.” And so he gave up the 52 of drinking wine.In this way, 53 the man thought of doing something bad, he 54 his promise to tell the truth. One by one, he gave up all his bad habits and became a very 55 person.36. A. always B. hardly C. sometimes D. never37. A. time B. money C. trouble D. energy38. A. great B. bad C. strange D. stupid39. A. educated B. bothered C. tested D. saved40. A. habits B. friends C. purposes D. collections41. A. take in B. bring back C. give up D. depend on42. A. stories B. truths C. reasons D. lies43. A. plan B. secret C. promise D. mistake44. A. Because B. Unless C. Since D. If45. A. stealing B. drinking C. walking D. dancing46. A. none B. someone C. anyone D. everyone47. A. controlled B. admired C. punished D. killed48. A. refused B. tried C. decided D. agreed49. A. talked about B. felt like C. adapted to D. broke down50. A. understand B. like C. hate D. respect51. A. allowed B. encouraged C. invited D. advised52. A. chance B. disadvantage C. adventure D. idea53. A. wherever B. whenever C. whatever D. however54. A. forgot B. doubted C. regretted D. remembered55. A. good B. attractive C. practical D. generous第三部分阅读理解（共20小题；每小题2分，满分40分）AI hated dinner parties. But I decided to give them another shot because I'm in London. And my friend Mallory invited me. And because dinner parties in London are very different from those back in New York. There, “I’m having a dinner party means: "I'm booking a table for 12 at a restaurant you can't afford and we'll be sharing the checkup evenly, no matter what you eat." Worse, in Manhattan there is always someone who leaves before the bill arrives. They'll throw down cash, half of what they owe, and then people like me, who don’t drink, end up paying even more. But if I try to use the same trick, the hostess will shout: "Where are you going?" And it's not like I can say I have somewhere to go: everyone know I have nowhere to go.But in London, dinner parties are in people's homes. Not only that, the guests is an interesting mix. The last time I went to one, the guests were from France, India. Denmark and Nigeria; it was like a gathering at the United Nations in New York. The mix is less striking. It's like a gathering at Bloomingdale's, a well-known department store.For New Yorkers, talking about other parts of the world means Brooklyn and Queens in New York. But at Mallory’s, when I said that I had been to Myanmar recently, people knew where it was. In New York people would think it was a usual new club56. What does the word "shot" in Paragraph 1 probably mean?A. choiceB. tryC. styleD. goal57. What does the writer dislike most about dinner parties in New York?A There is a strange mix of people. B. The restaurants are expensive.C. The bill is not fairly shared.D. People have to pay cash58. What does the author think of the parties in London?A. A bit unusual. B．Full of tricks.C．Less expensive. D. More interesting.59. What is the author's opinion of some New Yorkers from her experience？