吉林省长春市普通高中2020届高三一模考试英语试题Word版含答案.pdf

机密★考试结束前温州市普通高中2025届高三第一次适应性考试地理试题卷2024.11考生须知：1. 本试题卷分选择题和非选择题两部分，共8页，满分100分，考试时间90分钟。

2. 选择题的答案须用2B铅笔将答题卷上对应题目的答案标号涂黑，如要改动，须将原填涂处用橡皮擦净。

3. 非选择题的答案须用黑色字迹的签字笔或钢笔写在答题卷上相应区域内，答案写在试题卷上无效。

选择题部分一、选择题(本大题共25小题，每小题2分，共50分。

每小题列出的四个备选项中只有一个是符合题目要求的，不选、多选、错选均不得分)下图为北大西洋表层海水平均盐度分布图。

完成1、2题。

1. 图中洋流A. 甲参与副热带环流B. 乙由西风吹拂推动C. 丙按性质属于寒流D. 丁按成因是补偿流2. 图示海区表层海水盐度东西差异和南北差异的主要影响因素分别是A. 洋流气候B. 洋流径流C. 径流纬度D. 气候纬度下图为2019-2023年日本水稻、小麦供需统计图。

完成3、4题。

3. 造成日本水稻和小麦产量差异的主要因素是A. 消费习惯B. 政策补贴C. 气候条件D. 技术水平4. 为保障国内粮食安全，日本可以采取的措施有A. 小麦种植规模化B. 积极推进非粮化C. 进口渠道多元化D. 粮食生产机械化地理试题卷第1页共8页土壤总碳是指土壤中所有含碳化合物的总和，包括无机碳和有机碳。

祁连山国家公园位于青藏高原东北缘，山脉北坡某区域土壤受植被影响，总碳含量随海拔升高而下降。

下图为该区域不同植被类型土壤总碳含量变化图。

完成5、6题。

5. 图中甲、乙、丙植被类型分别对应的是A. 山地针叶林高山灌丛高山草甸B. 山地草原高山草甸山地针叶林C. 常绿阔叶林落叶阔叶林山地草原D. 高山草甸高山灌丛落叶阔叶林6. 随深度增加，土壤总碳含量降低的主要原因是A. 风化作用减弱B. 土壤水分减少C. 枯落物来源减少D. 微生物分解加快硝酸盐是氮在自然界中存在的主要形式之一。

长春市普通高中 2020 届高三质量监测(二)英语本试卷分第 I 卷(选择题)和第 II 卷(非选择题)两部分。

考试结束后，将本试卷和答题卡一并交回。

第I 卷注意事项：1.答第 I 卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2.选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

不能答在本试卷上，否则无效。

第二部分阅读理解 (共 2 节，满分 40 分)第一节(共 15 小题；每小题 2 分，满分 30 分)阅读下面短文，从每题所给的A、B、C 和D 四个选项中，选出最佳选项。

