广东六校2018届高三英语下学期第三次联考试题附答案

2023届高三六校第三次联考英语命题：深圳实验学校高中部审题：深圳实验学校高中部第二部分阅读（共两节，满分50分）第一节（共15小题；每小题2.5分，满分37.5分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项。

ADear Tommy,•I am Ole Orvér,Finnair’s chief commercial officer.It’s my pleasure to warmly welcome you back to the skies with Finnair.I’d like to reflect on some of the developments that we hope you find exciting and helpful:chief commercial officer首席商务官；reflect on回想，回顾reflection映像,反射,反映;审慎的思考She decided on reflection to accept his offer after all.经过审慎的思考，她决定还是接受他的提议。

分段注解。

段落中加粗蓝色重要词组。

难句型划线。

This summer season you can fly with Finnair to over70European and five US destinations.In Asia,we serve eight cities,including Guangzhou and newly added Mumbai starting6August.We operate over 300daily flights and I’m excited about the addition of Seattle and Dallas to our US network.•Travel is recovering everywhere,and airports around the world are working hard to manage increased traffic volumes.It is a good idea to reserve some extra time at the airport before your flight.We are doing our very best together with our partners both at Helsinki and in our outstations to offer you a smooth travel experience during this popular travel season.•You are again able to offset flight carbon emissions,this time with a service that combines sustainable aviation fuel and certified climate projects.We at Finnair have ambitious emissions targets and our customers wish for a simple and transparent way to contribute.•Finnair Plus turned30in May.We are committed to developing the programme further to serve you in the best possible way.To make your flight bookings smoother,we recently upgraded the experience of booking award flights in the Finnair app.Finally,I’d like to thank you for your patience when we haven’t got things quite right.Wherever you’re travelling in the next few months,I hope it’s memorable.Thank you for flying Finnair.Kind Regards,Ole Orvér21.Which city is a new addition to the Finnair’s Asian network?A.Guangzhou.B.Mumbai.C.Seattle.D.Dallas.22.What is Finnair doing to help the environment?unching a climate project.B.Developing sustainable fuels.C.Donatingto a green programme. D.Offering a carbon offset service.23.Why does Finnair write this letter to Tommy?A.To express sincere gratitude.B.To introduce new routes.C.To apologize for bad service.D.To keep a regular customer.BA few years ago,I spared a couple of hours from busy academic learning to work in a video store on a daily basis.There was something in the elderly woman’s behavior that caught my eye.Although slow and unsure of step,the woman moved with deliberation,and there was no hesitation in her gestures.And she had a job to do.The elderly woman had walked into the store along with a younger woman who guessed was her daughter.The daughter was displaying a serious case of impatience,checking her watch every few seconds.The older woman detached from the younger one and began to tick through the DVDs on the nearest shelf.After the slightest hesitation,I walked over and asked if I could help her find something.The woman smiled up at me and showed me a title scrawled on a crumpled(皱巴巴的)piece of paper.The title was a bit difficult to understand.Clearly a person looking for it knew a little about movies,about quality.Rather than rushing off to locate the DVD for the woman,I asked her to walk with me so I could show her where she could find it.Something about her deliberate movements reminded me of my own mother, who’d departed this life last Christmas.As we walked along the back of the store,I narrated its floor plan. The woman seemed glad of the unrushed company and casual conversation.We found the movie,and I complimented(称赞)her on her choice.Then,reluctantly,I had to return the elderly woman to her keeper, who was still tapping her foot at the front of the store.I walked over to the younger woman.“Is that your mom?”I asked.She rolled her eyes and said,“Yeah.”There was annoyance in her reply,half sigh and half complaint.Still watching the mother,I said,“Mind some advice?”“Sure,”said the daughter.I smiled to show her I wasn’t criticizing.I answered her curious expression by saying,“When she’s gone,it’s the little moments that will come back to you.Moments like this.I used to let it slip.I know.”24.What does the underlined sentence“she had a job to do”in paragraph1mean?A.She was thinking of what to buy.B.She had a regular job in the store.C.She wanted to buy a DVD. D.She wanted to ask for help.25.Which word can best describe the daughter’s behaviors towards her mom?A.Impolite.B.Uncaring.C.Tolerant.D.Considerate.26.What can we learn about the author?A.She was ill-informed of quality movies.B.She was a full-time employee in the store.C.She regretted not accompanying her mom.D.She criticized the younger woman seriously.27.What is the best title for the text?A.Lend a helping hand to elderly peopleB.Mother is not what we can substituteC.The past cannot be called back againD.Always treasure the ones you love C Forests give us shade,quiet and one of the harder challenges in the fight against climate change.Even as we humans count on forests to soak up a good share of the carbon dioxide we produce,we are threatening their ability to do so.The climate change we are quickening could one day leave us with forests that emit more carbon than they absorb.Thankfully,there is a way out of this trap—but it involves striking a subtle balance.Helping forests flourish as valuable“carbon sinks”long into the future may require reducing their capacity to absorb carbon now.California is leading the way,as it does on so many climate efforts,in figuring out the details. The state’s proposed Forest Carbon Plan aims to double efforts to thin out young trees and clear brush in parts of the forest.This temporarily lowers carbon-carrying capacity.But the remaining trees draw a greater share of the available moisture,so they grow and thrive,restoring the forest’s capacity to pull carbon from the air.Healthy trees are also better able to be spared from insects.The landscape is rendered (致使)less easily burnable.The need for such planning is increasingly urgent.Already,since2010, drought and insects have killed over100million trees in California,most of them in2016alone,and wildfires have burned hundreds of thousands of acres.California plans to treat35,000acres of forest a year by2020,and60,000by2030–financed from the proceeds of the state’s emissions-permit auctions(拍卖).That’s only a small share of the total land area that could benefit,about half a million acres in all,so it will be vital to prioritize areas at greatest risk of fire or drought.State governments are well accustomed to managing forests,but traditionally they’ve focused on wildlife,watersheds(分水岭)and opportunities for recreation.Only recently have they come to see the vital part forests will have to play in storing carbon.California’s plan,which is expected to be finalized by the governor next year,should serve as a model.28.What does the author imply in paragraph1?A.Global climate change may get out of control.B.People may misunderstand global warming.C.Extreme weather conditions may arise.D.Forests may become a potential threat.29.What does the California’s Forest Carbon Plan intend to do?A.To expand the forest planting area.B.To reduce the density of some of its forests.C.To find more effective ways to kill insects.D.To restore its forests quickly after wildfires.30.What is essential to California’s plan according to Paragraph4?A.To handle the areas in serious danger first.B.To carry it out before the year of2020.C.To perfect the emissions-permit auctions.D.To obtain enough financial support.31.According to the author,California’s Plan is________.A.impracticalB.worthlessC.promisingD.appealingDTo combat the trap of putting a premium on(重视)being busy,Cal Newport,author of Deep Work:Rules for Focused Success in a Distracted World,recommends building a habit of“deep work”—the ability to focus without distraction.There are a number of approaches to mastering the art of deep work—be it lengthy retreats dedicated to a specific task,developing a daily ritual,or taking a“journalistic”approach to seizing moments of deepwork when you can throughout the day.Whichever approach,it is critical to determine your duration of focus time and stick to it.Another approach to getting more done in less time is to rethink how you prioritise your day—in particular how we craft our to-do lists.Tim Harford,author of Messy:The Power of Disorder to Transform Our Lives,points to a study in the early1980s that divided undergraduates into two groups:some were advised to set out monthly goals and study activities;others were told to plan activities and goals in much more detail,day by day.While the researchers assumed that the well-structured daily plans would be most effective when it came to the implementation of tasks,they were wrong:the detailed daily plans demotivated students. Harford argues that inevitable distractions often leave the daily to-do list ineffective,while leaving room for improvisation(即兴创作)in such a list can reap the best results.In order to make the most of our focus and energy,we also need to embrace downtime,or as Newport suggests,“be lazy.”Srini Pillay,an assistant professor of psychiatry at Harvard Medical School,believes this counter-intuitive connection between downtime and productivity may be due to the way our brains operate. When our brains switch between being focused and unfocused on a task,they tend to be more efficient.“What people don’t realize is that in order to complete these tasks they need to use both the focus and unfocus circuits in their brain,”says Pillay.32.What contributes most to mastering deep work?A.Keeping to focus length.B.Seizing the working chance.C.Carrying out specific plans.D.Ensuring the task procedures.33.What can we learn from Harford’s research?A.Distractions may contribute to efficiency.B.Daily schedules are beneficial to studying.C.Performances are barely driven by monthly goals.D.Detailed plans might not be as fruitful as expected.34.Pillay believes that our brains’shift between being focused and unfocused_______.A.is motivated by well-planned tasksB.can bring about greater productivityC.is targeted at better working balanceD.will greatly affect the way brains work35.What’s the main idea of the text?A.The approach to easing distractions.B.The priority to embracing downtime.C.Solutions to relieving the life tension.D.Keys to getting more done in less time.第二节（共5小题；每小题2.5分,满分12.5分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2020届高三六校第三次联考英语试题试卷共10页，卷面满分120分，折算成135分计入总分。

考试用时120分钟。

注意事项：1.答题前，先将自己的姓名、准考证号填写在答题卡上。

2.选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

3.非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

4.考试结束后，请将本试卷和答题卡一并上交。

第一部分阅读理解（共两节，满分40分）第一节(共15小题；每小题2分，满分30分)阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