A. Easy-going.B. Self-centered.C. Generous.D. Traditional.BCan you communicate with others when you live in a foreign country with no or little knowledge of its language? Of course, it is possible. You can communicate your moods and intentions to one another without words, because all human beings share a lot of common visual signals. These signals are as effective as words during communication.The gestures of the head play a key role in body language. The movements of eyes and eyebrows are as important as head movements in body language.Besides the gestures of the head or the movements of the eyes and eyebrows, the action of arms, hands and legs is also a large part of body language. Extending one's arm and shaking hands with others is a greeting in both formal and informal cases. This part of body language might date back to primary tribes（原始部落）.Like handshaking, there are still many other forms of body language presented by hands. Raising one's hand and making a circle with his thumb（拇指）and for finger signals, that something is OK. Clasped（握紧的）hands raised above the head, a traditional picture accepted by sportsmen after winning a fight, is a display of triumph that grows out of a kind of feeling following a victory. Waving one's hands, a speaker can make his words more powerful and vigorous（有活力的）.Besides hand gestures, there are times when a person says something with his legs as well as with his head and eyes. The leg gestures often reflect one's attitude towards something or someone that person is with.According to the above facts, body language has offered a more reliable（可靠的）way to understand one's mind by means of gestures. Though it is soundless and wordless, once you understand it, you will feel the world is bigger than you realized.60. Which of the following is the proper title for this passage?A. Body LanguageB. How to Communicate with the People around YouC. The History of Body LanguageD. Gesturers And Languages61. After reading the passage we can conclude that ________.A. hand shaking suggests that the speaker is excitedB. head plays a less important part in body languageC. actors and actresses are good at gesturesD. people began to use body language long long ago62．What's the characteristic（特点、特征）of body language?A. Soundless and wordless.B. Difficult to understand.C. Powerful and vigorous.D. Effective and normal63．When sports men win a match, they probably ________.A. clasp their hands to announce their victoryB. clasp their hands to express their excited feelingC. have a picture taken as soon as possibleD. show a sign of thankfulnessCWhat to do if you don't feel popular？● Try to take part in activities. Call your friends. Plan to do something. The worst feeling is staying home alone, because it makes you feel even more lonely.● Try to make new friends. Choose friends carefully , not just because you think they're popular. And remember, making good friends takes time. Choosing a popular person to be friends with is okay. If they are nice.● Be yourself. If you want to become friends with someone who's popular, don't make yourself into someone you are not just to impress that person.● Be nice. Be friendly. Be outgoing. But don't overdo it！Talk to trusted friends if you are feeling really bad. Or you might want to write it down in a journal or diary.