吉林省长春市第二实验中学2020-2021学年高一上学期9月月考数学试卷 Word版含答案

2024-2025学年吉林省长春实验中学高一（上）期中数学试卷一、单选题：本题共8小题，每小题5分，共40分。

在每小题给出的选项中，只有一项是符合题目要求的。

1.已知集合A ={y|y =12x 2−52}，B ={x|x 2+5x +6<0}，则A ∩B =( )A. (−3,−2)B. [−52,−2)C. (−3,−52]D. R2.函数f(x)=(1−x)⋅|2−x|的单调递增区间为( )A. (32,2)B. (1,32)C. (−∞,32)D. (32,+∞)3.已知函数f(x)=a x +1(a >0，且a ≠1)，则函数图象过定点( )A. (1,1)B. (−1,−1)C. (−1,1)D. (1,−1)4.已知a =20.3，b =40.1，c =(13)0.2，则三个数的大小关系是( )A. a >b >cB. b >a >cC. b >c >aD. c ≥a >b5.已知a >b >0，p ：x <a +b 2，q ：x < ab ，则p 是q 成立的____条件( )A. 充分不必要B. 必要不充分C. 既不充分也不必要D. 充要6.已知10m =2，10n =3，则103m−2n 2=( )A. 49 B. 89 C. 23 D. 2 237.某工厂要建造一个长方形无盖贮水池，其容积为4800m 3，深为3m ，如果池底每平方米的造价为150元，池壁每平方米的造价为120元，若当贮水池一边长x 时，最低总造价z 最小，则( )A. x =40，z =268800B. x =20，z =297600C. x =40，z =297600D. x =20，z =2688008.已知定义在R 上的奇函数f(x)，其图象关于x =1轴对称，当0≤x ≤1时，f(x)=x 2，则f(73)=( )A. −259B. −19C. 259D. 19二、多选题：本题共3小题，共18分。

长春市实验中学2023-2024学年上学期期中试卷高一英语试卷一、选词填空-句子（本大题共1小题，共15分）1.On my way home， traffic was held up in front of the University stadium-it is a busy area (1) I saw a young woman trying (2) （ get） a tiny （maybe 8 weeks old） cat out of (3) road． The kitten （小猫） (4)（ terrify） and she finally got the little one but dropped him． The kitten ran to the roadside and lay there in shock． I pulled over and got out as she had gone back into her truck （maybe since the kitty was out of the road her part was done） and (5) （simple） took him to safety．As I was doing so， two beautiful young men pulled over and asked if I needed help． Well，I said，maybe． I showed them the kitten and put him (6) the cab of their truck． They were instantly in love． They also knew where the (7) （ shelter） were in town．I told them I could take the kitten to one if they couldn't， but they told me they would take the kitten and if they didn't keep him， they would take him to a shelter． As I left， I heard one say， "kittens deserve (8) （ well）than this．" There (9) （ be） some truly wonderful young people out there． My heart broke with (10)（ happy） to see these guys caring so obviously．二、阅读理解（本大题共20小题，共45分）AFar, far below your feet lies a source of nearly endless energy. Earth's core is about as hot as the surface of the Sun, so hot that it melts the rocky layers above it into magma, or liquid rock. Wouldn't it be great if we could tap into all that energy? In some places, we do!The Geysers is an area north of San Francisco in California where magma's heat turns a reservoir of underground water into steam. This region is home to 18 geothermal power plants. The steam rises up through spaces between the rocks underground, a bit like how steam pours from a teakettle boiling on a stove. The power plant has pipelines that send the steam into the turbines (涡轮机) where electricity flow is generated. Once the steam leaves the turbine, it goes into a cooling tower where it turns back into liquid. Then it's piped back into the reservoir to be reheated again. Other kinds of geothermal power plants pump hot groundwater into the power plant. Then thepressure is reduced, causing the liquid to flash into steam that turns the turbine and generates electricity flow. Once the steam cools and turns back into liquid, it's pumped back down into the reservoir to begin the cycle again.So why don't we all heat our homes with free steam from the earth? First, the heat has to be close enough to the surface for us to reach it. Next, there has to be plenty of underground water to be heated. Finally, there has to be a layer of rock that water or steam can flow through. So in places where all three of those things come together, geothermal energy can be a powerful renewable energy source. Besides, when a geothermal plant returns water back into the hot rocks of a reservoir, it makes the rock crack a bit, which can cause small earthquakes. There's another danger that comes with drilling near magma-pipes and other equipment might melt if they hit a pocket of magma or are caught in an eruption. One geothermal plant in Hawaii was partially buried by lava in 2018. But engineers are hopeful that the repaired plant will generate even more power. Geothermal energy isn't the answer for everywhere, but it's a piece of the puzzle to help slow climate change.2.In which part of power plants is the electricity made?A. The turbine.B. The reservoir.C. The pipeline.D. The tower.3.What prevents free steam from being widely developed according to paragraph 3?A. Hard surface and possible earthquakes.B. Changeable climate and unqualified equipment.C. Limited underground water and thin layers of rock.D. Unsuitable geological conditions and potential dangers.4.Why is the buried geothermal plant in Hawaii mentioned?A. To demonstrate the great effort that engineers made.B. To show the power that the repaired plant can generate.C. To illustrate the danger caused by drilling near magma.D. To praise the engineers who repaired the generate plant.5.What is the author's attitude towards geothermal energy?A. Unconcerned.B. Unclear.C. Doubtful.D. Approving.BBiological fieldwork can mean trips to exotic places. The most common method is to send a few eager graduate students armed with camera traps and several weeks of spare time. But perhaps not for much longer. A paper published in Current Biology suggests an easier method: simply swabbing(擦拭) nearby leaves for DNA.The DNA in question is called "environmental DNA" (eDNA for short). It refers to all the genetic