AHow cool can libraries be in an era of iPods and Kindles? More than you think. Only if you know where to go.Central Library: Seattle, Washington, United StatesThe Central Library in Seattle is modern and fashionable and has tourists from around the world paying visits and taking tours. It was designed by Dutch architect Rem Koolhaas and American designer Joshua Ramus. Tours began in 2006, two years after its opening. The library holds various art exhibitions, book signings and other events, while visitors can stop by the Chocolate cart for a coffee and scan through the gift shop anytime.Trinity College Library: Dublin, IrelandThe Trinity College Library in Dublin is in Ireland, founded at the end of the 16th century by Queen Elizabeth I. It is the largest single library in the world, also known as the Long Room, which contains more than 200,000 of the library's oldest books. The Long Room houses one of the oldest harps（竖琴）in Ireland.Dating to the 15th century, the old harp is the model for the symbol foreland.Geisel Library, University of California: San Diego, United StatesAt first glance, it looks like a spaceship. Architect William Pereira, who helped design actual space launch facilities at Cape Canaveral in Houston, Texas, designed the library in 1970. It has been featured in sci-fi films, short stories and novels. The library hosts “Dinner in the Library,” which invites readers for cocktails, and also special speeches from distinguished authors．TU Delft Library: The NetherlandsThe library at the Delft University of Technology was constructed in 1997 and has more than 862,000 books, 16,000 magazine subscriptions and its own museum. The building itself exists beneath the ground, so you can't really see the actual Library. What makes it interesting is the roof, which is a grassy hill. The roof covers 5,500 square meters. And it has become one of the most striking and greenest structures in the area.1. Which of the four libraries has the longest history?A. Central LibraryB. Trinity College LibraryC. Geisel LibraryD. TU Delft Library2. What makes Geisel Library different from the others is that _____.A. a spaceship designer founded the libraryB. it has a roof of grassy hillC. famous writers often deliver speeches thereD. it is the largest single library in the world3. In Central Library, you can _____.A. drink cocktailsB. buy souvenirsC. create paintingsD. book eventsBThe cracked step four years ago was the start of it. That day, I awoke tired—the children were tiny and needing so much—and I had a golden afternoon of rest ahead, my mother stepping in to allow me to catch up on my sleep. I dropped them off and drove home—the sun shining and my bed signaling. As I was about to enter the house, I caught sight of a deep crack beneath my feet.Without thinking, I turned around, walked back to the car and drove to a DIY store. Four hours later, I had all the tools, mixed my own cement, filled in the crack and repaired the foundation. Perfect. As I stood up to take a photo of my handiwork, I realized that I was trembling. I’d forgotten my shot at a nice long nap, and my children were already on their way home. That sleep... that promise to self was broken, because I had focused, instead, on the crack in the step.Suddenly, everything started to hurt. My head, my throat, my back. I couldn’t stop shaking. Whatearned then is that when we break the promises we make to our bodies they will not be silenced. This is when we overwork and overthink to the point of breaking down. Ironically (讽刺地), for many of us, it is only when we have no choice— when we fall ill—that we learn to listen. For me, when that crack ended in a hospital stay which sent me to bed for two unmoving weeks when my body worked to clear two different infections, the lesson is ever present. I did it to myself—a whole twisted spin on DIY.Sadly it took another two ridiculous DIY projects to finally get through. The cracks will never be fully filled. Focus, then, on your own inner core, the feeding of light, fire and strength.4．What made the author so sleepy in the first place?A. Taking care of the kids.B. Asking her mother for help.C. Driving to her mother’s houseD. Dealing with DIY projects.5．How did the author feel as soon as she finished her repair work?A. RegretfulB. UpsetC. ProudD. Thankful6．What can be implied from Paragraph 3?A. Our health is ignored deliberately.B. Our body will respond to what we do.C. The author took her mother’s advice.D. The author was infected before the DIY.7．What is the author’s purpose in writing the text?A. To describe an unfortunate event.B. To show the danger of DIY.C. To stress the importance of sleep.D. To encourage focusing on oneself.CI used to think the whole purpose of life was pursuing happiness. Everyone said the path to happiness was success, so I searched for that ideal job, that perfect boyfriend, and that beautiful apartment. But instead of ever feeling fulfilled, I felt anxious and lost. Eventually. I decided to go to graduate school for positive psychology to learn what truly makes people happy.And what's the difference between being happy and having meaning in life? Many psychologists describe happiness as a state of comfort and ease, feeling good in the moment. Meaning, though, is deeper. The famous psychologist Martin Seligman says meaning comes from belonging to and serving something beyond yourself and from developing the best within you. Our culture is obsessed with happiness, but Icame to see that seeking meaning is the more fulfilling path.There are four pillars of a meaningful life.The first pillar is belonging. Belonging comes from being in relationships where you're valued for who you are and where you value others as well. For many people, belonging is the most essential source of meaning.For others, the key to meaning is the second pillar: purpose. Finding your purpose is not the same thing as finding that job that makes you happy. A doctor told me her purpose is healing sick people. Many parents tell me, “My purpose is raising my children.” The key to purpose is using your strengths to serve others. Without something worthwhile to do, people flounder, thus losing the aim of life.The third pillar of meaning is also about stepping beyond yourself, but in a completely different way: transcendence (超然). Transcendent experiences can change you. Transcendent states are those rare moments when you're lifted above the hustle and bustle of daily life, your sense of self fades away, and you feel connected to a high er reality. For me, I’m a writer, and it happens through writing. Sometimes I get so in the zone that I lose all sense of time and place.The fourth pillar is storytelling, the story you tell yourself about yourself. Creating a narrative from the events of your life brings clarity. It helps you understand how you became you. But we don’t always realize that we're the authors of our stories and can change the way we’re telling them. Your life isn't just a list of events. You can edit, interpret and retell your story, even as you're constrained by the facts.That’s the power of meaning. Happiness comes and goes. But when life is really good and when things are really bad, having meaning gives you something to hold on to.8. What can we know from the first two paragraphs？A. Life might be fulfilled by landing ideal jobs．B. Life dilemma is challenging for us to get out of．C. Meaning is highly valued in our culture．D. Happiness is what most people try to achieve．9. Which word is the closest to the underlined word?A. ConfusedB. DistractedC. DisappointedD. Saddened10. Which pillar can describe an artist obsessed with her work despite repeated failures?A. BelongingB. PurposeC. TranscendenceD. Storytelling11. The passage aims to tell us that _______________．A. meaning is superior to happinessB. meaning is the way to successC. chasing meaning can make people happyD. meaning has deeper psychological significanceDIt often happens that a number of applicants with almost identical qualifications and experience all apply for the same position. In their educational background, special skills and work experience, there is little, if anything, to choose between half a dozen candidates. How then does the employer make a choice? Usually on the basis of an interview.There are many arguments about the interview as a selection procedure. One argument is that it gives rise to a wholly subjective decision. As often as not, employers do not choose the best candidate, but the one who makes a good first impression on them. Some employers, of course, reply to this argument by saying that they have become so experienced in interviewing staff that they are able to make a sound assessment of each candidate’s likely perfor mance. Unfortunately, both for the employers and applicants, there are many people of great ability who simply do not interview well. There are also, of course, people who interview extremely well, but are later found to be very unsatisfactory employees.Those in favour of the interview insist that the well-structured procedure is valid in assessing a candidate’s ability, an essential guarantee for the future job. They also argue that an employer is concerned not only with a candidate’s ability, but with th e suitability of his or her personality for the particular work situation. Many employers, for example, will overlook occasional inefficiencies from their secretary so long as she has a pleasant personality. Perhaps the real purpose of an interview is not to assess the assessable aspects of each candidate but to make a guess at the more intangible things, such as personality and social ability.Today, interview is still a common section of the entire selection procedure, though different employers have different standards for competence. Generally speaking, candidates who interview well tend to be quietly confident, but never boastful; direct and straight-forward in their questions and answers; cheerful and friendly, but never over-familiar; and sincerely enthusiastic and optimistic. Candidates who interview badly tend to be at either end of the spectrum of human behaviour. They are either very shy or over-confident. They show either a lack of enthusiasm or an excess of it. They either talk too little or never stop talking. They are either over-polite or rudely abrupt.12. According to the passage, which of the following statements is TRUE?A. Employers are experienced in assessing the interviewees’ performance.B. Interview is not always recognized as a sensible way to choose employees.C. The interview helps the employers to pick the desired employees.D. The remarkable candidates often distinguish themselves in an interview.13. Which may not be considered in an interview?A. PersonalityB. Communication skillsC. BackgroundD. Capability14. What is the author’s attitude towards the interview as a selection procedure?A. SupportiveB. NegativeC. ObjectiveD. Unconcerned15. The last paragraph indicates _________________.A. a link between success in interview and characterB. connections between work abilities and characterC. differences in interview experienceD. differences in personal behaviour第二节(共5小题；每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

广东五校2018届高三年级联考试题英语本试卷共10页，三大题，满分135分。

考试用时120分钟。

注意事项：1.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上，并用2B铅笔在答题卡上的相应位置填涂考生号。

2.选择题每小题选出答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。

3.非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原先的答案，然后再写上新的答案；不准使用铅笔和涂改液。

不按以上要求作答的答案无效。

Ⅰ 语言知识及应用(共两节，满分45分)第一节完形填空(共15小题；每小题2分，满分30分) 阅读下面短文，掌握其大意，然后从1~15各题所给的A、B、C和D项中，选出最佳选项，并在答题卡上将该项涂黑。

What are the basic elements of good manners? Certainlya strong sense of justice is one; modesty is often nothing more than a highly developed sense of fair play. A friendof mine once told me about a time he was 1 along a narrow, unpaved(未铺柏油的) mountain road. Ahead was another car that produced clouds of 2 , and it was a long way to the nearest 3 highway. Suddenly, at a 4 place, the car ahead pulled off the road. 5 that its owner might have engine trouble, my friend stopped and askedif anything was wrong. “No,” said the other driver, “but you’ve tolerated my dust this far; I’ll 6 with yours the rest of the way.”Another element of courtesy is considerate, a 7 that enables a person to see into the mind or heart of someone else, to understand the pain or 8 there and to do something to minimize it. A man 9 alone in a restaurant was trying to open the cap of a beer bottle, buthe couldn’t do it because of badly injured 10 . He asked a young busboy to help him. The boy took the bottle, turned his back 11 and loosened the cap without difficulty. Then he 12 it again. Turning back to the man, he 13 to make great efforts to open the bottlewithout success. 14 he took it into the kitchen and returned shortly, saying that he had managed to loosen it ----but only with a pair of pliers(钳子).Yet another element of politeness is the ability to treat all people 15 , in spite of all status or importance. Even when you have doubts about some people, act as if they are worthy of your best manners. You may also be astonished to find out what they really are.Courtesy is the key to a happier world.1. A. walking B. running C. riding D. driving2. A. dust B. smoke C. gas D. pollution3. A. opened B. used C. paved D. repaired4. A. smaller B. wider C. narrower D. bigger5. A. Hoping B. Seeing C.RecognizingD. Thinking6. A. do away B. catch up C. put up D. go on7. A. tool B. way C. behavior D. quality8. A.unhappinessB. joyC. feelingD. thought9. A. dining B. singing C. working D. sitting10. A. legs B. arms C. fingers D. ears11. A. hurriedly B. happilyC.momentarilyD. secretly12. A. loosened B. took C. hidD.tightened13. A. seemed B.pretendedC. managedD. tried14. A. Luckily B. Finally C. Happily D. Sadly15. A. alike B. kindly C. warmly D. nicely第二节语法填空 (共10小题；每小题1. 5分，满分15分) 阅读下面短文，按照句子结构的语法性和上下文连贯的要求，在空格处填入一个适当的词或使用括号中词语的正确形式填空，并将答案填写在答卷标号为16—25的相应位置上。