ATop 4 Things To Do in Pigeon Forge and Gatlinburg TN The Pigeon Forge and Gatlinburg areas of Tennessee are absolutely full of fun things to do and see. You are sure to have an amazing time.Dolly Parton’s StampedeOne of the most famous attractions in the Pigeon Forge and Gatlinburg areas, the Dolly Parton’s Stampede is a must-have attraction. This show features many special effects, horsemanship and a fun evening. Watch as you take in some of the best entertainment. Cheer on your favorite side. Then, top it all off with a delicious meal of roast chicken and tons of delicious sides. Ripley Aquarium (水族馆) of the SmokiesFor the animal lover in your family, you’ll definitely want to check out the Ripley’s Aquarium of the Smokies. This aquarium is one of the best attractions in Gatlinburg and features tons of beautiful animals for a fun and educational experience.Titanic MuseumVisit the Titanic in Pigeon Forge for a unique look into this tragic event. The Titanic Museum in the Great Smoky Mountains is the largest permanent museum. Upon arrival, you’ll be amazed by the giant reproduction of the ship. Here, guest will be able to explore a variety ofexhibits.Dollywood Theme ParkDollywood is a favorite among visitors of all ages because it provides tons of fun and different rides. There are lots of events during the year. Dolly Splash Country Water Park is sure to be a refreshing time during the summer months. Visit the park when it’s shining with Christmas lights and more. No matter when you visit, this park is sure to provide unforgettable fun during your Pigeon Forge getaway.21.Where are those who love animals likely to go?A.Dolly Parton’s Stampede.B.Ripley Aquarium of the Smokies.C.Titanic Museum.D.Dollywood Theme Park.22.Which place will make you feel refreshed during the hot months?A.Dolly Parton’s Stampede.B.Ripley Aquarium of the Smokies.C.Titanic Museum.D.Dollywood Theme Park.23.In which section of a magazine may this text appear?A.Science.B. Travel.C. Society.D. Education.BOur wedding was about to begin. My throat was tight and my cheeks got red, but I didn’t care. I was ready to marry David Sanchez. We’re a “nontraditional” couple: getting married not at a church but in a bookstore that supports a charity to fight H.I.V. and homelessness.“Kim! I could walk you down the aisle(走廊)if you like!” David’s father offered gently.“I’m OK. But I appreciate that,” I said with a smile. And I was reminded, again, of my dad’s absence.My father died of cancer six weeks ago. For the last two months, we tried to make him feel comfortable and loved as he departed from this world. He always told us that he didn’t like afuneral(葬礼) and insisted our wedding go forward as planned. But how could we honor him sincethe wedding would be the first time the family would gather after his death and some even didn’t know he was sick?During the ceremony, my dear friend Eva delivered a reading entitled “When Things Go Missing” by Kathryn Schulz. She paused and got everyone on the same page:“When we areexperiencing it, loss often feels like confusion in the usual order of things. In fact, the entire planof the universe consists of losing, and life amounts to a reverse(逆向的) savings account in which we are eventually robbed of everything.”I felt the energy full of the room. Everyone was listening. By choosing to accept the pain, we knew what a wedding does to join two families and mark the next chapter for a couple. Loss became a compass that pointed us away from a fantasy and toward celebrating the difficult realities of life.After rings were exchanged, fried chicken was served, our friends offered so many funny and touching toasts, and finally David sang “Married” on father’s guitar. I felt joy filling all the holes in my soul. Celebrating my father’s life at our wedding made me grateful for all the time I had spent with him, because it all goes by so fast.24.W hy did David's father offer to walk the author down the aisle?A.To relieve her tensionB.To welcome her to his family.C.To play the author's late father's role.D.To contribute something to thecharity. 25.What do we know about Kimat her wedding?A.She got a compass as a wedding gift.B.She enjoyed David's promise for their marriage.C.She received more sympathy from families and friends.D.She recalled the days spent with her father andunderstood life better. 26.Why did Kim feel energy full ofthe room?A.Because she could keep from the pain.B.Because she knew everyone was listening.C.Because she got more courage for marriage and life.D.Because she could read a piece of Kathryn Schulz'sworks. 