information that animals leave behind as they go about their daily business: breathing, urinating, or interacting with their environment in any way. In recent years, genesequencing(基因测序) technology has become quick and sensitive enough to pick out genetic sequences from particular animals including humans from this eDNA.One way of doing so is simply to blow air through filters(过滤器), and then analyse them to see which animals live nearby. Drs Gogarten and Lynggaard wondered if there might be a simpler approach. Air-sampling systems can take days to do their work. Maintenance must be done, and filters must be changed. But given that eDNA is literally blowing around ecosystems, the searchers wondered if it might be collecting on leaves.The leaves of many plants are waxy(蜡质的) and somewhat sticky. The researchers theorised that eDNA might end up stuck to leaves and that it could subsequently be collected by swabbing them. They tested their theory in the dense rain forests of Kibale National Park, in Uganda. Using simple cotton swabs, and wearing masks and gloves to prevent polluting the samples with their own DNA, they visited three areas of the park and collected eight swabs at each site, and then took them back to Copenhagen for analysis.The swabs revealed the presence of 26 birds, 24 mammals, one amphibian and one fish, with each swab containing DNA from eight animals on average. More than half the samples were good enough to work out the precise species they came from.Swabbing for animals, then, seems to work. Moreover, it is cheap, easy and fast. Graduate students will have to be content spending less time sample-hunting in distant parts of the world.6.Who will benefit most from the research findings?A. Forest farmers.B. Biological graduates.C. Ambitious scientists.D. Environmental activists.7.Why was the researchers armed with masks and gloves?A. To protect the leaves.B. To avoid getting stuck.C. To stay safe from wax.D. To ensure the quality of samples.8.How is eDNA method compared with the common ways?A. More animal-friendly.B. Free of complex analysis.C. More accurate and effective.D. Economical in time and money.9.What serves as the best title for the text?A. Swabbing leaves: an easier method to track animalsB. Testing eDNA: a useful tool for animal detectionC. What the function of leaves isD. How the field work goesCBegin your global journeyAt University of Wisconsin (UW) -Eau Claire, you'll find your investment pays off well before you graduate. Because here, we believe that your journey is just as important as your destination. You will have many opportunities to develop: from internships(实习) to undergraduate research to foreign cultural experiences. We seek students who are curious, innovative and compassionate. If this sounds like you, submit your application to join our big family!Admission application processTo complete an application for admission, submit the following:1. Online application;2. $25 USD application fee;3. Evidence of English proficiency;4. Financial documentation;5. Academic records;6. Passport copy.Submit the supporting documents listed above by including them with your UW-Eau Claire specific*********************************************************************.Paying for college2023-2024 undergraduate student estimated expenses (The numbers below are in USD per academic year): Tuition and fees: $18, 460Housing and meals: $8, 800Health insurance: $1, 900Application deadlinesWe accept applications February 1-June 1 for admission the upcoming fall term (September). and August 1-November 1 for admission the upcoming spring term (February). We must receive all of your required application materials prior to the deadline. Start applying early!Check your application statusTo check your application status, as well as other important steps in the enrollment process, you must first activate your Campus Account. The information you will be able to access through your Campus Account includes the following:•View your admission decision in real time;•Track the progress of your completed next steps after admission;•Pay your enrollment fee of $500;•Sign up for Orientation (迎新会) when you are qualified.Please note that official admission decisions will always be sent via US Mail.10.Where is this text probably taken from?A. A global travel journal.B. An undergraduate course plan.C. A welcome speech for freshman.D. A college application guide.11.Which is the right time for you to apply for 2024 spring semester admission?A. September 10, 2023.B. December 1, 2023.C. February 9, 2024.D. March 16, 2024.12.What can you do by using the Campus Account?A. Pay the tuition fees.B. Download official admission offer.C. Submit application documents.D. Know about your enrollment process.DMany of us are lonelier than ever. We can go shopping and avoid speaking to a single person. Automated voice son phones and machines suck the contact and relational element out of day-to-day life, so much so that experts say that we are experiencing a loneliness disease.According to Dr. Lalitaa, loneliness is the feeling we get when our need for rewarding social contact and relationships is not met. But loneliness is not always the same as being alone. Loneliness is a state of mind linked to wanting human contact but feeling alone. People can be alone and not feel lonely, or they can have contact with people