绝密★启用前2018届广东省六校第三次联考文科数学注意事项：1．答题前，考生务必将自己的姓名、准考证号、座位号、学校、班级等考生信息填写在答题卡上。

2．作答选择题时，选出每个小题答案后，用2B 铅笔把答题卡上对应题目的答案信息点涂黑。

如需改动，用橡皮擦干净后，再选涂其它答案，写在本试卷上无效。

3．非选择题必须用黑色字迹签字笔作答，答案必须写在答题卡各题指定的位置上。

4．考试结束后，将本试卷和答题卡一并交回。

一、选择题：本题共12小题，每小题5分，共60分. 在每题给出的四个选项中，只有一项符合题目要求. 1.函数()ln(1)f x x =++的定义域为（ ） A ．(2,)+∞ B ．(1,2)(2,)-+∞ C ．(1,2)- D ．(]1,2-2.如果复数ibi212+-(其中i 为虚数单位，b 为实数)的实部和虚部互为相反数，那么b 等于( ) A ．6- B ．32 C ．32- D ．23.高考结束后，同学聚会上，某同学从《爱你一万年》，《非你莫属》，《两只老虎》，《单身情歌》四首歌中选出两首歌进行表演，则《爱你一万年》未选取的概率为（ ）A ．13B ．12 C ．23 D ．564.圆22(2)4x y -+=关于直线y x =对称的圆的方程是（ ）A ．22((1)4x y +-=B ．22((4x y +=C ．22(2)4x y +-=D ．22(1)(4x y -+=5．某几何体的三视图如图所示，且该几何体的体积是3，则正视图中的x 的值是( )A ．2 B.29 C. 23D ．3 6.已知sin()3cos()sin()2πθπθθ++-=-，则2sin cos cos θθθ+=（ ）A ．15B ．25C ．35D7.实数x 、y 满足000x y x y c ≤⎧⎪≤⎨⎪+-≥⎩，且x y -的最大值不小于1，则实数c 的取值范围是( )A ．1c ≤-B ．1c ≥- C．c ≤．c ≥8.函数x x x f cos )(=的导函数)(x f '在区间],[ππ-上的图像大致是（ ）A. B. C. D.9.三棱锥ABC P -中，ABC PA 平面⊥且2=PA ，ABC ∆是边长为3的等边三角形，则该三棱锥外接球的表面积为( )A.34πB ．π4C ．π8D ．π20 10.自主招生联盟成行于2009年清华大学等五校联考，主要包括“北约”联盟，“华约”联盟，“卓越”联盟和“京派”联盟．在调查某高中学校高三学生自主招生报考的情况，得到如下结果： ①报考“北约”联盟的学生，都没报考“华约”联盟②报考“华约”联盟的学生，也报考了“京派”联盟③报考“卓越”联盟的学生，都没报考“京派”联盟④不报考“卓越”联盟的学生，就报考“华约”联盟根据上述调查结果，下列结论错误的是（ ）DA 1BAA ．没有同时报考“华约” 和“卓越”联盟的学生B ．报考“华约”和“京派”联盟的考生一样多C ．报考“北约” 联盟的考生也报考了“卓越”联盟D ．报考“京派” 联盟的考生也报考了“北约”联盟11.设120172016,log log a b c ===，则,,a b c 的大小关系为（ ）A ．a b c >>B ．a c b >> C. b a c >> D ．c b a >>12. 已知双曲线E ： 22x a﹣22y b =1（0,0>>b a ），点F 为E 的左焦点，点P 为E 上位于第一象限内的点，P 关于原点的对称点为Q ，且满足FQ 3PF =，若b =OP ，则E 的离心率为（ ）A.二．填空题：本题共4小题，每小题5分。