27.What do we know about Kim and David'swedding ceremony?A.It was held at a church.B.It was a touching and happy one.C.Kim and David turned it into a funeral.D.There was no other activity expect reading.CThere were far fewer cars on the streets and crowds were not seen in the shopping malls in Central China's Wuhan on Jan 24 - the Eve of the Chinese New Year. The scene was quitedifferent from the occasion in the previous years because of the novel coronavirus, which had resulted in 41 deaths in China by the end of New Year’s Eve, mostly in Wuhan, according to the National Health Commission.Chen Li, a doctor in a Wuhan hospital, spent the Chinese Lunar New Year's Eve at home to quarantine herself for having had contact with infected patients, but luckily, she has no signs of symptoms for the time being. Chen's husband is at the forefront of the fight against the epidemic(流行病). "We haven't seen each other for over a week," said Chen. On Saturdaymorning, she put on protective clothing again and returned to work.Wuhan is following Beijing's SARS treatment model in 2003 to build a makeshift hospital with 1,000 beds for receiving infected patients. It will be completed and put into use prior to Feb 3, less than 10 days away. "It's going to be another all-nighter. We need to speed up the work," said Lyu Jun, a young truck driver at the construction site. This is his first Spring Festival away from home.For ordinary people, this year's Lunar New Year's Eve lacks some gatherings. Yin Yeqiong, from Hunan Province, refunded( 退掉) her tickets back home after much debate. "I had it in mymind to still go home, but finally decided to stay in Wuhan," she said. "Ourstay will help reduce panic in other places."Doctors, nurses and experts from across the nation have been selected to join the battle, and manufacturers have restarted their plants to produce medical consumables that have been running short in many places."This is going to be an unforgettable Spring Festival," said Chen Ying, a writer. "Because I feel that at this moment, there are so many families that I do not know, in every corner of this city, praying for our home."28.What does the underlined word “quarantine” mean in paragraph 2?A.SupportB. Supply.C. Serve.D. Separate.29.W hy did Yin Yeqiong decide to stay in Wuhan?A.She couldn’t afford the ticket home.B.She was eager to work as a volunteer.C.She didn’t want to cause unnecessary trouble.D.She was not allowed to go back to her home.30.What does the text intend to tell us?A.The Chinese are fighting against the epidemic together.B.The epidemic is not so serious that we can enjoy our normal life.C.Coronavirus, a highly infectious disease, is spreading around china.D.Not until the makeshift hospital is completed will the doctors find the cure.31.What can we learn from the text?A.The Spring Festival in China this year is the same as before.B.Chen Li and her husband are fighting against coronavirus in Wuhan.C.Lyu Jun and his coworkers will help complete the hospital in Beijing.D.There is no need to worry because we have plenty of medical consumables.DAn argument is an exchange of views between people who do not agree. Some arguments turn into angry quarrels. Suppose, a friend borrowed your car and left it fill of fast-food rubbish. What if you dealt with the situation this way: YOU: Why do you leave all that trash in my car? It’s an absolute mess, and I'm tired of you always being so inconsiderate.FRIEND: Look who's talking. You're such a slob(邋遢鬼), I didn’t think you’d notice. How did aminor incident turn into such an unpleasant exchange? You were angry and feeling as though your kindness was being abused. So instead of talking with your friend, you yelled at him. “Why did you” was a challenge. That's why your friend immediately went on the defensive and yelled back.Now the argument is over. In fact, you don't feel satisfied that you’ve told him off! During the heat of the moment, he said something that hurt your feelings. And perhaps you didn't really mean what you said.How can you avoid such situation? Learn to argue in a better way. Trysomething like this: YOU: I don't like it when you leave trash in my car. It makes me feel like you don’t respect me. FRIEND: You're right. It was veryinconsiderate, I won't do it again.Before speaking, take a deep breath and get control of your anger. The words you use will let your friend know specifically what is bothering you and most importantly, treat him with respect. So he will respond in the same way.Also notice that begin the argument with the pronoun “I”. An argument beginning with “You did…” is generally a challenge. What usually follows is criticism or an insult. And it goes downhill fast from there.Using “I” in arguments won’t eliminate all disagreements. But it cancertainly cut down on the yelling.32.H ow may you feel after an unpleasant argument with your friend?A.Angry and hurt.B. Still wanting to argue.C. Satisfied with the yell.D. Challenged by the argument.33.Which can probably replace the underlined phrase “During the heat of themoment”?A.When the weather is hot outside.B.When the talk becomes exciting.C.When the argument gets emotional.D.When your friend is warmer than ever.34.Which sentence might be used in an “I” argument?A.You are making me feel bad.B.What's the matter with you?C.What on earth are you telling me?D.It makes me feel bad whenhearing that. 35.What is the textmainly about?A.Winning arguments with other people.B.Making sure that people do what you want.ing the “I” method to communicate better.D.Avoiding having disagreement with friends.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。