and still experience feelings of loneliness.Loneliness is a universal human emotion that is both complex and unique to each individual. There are many contributing factors to loneliness, such as illness, relationships breaking down, moving country, changing jobs ornot being understood by co-workers, retiring, starting university, etc.We cannot underestimate the impact loneliness can have on our physical and mental wellbeing. According to research, loneliness has comparable health risks to smoking 15cigarettes a day, and people who feel lonely are more likely to die earlier and suffer from heart attacks. Dr. Lalitaa says, "People often say to me, 'It's too late to meet new people as an adult.' Having human connect ion can look different for each person, but this can become a block, stopping them going out, trying new things and connecting with new people. Remember, it is never too late to make good, meaningful connections."However, don't put pressure on yourself. A meaningful relationship takes time. It is not just created overnight. Also, take some time to sit with yourself and venture(冒险) into some of the things that you like doing. "The first thing I would say is not to deny or distance the feeling. Acknowledge it and then you can choose to focus on ways to help yourself," says Dr. Lalitaa.13.How does the author clarify what loneliness is?A. By stating arguments.B. By giving examples.C. By making comparisons.D. By employing figures.14.Why is smoking cigarettes mentioned in the text?A. To explain the causes of loneliness.B. To illustrate the harm from loneliness.C. To overestimate the impact of loneliness.D. To emphasize the universality of loneliness.15.What does the underlined word "this" in paragraph 4 refer to?A. Lack of appealing reward.B. Dependence on the network.C. The regret for the passing youth.D. The idea of being too late for new relations.16.What does Dr. Lalitaa consider as priority when dealing with loneliness?A. Having new experience.B. Telling it from being alone.C. Being aware of and recognizing it.D. Making friends from all walks of life.EThere is a festival in China that has three names. Itˈs known as the Chongyang Festival. Also, it is called the Double Ninth Festival because it falls on the ninth day of the ninth month of the Chinese lunar calendar (阴历). Finally it has been Seniorˈs Day (老人节) since 1989. This year, it fell on Oct 23rd.There are many traditions for this festival. In the past, people climbed mountains, drank chrysanthemum (菊花) wine, and wore a plant called zhuyu to celebrate it. Climbing mountains in autumn brings people close to nature and itˈs good for health. Both chrysanthemum and zhuyu are also clean plants and they can clean houses and make people healthy.In China, nine has the similar pronunciation with the word "forever", meaning long life. So the Chinese government set the day as the Seniorˈs Day in 1989—a day to respect the old. Many companies and communities organize autumn trips for old people. Young people bring elders to the countryside to enjoy nature. They also give them gifts.In China, it is a tradition to respect old people. In the past, if young people didnˈt take good care of their parents, they would be seriously punished. Now we have the 24 Filial Exemplars (《新二十四孝》). It includes 24 things we should do for elders, such as calling them up every week and going to see them more often. On this three-named festival, remember to show your love to your elders.17.Which is NOT a name for the festival?A. Chongyang Festival.B. the Double Ninth Festival.C. Seniorˈs Day.D. Youth Day.18.Which was not a tradition for this festival in the past?A. Climbing mountains.B. Calling them up every week.C. Drinking chrysanthemum wine.D. Wearing a plant called zhuyu.19.What does the underlined word "respect" in Paragraph 3 mean in Chinese?A. 思念B. 尊重C. 保护D. 照顾20.What is the main idea of the passage?A. History of Chongyang Festival.B. Introduction of Chongyang Festival.C. Traditions of Chongyang Festival.D. Symbols of Chongyang Festival.21.We can read the passage from a magazine called ______.A. American HistoryB. Chinese HistoryC. Western FestivalsD. Traditional Festivals三、阅读七选五（本大题共5小题，共12.5分）How to Be More Present Many people have a tendency to live in the past or the future. They constantly think about the past and worry about the future, and thus find it difficult to enjoy the good things in life in the here and now. You might unfortunately be one of these people. (22) Here are some tips that might help you.Notice Your SurroundingsOne way to be in the present moment is by noticing your surroundings. How often do you take time out of your day to actually look around and see what's going on? Now close your eyes and take a deep breath. (23) When you do, it's easier to be more present in the moment.Be Grateful for What You Have Now(24) If you are constantly focused on things you don't have, you aren't taking the time to appreciate what you have at this moment. One way to practice gratitude is to write a list of things you are grateful for and review that list on a daily basis. Try to write at least three things you are grateful for in your life right now.Show AcceptanceIf you want to learn how to be more present, you need to let go of how you think things should be and accept them for what they are. (25) Sometimes life is going to be different than how you want it to be. Practicing acceptance will help you let go of the things in your life that are out of your control.Find Positive Social SupportThe kind of social support you have in your life can also play an important role. Surrounding yourself with positive, supportive people will increase your own positivity and happiness levels. (26)A. Then open them and really take in where you are.B. You should focus your attention on one thing at a time.C. You cannot control everything that happens around you.D. This is one way to distance yourself from what you are enjoying.E. In turn, this will allow you to focus on what is going on right now.F. Part of living in the present moment is to appreciate what you have now.G. So learning how to live in the moment can greatly improve your well-being.