广东省珠海等六校2018届高三第三次联考数学文试题含答案2018届广东省六校第三次联考文科数学 第Ⅰ卷（共60分）一、选择题：本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中，只有一项是符合题目要求的. 1.函数())1ln(21++=-=x xx f 的定义域为( )A ．()∞+，2 B ．()()+∞-,22,1Y C ．()2,1- D ．(]2,1-2.如果复数ibi212+-（其中i 为虚数单位，b 为实数）的实部和虚部互为相反数，那么b 等于( )A ．-6B ．32C ．32- D ．23.高考结束后，同学聚会上，某同学从《爱你一万年》，《非你莫属》，《两只老虎》，《单身情歌》四首歌中选出两首歌进行表演，则《爱你一万年》未选取的概率为( ) A ．31 B ．21 C ．32 D ．654.圆()4222=+-y x 关于直线x y 33=对称的圆的方程是( ) A ．()()41322=-+-y x B ．()()42222=-+-y xC. ()4222=-+y xD ．()()43122=-+-y x5.某几何体的三视图如图所示，且该几何体的体积是3，则正视图中的x 的值是( )A ．2B ．29 C. 23D ．3 6.已知()()θ-=θ-π+⎪⎭⎫⎝⎛θ+πsin cos 32sin ，则=θ+θθ2cos cos sin ( ) A ．51 B ．52 C. 53D ．557.实数y x 、满足⎪⎩⎪⎨⎧≥-+≤000c y x y x π，且y x -的最大值不小于1，则实数c 的取值范围是( ) A ．1-≤c B ．1-≥c C.2-≤c D ．2-≥c8.函数()x x x f cos =的导函数)('x f 在区间[]ππ-,上的图象大致是( )A ．B ．C. D ．9.三棱锥ABC P -中，⊥PA 平面ABC 且ABC PA ∆=,2是边长为3的等边三角形，则该三棱锥外接球的表面，积为( )A ．34πB ．π4 C.π8 D ．π20 10.自主招生联盟成行于2009年清华大学等五校联考，主要包括“北约”联盟，“华约”联盟，“卓越”联盟和“京派”联盟，在调查某高中学校高三学生自主招生报考的情况，得到如下结果：①报考“北约”联盟的学生，都没报考“华约”联盟②报考“华约”联盟的学生，也报考了“京派”联盟 ③报考“卓越”联盟的学生，都没报考“京派”联盟斯不报考“卓越”联盟的学生，就报考“华约”联盟 根据上述调查结果，下列结论错误的是( )A ．没有同时报考“华约”和“卓越”联盟的学生B ．报考“华约”和“京派”联盟的考生一样多 C.报考“北约”联盟的考生也报考了“卓越”联盟 D ．报考“京派”联盟的考生也报考了“北约”联盟 11.设201620172017201620171log ,log ,2016===c b a，则c b a ,,的大小关系为( )A ．c b a >>B ．b c a >> C. c a b >> D ．a b c >>12.已知双曲线()0,01:2222>>=-b a by a x E ，点F 为E 的左焦点，点P 为E 上位于第一象限内的点，P 关于原点的对称点为Q ，且满足FQ PF 3=，若b OP =，则E 的离心率为( )A ．2 B ．3 C. 2 D ．5第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上） 13.若向量b a ,()⊥-==,2,2，则向量与的夹角等于 ．14.执行如图所示的程序框图，则输出S 的结果为 ．15.已知函数()x f y =在点()()22f ，处的切线方程为12-=x y ，则函数())(2x f x x g +=在点()()22g ，处的切线方程为 ． 16.已知平面四边形ABCD 为凸四边形（凸四边形即任取平面四边形一边所在直线，其余各边均在此直线的同侧），且3,5,4,2====DA CD BC AB ，则平面四边形ABCD 面积的最大值为 ．三、解答题 （本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤.） 17.已知数列{}n a 的前n 项和为n S ，且满足()*∈-=N n n n S n ,22(1)求数列{}n a 的通项公式；(2)设()(),11222⎪⎩⎪⎨⎧--+n n b n a a b n()()()*∈=-=N k k n k n 212，求数列{}n b 的前n 2项和n T 2. 18. 如图，在三棱柱111C B A ABC -中，侧棱⊥1AA 底面ABC ,D BC AB ,⊥为AC 的中点，3,21===BC AB A A .(1)求证：//1AB 平面D BC 1； (2)求四棱锥D C AA B 11-的体积.19.随着社会的发展，终身学习成为必要，工人知识要更新，学习培训必不可少，现某工厂有工人1000名，其中250名工人参加短期培训（称为A 类工人），另外750名工人参加过长期培训（称为B 类工人），从该工厂的工人中共抽查了100名工人，调查他们的生产能力（此处生产能力指一天加工的零件数）得到A 类工人生产能力的茎叶图（左图），B类工人生产能力的频率分布直方图（右图）.(1)问A 类、B 类工人各抽查了多少工人，并求出直方图中的x ；(2)求A 类工人生产能力的中位数，并估计B 类工人生产能力的平均数（同一组中的数据用该组区间的中点值作代表）；(3)若规定生产能力在[]150130，内为能力优秀，由以上统计数据在答题卡上完成下面的22⨯列联表，并判断是否可以在犯错误概率不超过0.1%的前提下，认为生产能力与培训时间长短有关.能力与培训时间列联表参考数据：参考公式：))()()(()(22d b c a d c b a bc ad n K ++++-=，其中d c b a n +++=.20. 已知动点M 到定点()0,1F的距离比M 到定直线2-=x 的距离小1.(1)求点M 的轨迹C 的方程；(2)过点F 任意作互相垂直的两条直线1l 和2l ，分别交曲线C 于点B A ,和N K ,.设线段KN AB ,的中点分别为Q P ,，求证：直线PQ 恒过一个定点.21. 已知函数())1(ln 122+-++-=x x a x x x f （其中R a ∈,且a 为常数）.(1)若对于任意的()+∞∈,1x ，都有()0>x f 成立，求a 的取值范围；(2)在(Ⅰ)的条件下，若方程()01=++a x f 在(]2,0∈x 上有且只有一个实根，求a 的取值范围.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分. 22.选修4-4：坐标系与参数方程在直角坐标系xOy 中，曲线1C 的参数方程为t ty t x (542532⎪⎩⎪⎨⎧+-=-为参数）.以坐标原点为极点，以x 轴正半轴为极轴，建立极坐标系，曲线2C 的极坐标方程为θ=θρtan cos .(1) 求曲线1C 的普通方程和曲线2C 的直角坐标方程； (2) 若1C 与2C 交于B A ,两点，点P 的极坐标为⎪⎭⎫ ⎝⎛π-422，，求PB PA 11+的值.23.选修4-5：不等式选讲 设函数()()0122>++-=a x a x x f ，()2+=x x g .(Ⅰ)当1=a 时，求不等式()()x g x f ≤的解集；(Ⅱ)若()()x g x f ≥恒成立，求实数a 的取值范围.2018 届广东省六校第三次联考 文科数学参考答案与评分标准一、选择题1-5: CCBDD 6-10:CAACD 11、12：AB 二、填空题 13.4π14. 30 15. 056=--y x 16.302三、解答题17.解：(1)当2≥n 时，()()[]n n n n n S S a n n n2211222221-=-----=-=-()21≥-=n n a n ，当1=n 时，由21112-=S 得01=a ，显然当1=n 时上式也适合， ∴n a n-=1(2)∵()()()211221122+-=+=--+n n n n a a n n ，∴()()n n nb b b b b b T 24212312+++++++=-ΛΛ()⎥⎦⎤⎢⎣⎡⎪⎭⎫ ⎝⎛+-++⎪⎭⎫ ⎝⎛-+⎪⎭⎫ ⎝⎛-++++=--22121614141212222220n n n ΛΛ22121411411+-+-⎪⎭⎫⎝⎛-n n2214134611+-⎪⎭⎫ ⎝⎛⋅-=n n. 18.解：(1)证明：连接C B 1，设C B 1与1BC 相较于点O ，连接OD ，∵四边形11B BCC 是平行四边形，∴点O 为C B 1的中点. ∵D 为AC 的中点，∴OD 为C AB 1∆的中位线， ∴1//AB OD .∵⊂OD 平面D BC 1，⊄1AB 平面D BC 1,∴//1AB 平面D BC 1.(2)解法1:∵⊥1AA 平面⊂1,AA ABC 平面C C AA 11，∴平面⊥ABC 平面C C AA 11，且平面I ABC 平面AC C C AA =11.作AC BE ⊥,垂足为E ，则⊥BE 平面C C AA 11，∵3,21===BC BB AB ,在ABC Rt ∆中，139422=+=+=BC AB AC ,136=•=AC BC AB BE ,∴四棱锥D C AA B 11-的体积()BE AA AD C A V ••+⨯=111213131362132361=⨯⨯⨯=. ∴四棱锥D C AA B 11-的体积为3.解法2：⊥1AA 平面⊂AB ABC ,平面ABC ,∴AB AA ⊥1.∵11//AA BB ,∴AB BB ⊥1.∵DB BB BC BC AB =⊥1,I ,∴⊥AB 平面C C BB 11.取BC 的中点E ,连接DE ,则AB DE AB DE 21,//=,∴⊥DE 平面C C BB 11. 三棱柱111C B A ABC -的体积为6211=•••=AA BC AB V ,则2312131,16121311111111111==•••⨯===•••⨯=--V B A BB C B V V DE CC BC V C BB A BCC D . 而D C AA B C BB A BCC D V V V V111111---++=,∴D C AA B V 11216-++=. ∴311=-D C AA B V .∴四棱锥D C AA B 11-的体积为3.19.解：（1）由茎叶图知A 类工人中抽查人数为25名,∴B 类工人中应抽查7525100=-名.由频率分布直方图得()1=10x )+0.048+0.02+0.008⨯，得024.0=x .(2)由茎叶图知A 类工人生产能力的中位数为 122由(1)及频率分布直方图，估计B 类工人生产能力的平均数为133.8100.024********.013510020.012510008.0115=⨯⨯=⨯⨯+⨯⨯+⨯⨯=θ由上表得()828.10733.126238752575010062387525541721810022>≈⨯⨯⨯⨯=⨯⨯⨯⨯-⨯⨯=k因此,可以在犯错误概率不超过 0.1%的前提下,认为生产能力与培训时间长短有关. 20.解：(1)由题意可知：动点M 到定点()0,1F 的距离等于M 到定直线1-=x 的距离，根据抛物线的定义可知，点M 的轨迹C 是抛物线. ∵2=p ，∴ 抛物线方程为：x y 42=(2)设B A ,两点坐标分别为()()2211,,,y x y x ，则点P 的坐标为⎪⎭⎫⎝⎛++2,22121y y x x .由题意可设直线1l 的方程为)0)(1(≠-=k x k y ，由()⎩⎨⎧-==142x k y x y 得0)42(2222=++-k x k x k . ()016164422422>+=-+=∆k k k .因为直线1l 与曲线C 于B A ,两点，所以()kx x k y y k x x 42,422121221=-+=++=+， 所以点P 的坐标为⎪⎭⎫ ⎝⎛+k k 2,212. 由题知，直线2l 的斜率为k1-，同理可得点Q 的坐标为()k k 2,212-+. 当1±≠k 时，有222121k k +≠+，此时直线PQ 的斜率2221212122k k k kkk k PQ -=--++=.所以，直线PQ 的方程为()222112k x kk k y ---=+， 整理得()032=--+y k x yk .于是，直线PQ 恒过定点()0,3E ；当1±=k时，直线PQ 的方程为3=x ，也过点()0,3E .综上所述，直线PQ 恒过定点()0,3E .21.解(1)()()xa x x x a x x f --=-+-=21)11()1(2)(' 当2≤a 时，∵0)('>x f 对于()+∞∈,1x 恒成立，∴)(x f 在()∞+，1上单调递增 ∴()0)1(=>f x f ，此时命题成立；当2>a时，∵)(x f 在⎪⎭⎫ ⎝⎛21a ，上单调递减,在⎪⎭⎫ ⎝⎛+∞,2a 上单调递增，∴当⎪⎭⎫⎝⎛∈2,1a x 时，有0)1()(=<f x f .这与题设矛盾. 故a 的取值范围是(]2,∞-(2)依题意(]2,∞-∈a ，设1)()(++=a x f x g .原题即为若)(x g 在(]20，上有且只有一个零点,求a 的取值范围.显然函数()x g与()x f 的单调性是一致的.①当0≤a 时,因为函数)(x g 在区间()10，上递减，(]21，上递增，所以()x g在(]20，上的最小值为1)1(+=a g ，由于011112222>+-⎪⎭⎫⎝⎛-=⎪⎭⎫ ⎝⎛ea e e g ，要使()x g 在(]20，上有且只有一个零点, 需满足()01=g 或()02<g ，解得1-=a 或2ln 2-<a ； ②当2=a 时，因为函数()x g 在(]20，上单调递增，0 且()02ln 22)2(,0241484>+=<--=-g e e e g，所以此时()x g在(]20，上有且只有一个零点；③当20<<a 时,因为函数()x g在⎪⎭⎫ ⎝⎛20a ，上单调递增,在⎪⎭⎫ ⎝⎛1,2a 上单调递减,在 (]21，上单调递增, 又因为()011>+=a g，所以当⎪⎭⎫⎝⎛∈2,2a x 时，总有()0>x g ，∵2122+<<+a eaa ∴022ln )2(22222222<⎪⎪⎭⎫ ⎝⎛+++⎥⎦⎤⎢⎣⎡+-=⎪⎪⎭⎫ ⎝⎛++++a e a a e e e g a a a a a a a a ， 所以()x g在⎪⎭⎫ ⎝⎛20a ，上必有零点,又因为()x g 在⎪⎭⎫⎝⎛20a ，上单调递增,从而当20<<a 时，()x g在(]20，上有且只有一个零点综上所述,当20≤<a 或2ln 2-<a 或1-=a 时， 方程01)(=++a x f 在(]2,0∈x 上有且只有一个实根.22.解：(1)曲线1C 的普通方程为0234=-+y x ； 曲线2C 的直角坐标方程为:2x y =.(2)1C 的参数方程的标准形式为⎪⎩⎪⎨⎧+-=-=ty t x 542532（t 为参数）代入2x y =得01508092=+-t t ，设21,t t 是B A 、对应的参数,则0350,9802121>==+t t t t . ∴1581PA 12121=+=⋅+=+t t t t PB PA PB PA PB . 23.解：(1)当1=a 时，21212+≤++-x x x所以⎪⎩⎪⎨⎧+≤--≤2421x x x 或⎪⎩⎪⎨⎧+≤<<-222121x x 或⎪⎩⎪⎨⎧+≤≤2421x x x 解得∅∈x 或210<≤x 或3221≤≤x 综上，不等式的解集为⎥⎦⎤⎢⎣⎡320，. (2)2122+≥++-x x a x ，转化为02122≥--++-x x a x 令()2122--++-=x x a x x h ，⎪⎪⎪⎩⎪⎪⎪⎨⎧≥--<<--+--≤-+-=2,13221,121,35)(ax a x a x a x x a x x h ， 0>a 时，12)(min -=a x h ， 令012≥-a ，得2≥a .。