● Do something special for yourself. You could take pictures of your friends, or collect their school pictures, and take a collage to hang on your wall. This will remind you, when you are feeling unpopular, that you really do have friends.● Think up your own ideas. These suggestions might not work for everyone.What to do if you have a problem with your teacher？●Talk to your parents, or another adult who will listen to you and perhaps can help. Talk to your friends. Maybe they have had problems with the same teacher, too.● Don't give the teacher a reason to have problems with you. Do your work, complete your task, attend the class seriously and take notes. Maybe you just need to give the teacher a chance.● Try to find out what the problem is.●Talk to the teacher if you feel comfortable doing this. Don't be nasty, but express your concerns. Listen to the teacher, as well.● Just accept the fact that you're not going to love all your teachers.64. What do we mean by saying“ not feeling popular？”A. Not liked by our classmates or workmates.B. Not doing what we want.C. Not showing any interest in anything.D. Not so happy.65. What does the underlined word “overdo” mean?A. Do something too much or in an extreme way.B. Try your best to do something.C. Do something carefully.D. Work too hard.66. The writer ___________.A. believes that your friend will help you out if you take their picturesB. suggests that you discuss the reason of problem with your teacher when you feel uncomfortableC. wants you to know that students usually hate teachersD. is not too sure if his advice will certainly work on you67. What's the best title of this passage？A. Why We Have Problems at School？B. Always be Yourself.C. How to Handle Problems at School？D. Don't Be Afraid of Problems With Others.DThe private automobile （私家车）has long played an important role in the United States. In fact, it has become a necessary and important part of the American way of life. In 1986, sixty-nine percent of American families owned at least one car, and thirty-eight percent had more than one. By giving workers rapid transportation, the automobile has freed them from having to live near their place of work. This has encouraged the growth of the cities, but it has also led to traffic problems.For farm families the automobile is very helpful. It has made it possible for them to travel to town very often for business and for pleasure, and also to transport their children to distant schools.Family life has been affected in various ways, The car helps to keep families together when it is used for picnics, outings, and other shared experiences. However, when teenage children have the use of the car, their parents can't keep an eye on them. There is a great danger if the driver has been drinking alcohol or taking drugs, or showing off by speeding or breaking down traffic laws. Mothers of victims of such accidents have formed an organization called MADD （Mothers Against Drunk Driving）. These women want to prevent further tragedies （悲剧）. They have worked to encourage the government to limit the youngest drinking age, Students have formed a similar organization, SADD （Students Against Drunk