四、完形填空（本大题共15小题，共15分）In the fall of 2008, I was looking to leave my current job in a doctor's office to explore something more (27) . So I started investigating the new world of travel nursing. With a bit of (28) , I was connected to Carlyn.At this time, I am working on all areas of my life......in the (29) of becoming a stronger, more confident person, and (30) more about who I am. Without amazing, enthusiastic and supportive Carlyn, I wouldn't be where I am today. For the past 2 years, Carlyn and I stayed in (31) through email, facebook, and a periodic phone call, becoming friends…. I had a whole view of all the things she was (32) in her life and it inspired me much.I was anxious to (33) Carlyn face-to-face for the first time. But, as soon as she (34) in front of my house, it was like we had done it a million times before. This "my friends" is the (35) of the human connection that she talks about. It takes two people from (36) to friends!Now as fate would have it, Carlyn has (37) my world. So now, I hope to repay her (38) for all that she has helped me (39) . I am fortunate to be part of a friendship that is a by-product of her (40) . She continues to inspire me and I hope to learn and meet more through her (41) .27.A. complicated B. universal C. challenging D. profitable28.A. confidence B. luck C. fear D. pride29.A. power B. hope C. absence D. sense30.A. learning B. complaining C. discussing D. worrying31.A. shape B. order C. place D. touch32.A. abandoning B. explaining C. experiencing D. delivering33.A. meet B. phone C. persuade D. inform34.A. put away B. backed down C. carried on D. pulled up35.A. trick B. power C. choice D. origin36.A. students B. workmates C. strangers D. learners37.A. influenced B. left C. explored D. enjoyed38.A. as a result B. by accident C. with a bang D. in a way39.A. suspect B. accomplish C. witness D. appreciate40.A. anxiety B. persistence C. charity D. passion41.A. recovery B. comparison C. example D. diligence五、语法填空（本大题共1小题，共15分）42. When China's first astronaut Yang Liwei blasted off into space in 2003, it was a history- making moment that declared his country's arrival (1) an emerging space power.So far, China (2) (become) a major presence in space. It now has its own permanent outpost in orbit—a (3) (full) operational space station-and routinely rotates(轮值) crews to live and work there.On Thursday, three Chinese astronauts lifted off on the Shenzhou-17 spacecraft from the Jiuquan Satellite Launch Center deep in the Gobi Desert, (4) (head) for the Tiangong space station for a six-month stay.They are the (5) (young) crew China has ever sent to space—with (6) average age of 38. Among their tasks on board is to repair the solar panels which (7) (destroy) by space debris years ago—the first time Chinese astronauts will carry out repair work outside the station.This is China's sixth manned mission to its space station since 2021. The new crew will take over from the Shenzhou-16 astronauts, (8) have been on board since May.(9) (complete) late last year, the Tiangong—or "heavenly palace" in Chinese—is one of the twospace (10) (station) currently in orbit. With a lifespan of 15 years, it could become the only one left when the NASA-led International Space Station (ISS) retires in 2030.六、书面表达（本大题共1小题，共15分）43.假定你是李华，你的英国朋友 Peter看了你在社交平台上发布的“全国爱眼日”班级活动图片后，向你了解相关情况。

2024级高一新生假期验收测试英语(满分100分)班级：______姓名：______分数：______I.单项选择(每题1分，共20分)一.分析下列划线单词或短语的成分1. The cars made in Japan are better than those in Germany.A. 谓语B. 宾语C. 状语D. 定语2. It is a great pleasure to talk with you.A.主语B. 表语C. 定语D. 状语3. All of us considered him honest.A.谓语B. 宾语C. 宾补D. 定语4. My grandfather bought me a pair of sports shoes.A.主语B. 定语C. 宾补D. 宾语5. He broke a piece of glass.A.谓语B. 宾语C. 主语D. 定语6. He made it clear that he would leave the city.A.宾语B. 表语C. 宾补D. 状语7. Trees turn green when spring comes.A.谓语B. 状语C. 表语D. 定语8. Grandma told me an interesting story last night.A.定语B. 宾语C. 状语D. 主语9. It’s hard for me to find him.A.主语B. 宾语C. 表语D. 定语10. No matter how difficult the task may be, we must fulfil it this monthA.谓语B. 表语C. 宾语补足语D. 状语二. 词汇语法知识11. Nowadays, more people are paying attention to the ______ of the environment.A. populationB. pressureC. protectionD. performance12.— Nearly three years ______ since we first entered this school.—It’s so hard to say goodbye to our teachers and classmates.A. are passingB. passedC. will passD. has passed13.— Peter failed the online exam yesterday.