绝密★启用前2018届广东省六校第三次联考理科数学满分：150分 考试时间：120分钟命题学校：深圳实验学校注意事项：1．答卷前，考生务必将自己的姓名、考生号、考场号和座位号填写在答题卡上．用2B铅笔将试卷类型（B ）填涂在答题卡相应位置上。

将条形码横贴在答题卡右上角“条形码粘贴处”．2．作答选择题时，选出每小题答案后，用2B 铅笔在答题卡上对应题目选项的答案信息点涂黑；如需要改动，用橡皮擦干净后，再选涂其他答案．答案不能答在试卷上． 3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液．不按以上要求作答无效．4．考生必须保证答题卡的整洁．考试结束后，将试卷和答题卡一并交回．一、选择题：本题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．已知集合{(,)|,M x y x y =为实数，且222}x y +=，{(,)|,N x y x y =为实数，且2}x y +=，则M N 的元素个数为A ．0B ．1C ．2D ．3 2．设等差数列{}n a 的前n 项和为n S ，若39S =，530S =，则789a a a ++=A ．63B ．45C ．36D ．273．若变量满足约束条件，则的取值范围是A ．B ．C ．D ．4．函数1ln sin 1ln xy xx-=⋅+的部分图象大致为,x y 0210430y x y x y ≤⎧⎪--≥⎨⎪--≤⎩35z x y =+[)3,+∞[]8,3-(],9-∞[]8,9-A ．B ．C ．D ．5．设函数())f x ϕ=+，其中常数ϕ满足0πϕ-<<．若函数()()(g x f x f x '=+（其中()f x '是函数()f xA ．3π-B ．56π-C ．6π-D ．23π-6．执行右面的程序框图，如果输入的a ，b ，k 分别为1，2输出的158M =，那么，判断框中应填入的条件为 A ．n k < B ．n k ≥ C ．1n k <+ D ．1n k ≤+7．已知02012(1i)(2i)(2i)(2i)(2i)n nn b b b b -+=-++-++-+++-+ （2n ≥，i 为虚数单位），又数列{}n a 满足：当1n =时，12a =-；当2n ≥，n a 为22(2i)b -+的虚部．若数列2{}n a -的前n 项和为n S ，则2018S =A ．20172018B ．20182017C ．40352018D ．403320178．如图，在同一个平面内，三个单位向量OA ，OB ，OC满足条件：OA 与OC 的夹角为α，且tan α=7，OB 与OC与的夹角为45°． 若OC mOA nOB =+（,m n R ∈），则m n +的值为A ．3B．．29．四面体ABC S -中，三组对棱的长分别相等，依次为5，4，x ，则x 的取值范围是A ．)41,2(B ．)9,3(C ．)41,3(D ．)9,2(10．从2个不同的红球、2个不同的黄球、2个不同的蓝球共六个球中任取2个，放入红、黄、蓝色的三个袋子中，每个袋子至多放入一个球，且球色与袋色不同，那么不同的放法有 A ．42种B ．36种 C ．72种 D ．46种11．已知点F 为双曲线2222:1(,0)x y E a b a b -=>的右焦点，直线(0)y kx k =>与E 交于M ，N 两点，若MF NF ⊥，设MNF β∠=，且[,]126ππβ∈，则该双曲线的离心率的取值范围是A．B．1] C． D．1] 12．已知()()2211,,y x B y x A 、是函数x x x f ln )(=与2)(x kx g =图象的两个不同的交点，则()21x x f +的取值范围是A ．2ln ,2e e⎛⎫+∞ ⎪⎝⎭ B ．⎪⎭⎫ ⎝⎛e e e 1,2ln 2 C ．⎪⎭⎫ ⎝⎛e 1,0 D ．⎪⎭⎫ ⎝⎛0,2ln 2e e二、填空题：本题共4小题，每小题5分，共20分．13．已知函数()y f x =是定义在R 上的奇函数，则311[(2)]f x dx x -+=⎰．14．已知函数()sin cos f x a x b x =-，若()()44f x f x ππ-=+，则函数13ax b y ++=恒过定点_____．15．已知几何体的三视图如图所示，其中俯视图为一正方形，则该几何体的表面积为．16．若函数()f x 的图象上存在不同的两点11(,)A x y ，22(,)B x y ，其中1122,,,x y x y 使得1212x x y y +的最大值为0，则称函数()f x 是“柯西函数”．给出下列函数：①()ln (03)f x x x =<<； ②1()(0)f x x x x =+>；③()f x =④()f x =. 其中是“柯西函数”的为（填上所有正确答案的序号）三、解答题：共70分．解答应写出文字说明、证明过程或演算步骤．第17 21题为必考题，每个试题考生都必须作答．第22、23题为选考题，考生根据要求作答． （一）必考题：共60分. 17.（12分）设数列{}n a 的前n 项和为n S ，数列{}n S 的前n 项和为n T ，满足2*2n n T S n n N =-∈，．（Ⅰ）求123,,a a a 的值；（Ⅱ）求数列{}n a 的通项公式．18.（12分）某小店每天以每份5元的价格从食品厂购进若干份食品，然后以每份10元的价格出售．如果当天卖不完，剩下的食品还可以每份1元的价格退回食品厂处理． （Ⅰ）若小店一天购进16份，求当天的利润y (单位：元)关于当天需求量n (单位：份，N n ∈)的函数解析式；（Ⅱ）小店记录了100天这种食品的日需求量(单位：份)，整理得下表：以100天记录的各需求量的频率作为各需求量发生的概率．（1）小店一天购进16份这种食品，X 表示当天的利润（单位：元），求X 的分布列及数学期望；（2）以小店当天利润的期望值为决策依据，你认为一天应购进食品16份还是17份？19.（12分）如图，在四棱锥P ABCD -中，ABCD 是平行四边形，1AB BC ==，120BAD ∠=，PB PC ==，2PA =，E ，F 分别是AD ，PD 的中点．（Ⅰ）证明：平面EFC ⊥平面PBC ； （Ⅱ）求二面角A BC P --的余弦值．20.（12分）已知椭圆2222:1(0)x y C a b a b +=>>的离心率为，1A 、2A 分别为椭圆C 的左、右顶点，点(2,1)P -满足121PA PA ⋅=．（Ⅰ）求椭圆C 的方程；（Ⅱ）设直线l 经过点P 且与C 交于不同的两点M 、N ，试问：在x 轴上是否存在点Q ，D CPABEF使得直线QM 与直线QN 的斜率的和为定值？若存在，请求出点Q 的坐标及定值；若不存在，请说明理由．21.（12分）已知函数2()(1)e 2x a f x x x=--，其中a ∈R ．（Ⅰ）函数()f x 的图象能否与x 轴相切？若能，求出实数a ，若不能，请说明理由；（Ⅱ）求最大的整数a ，使得对任意12,(0,)x x ∈∈+∞R ，不等式1212()()2f x x f x x x+-->-恒成立．（二）选考题：共10分.请考生在第22、23题中任选一题作答.如果多做，则按所做的第一题计分.22.[选修4-4：坐标系与参数方程]（10分）已知直线l 的参数方程为cos sin x m t y t αα=+⎧⎨=⎩(t 为参数，0)απ≤<，以坐标原点为极点，轴的正半轴为极轴建立极坐标系，曲线C 的极坐标方程为4cos ρθ=，射线()44ππθϕϕ=-<<，4πθϕ=+，4πθϕ=-分别与曲线C 交于A B C 、、三点(不包括极点O )．（Ⅰ）求证：OB OC OA+=；（Ⅱ）当12πϕ=时，若B C 、两点在直线l 上，求m 与α的值．23. [选修4-5：不等式选讲]（10分）已知函数()222f x x a x a=+-+-．（Ⅰ）若()13<f ，求实数a 的取值范围；（Ⅱ）若不等式()2≥f x 恒成立，求实数a 的取值范围．2018届广东省六校第三次联考理科数学参考答案一、选择题：本大题共12小题，每小题5分．二填空题：本大题共4小题，每小题5分．13．；14．；15．；16．① ④说明：本参考答案给出一种解法的评分标准，其它解法可参照本评分标准相应评分.三、解答题：共70分．17.（12分）解：（Ⅰ）∵，，∴. ……………1分∵，∴. …………………………………………………2分∵，∴. ……………………………………………4分（Ⅱ）∵…①，…②，∴①-②得，，∵，……………………6分∴…③，……………………………………………………8分…④，③-④得，，. ……………………………………………………………………10分∵，∴是首项3公比的等比数列，，故. ……………………………………………………………………12分18.（12分）解：（Ⅰ）当日需求量时，利润，…………………………1分当日需求量时，利润，…………………………2分所以关于的函数解析式为．……………………3分（Ⅱ）（i）可能的取值为62，71，80，………………………………………………4分并且，，．的分布列为：……………………………………………………7分的数学期望为元．……………………8分（ii）若小店一天购进17份食品，表示当天的利润(单位：元)，那么的分布列为Y 58677685的数学期望为元．………11分由以上的计算结果可以看出，，即购进17份食品时的平均利润大于购进16份时的平均利润．所以，小店应选择一天购进17份．………………………………12分19.（12分）解法一：（Ⅰ）取中点，连，∵，∴，∵是平行四边形，，，∴，∴是等边三角形，∴，∵，∴平面，∴. ………………………3分∵分别是的中点，∴∥，∥，∴，，∵，∴平面，…………………5分∵平面，∴平面平面. …………………………………………6分（Ⅱ）由（Ⅰ）知，，∴是二面角的平面角.…………………………………………………7分,，，……………………………………………9分在中，根据余弦定理得，, ………11分∴二面角的余弦值为.…………………………………………………12分解法二：（Ⅰ）∵是平行四边形，，，∴，∴是等边三角形，∵是的中点，∴，∵∥，∴. ………………………………………………………………………………1分分别以，的方向为轴、轴的正方向，为坐标原点，如图建立空间直角坐标系. ……………………………………………………………2分则，，，，，设，∵，，解得，，，∴可得，………………………………………………………………4分∵是的中点，∴，∵，∴，∵，，∴平面，∵平面，∴平面平面.…………………………………………………………………6分（Ⅱ）由（Ⅰ）知，，，设是平面的法向量，则，∴，…………………………8分令，则，………………………………………………………9分又是平面的法向量，…………………………………………………10分∴，………………………………………………………11分∴二面角的余弦值为.…………………………………………………12分注：直接设点，或者说平面，，酌情扣分.20.（12分）解：（Ⅰ）依题意，、，，∴，………………………………………………2分由，，得，∵，∴，，………………………………………………………………4分故椭圆的方程为．……………………………………………………5分（Ⅱ）假设存在满足条件的点. 当直线与轴垂直时，它与椭圆只有一个交点，不满足题意. …………………………………………………6分因此直线的斜率存在，设：，由，消得，…………………………………………7分设、，则，，∵，………10分∴要使对任意实数，为定值，则只有，此时，．故在轴上存在点，使得直线与直线的斜率的和为定值．…………12分21.（12分）解：（Ⅰ）由于．…………………………………………1分假设函数的图象与轴相切于点，则有，即．………………………………………………3分显然，代入方程中得，．…………5分∵，∴无解．故无论a取何值，函数的图象都不能与轴相切．……6分（Ⅱ）依题意，恒成立．……………………………7分设，则上式等价于，要使对任意恒成立，即使在上单调递增，∴在上恒成立．…………………………………………8分则，，∴在上恒成立的必要条件是：．下面证明：当时，恒成立．…………10分设，则，当时，，当时，，∴，即．那么，当时，，；当时，，．∴恒成立．因此，的最大整数值为3．……………………………………………………12分22. [选修4-4：坐标系与参数方程]（10分）解：（Ⅰ）证明：依题意，，………………………………………………1分，，…………………………………………3分则．…………5分（Ⅱ）当时，两点的极坐标分别为，，…………6分化直角坐标为，. ………………………………………………7分经过点的直线方程为，…………………………………………8分又直线经过点，倾斜角为，故，. ………………………10分23.[选修4-5：不等式选讲]（10分）解：（Ⅰ）∵，∴，……………………………………………1分①当时，得，，∴；…………2分②当时，得，，∴；…………3分③当时，得，，∴. …………4分综上所述，实数的取值范围是．……………………………………5分（Ⅱ）∵，根据绝对值的几何意义知，当时，的值最小，……………………………………………………………………7分∴，即，……………………………………………………8分解得或．∴实数的取值范围是. …………10分。