2020届长春市第一中学高三英语模拟试卷及参考答案第一部分阅读（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，从每题所给的A、B、C、D四个选项中选出最佳选项ADive with Big SharksOur shark dive adventures make use of hookah systems and shark cages. A hookah system is a system of providing air from the surface to divers down below. Cage divers breathe by using a regulator connected to an air hose.Is SharkDiving Dangerous?Yes. You could get sunburnt. You could hit your head on the top bunk getting out of bed. You could fall overboard. As for a shark attack,according to the International Shark Attack File,you are far more likely to be killed by a dog or a deer.Pricing & DetailsOne day Cage Diver Adventure S 875Our expert shark diver team will accompany you to the best viewing areas within the Marine Sanctuary.There,we'll drop our cage and prepare to provide you with a view you'll never forget.No dive experience is necessary.Our cages sit just below the surface.You'll be able to breathe comfortably from your snorkel or air hose while you move about the cage,taking photos and having fun.Top Shark Adventure S 375If you want to see great white sharks but prefer them a little further away,we offer great top-side shark viewing from our observation deck. Help scan the horizon for fins and watch for sharks attacking their prey（猎物）.Important NoteThere's No Shark GuaranteeAlthough we go to the best places at the best time of year, we cannot guarantee you'll see sharks. We've been very successful in past shark seasons and expect another incredible year. However, if we see nosharks, there is no refund.1.Which of the following isTRUEabout the two adventures?A.Top Shark Adventure makes use of hookah systems.B.Cage Diver Adventure offers you a view of the bottom of the sea.C.Cage Diver Adventure is less interesting than the other.D.Top Shark Adventure is suitable for those worried about danger.2.What is most likely to happen according to the advertisement?A.you fail to achieve your purpose of the trip.B.you are out of breath deep down in the sea.C.you are hurt by a shark while diving there,D.you suffer from lack of skill in shark diving.3.It can be inferred from the advertisement that shark diving is ________A.difficult but excitingB.challenging and tiringC.amazing and enjoyableD.expensive but popularBAge has never been a problem for 16-year-old Thessalonika Arzu-Embry. After all, she’s already got her master’s degree.The North Chicago-area teen started homeschooling at the age of 4. She began having an influence on others soon after. When she was 6 years old, she was an inspirational speaker at an organization called Tabitha House Community Service, which is for people who were forced to leave their homes because of earthquake, flood and other natural disasters.At the age of 11, she graduated from high school and then earned her bachelor’s degree in psychology in 2013. She completed those classes online as she was traveling for church events and leadership meetings.She doesn’t stop there, though. The teen plans to focus on aviation psychology (航空心理学) for her further study, a decision inspired by her father who is a pilot. She grew up around airplanes and took fights all the time. Her goal is to use it to help pilots deal with problems that could have deadly results once the plane takes off — a topic that has been in the news lately. For her, it’s a mix of two of her interests.In her free time, Thessalonika enjoys playing tennis, swimming and being active in her youth group at church. She also has three self-published books, which are on her site. Jump the Education Barrier is written to help students finish college, and in the future aims to help business owners with trends. Her third book The Genius Race is designed to help people to be talents in various areas of life.4. Which of the following is TRUE about Thessalonika?A. When she was 6 years old, she started homeschooling.B. She gained her master’s degree at the age of 11.C. She majored in science and technology.D. In 2013 she got her bachelor’s degree through completing courses online.5. What is her next plan according to the passage?A. Major in aviation psychology.B. Deliver inspiring speeches for church events and leadership meetings.C. Be active in her youth group at church.D. Write another book to help people to be talents.6. Why does she write the book Jump the Education Barrier?A. It aims to help people to be geniuses.B. It is intended to give students a hand to complete college.C. It is designed to arouse people’s awareness of psychology.D. The author hope to share her own experience with others.7. Which ofthe following can be the best title for the text?A. The Story of ThessalonikaB. To be a talentC. Three Published