—That’s not surprising. Computer games ______ too much of his time.A. take outB. take inC. take offD. take up14. To my ______, my deskmate disturbed me over and over againA. annoyingB. annoyanceC. annoyD. annoyed15. I have exchanged my ideas ______ the famous novelist, so I feel more confident about my future.A. withB. ofC. inD. for16. It was ______ of me to break his cup.A. outgoingB. awkwardC. sincereD. annoyed17. —Tony, what are you doing?—I have just finished my work and ______a shower.A. have takenB. will takeC. tookD. am taking18. The teacher and writer ______ coming to our school this afternoon.A. isB. areC. beD. was19. In my opinion, this learning style ______ you and you can make progress.A. is responsible forB. is scheduled forC. is suitable forD. is confusing about20. The beautiful girl ______ ballet since her early age.A. has been addicted toB. has been addicting toC. has been addicting toD. has been addicted withII. 阅读理解(每题2分，共20分)ACentral ParkOutside among the trees, watch the wildlife--- both the human and animal varieties. Call (212)360-3465 or (212)360-2726 for events and tours. Central Park stretches from 59th to 110th Sts., and from 5th Ave. to Central Park. West.Empire State BuildingThis is among the most striking buildings in the city, the nation, even the world. The observation deck (瞭望台) on the 86th floor is open to general public, offering a wonderful view of the second floor. You’ll find the New York Skyride, a simulated (模拟的) helicopter ride. Over Manhattan.5th Ave. at 34th St., Midtown/ (212)736-3100. Intrepid Sea- Air- Space MuseumFive blocks west of Times Square, this museum has hundreds of air, deep- sea and space exhibits. Walk the flight deck of the 900- foot- long aircraft carrier(航母) Intrepid, see dozens of old and modern aircrafts and ride the Intrepid Navy Flight Simulator. Pier 86, W.46th St. and 12th Ave./ (212)245-0072.Madison Square GardenIf it’s big, it probably happens at the Garden. Check out sporting events, concerts and much more. Tours are available.7th Ave, btwn.31st and 33rd Sts., Midtown / (212)465-6741.21. The New York Skyride is for ______.A. sightseeingB. flight trainingC. model plane sportsD. city transportation22. If a visitor is interested in music, he will probably go to ______.A. Central ParkB. Empire State BuildingC. Intrepid Sea- Air- Space MuseumD. Madison Square Garden23. What is the purpose of these texts?A. To provide information of living in New York.B. To provide directions of city traffic in New York.C. To give visitors a guide to New York.D. To give a brief introduction to the history of New York.BMany families take their children on vacation. They will usually travel for a few days or weeks during school breaks. But Julie and Tim Smith have planned a longer vacation with their two children. The Smith family is on a one- year trip around the world. They plan to visit 30 countries in all. Right now, the four travelers are about halfway through their trip.Ms. Smith says they are trying to see as much of their world as they can. Mr. Smith says one of the most interesting experiences of the trip has been meeting new people. He says people have been extremely friendly, very welcoming and love their kids. Eleven- year- old Tyler says he has enjoyed learning about the people they have met. He says, “I learned in Africa that people have very different lifestyles than in America.” His sister, 9- year- old Kara, discovers that she likes Thai food. Ms. Smith says that the trip teaches the children a lot.It took the family a year to prepare for the trip. They had to sell their house and cars. Ms. Smith left her job and her husband is using unpaid leave. They carry small bags filled with lightweight clothing and whatever else they need. Ms. Smith says she enjoys being able to carry everything she needs on her back. She says she does not miss the things she has back home. “What has become more important is making these memories as a family and taking’ those’ with us instead.”The Smiths will continue to head east for the next six months.24. In what way is the Smith family’s trip different from many others’ according to Paragraph 1?A. They take their children on vacation.B. They travel around the world for a year with children.C. They travel during school breaks with children.D. They travel for a few weeks with children.25. Which of the following is NOT true about the Smiths’ preparation for the trip?A. They left their jobs.B. It took the Smith family a year.C. They sold their house and cars.D. They put lightweight clothing in small bags.26. What does the underlined word “those” in Paragraph3 refer to?A. The small bags they carry.B. The memories of the family.C. The things on her back.D. The things back home.CFreshman year of high school is a big transition (过渡) for any student.Luckily, you’re not the only person going through this, and plenty of others have made the transition before you too.One of the ways in which high school is different from middle school or junior high the most is the higher expectations. You’ll find that you’re expected to keep closer track of your own schedule and responsibilities with fewer people checking up on you. At the same time, your classes are likely to become more challenging, and youmight be participating in new school activities as well.Some students find it hard to keep up with everything at first, which is totally normal. One way to prepare in advance for these higher expectations is to make sure that you have organized schedules in place