Driving）and are spreading the same message among their friends.For many Americans the automobile is a necessity. But for some, it is also a mark of social position and for young people, a sign of becoming an adult. Altogether, cars mean very much to Americans.68. Which of the following is NOT mentioned in the text?A. Cars have encouraged the growth of the cities.B. Cars can bring families together when they go for picnics.C. Cars have enabled people to live far from their place of work.D. Cars help city families to transport their children to faraway schools.69. What has been done to deal with the problem of drunk driving?A. Patents have paid more attention to their children.B. Some organizations have been set up against drunk driving.C. Mothers have tried to persuade their children not to drink alcohol.D. University students have asked the government to solve the problem.70. We can infer from the text that ____________ in America.A. it will be more difficult for people to get new carsB. parents will not allow their children to have their own carsC. the government will encourage people to use public transportationD. cars will still be popular though they have caused many problemsEEveryone has got two personalities—the one that is shown to the world and the other that is secret and real．You don't show your secret personality when you're awake because you can control your behavior，but when you're asleep，your sleeping position shows the real you．In a normal night，of course，people frequently change their position．The important position is the one that you go to sleep in．If you go to sleep on your back，you're a very open person．You normally trust people and you are easily influenced by fashion or new ideas．You don't like to upset people，so you never express your real feelings．You're quite shy and you aren't very confident．If you sleep on your stomach，you are a rather secretive（不坦率的）person．You worry a lot and you're always easily upset．You're very stubborn（顽固的），but you aren't very ambitious．You usually live for today not for tomorrow．This means that you enjoy having a good time．If you sleep curled up（卷曲），you are probably a very nervous person．You have a low opinion of yourself and so you're often defensive．You're shy and you don't normally like meeting people．You prefer to be on your own．You're easily hurt．If you sleep on your side，you have usually got a well-balanced personality．You know your strengths and weaknesses．You're usually careful．You have a confident personality．You sometimes feel anxious，but you don't often get depressed．You always say what you think even if it annoys people．71．According to the writer，you naturally show your secret and real personality _____.A．only in a normal nightB．only when you go to sleepC．only when you refuse to show yourself to the worldD．only when you change sleeping position72．Which is NOT mentioned in the second paragraph about a person's personality？A．He or she is always open with others．B．He or she always likes new ideas earlier than others．C．He or she is always easily upset．D．He or she tends to believe in others．73．Point out which sentence is used to show the personality of a person who is used to sleeping on his or her stomach？