BooksD. HomeschoolingCMichele Gentile, an Italian bookseller, is offering free books to children in exchange for plastic bottles to recycle.Michele owns Ex Libris Cafe in Polla，a small town in southern Italy. He said he thought of the recycling program, because he wanted to inspire children in the small town to read and pay attention to the environment.''My goal is to spread the passion and love for books among those people in Italy who do not usually read while at the time helping the environment," Gentile explained.The idea for the initiative (倡议) came after Gentile collaborated with a nearby middle school on an aluminum recycling project. Working together, the schoolchildren and Gentile collected enough cans to purchase books for an entire classroom. His new program too off from there and has already spread into northern Italy: Gentile's hopes his work will continue to make headlines and become a worldwide initiative.The free books come from customers in Gentile's shop who have donated money to purchase a ''suspended" book. The idea comes from a World War II practice in which customers would buy two Coffees: one for themselves and another for the next person in line. Gentile has been using the extra books as part of his recycling initiative, While Gentile's program is a great way to recycle and get kids to read, it also brings awareness to the growingproblem of plastic waste. Single-use plastics make up around 26 percent of all the plastics in the world, only 14 percent of which are recycled. Plastics that end up in landfills take around 500 years to decompose (分解),is a major concern for environmentalists.Cutting down on plastic waste is important if we want to better the environment for future generations, and recycling programs like Gentile's book giveaway are a great way to meet that goal.8. What is the purpose of Gentile's book giveaway?A. To sell more coffee and books.B. To attract more customers.C. To collect money for a new project.D. To inspire reading and recycling.9. How did Gentile come up with the idea?A. Working with a school to recycle cans.B. Seeing school kids don't like reading.C. Donating books for a local school.D. Buying a “suspended” book for a child.10. Who pay for the books of the project?A. The local government.B. Gentile himself.C. Some publishers.D. His customers.11. Whichof the following is the best title for the text?A. An Italian's Reading InitiativeB. Recycling Can Get Kids Free BooksC. Michele's Way of Doing BusinessD. A New Way to Deal with Plastic WasteDMy wife and I recently completed a day-long tour of the Great Wall with Jessie. In addition to being very knowledgeable about the history of theareas that we toured, she spoke excellent English and was able to answer all of our questions. Her driver was very experienced and polite, and we really enjoyed being able to have a customized tour that avoided the tourist traps and forced shopping that seem to be a part of the larger group tours.The attractions themselves were fantastic. I was a little worried that the snowy weather might impact our trip to the Great Wall, but everything went fine, and there weren’t many people out at all that day. I suggest wearing strong shoes—the Great Wall is really a hike. And in snowy or rainy days, the surfaces are pretty slippery (滑的)! Seeing this area in winter was really unique, and the snow made for great pictures. Jessie kept us entertained with stories and facts about the construction of the Wall, and always pointed out great spots for taking pictures. Even though she’s in fantastic shape, she cared about our level of fitness and often stopped to let us catch our breath.When we got back to our hotel, Jessie gave us a great recommendation for dinner and some tips for ourplanned stops the next day. If I find myself in Beijing in the future, I will certainly be contacting Jessie for more tour opportunities, and I’ve already recommended her to some friends who are visiting the area later in the year. I can’t say enough about how kind and knowledgeable she was, and she really gave us a great tour experience.12. What can we infer about Jessie?A. She is a tour advisor.B. She is a tour guide.C. She is a foreign traveler.D. She is a skilled driver.13. When did the writer visit the Great Wall?A. In spring.B. In summer.C. In autumn.D. In winter.14. What did the writer think of his tour?A. Adventurous.B. Disappointing.C. Satisfactory.D. Improvable.15. What is the probable title for the text?A. A Wonderful Tour Day with JessieB. An Extraordinary Tour CompanyC. The Great Wall, an Excellent AttractionD. Jessie, a Kind and Knowledgeable Guide第二节（共5小题；每小题2分，满分10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。