before you start high school.Another important skill for meeting these higher expectations is building a strong support network. No matter how strong a student you are, at some point you will need some help. Keeping healthy relationships with your friends and teachers is a great way to make sure that you have people who are willing to help when you need them, Try to get to know at least some of your teachers beyond your classroom communication. Be an active learner during class and stay after class to ask questions. Take advantage of email or class messaging systems. The better your teachers know you, the better prepared they’ll be to help when you need them.It’s important for you to keep in mind as you start high school that no one is perfect. Transitions are hard for everyone, and starting high school is a big transition. These challenges provide a great chance to reinvent (重塑) yourself.27. In the author’s view, the biggest difference between high school and middle school is ______.A. different relationshipsB. the higher pressureC. high academic (学术的) achievementD. the higher expectations28. Which of the following suggestion is not mentioned in the text?A. Careful schedules.B. Healthy relationships.C. Reviewing notes.D. Using network information.29. Who is the article written for?A. Students in junior school.B. Teachers in high school.C. Parents of high school students.D. Students in senior high school.30. What is the best title for the text?A. How to Get Through the Transition of Freshman Year of High SchoolB. How to Become an Active Learner in High SchoolC. What to Prepare to Keep up with Everything in High SchoolD. How to Meet Your Teacher’s High ExpectationsIII.完形填空(每题1分，共15分)When I was young, I often went to my grandfather’s farm and helped with the farm work. Afterwards we would walk to the irrigation (灌溉) 31 . There we would sit and talk about school, sports, friends and life in general.Sometimes 32 I was sitting and talking with my grandfather, I would 33 a rock and throw it into the middle of the pond. This would cause ripples (波纹) to start at the 34 and extend outward until the ripples would 35 the entire pond. Those childhood memories were so 36 that I would treasure them forever.Now some forty years 37 , I have almost forgotten about those long ago 38 days with my grandfather. When one day I was 39 for an afternoon walk, I passed by a still small pond. I stopped and 40 a stone into the center of the pond and watched as the 41 took effect.As I stood there very calm and quiet, I 42 this rippling effect was much like my life. Although perhaps very small and insignificant (微不足道的) compared to the rest of the world, it did in fact over time have a profound 43 on my family, friends, neighbors, and community. We must always remember that whatever we say or do, good or bad, does 44 cause a rippling effect that 45 far beyond ourselves.31. A. river B. lake C. pond D. sea32. A. after B. while C. as D. before33. A. break up B. get up C. come up D. pick up34. A. edge B. side C. bank D. center35. A. cover B. extend C. lengthen D. widen36. A. sweet B. bitter C. tasty D. pretty37. A. latter B. late C. latest D. later38. A. difficult B. happy C. troublesome D. awesome39. A. out B. off C. down D. up40. A. dropped B. turned C. threw D. divided41. A. results B. ripples C. waves D. waters42. A. guessed B. assumed C. realized D. dreamed43. A. effect B. look C. change D. talk44. A. in all B. in fact C. in brief D. in general45. A. exchanges B. searches C. reaches D. teachesIV.单词拼写(每题1分，共10分)46 国籍n. ______ 47 校园n. ______48 印象n. ______ 49 性格n. ______50 交换v. n. ______ 51 挑战v. n. ______52: 流利的adj. ______ 53 有瘾的adj. ______54 明显地adv. ______ 55 温室n. ______V.语法填空(每题1.5分，共15分)56. I found most of my classmates and teachers friendly and ______ (help).57. I was wrong. But I didn’t feel awkward or ______ (frighten) at all.58. While the first week was a little ______ (confuse), I’m still confident.59. Every Wednesday, we work at a soup kitchen and hand out food to ______ (home) people in the community.60. He thought I didn’t like his writing. Actually, I liked it so much, so he ______ (understand) me.61. The little girl is ______ (extreme) eager to know the result of the exam.62. A disaster is a very bad accident or a sudden event ______ usually causes great damage and can ruin many people’s lives.63. The woman wanted to find and thank the firefighter ______ rescued her from the fire.64. The film brought the hours back to me ______ I was taken good care of in that small village.65. I have reached a point in my life ______ I am supposed to make decisions of my own.VI.英汉互译(每题2分，共20分)66. I dislike __________________. (你对待我的方式)67. It is not known __________________ tomorrow. (他是否会去)68. If you want to use Tom’s computer, __________________. (别忘要密码)69. Our English teacher asks us to __________________. (尽可能经常讲英语)70. Alex jumped with joy __________________! (当他听到那个令人兴奋的消息)71. She always wears a smile. ________________________72. The military training is tiring.________________________73. He is senior to me by 2 years.________________________74. I’m looking forward to your reply.________________________75. I took part in an extra- curricular activity.________________________2024级高一新生假期验收测试答案1-5 DACDA 6-10 ACCAA 11-15 CDDBA 16-20 BDACA21-23 ADC 24-26 BAB 27-30 DCDA31-35CBDDA 36-40ADBAC 41-45 BCABC46. nationality 47. campus 48. impression 49. personality50. exchange 51. challenge 52. fluent 53. addicted 54. obvious 55. greenhouse 56. helpful 57. frightened 58. confusing59. homeless60. misunderstood61. extremely 62. which/ that 63. that/ who64. when 65. where66. the way you treat me67. whether he will go68. don’t forget to ask for the password69. speak English as often/ much as possible/ as we can70. when he heard / hearing the exciting news71. 她总面带微笑。