2020届高三六校第三次联考英语试题试卷共10页，卷面满分120分，折算成135分计入总分。

考试用时120分钟。

注意事项：1.答题前，先将自己的姓名、准考证号填写在答题卡上。

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第一部分阅读理解（共两节，满分40分）第一节(共15小题；每小题2分，满分30分)阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

AHow cool can libraries be in an era of iPods and Kindles? More than you think. Only if you know where to go.Central Library: Seattle, Washington, United StatesThe Central Library in Seattle is modern and fashionable and has tourists from around the world paying visits and taking tours. It was designed by Dutch architect Rem Koolhaas and American designer Joshua Ramus. Tours began in 2006, two years after its opening. The library holds various art exhibitions, book signings and other events, while visitors can stop by the Chocolate cart for a coffee and scan through the gift shop anytime.Trinity College Library: Dublin, IrelandThe Trinity College Library in Dublin is in Ireland, founded at the end of the 16th century by Queen Elizabeth I. It is the largest single library in the world, also known as the Long Room, which contains more than 200,000 of the library's oldest books. The Long Room houses one of the oldest harps（竖琴）in Ireland. Dating to the 15th century, the old harp is the model for the symbol foreland.Geisel Library, University of California: San Diego, United StatesAt first glance, it looks like a spaceship. Architect William Pereira, who helped design actual space launch facilities at Cape Canaveral in Houston, Texas, designed the library in 1970. It has been featured in sci-fi films, short stories and novels.The library hosts “Dinner in the Library,” which invites readers for cocktails, and also special speeches from dis tinguished authors．TU Delft Library: The NetherlandsThe library at the Delft University of Technology was constructed in 1997 and has more than 862,000 books, 16,000 magazine subscriptions and its own museum. The building itself exists beneath the ground, so you can't really see the actual Library. What makes it interesting is the roof, which is a grassy hill. The roof covers 5,500 square meters. And it hasbecome one of the most striking and greenest structures in the area.1. Which of the four libraries has the longest history?A. Central LibraryB. Trinity College LibraryC. Geisel LibraryD. TU Delft Library2. What makes Geisel Library different from the others is that _____.A. a spaceship designer founded the libraryB. it has a roof of grassy hillC. famous writers often deliver speeches thereD. it is the largest single library in the world3. In Central Library, you can _____.A. drink cocktailsB. buy souvenirsC. create paintingsD. book eventsBThe cracked step four years ago was the start of it. That day, I awoke tired—the children were tiny and needing so much—and I had a golden afternoon of rest ahead, my mother stepping in to allow me to catch up on my sleep. I dropped them off and drove home—the sun shining and my bed signaling. As I was about to enter the house, I caught sight of a deep crack beneath my feet.Without thinking, I turned around, walked back to the car and drove to a DIY store. Four hours later, I had all the tools, mixed my own cement, filled in the crack and repaired the foundation. Perfect. As I stood up to take a photo of my handiwork, I realized that I was trembling. I’d forgotten my shot at a nice long nap, and my children were already on their way home. That sleep... that promise to self was broken, because I had focused, instead, on the crack in the step.Suddenly, everything started to hurt. My head, my throat, my back. I couldn’t stop shaking. What earned then is that when we break the promises we make to our bodies they will not be silenced. This is when we overwork and overthink to the point of breaking down. Ironically (讽刺地), for many of us, it is only when we have no choice— when we fall ill—that we learn to listen. For me, when that crack ended in a hospital stay which sent me to bed for two unmoving weeks when my body worked to clear two different infections, the lesson is ever present. I did it to myself—a whole twisted spin on DIY.Sadly it took another two ridiculous DIY projects to finally get through. The cracks will never be fully filled. Focus, then, on your own inner core, the feeding of light, fire and strength.4．What made the author so sleepy in the first place?A. Taking care of the kids.B. Asking her mother for help.C. Driving to her mother’s houseD. Dealing with DIY projects.5．How did the author feel as soon as she finished her repair work?A. RegretfulB. UpsetC. ProudD. Thankful6．What can be implied from Paragraph 3?A. Our health is ignored deliberately.B. Our body will respond to what we do.C. The author took her mother’s advice.D. The author was infected before the DIY.7．What is the author’s purpose in writing the text?A. To describe an unfortunate event.B. To show the danger of DIY.C. To stress the importance of sleep.D. To encourage focusing on oneself.CI used to think the whole purpose of life was pursuing happiness. Everyone said the path to happiness was success, so I searched for that ideal job, that perfect boyfriend, and that beautiful apartment. But instead of ever feeling fulfilled, I felt anxious and lost. Eventually. I decided to go to graduate school for positive psychology to learn what truly makes people happy.And what's the difference between being happy and having meaning in life? Many psychologists describe happiness as a state of comfort and ease, feeling good in the moment. Meaning, though, is deeper. The famous psychologist Martin Seligman says meaning comes from belonging to and serving something beyond yourself and from developing the best within you. Our culture is obsessed with happiness, but I came to see that seeking meaning is the more fulfilling path.There are four pillars of a meaningful life.The first pillar is belonging. Belonging comes from being in relationships where you're valued for who you are and where you value others as well. For many people, belonging is the most essential source of meaning.For others, the key to meaning is the second pillar: purpose. Finding your purpose is not the same thing as finding that job that makes y ou happy. A doctor told me her purpose is healing sick people. Many parents tell me, “My purpose is raising my children.” The key to purpose is using your strengths to serve others. Without something worthwhile to do, people flounder, thus losing the aim of life.The third pillar of meaning is also about stepping beyond yourself, but in a completely different way: transcendence (超然). Transcendent experiences can change you. Transcendent states are those rare moments when you're lifted above the hustle and b ustle of daily life, your sense of self fades away, and you feel connected to a higher reality. For me, I’m a writer, and it happens through writing. Sometimes I get so in the zone that I lose all sense of time and place.The fourth pillar is storytelling, the story you tell yourself about yourself. Creating a narrative from the events of your life brings clarity. It helps you understand how you became you. But we don’t always realize that we're the authors of our stories and can change the way we’re tellin g them. Your life isn't just a list of events. You can edit, interpret and retell your story, even as you're constrained by the facts.That’s the power of meaning. Happiness comes and goes. But when life is really good and when things are really bad, having meaning gives you something to hold on to.8. What can we know from the first two paragraphs？A. Life might be fulfilled by landing ideal jobs．B. Life dilemma is challenging for us to get out of．C. Meaning is highly valued in our culture．D. Happiness is what most people try to achieve．9. Which word is the closest to the underlined word?A. ConfusedB. DistractedC. DisappointedD. Saddened10. Which pillar can describe an artist obsessed with her work despite repeated failures?A. BelongingB. PurposeC. TranscendenceD. Storytelling11. The passage aims to tell us that _______________．