A．He or she is careful not to offend others．B．He or she doesn't want to stick to his or her opinion．C．He or she can't be successful in any business．D．He or she likes to bring others happiness．74．Maybe you don't want to make friends with a person who sleeps curled up．Why？A．He or she would rather be alone than communicate with you．B．He or she is rarely ready to help you．C．He or she prefers staying at home to going out．D．He or she wouldn't like to get help from you．75．It appears that the writer tends to think highly of the person who sleeps on one side because ______ ．A．he or she always shows sympathy for peopleB．he or she is confident，but not stubbornC．he or she has more strengths than weaknessesD. he or she often considers annoying people姓名班级。
专题02 一元二次函数、方程和不等式考点一：不等式性质及应用1．若A ＝a 2＋3ab ，B ＝4ab －b 2，则A ，B 的大小关系是( ) A ．A ≤B B ．A ≥B C ．A <B 或A >B D ．A >B 答案 B解析 ∵A －B ＝a 2＋3ab －(4ab －b 2)＝⎝⎛⎭⎫a －b 22＋34b 2≥0， ∴A ≥B . 2．若110a b<<，则下列不等式成立的是( ) A ．a b ab -> B ．a b ab -<C ．b a ab ->D ．b a ab -<【解答】解：由110a b<<， 对于A 、B ，因为110a b <<，则0a <，0b <，a b >，从而0ab >，0a b ->，即0a b ab ->，则可取1a bab-=，即a b ab -=，故A 、B 错误，对于C 、D ，因为110a b <<，则0a <，0b <，从而0ab >．又110b a->，即0a bab->，则0a b ->，所以0b a ab -<<，故D 正确，C 错误． 故选：D ．3.对于任意实数a ，b ，c ，则下列四个命题：①若a b >，0c ≠，则ac bc >；②若a b >，则22ac bc >； ③若22ac bc >，则a b >；④若a b >，则11a b<. 其中正确命题的个数为( ) A ．3 B ．2C ．1D ．0【答案】C【解析】a b >时，若0c <，则ac bc <，①错误；若0c，则22ac bc =，②错误；若22ac bc >，则20c >，∴a b >，③正确；a b >，若0a b >>，仍然有11a b>，④错误． 正确的只有1个．故选：C ．4.已知11x y -≤+≤，13x y ≤-≤，则182yx ⎛⎫⋅ ⎪⎝⎭的取值范围是( ) A ．82,2⎡⎤⎣⎦B ．81,22⎡⎤⎢⎥⎣⎦C ．72,2⎡⎤⎣⎦D ．71,22⎡⎤⎢⎥⎣⎦【答案】C【解析】令()()()()3x y s x y t x y s t x s t y -=++-=++-则31s t s t +=⎧⎨-=-⎩，∴12s t =⎧⎨=⎩，又11x y -≤+≤，…∴①13x y ≤-≤，∴()226x y ≤-≤…②∴①+②得137x y ≤-≤．则371822,22yxx y -⎛⎫⎡⎤⋅=∈ ⎪⎣⎦⎝⎭．故选C ．5.证明不等式22222a b a b ++⎛⎫≤⎪⎝⎭(,a b ∈R ). 【答案】证明见解析.【解析】证明：因为222a b ab +≥，所以22222()2a b a b ab +≥++， 所以()()2222a ba b +≥+两边同除以4，即得22222a b a b ++⎛⎫≤⎪⎝⎭，当且仅当a b =时，取等号. 考点二：利用基本不等式求最值 6.函数413313y x x x ⎛⎫⎪⎝=>-⎭+的最小值为（ ） A ．8 B ．7 C ．6 D ．5【答案】D因为13x >，所以3x －1>0，所以()443311153131y x x x x =+=-++≥=--， 当且仅当43131x x -=-，即x =1时等号成立，故函数413313y x x x ⎛⎫ ⎪⎝=>-⎭+的最小值为5． 故选：D ．7.设0a >，0b >，41a b +=，则11a b+的最小值为( )A ．7B ．9C D 3【解答】解：0a >，0b >，41a b +=，111144()(4)()552549b a b a b a b a b a b a ∴+=++=++++=， 当且仅当4b a a b =，即126a b ==时取等号，∴11a b +的最小值为9．故选：B ．8．已知a ，b R +∈，且23a b ab +=，则2a b +的最小值为( ) A ．3B ．4C ．6D ．9【解答】解：a ，b R +∈，且23a b ab +=，∴213a b+=，12152522(2)()()333333a b a b a b a b b a ∴+=++=+++⨯（当且仅当a b =时取“= “)，即2a b +的最小值为3．故选：A ．9．函数233(1)1x x y x x ++=<-+的最大值为（ ）A ．3B ．2C ．1D ．-1【答案】D2233(1)(1)111x x x x y x x ++++++==++1[(1)]1(1)x x =--+++-+11≤-=-， 当且仅当1111x x +==-+,即2x =-等号成立. 故选：D.10.已知0x >，0y >，若28x y xy +=，则xy 的最小值是（ ）A B C ．18D ．14【答案】C因为0x >，0y >，由基本不等式得：2x y +≥所以8xy ≥解得：18xy ≥，当且仅当2x y =，即14x =，12y =时，等号成立故选：C11.已知0x >，0y >且141x y+=，若28x y m m +>+恒成立，则实数m 的取值范围是_________.【答案】(9,1)- 【详解】0,0x y >> ，且141x y+=，()144149y xx y x y x y x y ⎛⎫∴+=++=+++≥ ⎪⎝⎭，当且仅当4y x x y =,即36x y ==，时取等号.()min 9x y ∴+=，由28x y m m +>+ 恒成立，即()2min 89m m x y +<+=，解得：91m -<<， 故答案为：(9,1)-12.已知正数a ，b 满足21a b +=，则( ) A ．ab 有最大值18 B ．12a b +有最小值8 C ．1b b a +有最小值4 D ．