2022-2023学年吉林省长春市第二实验中学高一上学期期中考试数学试题一、单选题1．已知集合{}0,1,2A =，{},B ab a A b A =∈∈，则集合B 中元素个数为（ ） A ．2 B ．3 C ．4 D ．5【答案】C【分析】由列举法列出集合B 的所有元素，即可判断；【详解】解：因为{}0,1,2A =，a A b A ∈∈,，所以0ab =或1ab =或2ab =或4ab =， 故{}{},0,1,2,4B ab a A b A =∈∈=，即集合B 中含有4个元素； 故选：C2．“1a >”的一个必要不充分条件是（ ） A ． 2a < B ． 2a > C ． 0a < D ．0a >【答案】D【分析】根据必要不充分条件的定义判断．【详解】1a >时，只有D 一定成立，只有D 是必要条件，但D 成立时，1a >不一定成立， 故选：D ．3．化简211133225166()(2)13a b a b a b -（其中0,0a b >>）＝（ ） A ．6ab - B ．6b -C ．23ab -D ．23b -【答案】B【分析】根据幂的运算法则计算．【详解】211111521133222363265166()(2)6613a b a b a b b a b +-+--=-=-． 故选：B ．4．若0.22a =，4log 3.2b =，2log 0.5c =，则（ ） A ．a b c >>B ．b a c >>C ．c a b >>D ．b c a >>【答案】A【分析】根据题意，借助中间量0,1比较大小即可.【详解】解：因为0.422241log 4log 3.2log 0l 2og 1log 0.5b c a >=>==>=>== 所以a b c >>. 故选:A.5．已知7(12)5,1()log ,1a x a x f x x x -+<⎧=⎨≥⎩的值域为R ，那么实数a 的取值范围是（ ）A ．11[,)32-B ．1,2∞⎛⎫- ⎪⎝⎭C ．1,2∞⎡⎫+⎪⎢⎣⎭D ．11(,)32-【答案】A【分析】求出函数()f x 在[1,)+∞上的取值集合，再根据给定的值域确定函数()f x 在(,1)-∞上的取值集合，列式求解作答.【详解】当1x ≥时，函数7()log f x x =在[1,)+∞上单调递增，其取值集合为[0,)+∞，而函数()f x 的值域为R ，因此函数()f x 在(,1)-∞上的取值集合包含(,0)-∞，当120a -=时，函数()(12)5f x a x a =-+在(,1)-∞上的值为常数，不符合要求， 当120a -<时，函数()f x 在(,1)-∞上单调递减，取值集合是(13,)a ++∞，不符合要求， 于是得120a ->，函数()f x 在(,1)-∞上单调递增，取值集合是(,13)a -∞+，则120130a a ->⎧⎨+≥⎩，解得1132a -≤<， 所以实数a 的取值范围是11[,)32-.故选：A6．已知函数f (x )＝e ,031,0x a x x x ⎧+⎨->⎩(a ∈R )，若函数f (x )在R 上有两个零点，则a 的取值范围是（ ）A ．(－∞，－1)B ．(－∞，1)C ．(－1，0)D ．[－1，0)【答案】D【分析】当x >0时，f (x )有一个零点，故当x ≤0时只有一个实根，变量分离后进行计算可得答案.【详解】当x >0时，f (x )＝3x －1有一个零点x ＝13.因此当x ≤0时，f (x )＝ex ＋a ＝0只有一个实根， ∴a ＝－ex (x ≤0)，函数y=－ex 单调递减，则－1≤a <0. 故选：D【点睛】本题考查由函数零点个数确定参数的取值，考查指数函数的性质，属于基础题. 7．若两个正实数x ，y 满足4x y xy +=且存在这样的x ，y 使不等式2++34yx m m <有解，则实数m 的取值范围是（ ） A ．(1,4)- B ．(4,1)- C ．(,4)(1,)∞∞--⋃+ D ．(,3)(0,)∞∞--⋃+【答案】C【分析】利用基本不等式求得+4yx 的最小值，再解一元二次不等式求得m 的取值范围. 【详解】414,1x y xy y x+=+=，414224444x y y x y x y y x x ⎛⎫+=++≥+= ⎪⎝⎭⎛⎫+=+⋅ ⎪⎝⎭， 当且仅当224,16,484x y y x y x y x====时等号成立. 所以()()2234,34410m m m m m m +>+-=+->，解得4m <-或1m >，所以m 的取值范围是(,4)(1,)∞∞--⋃+. 故选：C8．已知函数()()2ln ,0,41,0x x f x x x x ⎧-<⎪=⎨-+≥⎪⎩.若1x ，2x ，3x ，4x 是方程()f x t =的四个互不相等的解，则1234x x x x +++的取值范围是（ ）A ．[)6,+∞B ．(],2-∞C ．14,2e e ⎛⎤-- ⎥⎝⎦D ．14e ,2e ⎡⎫--⎪⎢⎣⎭【答案】D【分析】根据给定函数画出其图象，结合图象可得1234|ln()||ln()|,4x x x x -=-+=，再借助对勾函数的单调性即可计算判断作答.【详解】作出函数()f x 的图象，如图，()f x 的递减区间是(,1)-∞-和[0,2]，递增区间是(1,0)-和(2,)+∞因1x ，2x ，3x ，4x 是方程()f x t =的四个互不相等的解，则01t <≤，不妨令1234x x x x <<<， 则有3x ，4x 是方程241,0x x t x -+=≥的两个根，必有344x x +=，1x ，2x 是方程()ln ,0x t x -=<的两个不等根，则12|ln()||ln()|x x -=-，12ln()ln()0x x -+-=，整理得121=x x ，即121x x =，由|ln()|1x -=得：e x =-或1e x =-，因此有121x x =，211ex -<≤-， 则有12221x x x x +=+，211e x -<≤-，而函数1y x x =+在1(1,]e--上单调递减，从而得2211e 2e x x --≤+<-，于是得123422114[4e ,2)ex x x x x x +++=++∈--， 所以1234x x x x +++的取值范围是1[4e ,2)e --.故选：D二、多选题9．若函数()221)20(1x f x x x--=≠，则（ ）A ．1152f ⎛⎫= ⎪⎝⎭B ．()324f =-C ．()()24101()f x x x =-≠-D ．()2214()1011x f x x x x =-≠≠-⎛⎫⎪⎝⎭且 【答案】AD【分析】由换元法求出()f x ，可判断C ；分别令2x =或12x =可判断A ，B ；求出1f x ⎛⎫⎪⎝⎭可判断D.【详解】令()121x t t -=≠，则12t x -=，所以2221142()1(1)12t f t t t -⎛⎫- ⎪⎝⎭==---⎛⎫⎪⎝⎭，则24()1(1)(1)f x x x =-≠-，故C 错误；1152f ⎛⎫= ⎪⎝⎭，故A 正确；()23f =，故B 错误； 22214411(1)11x f x x x ⎛⎫=-=- ⎪-⎝⎭⎛⎫- ⎪⎝⎭（0x ≠且1x ≠），故D 正确． 故选：AD ．10．若0a b >>，则下列不等式中一定不成立的是（ ） A ．11a b a b+>+ B ．11b b a a +>+ C ．22a b aa b b+>+ D ．11a b b a+>+ 【答案】BC【分析】利用不等式的基本性质，即可判断正误. 【详解】对于A ，因为0a b >>，且()111ab a b a b a b ab -⎛⎫+--=- ⎪⎝⎭， 当1ab >时，110a b a b +-->，即11a b a b +>+； 当1ab =时，110a b a b +--=，即11a b a b +=+； 当01ab <<时，110a b a b+--<，即11a b a b +<+；故11a b a b+>+可能成立； 对于B ，因为0a b >>，则1(1)(1)01(1)(1)b b b a a b b aa a a a a a ++-+--==<+++， 所以11b b a a +>+一定不成立； 对于C ，因为0a b >>，则22202(2)a b a b a a b b b a b +--=<++， 故22a b aa b b+>+一定不成立； 对于D ，因为0a b >>，则111()10a b a b b a ab ⎛⎫+--=-+> ⎪⎝⎭，故11a b b a +>+恒成立.故选：BC.11．已知函数()x x f x a a -=-其中0a >且1a ≠，则下列结论正确的是（ ） A ．函数()f x 是奇函数B ．函数 ()f x 的图象过定点()0,1C ．函数 ()f x 在其定义域上有零点D ．当1a >时，函数()f x 在其定义域上为增函数 【答案】ACD【分析】根据奇偶性的定义，零点的定义，以及单调性的判断方法，结合函数解析式，对每个选项进行逐一分析，即可判断和选择.【详解】对A ：()f x 定义域为R ，且()()()x xf x a a f x --=--=-，故()f x 为奇函数，A 正确；对B ：()00f =，则()f x 过定点()0,0，B 错误； 对C ：由B 可知，0为()f x 的零点，C 正确；对D ：当1a >时，x y a =，x y a -=-都是单调增函数，故()f x 在定义域上是增函数，D 正确. 故选：ACD.12．下列命题中正确的是（ ）A ．函数212xy x ⎛⎫ ⎪⎭-⎝=在区间（0，1）上有且只有1个零点 B ．若函数f （x ）＝x 2＋ax ＋b ，则f 12)(2x x +≤12()()2f x f x + C ．如果函数y ＝x ＋1x在[a ，b ]上单调递增，那么它在[－b ，－a ]上单调递减D ．若定义在R 上的函数y ＝f （x ）的图象关于点（a ，b ）对称，则函数y ＝f （x ＋a ）－b 为奇函数 【答案】ABD【分析】根据函数的相关知识，对各选项逐个判断.【详解】对于选项A ，作出函数12xy ⎛⎫= ⎪⎝⎭和2yx 的图像，由图可知，它们在(0,1)上有且只有1个交点，所以选项A 正确；对于选项B ，作出函数2()f x x ax b =++的图像，设1(A x ，1)y ，2(B x ，2)y ，由图可知，点1212()(),22x x f x f x D ++⎛⎫⎪⎝⎭，总在点1212,22x x x x C f ⎛++⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭，的上方，所以1212()()22x x f x f x f ++⎛⎫≤ ⎪⎝⎭，所以选项B 正确；对于选项C ，因为函数1y x x =+为奇函数，所以函数1y x x=+在[a ，]b 上单调递增，在[b -，]a -上也单调递增，所以选项C 错误；对于选项D ，根据函数()y f x =的图像关于点(,)a b 对称，所以()()2f x a f a x b ++-=，于是()()()f x a b f x a b -+-=-+-，所以函数()y f x a b =+-为奇函数．选项D 正确故选：ABD ．三、填空题13．已知集合A ＝{1，3m ，B ＝{1，m }，A ∪B ＝A ，则m ＝________. 【答案】0或3【解析】由并集结果推出B A ⊆，则3m =m ，求解出m 代入集合中验证是否满足条件即可. 