A. meaning is superior to happinessB. meaning is the way to successC. chasing meaning can make people happyD. meaning has deeper psychological significanceDIt often happens that a number of applicants with almost identical qualifications and experience all apply for the same position. In their educational background, special skills and work experience, there is little, if anything, to choose between half a dozen candidates. How then does the employer make a choice? Usually on the basis of an interview.There are many arguments about the interview as a selection procedure. One argument is that it gives rise to a wholly subjective decision. As often as not, employers do not choose the best candidate, but the one who makes a good first impression on them. Some employers, of course, reply to this argument by saying that they have become so experienced in interviewing s taff that they are able to make a sound assessment of each candidate’s likely performance. Unfortunately, both for the employers and applicants, there are many people of great ability who simply do not interview well. There are also, of course, people who interview extremely well, but are later found to be very unsatisfactory employees.Those in favour of the interview insist that the well-structured procedure is valid in assessing a candidate’s ability, an essential guarantee for the future job. They also argue that an employer is concerned not only with a candidate’s ability, but with the suitability of his or her personality for the particular work situation. Many employers, for example, will overlook occasional inefficiencies from their secretary so long as she has a pleasant personality. Perhaps the real purpose of an interview is not to assess the assessable aspects of each candidate but to make a guess at the more intangible things, such as personality and social ability.Today, interview is still a common section of the entire selection procedure, though different employers have different standards for competence. Generally speaking, candidates who interview well tend to be quietly confident, but never boastful; direct and straight-forward in their questions and answers; cheerful and friendly, but never over-familiar; and sincerely enthusiastic and optimistic. Candidates who interview badly tend to be at either end of the spectrum of human behaviour. They are either very shy or over-confident. They show either a lack of enthusiasm or an excess of it. They eithertalk too little or never stop talking. They are either over-polite or rudely abrupt.12. According to the passage, which of the following statements is TRUE?A. Employers are experienced in a ssessing the interviewees’ performance.B. Interview is not always recognized as a sensible way to choose employees.C. The interview helps the employers to pick the desired employees.D. The remarkable candidates often distinguish themselves in an interview.13. Which may not be considered in an interview?A. PersonalityB. Communication skillsC. BackgroundD. Capability14. What is the author’s attitude towards the interview as a selection procedure?A. SupportiveB. NegativeC. ObjectiveD. Unconcerned15. The last paragraph indicates _________________.A. a link between success in interview and characterB. connections between work abilities and characterC. differences in interview experienceD. differences in personal behaviour第二节(共5小题；每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2018 届广东省六校第三次联考理科数学第Ⅰ卷（共60 分）一、选择题：本大题共12 个小题 , 每小题 5 分 , 共 60 分 . 在每小题给出的四个选项中，只有一项是符合题目要求的.1. 已知集合 M {( x, y) | x, y 为实数，且x2 y2 2} ，N {( x, y) | x, y为实数，且 x y 2} ，则 M N 的元素个数为( )A． 0 B ． 1 C．2 D．32. 设等差数列a n的前n 项和为S n，若S3 9，S5 30 ,则 a7 a8 a9 ( )A． 63 B ． 45 C ． 36 D ． 27y 03. 若变量 x, y 满足约束条件x 2 y 1 0 ，则 z 3x 5 y 的取值范围是( )x 4 y 3 0A．3， B ．8,3 C ．,9 D．8,94.1 ln | x |) 函数ysin x 的部分图象大致为(1 ln | x |A．B．C.D．5. 设函数f x cos 3x，其中常数满足0 .若函数 g(x) f ( x) f ' (x)（其中 f ' ( x) 是函数 f (x) 的导数）是偶函数，则等于()1A． B ．5D2C. ．3 6 6 36. 执行下面的程序框图，如果输入的a, b, k 分别为1，2，3，输出的M 15, 那么，判断框中8应填入的条件为 ( )A．n k B ． n k C. n k 1 D ． n k 17. 已知nb0 20 b1 2 i b2 22b n 2n1 i i i i （n 2,i 为虚数单位），又数列a n满足：当 n 1 2 ；当 n 2 an2 21为b2 2i的虚部，若数列时，a ，a n 的前 n 项和为S n，则S2018 ( )A． 2017 B ． 2018 C. 4035 D ． 40332018 2017 2018 20178. 如图，在同一个平面内，三个单位向量OA, OB, OC 满足条件： OA 与 OC 的夹角为，且tan7 ， OB 与 OC 与的夹角为45°. 若OC mOA nOB m,n R ，则 m n 的值为( )32C. 3 2 D．2A．3B．2229. 四面体SABC 中，三组对棱的长分别相等，依次为5，4， x ，则x 的取值范围是() A ．2，41B ． 3，9C.3， 41D ． 2，910. 从 2 个不同的红球、 2 个不同的黄球、 2 个不同的篮球共六个球中任取2 个，放入红、 黄、 蓝色的三个袋子中，每个袋子至多放入一个球， 且球色与袋色不同， 那么不同的放法有( ) A ．42 种B ．36 种C.72种D ．46 种 11. 已知点 F 为双曲线 E :x 2y 2 1 a, b 0 的右焦点，直线 y kx(k 0)与 E 交于 M,Na 2b 2两点，若 MFNF ,设MNF, 且12 ， ，则该双曲线的离心率的取值范围是6( )A ． 2,26B．2,31C.2, 2 6D．2,3112. 已知 A x 1, y 1 、 B x 2 , y 2 是函数 f xln x与 k图象的两个不同的交点，则xg xx 2f x 1 x 2 的取值范围是()A ． e 2B ．e 2 1C.1 2 ln ,2 ln , e0， eeee 2 D ．ln ,02e第Ⅱ卷（共 90 分） 二、填空题（每题 5 分，满分 20 分，将答案填在答题纸上）13. 已知函数 yf ( x) 是定义在 R 上的奇函数，则3 21 dx ．f x1x14. 已知函数 f xa sin xb cosx ，若 fx f x ，则函数 y 3ax b 1 恒过定点．4415. 已知几何体的三视图如图所示，其中俯视图为一正方形，则该几何体的表面积为．316. 若函数 f x 的图象上存在不同的两点A x 1 , y 1 ,B x 2 , y 2 ，其中 x 1 , y 1, x 2 ,y 2 使得 x 1x 2 y 1 y 2x 12 y 12x 22 y 22 的最大值为 0，则称函数 f x 是“柯西函数” . 给出下列函数：① f x ln x 0 x 3 ；② f xx 1 x0 ；x③ f x2 x 2 8 ；④ f x2 x 28 .其中是“柯西函数”的为（填上所有正确答案的序号）．三、解答题 （本大题共 6 小题，共 70 分 . 解答应写出文字说明、证明过程或演算步骤 . ）17. 设数列 a n 的前 n 项和为 S n ，数列 S n 的前 n 项和为 T n ，满足 T n 2S n n 2, n N.( Ⅰ ) 求 a 1 , a 2, a 3 的值；( Ⅱ ) 求数列a n 的通项公式.18. 某小店每天以每份 5 元的价格从食品厂购进若干份食品，然后以每份10 元的价格出售 . 如果当天卖不完，剩下的食品还可以每份1 元的价格退回食品厂处理 .( Ⅰ 若小店一天购进 16 份，求当天的利润 y （单位：元）关于当天需求量 （单位：份，n N ） )n的函数解析式；4( Ⅱ ) 小店记录了 100 天这种食品的日需求量（单位：份），整理得下表：日需求量 n 14 15 16 17 18 19 20 频数10 20 16 16 15 13 10 以 100 天记录的各需求量的频率作为各需求量发生的概率.(i)小店一天购进16 份这种食品，X 表示当天的利润（单位：元），求X的分布列及数学期望；(ii) 以小店当天利润的期望值为决策依据，你认为一天应购进食品16 份还是 17 份？19 如图，在四棱锥P A BCD 中， ABCD 是平行四边形，AB BC 1, BAD 120 ，PB PC2,PA 2, E,F 分别是 AD, PD 的中点.( Ⅰ ) 证明：平面EFC平面PBC；5( Ⅱ) 求二面角A BC P 的余弦值.20. 已知椭圆 C :x2y 2 1 a b 0 的离心率为 3， A 1、A 2 分别为椭圆 C 的左、右顶点a 2b 22点P2, 1 满足 PA 1 PA 2 1. ( Ⅰ) 求椭圆C 的方程；( Ⅱ ) 设直线l 经过点P 且与C 交于不同的两点M 、 N ，试问：在x 轴上是否存在点Q ，使得 QM 与直线 QN 的斜率的和为定值？若存在，请求出点Q 的坐标及定值；若不存在，请说明 理由 .21. 已知函数f xx1 exax 2，其中a R .2( Ⅰ ) 函数fx 的图象能否与x 轴相切？若能，求出实数a ，若不能，请说明理由；6( Ⅱ ) 求最大的整数 a ，使得对任意 x 1 R, x 2 0,，不等式 f x 1 x 2 f x 1 x 22x 2恒成立 .请考生在 22、 23 两题中任选一题作答，如果多做，则按所做的第一题记分. 22. 选修 4-4 ：坐标系与参数方程x m t cos），以坐标原点为极点，以 x已知直线 l 的参数方程为（ t 为参数，y t sin轴正半轴为极轴建立极坐标系，曲线 C 的极坐标方程为4cos ，射线 4, ， 分别与曲线 C 交于 A 、 B 、 C 三点（不包括极点 444O ） .(Ⅰ)求证：OBOC 2OA ；7( Ⅱ ) 当时，若B、C两点在直线l 上，求m与的值.12已知函数 f x 2x a 2 x 2a .( Ⅰ ) 若f 13 ，求实数a的取值范围；( Ⅱ ) 若不等式f x 2恒成立，求实数a的取值范围.2018 届广东省六校第三次联考理科数学参考答案一、选择题1-5: BADAA6-10: CCBCA 11、12：DD8二、填空题13. ln 314.1，315.42 23 216.①④三、解答题17.解：(Ⅰ)∵ S 1 T 12 S 1 1 , S 1 1 a 1 ，∴ a 1 1. ∵ S 1 S 2 T 2 2S 2 4 , ∴ a 2 4 .∵ S 1S 2 S 3 T 3 2S 3 9 , ∴ a 3 10 .( Ⅱ ) ∵ T n 2S n n 2①， T n12S n 1x 1 2, ②，∴① - ②得， S n 2a n 2n 1 n2，∵S 12a 1 2 1 1 ，∴ S n2a n 2n 1 n 1 , ③，Sn 1 2a n 1 2n 3,④，③ - ④得， a n2a n12 n2 ，a n 2 2(a n 1 2) .12 3 ，∴a n 2是首项3 公比 2 的等比数列，a n 23 2n 1 ，∵ a故a n 32n 12 .18. 解： ( Ⅰ ) 当日需求量 n 16 时，利润 y 80 ，当日需求量 n16 时，利润 y 5n 4(16 n) 9n 64 ，所以 y 关于 n 的函数解析式为y9n 64, n16N .80, n 16 n( Ⅱ )(i) X 可能的取值为 62， 71，80，并且PX62 0.1, P X 710.2, P X80 0.7 . X 的分布列为：X 62 71 80 P0.10.20.7X 的数学期望为 E X62 0.1 71 0.2 80 0.7 76.4 元 .(ii) 若小店一天购进17 份食品， Y 表示当天的利润（单位：元） ，那么 Y 的分布列为9Y 58 67 76 85 P0.10.20.160.54Y 的数学期望为 E Y 58 0.1 67 0.2 76 0.16 85 0.54 77.26 元.由以上的计算结果可以看出，E X E Y , 即购进 17 份食品时的平均利润大于购进 16 份时的平均利润．所以，小店应选择一天购进17份. 19.解法一： (Ⅰ)取BC 中点G ，连PG,AG,AC ,∵PBPC ,∴ PG BC , ∵ ABCD 是平行四边形， AB BC 1 , BAD 120,∴ ABC 60,∴ ABC 是等边三角形，∴ AG BC ,∵ AG PG G ,∴BC 平面 PAG ,∴ BCPA .∵ E,F 分别是 AD,PD 的中点 ,∴ EF // PA ,EC// AG , ∴BC EF , BC EC ,∵EF EC E ,∴BC 平面EFC , ∵ BC 平面 PBC , ∴平面 EFC 平面 PBC . (Ⅱ)由(Ⅰ)知PGBC,AG BC , ∴ PGA 是二面角 A BC P 的平面角.∵PG21 7,AG3,PA 2,422在 PAG 中，根据余弦定理得PG 2 AG 2 PA 221,cos PGA,2PG AG 7102018 届广东省六校第三次联考理科数学及答案解析∴二面角 A BC P 的余弦值为21. 7解法二：( Ⅰ ) ∵ABCD是平行四边形，AB BC1 ,BAD 120 ，∴ADC60 ,∴ADC 是等边三角形，∵E是AD的中点，∴CE AD,∵AD//BC,∴CE BC.分别以 CE,CB 的方向为x轴、y轴的正方向，C 为坐标原点，如图建立空间直角坐标系.则C 0,0,0 ,E3,0,0 ,A3,1,0 , D 3 ,1,0 ,2 2 2 2 22 2 23 , y 1 , z 1，设 P x, y, z ，∵ PB PC 2 , PA 4 ,解得x2 2∴可得 P3,1,1 , 2 2∵ F 是 PD 的中点，∴F 0,0,1,∵CB CF 0,∴CB CF,∵CE BC,2CE CF C,∴BC 平面 EFC ,∵ BC 平面 PBC ,∴平面 EFC 平面 PBC .(Ⅱ)由(Ⅰ)知，CB 0,1,0 , CP 3,1,1 , 设n x, y, z 是平面 PBC 的法向量，则2 2112018 届广东省六校第三次联考理科数学及答案解析 CB n ，∴ CB n y 03 x ，CP n CP n 1 y z 02 2令 x 2 ，则n ( 2,0, 3) ，又 m (0,0,1) 是平面ABC 的法向量，∴ cos m, n m n 21m n ，7∴二面角 A BC P 的余弦值为 21 .7注：直接设点 F 0，0，z ，或者说 CF 平面 ABCD , PA AD ，酌情扣分 .20. 解： ( Ⅰ ) 依题意， ,0 、 ， ， ，A 1a A 2 a,0 P 2 1∴ PA 1 PA 2 （ a 2,1) a 2,1 5 a 2 ,由 PA 1PA 2 1, a 0 , 得 a 2 ，∵ e c 3a ，2∴ c 3,b 2 a 2 c 2 1 ，故椭圆 C 的方程为 x 2 y 2 1 .4( Ⅱ ) 假设存在满足条件的点 Q t,0 . 当直线 l 与 x 轴垂直时，它与椭圆只有一个交点，不满足题意.因此直线 l 的斜率 k 存在，设 l : y y 1 k(x 2)1 k( x 2) ，由 x2 y 2，消 y 得141 4k2 x 2 16k 2 8k x 16k2 16k 0 ，设 M x 1 , y 1 、N x 2 , y 2 ，则 x 1 x 2 16k 2 8k , x 1x 2 16k 2 16k1 4k2 1 4k 2，∵ k QM k QN y 1 y 2 kx 1 2k 1 x 2 t kx 2 2k 1 x 1 tx 1 t x 2 t x 1 t x 2 t122kx1x2 2k 1 kt x1 x2 2 2k 1 t 4t 8 k 2t，x1x2 t x1 x2 t 2 4 t 2 2 k 2 8 2 t k t 2∴要使对任意实数k,k QMk QN为定值，则只有t 2 ，此时， k QMkQN 1 .故在 x 轴上存在点Q2,0 , 使得直线QM与直线QN的斜率的和为定值 1.21.解： ( Ⅰ ) 由于f '( x) xe x ax .假设函数 f x 的图象与 x 轴相切于点t,0 ，f (t ) 0t 1e'at20.2则有f '(t)，即0 te' at 0显然 t 0, e' a 0 代入方程t 1 e' at2 0 中得， t 2 2t 2 0 . 2∵ 4 0 ，∴无解．故无论 a 取何值，函数 f x 的图象都不能与x 轴相切. ( Ⅱ ) 依题意，f x1 x2 f x1 x2 x1 x2 x1 x2f x1 x2 x1 x2 f x1 x2 x1 x2 恒成立 .设 g x f (x) x ，则上式等价于g x1 x2 g x1 x2 ，要使 gx1 x2 g x1 x2, 0, 恒成立，即使 g x x a 2x 在R上单调递增，对任意x 1 e x x1 R x2 2∴ g'( x) xe x ax 1 0在R上恒成立.则 g' (1) e a 1 0, a e 1 ，∴ g' ( x) 0 在R上成立的必要条件是： a e 1 . 下面证明：当 a 3时， xe x 3x 1 0恒成立.设x，则xh x e x 1'(x)e1 ，当x 0时， h' (x) 0，当x 0时， h' ( x) 0 ，h∴ h(x)min h(0) 0 ，即x R,e x x 1. 那么，当 x 0 时，xe x x2 x, xe x 3x 1 x2 2x 1 x 1 2 0 ；当 x 0 时， e x 1, xe x 3x 1 x(e x 3 1 ) 0 ，∴ xe x 3x 1 0 恒成立 .x因此， a 的最大整数值为 3.22. 解： ( Ⅰ ) 证明：依题意，OA 4cos ，13OB 4 cos , OC 4 cos4 ，4则 OB OC 4 cos4 4 cos44 2 cos 2OA .(Ⅱ)当12 时， B、 C 两点的极坐标分别为2，，2 3，，3 6化直角坐标为B1，3，C 3， 3 .经过点 B、 C 的直线方程为y 3 x 2 ，又直线 l 经过点m,0 ，倾斜角为，故 m 2, 2. 323. 解： ( Ⅰ ) ∵f 1 3 ，∴ a 1 2a 3 ，①当 a 0 时，得 a (1 2a) 3, a 2，∴2a 0 ；3 3②当 01时，得 a (1 2a) 3, a2 ，∴0 a1a ；2 2③当 a 1(1 2a) 3, a4 1a4 时，得 a3，∴.2 2 3综上所述，实数 a 的取值范围是2 4. 3，3( Ⅱ ) ∵f xa1 x 2a ，根据绝对值的几何意义知，当x 1ax 的值2 x 时， f2 2最小 ,∴ f 1 a 2，即1 5a 2 ，2 2解得 a 6 2, 26,.或 a . ∴实数a的取值范围是5 5 5 514。