长春市普通高中2020届高三质量检测(一)英语本试卷共150分，共10页。

考试结束后，将本试卷和答题卡一并交回。

注意事项:1. 答题前，考生先将自己的姓名、准考证号码填写清楚，将条形码准确粘贴在条形码区域内。

2. 选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑字迹的签字笔书写，字迹工整，笔记清楚。

3. 请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

4. 作图可先用铅笔画出，确定后必须用黑色字迹的签字笔描黑。

5. 保持卡面清洁，不要折叠、不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。

第一部分听力(1—20小题)在笔试结束后进行。

第二部分阅读理解(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，从每题所给的A、B、C、D四个选项中，选出最佳选项。

ABackcountry for beginners: the best destinations in Canada When carried out safely, your first backcountry trip will leave you lifelong memories, opening a getaway into nature. But the leap from car camping to backcountry requires preparation and learning. Here are some recommended trips for backcountry beginners:Grundy Lake Provincial ParkThe park’s 9 ba ckcountry sites are a 30-minute paddle (划船) away. Grundy Lake is motor-boat free. Your sites are quiet enough for a true backcountry trip. Each site comes equipped with a fire pit (坑) and a picnic table.Bon Echo Provincial ParkMany visitors don’t know ab out the 25 canoe-in campsites located on Joeperry and Pearson Lakes. A short canoe trip of 30-minute will get you to your campsite. At each campsite, you will find a picnic table, tent space and a toilet nearby.Charleston Lake Provincial ParkExperience the best of the Canadian Shield, and hike or paddle your way to 10 backcountry campsites. Travel time can range from 10 minutes to 2 hours. All sites come equipped with elevated tent platforms, a picnic table, a fire grill, and a toilet.Murphys Point Provincial ParkPaddle through Big Rideau Lake (part of the historic Rideau waterway) to access 14 backcountry campsites. Most are located 5-45 minutes away from the boat launch. You’ll find a picnic table, tent space, and a pit toilet nearby each site. Paddle back to visit Murphys’ piece of living history: the Mica Mine!Remember: backcountry travel requires careful consideration of packing, route planning, meal planning, safety, and your skill level.1. You can do the followings at Grundy Lake Provincial Park EXCEPT _______.A. Paddling.B. Having a picnic.C. Cooking.D. Taking a motor-boat.2. Which park has the most campsites?A. Grundy Lake Provincial Park.B. Bon Echo Provincial Park.C. Charleston Lake Provincial Park.D. Murphys Point Provincial Park.3. In which section of a newspaper can you probably find this passage?A. Health.B. Travel.C. Education.D. Science. 【答案】1. D 2. B 3. B【解析】本文是一篇应用文，介绍了加拿大的四个野外旅游地。

吉林省实验中学2017届高三年级第四次模拟考试英语学科试卷考试时间：120分钟满分：150分命题人：刘妍君审题人：马中午2016年12月24日本试卷分为第I卷（选择题）和第II卷（非选择题）两部分。

第I卷（选择题共100分）第一部分听力（共两节，共20小题；每小题1.5分，满分30分）做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分, 满分7.5分）听下面5段对话。

每段对话后有一个小题, 从题中所给的A、B、C三个选项中选出最佳选项, 并标在试卷的相应位置。

听完每段对话后, 你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What does the man like about the play?A. The story.B. The ending.C. The actor.2.Which place are the speakers trying to find?A. A hotel.B. A bank.C. A restaurant.3.At what time will the two speakers meet?A. 5 : 20.B. 5 : 10.C. 4 : 40.4.What will the man do?A. Chang the plan.B. Wait for a phone call.C. Sort things out.5.What does the woman want to do?A. See a film with the man.B. Offer the man some help.C. Listen to some great music.第二节（共15小题；每小题1.5分，满分22.5分）听下面五段对话或独白，每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