22a b +有最小值15【解答】解：根据题意，依次分析选项： 对于A ，22112()248a b a b ab+⋅=⇒，当且仅当12a =，14b =时取等号，则A 正确； 对于B ，121222(2)()5459b aa b a b a b a b +=++=+++=，当且仅当13a b ==时取等号，B 错误；对于C ，12224b a bb a b a+=+++=，当且仅当13a b ==时取等号，则C 正确；对于D ，222222211(12)5415()(0)552a b b b b b b b +=-+=-+=-+<<，故最小值为15，则D 正确；故选：ACD ．13.已知20a b >>，则4(2)a b a b +-的最小值为______________思路一：所求表达式为和式，故考虑构造乘积为定值以便于利用均值不等式，分母为()2b a b -，所以可将a 构造为()112222a ab b ⋅=⋅-+⎡⎤⎣⎦，从而三项使用均值不等式即可求出最小值：4181(2)3(2)2(2)2a a b b b a b b a b ⎡⎤+=-++≥⋅=⎢⎥--⎣⎦ 思路二：观察到表达式中分式的分母()2b a b -，可想到作和可以消去b ，可得()()2222b a b b a b a +-⎡⎤-≤=⎢⎥⎣⎦，从而244(2)a a b a b a +≥+-，设()24f a a a =+，可从函数角度求得最小值（利用导数），也可继续构造成乘积为定值：()24322a a f a a =++≥= 答案：314.某项研究表明：在考虑行车安全的情况下，某路段车流量F (单位时间内经过测量点的车辆数，单位：辆/时)与车流速度v (假设车辆以相同速度v 行驶，单位：米/秒)、平均车长l (单位：米)的值有关，其公式为F＝76 000v v 2＋18v ＋20l . (1)如果不限定车型，l ＝6.05，则最大车流量为________辆/时；(2)如果限定车型，l ＝5，则最大车流量比(1)中的最大车流量增加________辆/时． 答案 (1)1 900 (2)100解析 (1)当l ＝6.05时，F ＝76 000v v 2＋18v ＋121＝76 000v ＋121v ＋18≤76 0002v ·121v ＋18＝1 900(辆/时)．当且仅当v ＝121v ，即v ＝11时，等号成立．(2)当l ＝5时，F ＝76 000vv 2＋18v ＋100＝76 000v ＋100v ＋18≤76 0002v ·100v ＋18＝2 000(辆/时)．当且仅当v ＝100v ，即v ＝10时，等号成立．∴最大车流量为2 000(辆/时)． 2 000－1 900＝100(辆/时)．∴最大车流量比(1)中的最大车流量增加100(辆/时)． 考点三：含参数与不含参数的不等式解法15.已知集合{}2230A x x x =-+≥，302x B x x ⎧⎫-=∈≤⎨⎬+⎩⎭Z，则A B =（ ） A ．{}23x x -<≤ B ．{}1,0,1,2,3-C ．{}2,1,1,2,3--D ．R【答案】B解不等式2230x x -+≥ ，()2223120,x x x x R -+=-+>∈ ，解不等式302x x -≤+ 得23x -<≤，}{1,0,1,2,3B =- ，}{1,0,1,2,3A B ∴⋂=- ； 故选：B.16.不等式()()()21350x x x ++->的解集为___________. 【答案】1(,3),52⎛⎫-∞-- ⎪⎝⎭⋃【详解】不等式()()()()()()2135021350x x x x x x ++->⇔++-<，由数轴标根法画出图线，可得不等式的解集为1(,3),52⎛⎫-∞-- ⎪⎝⎭⋃.故答案为：1(,3),52⎛⎫-∞-- ⎪⎝⎭⋃.17.已知二次不等式220x bx c -++<的解集为1{|3x x <或1}2x >，则关于x 的不等式220cx bx -->的解集为( )A ．{|23}x x <<B ．{|23}x x -<<C ．{|32}x x -<<D ．{|32}x x -<<-【解答】解：二次不等式220x bx c -++<的解集为1{|3x x <或1}2x >， 所以二次方程220x bx c -++=的解是13和12，由根与系数的关系知，1132211322bc ⎧+=⎪⎪⎨⎪⨯=-⎪⎩，解得53b =，13c =-；所以不等式220cx bx -->化为2152033x x --->， 即2560x x ++<，解得32x -<<-；所以所求不等式的解集为{|32}x x -<<-． 故选：D ．18．25．已知关于x 的不等式20ax bx c ++>解集为{}23x x -<<，则下列说法错误的是（ ） A ．0a < B ．不等式0ax c +>的解集为{}6x x <C ．0a b c ++>D ．不等式20cx bx a -+<的解集为1132x x ⎧⎫<<⎨⎬⎩⎭【答案】D 【详解】由已知可得－2，3是方程20ax bx c ++=的两根，则由根与系数的关系可得23,23,b ac a ⎧-+=-⎪⎪⎨⎪-⨯=⎪⎩且0a <，解得,6b a c a =-=-，所以A 正确；对于B ，0ax c +>化简为60x -<，解得6x <，B 正确；对于C ，660a b c a a a a ++=--=->，C 正确； 对于D ，20cx bx a -+<化简为：2610x x --<，解得1132x -<<，D 错误．故选：D.19.已知关于x 的不等式：()23130ax a x -++<．(1)当2a =-时，解此不等式； (2)当0a >时，解此不等式．【答案】(1)1{|2x x <-或}3x >(2)当13a =时，解集为∅；当103a <<时，解集为1{|3}x x a <<；当13a >时，解集为1{|3}x x a <<(1)当a ＝－2时，不等式－2x 2＋5x ＋3＜0整理得(2x ＋1)(x －3)＞0，解得x ＜－12或x ＞3， 当a ＝－2时，原不等式解集为{x |x ＜－12或x ＞3}．(2)当a ＞0时，不等式ax 2－(3a ＋1)x ＋3＜0整理得：(x －3)(x －1a )＜0， 当a ＝13时，1a ＝3，此时不等式无解；当0＜a ＜13时，1a ＞3，解得3＜x ＜1a ；当a ＞13时，1a ＜3，解得1a ＜x ＜3；综上：当a ＝13时，解集为∅；当0＜a ＜13时，解集为{x |3＜x ＜1a }；当a ＞13时，解集为{x |1a ＜x ＜3}.20．已知22()(3)3f x ax a x a =+--．（1）若关于x 的不等式()0f x <的解集为{|1x x >或3}x <-，求实数a 的值； （2）若关于x 的不等式()0f x x a ++<的解集中恰有2个整数，求正整数a 的值． 【解答】解：22()(3)3(3)()f x ax a x a ax x a =+--=-+，（1）若不等式()0f x <的解集为(-∞，3)(1-⋃，)+∞，则0a <，且1a -=，33a=-，解得1a =-； （2）不等式()0f x x a ++<，即22(2)20ax a x a +--<有两整数解， 所以(2)()0ax x a -+<；又a 为正整数，所以2a x a-<<， 由解集中必含0，两整数解为1-，0或0，1；当2a >时，整数解为2-，1-，0，不符合； 所以1a =或2a =．