2018届广东省六校高三第三次联考理科综合化学试题一、单项选择题7．下列说法正确的是A．石油的分馏和煤的气化都是发生了化学变化B．纤维素、油脂和蛋白质在一定条件下都能水解C．二氧化硅是半导体材料，可将太阳能直接转化为电能D．乙烯和苯都能使酸性KMnO溶液褪色48．下列离子在溶液中能大量共存的一组是A．K＋、H＋、ClO－、SO32－ B．Fe3＋、Mg2＋、NO3－、CO32－C．Na＋、Ca2＋、HCO3－、OH－ D．Al3＋、NH4＋、Cl－、SO42－9．设n A表示阿伏加德罗常数的数值。

下列说法正确的是A．标准状况下，11.2L CHCl3含有0.5 n A个CHCl3分子B．常温常压下，16 g O3含有8n A个电子C．1L 0.1 mol/L醋酸溶液中含有0.1n A个氢离子D．27g铝片投入足量浓HNO3中生成n A个NO分子10．下列有关物质性质的描述和该性质的应用均正确的是A．氨气具有氧化性，用浓氨水检验氯气管道是否泄漏B．铜的金属活泼性比铁的弱，可在铁闸上装若干铜块以减缓其腐蚀C．二氧化硫具有还原性，用二氧化硫水溶液吸收溴蒸气D．二氧化锰具有较强的的氧化性，可作H2O2分解的氧化剂11．下列有关说法正确的是A．AlCl3溶液蒸干、灼烧至恒重，最终剩余固体是AlCl3 B．向煮沸的1 mol·L－1 NaOH溶液中滴加FeCl3饱和溶液可制备Fe(OH)3胶体C．等体积pH＝12的氨水和pH＝12的NaOH溶液可中和含等物质的量HCl的盐酸D．锅炉中沉积的CaSO4可用饱和Na2CO3溶液浸泡，再将不溶物用酸去除12．50℃时，0.1mol·L－1Na2CO3溶液pH＝12，下列判断正确的是A．c(OH－)＝10－2mol·L－1B．加入少量NaOH固体，c(Na＋)和c(CO32－)均增大C．c(Na＋)＋c(H＋)＝c(HCO3－)＋c(OH－)＋c(CO32－)D．2c(Na＋)＝c(HCO3－)＋c(CO32－)＋c(H2CO3)二、双项选择题22．短周期主族元素X、Y、Z、W的原子序数依次增大，原子半径r(W)＞r(Y)＞r(Z)＞r(X)。