2020届吉林省延边第二中学高三上学期第一次调研英语试题注意事项：答案必须写在答题卡上，答在试卷上无效。

本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，本试卷满分150分。

考试时间120分钟。

第Ⅰ卷（选择题共100分）第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有1个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What color is the man’s bike?A. Red.B. Blue.C. Black.2. What does the girl want to do next?A. Change her clothes.B. Do some shopping.C. Choose another high school.3. What is the relationship between the speakers?A. Sister and brother.B. Father and daughter.C. Mother and son.4. What does the man think of his gift?A. It is of use.B. It is of poor quality.C. It is too expensive.5. What will the man do this fall?A. Go to school.B. Travel to France.C. Find a job.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给出的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话或独白前，你将有时间来阅读各个小题，每小题5秒钟；听完后，各个小题将给出5秒钟的作答时间。

2020届高三适应性训练1 英语本试题卷分为听力、阅读理解、语言知识运用和写作四个部分，共14页。

时量120分钟。

满分150分。

第一部分听力(共两节，满分30分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题；每小题1.5分，满分7.5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A．￡19.15. B．￡9.18. C．￡9.15.答案是C。

(A)1. What will the man do next?A. Give Sam a call.B. Find an expert.C. Buy a computer.(B)2. What does the woman want to be now?A. A singer.B. A doctor.C. A teacher.(C)3. How will Sophie spend her weekend?A. Doing her job.B. Staying at home.C. Visiting her friend.(A)4. Where did the woman buy her shoes?A. In a store.B. In a supermarket.C. On the Internet.(C)5. What's the relationship between the speakers?A. Friends.B. Salesman and customer.C. Boss and employee.第二节(共15小题；每小题1.5分，满分22.5分)听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。

2023—2024学年度第二学期高三年级质量监测（一）语文学科试卷语文试卷分为第Ⅰ卷（选择题）和第Ⅱ卷两部分，共150分，考试用时150分钟。

第Ⅰ卷本试卷共11小题，每小题3分，共33分。

在每小题给出的四个选项中，只有一项是最符合题目要求的。

一、（9分）阅读下面一段文字，完成1～3题。

闽江自武夷山麓一路南下，建溪、沙溪，诸多的碧水清滩汇聚于山城南平，遂成巨流。

这一派流水，（），直奔东海。

花果香一路伴随，就到了三塔鼎立的福州，人称此乃有福之州。

“①”，这里说的是除了花香果香之外，由满城的读书声a夹带而来的另一种迷人的香气：这就是书香。

幼时，我家在城中如今被称为a“三坊七巷”的郎官巷。

晚上，家家亮起灯火，四围响起了琅琅书声。

那是童蒙识字的读书之声，b其声悠悠，其乐融融，我在其中。

闽省旧称“蛮荒之地”，晋室东迁，带来了中原文化。

在宋代，一代大儒朱熹在八闽大地开坛授徒，极大地传播了儒家文化。

有宋一代，蔡襄、曾巩、陆游、辛弃疾这些名家，都在福州留下了足迹。

正是他们的到来，为这片大地增添了生机和活力：“②”。

跟随着前人的足迹，这里走出众多学者、作家和诗人。

我的家是平常人家，母亲是平常的乡间女子，没有上过学，不识字，甚至没有一个正式的名字。

但她十分敬重文化，c“敬惜字纸”是她给我们的最初的，也是始终的家训。

她（），却随时俯身捡拾有字的纸张。

在福州，（）、目光向着世界是一个传统。

我常想，d决定一个城市的悠久生命力的，是它的历史文化。

文化的传承是无形的，却是永恒的。

1．依次填入文中括号内的词句，最恰当的一组是（）A．洋洋洒洒目不识丁知书达礼B．纷纷扬扬目不识丁腹有诗书C．纷纷扬扬胸无点墨知书达礼D．洋洋洒洒胸无点墨腹有诗书2．关于文中画波浪线部分的解说，正确的一项是（）A．a处“夹带”中“夹”应读“jiā”，“三坊七巷”中“坊”应读“fáng”。