考点四：恒成立、有解与根分布问题21．函数()()20.8log 23f x x ax =-+在()1,-+∞有意义，则a 的取值范围（ ）A ．(-B ．5,⎡-⎣C ．[]5,4--D ．(],4-∞-【答案】B 【详解】由题意可知2230x ax -+>对任意的1x >-恒成立，令223u x ax =-+， 二次函数223u x ax =-+的图象开口向上，对称轴为直线4ax =. ①当14a≤-时，即当4a ≤-时，此时函数223u x ax =-+在()1,-+∞上单调递增， 所以，230a ++≥，解得5a ≥-，此时54a -≤≤-；②当14a>-时，即当4a >-时，则有2240a ∆=-<，解得a -<4a -<<综上所述，实数a 的取值范围是5,⎡-⎣. 故选：B.22.已知函数y ＝x 2＋ax ＋3.(1)当x ∈R 时，y ≥a 恒成立，求a 的取值范围； (2)当a ∈[4,6]时，y ≥0恒成立，求x 的取值范围．解 (1)当x ∈R 时，x 2＋ax ＋3－a ≥0恒成立，则Δ＝a 2－4(3－a )≤0，即a 2＋4a －12≤0， 解得－6≤a ≤2，故a 的取值范围为{a |－6≤a ≤2}．(2)将y ＝xa ＋x 2＋3看作关于a 的一次函数，当a ∈[4,6]时，y ≥0恒成立，只需在a ＝4和a ＝6时y ≥0即可，即⎩⎪⎨⎪⎧x 2＋4x ＋3≥0，x 2＋6x ＋3≥0， 解得x ≤－3－6或x ≥－3＋6，故x 的取值范围是{x |x ≤－3－6或x ≥－3＋6}． 23.已知a R ∈，“2210ax ax +-<对x R ∀∈恒成立”的一个充要条件是（ ） A ．10a -<< B ．10a -<≤C ．10a -≤<D ．10a -≤≤【答案】B当0a =时，221=10ax ax +--<，对x R ∀∈恒成立；当0a ≠时，若2210ax ax +-<，对x R ∀∈恒成立，则必须有20(2)4(1)0a a a <⎧⎨-⨯-<⎩，解之得10a -<<， 综上，a 的取值范围为10a -<≤.故“2210ax ax +-<对x R ∀∈恒成立”的一个充要条件是10a -<≤，故选：B24.若命题“R x ∃∈，使得不等式22(3)0mx m x m +-+<”成立，则实数m 的取值集合是（ ） A ．(3,1)-- B ．(,1)(3,)-∞+∞C ．(,0]-∞D ．(3,1)(1,3)--【答案】B命题“R x ∃∈，使得不等式22(3)0mx m x m +-+<”成立， 当0m =时，不等式为30x -<，显然有解，成立；当0m <时，开口向下，必然R x ∃∈，使得不等式22(3)0mx m x m +-+<成立，； 当0m >，0∆>即222(3)40m m -->，解得29m >或21m <，所以01m <<或3m >． 综上可得1m <或3m >． 故选：B ．25.已知关于x 的不等式²4x x m -≥对任意(]0,3x ∈恒成立，则有（ ） A ．4m ≤- B ．3m ≥- C ．30m -≤< D ．40m -≤<【答案】A因为关于x 的不等式²4x x m -≥对任意(]0,3x ∈恒成立，所以2min (4)m x x ≤-， 令224(2)4y x x x =-=--，(]0,3x ∈，所以当2x =时，24y x x =-取得最小值4-， 所以4m ≤- 故选：A26.若关于x 的一元二次方程2240x ax -+=有两个实根，且一个实根小于1，另一个实根大于2，则实数a 的取值范围是________． 【答案】（52，＋∞）【详解】设2()24f x x ax =-+，由题意2Δ4160(1)1240(2)4440a f a f a ⎧=->⎪=-+<⎨⎪=-+<⎩，解得52a >，故答案为：5(,)2+∞．27.2022年11月23日，贵州宣布最后9个深度贫困县退出贫困县序列，这不仅标志着贵州省66个贫困县实现整体脱贫，这也标志着国务院扶贫办确定的全国832个贫困县全部脱贫摘帽，全国脱贫攻坚目标任务已经完成.在脱贫攻坚过程中，某地县乡村三级干部在帮扶走访中得知某贫困户的实际情况后，为他家量身定制了脱贫计划，政府无息贷款10万元给该农户种养羊，每万元可创造利润0.15万元.若进行技术指导，养羊的投资减少了x ()0x >万元，且每万元创造的利润变为原来的()10.25x +倍.现将养羊少投资的x 万元全部投资网店，进行农产品销售，则每万元创造的利润为()0.150.875a x -万元，其中0a >. （1）若进行技术指导后养羊的利润不低于原来养羊的利润，求x 的取值范围； （2）若网店销售的利润始终不高于技术指导后养羊的利润，求a 的最大值. 【答案】（1）x 的取值范围为06x <≤；（2）a 的最大值为6.5． 【详解】解：（1）由题意，得()()0.1510.25100.1510x x +-≥⨯，整理得260x x -≤，解得06x ≤≤，又0x >，故06x <≤． （2）由题意知网店销售的利润为()0.150.875a x x -万元，技术指导后，养羊的利润为()()0.1510.2510x x +-万元，则()()()0.150.8750.1510.2510a x x x x -≤+-恒成立，又010x <<，∴5101.58x a x≤++恒成立， 又51058x x +≥，当且仅当4x =时等号成立，∴0 6.5a <≤，即a 的最大值为6.5． 答：（1）x 的取值范围为06x <≤；（2）a 的最大值为6.5．对点练习一、单选题1．不等式21560x x +->的解集为（ ）A ．{1x x 或1}6x <- B ．116x x ⎧⎫-<<⎨⎬⎩⎭ C ．{1x x 或3}x <- D ．{}32x x -<<【答案】B【分析】解一元二次不等式，首先确保二次项系数为正，两边同时乘1-，再利用十字相乘法，可得答案， 【详解】法一：原不等式即为26510x x --<，即()()6110x x +-<，解得116x -<<，故原不等式的解集为116x x ⎧⎫-<<⎨⎬⎩⎭．法二：当2x =时，不等式不成立，排除A ，C ；当1x =时，不等式不成立，排除D ．故选：B ．2．已知正数x y ，满足 4x y +=，则xy 的最大值（ ）A ． 2B ．4C ． 6D ．8【答案】B【分析】直接使用基本不等式进行求解即可. 【详解】因为正数x y ，满足 4x y +=，所以有424x y xy =+≥⇒≤，当且仅当2x y ==时取等号， 故选：B3．已知二次函数2y ax bx c =++的图象如图所示，则不等式20ax bx c ++>的解集是（ ）A ．{}21x x -<<B ．{|2x x <-或1}x >C ．{}21x x -≤≤D ．{|2x x ≤-或1}x ≥ 【答案】A【分析】由二次函数与一元二次不等式关系，结合函数图象确定不等式解集. 【详解】由二次函数图象知：20ax bx c ++>有2<<1x -. 故选：A4．已知02x <<，则y =的最大值为（ ） A ．2B ．4C ．5D ．6【答案】A【分析】由基本不等式求解即可【详解】因为02x <<，所以可得240x ->，则()22422x x y +-==，当且仅当224xx =-，即x =y =的最大值为2．故选：A ．5．