【详解】A B A ⋃＝，B A ∴⊆，则3m =m若3m =，A ＝{1，33，B ＝{1，3}，满足B A ⊆； 若m m =0m =或1m =，0m =时，A ＝{1，3，0}，B ＝{1，0}，满足B A ⊆； 1m =时，A 、B 不满足集合中元素的互异性，舍去.综上所述，0m =或3. 故答案为：0或3【点睛】本题考查根据集合并集运算结果求参数、集合中元素的互异性，属于基础题.14．函数2()log 26xf x x =+-，函数()f x 的零点所在的区间为(),1N n n n +∈且，则n =____【答案】2【分析】探讨给定函数的单调性，再由零点存在性定理确定零点所在区间作答.【详解】函数2()log 26xf x x =+-定义域为(0)+∞，且在(0)+∞上单调递增，23222(2)log 22610,(3)log 326log 320f f =+-=-<=+-=+>，因此函数()f x 的唯一零点在(2,3)内，所以2n =. 故答案为：215．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--16．已知函数()()2212ln log 1f x x x =-+，则满足不等式13log 1f x ⎛⎫> ⎪⎝⎭的x 范围是________. 【答案】()10,3,3⎛⎫+∞ ⎪⎝⎭【解析】分析出函数()()2212ln log 1f x x x =-+是定义域为{}0x x ≠的偶函数，且在区间()0,∞+上为增函数，由13log 1f x ⎛⎫> ⎪⎝⎭得出()13log 1f x f ⎛⎫> ⎪ ⎪⎝⎭，可得出13log 1x >，解此不等式即可得出结果. 【详解】函数()()2212ln log 1f x x x =-+的定义域为{}0x x ≠，()()()()()22221122ln log 1ln log 1f x x x x x f x ⎡⎤-=---+=-+=⎣⎦，该函数为偶函数，因为函数21ln y x =在区间()0,∞+上为增函数，函数()212log 1y x =+在区间()0,∞+上为减函数，所以，函数()()2212ln log 1f x x x =-+在区间()0,∞+上为增函数，且()11f =，若13log 1f x ⎛⎫> ⎪⎝⎭，即()13log 1f x f ⎛⎫> ⎪⎝⎭，即()13log 1f x f ⎛⎫> ⎪ ⎪⎝⎭，可得13log 1x >，可得13log 1x >或者13log 1x <-，解得103x <<或3x >.故答案为：()10,3,3⎛⎫+∞ ⎪⎝⎭.【点睛】本题考查利用函数的单调性与奇偶性解函数不等式，同时也考查了对数不等式的求解，考查分析问题和解决问题的能力，属于中等题.四、解答题17．已知命题p ：关于x 的方程222260x ax a a -+--=有实数根， 命题:13q m a m -≤≤+． (1)若命题p ⌝是真命题， 求实数a 的取值范围； (2)若p 是q 的必要不充分条件， 求实数m 的取值范围． 【答案】(1)(,2)(3,)-∞-⋃+∞ (2)10m -≤≤【分析】（1）依题意命题p 是假命题，即可得到Δ0<，从而求出参数a 的取值范围；（2）记{}23|A a a -=≤≤，{}|13B a m a m =-≤≤+，依题意可得B A ，即可得到不等式组，解得即可.【详解】（1）解：因为命题p ⌝是真命题，所以命题p 是假命题． 所以方程222260x ax a a -+--=无实根，所以222Δ(2)4(26)44240a a a a a =----=-++<． 即260a a -->，即()()320a a -+>，解得3a >或2a <-， 所以实数a 的取值范围是(,2)(3,)-∞-⋃+∞． （2）解：由（1）可知p ：23a -≤≤， 记{}23|A a a -=≤≤，{}|13B a m a m =-≤≤+， 因为p 是q 的必要不充分条件，所以B A ，所以1233m m -≥-⎧⎨+≤⎩（等号不同时取得），解得10m -≤≤，所以实数m 的取值范围是10m -≤≤．18．（1）计算：()2lg 2lg5lg 20lg100+⋅+ （2）已知11223a a-+=，求22112a a a a --++++的值.【答案】（1）3；（2）9.【分析】（1）利用对数的性质及运算法则直接求解．（2）利用平方公式得，a +a -1=11222()2a a -+-，a 2+2+a -2=49，代入可求得答案． 【详解】解：（1） ()2lg 2lg5lg 20lg100+⋅+ ()()22lg 2lg5lg 210lg10=+⋅⨯+ ()()2lg 2lg5lg 2+12lg10=+⋅+ ()2lg 2lg5lg 2+lg52=+⋅+()lg2lg5lg2+lg52=+⋅+lg 2+lg52=+123=+=，所以()2lg 2lg5lg 20lg1003+⋅+=；(2)由11223a a -+=，得11222()9a a -+=，即a +2+a -1=9．∴a +a -1=7． 两边再平方得：a 2+2+a -2=49，∴a 2+a -2=47． ∴22122a a a a --+-+-=472972-=-． 所以221192a a a a --++=++. 19．已知幂函数()()2133m f x m m x +=+-在()0,∞+上是减函数，R m ∈．(1)求()f x 的解析式；(2)若()()11521mma a ->-， 求a 的取值范围． 【答案】(1)()31f x x = (2)()2,5【分析】（1）根据幂函数定义及单调性可得参数m 的值；（2）根据（1）可得4m =-，构造函数()14g x x -=，结合定义域与单调性解不等式.【详解】（1）由函数()()2133m f x m m x +=+-为幂函数得2331m m +-=，解得1m =或4m =-， 又函数在()0,∞+上是减函数，则10+<m ，即1m <-，所以4m =-，()331f x x x -==； （2）由（1）得4m =-，所以不等式为()()4411521a a --->-， 设函数()14g x x -=，则函数()g x 的定义域为()0,∞+，且函数()g x 在()0,∞+上单调递减，所以50210521a a a a ->⎧⎪->⎨⎪-<-⎩，解得25a <<，所以a 的取值范围是()2,5.20．攀枝花是一座资源富集的城市，矿产资源储量巨大，已发现矿种76种，探明储量39种，其中钒、钛资源储量分别占全国的63%和93%，占全球的11%和35%，因此其素有“钒钛之都”的美称．攀枝花市某科研单位在研发钛合金产品的过程中发现了一种新合金材料，由大数据测得该产品的性能指标值y (y 值越大产品的性能越好)与这种新合金材料的含量x (单位：克)的关系为：当07x ≤<时，y 是x 的二次函数；当7x ≥时，1()x m y -=.测得部分数据如表：（1）求y 关于x 的函数关系式()y f x =；（2）求该新合金材料的含量x 为何值时产品的性能达到最佳.【答案】（1）2884,071,73x x x x y x -⎧-+-≤<⎪=⎨⎛⎫≥⎪ ⎪⎝⎭⎩；（2）当x ＝4时产品的性能达到最佳． 【解析】（1）结合待定系数法，代入数据运算即可得解；（2）按照0≤x <7、x ≥7分类，结合指数函数、二次函数的性质即可得解.【详解】（1）当07x ≤<时，设2,(0)y ax bx c a =++≠，由x ＝0，y ＝－4可得c ＝－4，由x ＝2，y ＝8得4a ＋2b ＝12，①由x ＝6，y ＝8得36a ＋6b ＝12，②联立①②解得a ＝－1，b ＝8，则y ＝－x 2＋8x －4；当x ≥7时，y ＝13x m -⎛⎫ ⎪⎝⎭，由x ＝10，y ＝19，可得101139m -⎛⎫= ⎪⎝⎭，解得m ＝8，即有y ＝813x -⎛⎫ ⎪⎝⎭. 综上可得2884,071,73x x x x y x -⎧-+-≤<⎪=⎨⎛⎫≥⎪ ⎪⎝⎭⎩ ； （2）当0≤x <7时，2284(4)12y x x x =-+-=--+，即有x ＝4时，性能取得最大值12；当x ≥7时， 813x y -⎛⎫= ⎪⎝⎭单调递减，所以当x ＝7时，性能取得最大值3；综上可得，当x ＝4时产品的性能达到最佳．21．已知函数223(),x x a f x a x++=∈R ． (1)若函数()()3g x f x =-， 判断()g x 的奇偶性并加以证明；(2)当2a =时， 先用定义法证明函数()f x 在[1,)+∞上单调递增；(3)若对任意(2,3)x ∈，都有223220x x ax +-+>恒成立，求实数a 的取值范围【答案】(1)()g x 为奇函数，证明见解析；(2)证明见解析；(3)4a ≤【分析】（1）由奇偶函数定义即可证明；（2）任取12,[1,)x x ∈+∞且12x x <，结合因式分解证12())0(f x f x -<即可；（3）参变分离得132a x x <++，结合对勾函数求()132h x x x =++最小值即可求 【详解】（1）因为()()32332(0)a a g x f x x x x x x =-=++-=+≠， 定义域为()(),00,∞-+∞关于原点对称，且()22()a a g x x x g x x x ⎛⎫-=--=-+=- ⎪⎝⎭，所以()g x 为奇函数. （2）当2a =时，2()23,[1,)f x x x x∞=++∈+， 任取12,[1,)x x ∈+∞且12x x <， 有()()2112211212121212122(1)()22()()2222x x x x x x f x f x x x x x x x x x x x -⎛⎫---=+-+=-+=- ⎪⎝⎭. 因为1212211,10,0,x x x x x x >->-> 所以12211212(1)()()()20x x x x f x f x x x ---=-<，即12()()f x f x <， 所以函数()f x 在[)1,+∞上单调递增.（3）(2,3)x ∈，则22232132322022x x x x ax a x x x +++-+>⇔<=++， 根据对勾函数性质，()132h x x x =++在()1,+∞单调递增，故当(2,3)x ∈，()()24h x h >=， 故对任意(2,3)x ∈，都有223220x x ax +-+>恒成立时，4a ≤.22．已知·22()(R)21x x a a f x x +-=∈+， (1)若函数()f x 满足()()f x f x -=-，求实数a 的值；(2)（i ）在（1）的条件下，判断函数()f x 在[1,1]-上是否有零点，并说明理由：（ii ）若函数()f x 在R 上有零点，求a 的取值范围.【答案】(1)1a =(2)（i ）有零点，证明见解析；（ii ）()0,2.【分析】（1）根据函数奇偶性的定义,由()()f x f x -=-，采用比较系数法,可解出a =1；（2）（i ）先判断出函数()f x 单调递增，利用零点存在定理即可求得；（ii ）把题意转化为方程221x a =+有根，求出221x y =+在R 上的值域，即可求得. 【详解】（1）因为22()21x x a a f x +-=+·，所以()22·22()2121x x x x a a a a f x --+-+--==++. 而·22()21x x a a f x +--=-+，所以22a a a a =-⎧⎨-=-⎩，解得：1a =. （2）（i ）由（1）可得：212()12121x x x f x -==-++. 因为12x y =在[1,1]-上为减函数，所以221x y =+在[1,1]-上为减函数，所以221x y =-+在[1,1]-上为增函数，所以212()12121x x x f x -==-++在[1,1]-上为增函数. 又11(1)0,(1)0,(0)033f f f -=-<=>=， 所以()f x 在[1,1]-上有唯一的零点0.（ii ）222()2121x x x a a f x a ⋅+-==-++. 函数()f x 在R 上有零点，即方程221x a =+有根. 因为221x y =+在R 上为减函数，211x +>，所以(),22210x y =∈+. 由此可得：若函数()f x 在R 上有零点，则a 的取值范围为()0,2.【点睛】（1）函数奇偶性的应用:①一般用()()f x f x =-或()()f x f x =-;②有时为了计算简便,我们可以对x 取特殊值: (1)(1)f f =-或(1)(1)f f =-.（2）分离参数法是求参数范围的一种非常常用的方法.。