关于x 的不等式()210x a x a -++< 的解集中恰有1个整数，则实数a 的取值范围是（ ）A ．(][)1,02,3-B ．[)(]2,13,4--C ．[)(]2130,-⋃，D ．()()2134--⋃，， 【答案】C【分析】分类讨论一元二次不等式的解，根据解集中只有一个整数，即可求解.【详解】由()210x a x a -++<得()()10x x a --< ，若1a =，则不等式无解．若1a >，则不等式的解为1x a <<，此时要使不等式的解集中恰有1个整数解，则此时1个整数解为2x =，则23a <≤．若1a <，则不等式的解为1<<a x ，此时要使不等式的解集中恰有1个整数解，则此时1个整数解为0x =，则10a -≤<．综上，满足条件的a 的取值范围是[)(]2130,-⋃， 故选：C ．6．已知关于x 的不等式20ax bx c ++<的解集为{|1x x <-或4}x >，则下列说法正确的是（ ）A ．0a >B ．不等式20ax cx b ++>的解集为{|22x x <<C ．0a b c ++<D ．不等式0ax b +>的解集为{}|3x x >【答案】B【分析】根据解集形式确定选项A 错误；化不等式为2430,x x --<即可判断选项B 正确；设2()f x ax bx c =++，则(1)0f >，判断选项C 错误；解不等式可判断选项D 错误.【详解】解：因为关于x 的不等式20ax bx c ++<的解集为{|1x x <-或4}x >，所以a<0，所以选项A 错误； 由题得014,3,414a b b a c a a c a ⎧⎪<⎪⎪-+=-∴=-=-⎨⎪⎪-⨯=⎪⎩，所以20ax cx b ++>为2430,22x x x --<∴<所以选项B 正确；设2()f x ax bx c =++，则(1)0f a b c =++>，所以选项C 错误；不等式0ax b +>为30,3ax a x ->∴<，所以选项D 错误.故选：B二、多选题7．(多选)给出下列命题，其中正确的命题是( )A ．a >b ⇒ac 2>bc 2B ．a >|b |⇒a 2>b 2C ．a >b ⇒a 3>b 3D ．|a |>b ⇒a 2>b 2答案 BC解析 A 当c 2＝0时不成立；B 一定成立；C 当a >b 时，a 3－b 3＝(a －b )(a 2＋ab ＋b 2)＝(a －b )·⎣⎡⎦⎤⎝⎛⎭⎫a ＋b 22＋34b 2>0成立； D 当b <0时，不一定成立．如|2|>－3，但22<(－3)2.a b >，则222a b b >=，D 正确．故选：BD ．8．对任意两个实数,a b ，定义{},,min ,,a ab a b b a b ≤⎧=⎨>⎩，若()22f x x =-，()2g x x =，下列关于函数()()(){}min ,F x f x g x =的说法正确的是（ ）A ．函数()F x 是偶函数B ．方程()0F x =有三个解C ．函数()F x 在区间[1,1]-上单调递增D ．函数()F x 有4个单调区间【答案】ABD【分析】结合题意作出函数()()(){}min ,F x f x g x =的图象，进而数形结合求解即可.【详解】解：根据函数()22f x x =-与()2g x x =，，画出函数()()(){}min ,F x f x g x =的图象，如图．由图象可知，函数()()(){}min ,F x f x g x =关于y 轴对称，所以A 项正确；函数()F x 的图象与x 轴有三个交点，所以方程()0F x =有三个解，所以B 项正确；函数()F x 在(,1]-∞-上单调递增，在[1,0]-上单调递减，在[0,1]上单调递增，在[1,)+∞上单调递减，所以C 项错误，D 项正确．故选：ABD三、填空题9．函数()1311y x x x =+>-的最小值是_____【答案】3+【分析】利用基本不等式可求得原函数的最小值.【详解】因为1x >，则10x ->，所以()1313331y x x =-++≥=-，当且仅当()1311x x -=-，因为1x >，即当x =.所以函数()1311y x x x =+>-的最小值是3.故答案为：3+10．已知[]0,2a ∀∈时，不等式()231102ax a x a +++-<恒成立，则x 的取值范围为__________． 【答案】()2,1--【分析】由题意构造函数关于a 的函数()f a 2312x x a x ⎛⎫=+-++ ⎪⎝⎭，则可得(0)0(2)0f f <⎧⎨<⎩，从而可求出x 的取值范围.【详解】由题意，因为当[]0,2a ∈，不等式()231102ax a x a +++-<恒成立， 可转化为关于a 的函数()f a 2312x x a x ⎛⎫=+-++ ⎪⎝⎭，则()0f a <对任意[]0,2a ∈恒成立， 则满足2(0)10(2)22310f x f x x x =+<⎧⎨=+-++<⎩，解得2<<1x --， 即x 的取值范围为()2,1--．故答案为：()2,1--四、解答题11．（1）已知一元二次不等式20x px q ++<的解集为11|23x x ⎧⎫-<<⎨⎬⎩⎭，求不等式210qx px ++>的解集； （2）若不等式2(7)0x mx m -++>在实数集R 上恒成立，求m 的范围.【答案】（1）{|23}x x -<<；（2）22m -<+【分析】（1）先将不等式问题转化为方程问题求出,p q 的值，然后就可以解不等式了；（2）一元二次不等式恒成立，即考虑其判别式.【详解】（1）因为20x px q ++<的解集为11|23x x ⎧⎫-<<⎨⎬⎩⎭， 所以112x =-与213x =是方程20x px q ++=的两个实数根， 由根与系数的关系得11,3211,32p q ⎧-=-⎪⎪⎨⎛⎫⎪⨯-= ⎪⎪⎝⎭⎩解得1,61.6p q ⎧=⎪⎪⎨⎪=-⎪⎩不等式210qx px ++>， 即2111066x x -++>，整理得260x x --<，解得23x -<<.即不等式210qx px ++>的解集为{|23}x x -<<. （2）由题意可得，∆<0，即241(7)0-⨯⨯+<m m ，整理得24280m m --<，解得22m -<+12．为持续推进“改善农村人居环境，建设宜居美丽乡村”，某村委计划在该村广场旁一矩形空地进行绿化.如图所示，两块完全相同的长方形种植绿草坪，草坪周围（斜线部分）均摆满宽度相同的花，已知两块绿草坪的面积均为400平方米.（1）若矩形草坪的长比宽至少多9米，求草坪宽的最大值；（2）若草坪四周及中间的花坛宽度均为2米，求整个绿化面积的最小值.【答案】（1）最大值为16米；（2）最小值为(824+平方米.【分析】（1）设草坪的宽为x 米，长为y 米，依题意列出不等关系，求解即可；（2）表示400(26)(4)(26)(4)S x y x x=++=++，利用均值不等式，即得最小值. 【详解】（1）设草坪的宽为x 米，长为y 米，由面积均为400平方米，得400y x =. 因为矩形草坪的长比宽至少大9米，所以4009x x +，所以294000x x +-，解得2516x -. 又0x >，所以016x <.所以宽的最大值为16米.（2）记整个的绿化面积为S 平方米，由题意可得400300(26)(4)(26)(4)8248()(824S x y x x x x=++=++=+++（平方米）当且仅当x =.所以整个绿化面积的最小值为(824+平方米.。