B．b处句中三个“其”指代内容皆不同。

C．c句中的逗号应改为顿号。

长春市2020届高三质量监测（一）文科数学本试卷共4页．考试结束后，将答题卡交回． 注意事项：1．答题前，考生先将自己的姓名、准考证号码填写清楚，将条形码准确粘贴在考生信息条形码粘贴区．2．选择题必须使用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚．3．请按照题号顺序在答题卡各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试卷上答题无效．4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑．5．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀． 一、选择题：本题共12小题，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.复数2z i +=-，则它的共轭复数z 在复平面内对应的点位于（ ） A. 第一象限 B. 第二象限 C. 第三象限 D. 第四象限【答案】C 【解析】试题分析：复数2z i =-+的共轭复数为2z i =--，在复平面内对应点的坐标为，所以位于第三象限．选C 考点：复数的概念及运算2.已知集合{2A x x =≥或}2x ≤-，{}230B x x x =->，则AB =（ ）A. ∅B. {3x x >或}2x ≤-C. {3x x >或}0x < D. {3x x >或}1x <【答案】B 【解析】 【分析】可以求出集合B ，然后进行交集的运算即可．【详解】解：{}230B x x x =->{|0B x x ∴=<或3}x >，{2A x x =≥或}2x ≤-，{|2AB x x ∴=-或3}x >．故选：B ．【点睛】考查描述法的定义，绝对值不等式和一元二次不等式的解法，以及交集的运算,属于基础题．3.已知等差数列{}n a 的前n 项和为n S ， 515S =，45a = ，则9S =( ) A. 45 B. 63C. 54D. 81【答案】B 【解析】 【分析】根据给出条件求出3a ，利用3a ，4a ，5a 成等差数列计算5a ，再根据前n 项和性质计算9S 的值.【详解】由515S =得33a =，45a =,∴57a = ∴95963S a == 故选B.【点睛】等差数列性质：2(2)m n p q c a a a a a m n p q c +=+=+=+=； 等差数列前n 项和性质：12121()(21)(21)2n n n a a n S n a --+-==-.4.已知条件:1p x >，条件:2q x ≥，则p 是q 的( ) A. 充分不必要条件 B. 必要不充分条件 C. 充要条件 D. 既不充分也不必要条件【答案】B 【解析】 【分析】利用集合间的关系推出p q 、之间的关系.【详解】{|1}x x>{|2}x x ≥，则p 是q 的必要不充分条件,故选B.【点睛】p 成立的对象构成的集合为A ，q 成立的对象构成的集合为B ：p 是q 的充分不必要条件则有：A B ；p 是q 的必要不充分条件则有：BA .5.2019年是新中国成立七十周年，新中国成立以来，我国文化事业得到了充分发展，尤其是党的十八大以来，文化事业发展更加迅速，下图是从2013 年到 2018 年六年间我国公共图书馆业机构数（个）与对应年份编号的散点图（为便于计算，将 2013 年编号为 1，2014 年编号为 2，…，2018年编号为 6，把每年的公共图书馆业机构个数作为因变量，把年份编号从 1到 6 作为自变量进行回归分析），得到回归直线ˆ13.7433095.7yx =+，其相关指数2R 0.9817=，给出下列结论，其中正确的个数是( )①公共图书馆业机构数与年份正相关性较强 ②公共图书馆业机构数平均每年增加13.743个 ③可预测 2019 年公共图书馆业机构数约为3192个 A. 0 B. 1C. 2D. 3【答案】D 【解析】 【分析】根据ˆb和2R 确定是正相关还是负相关以及相关性的强弱；根据ˆb 的值判断平均每年增加量；根据回归直线方程预测2019年公共图书馆业机构数.【详解】由图知点散布在从左下角到右上角的区域内，所以为正相关，又2R 0.9817=趋近于1，所以相关性较强，故①正确；由回归方程知②正确； 由回归方程，当7x =时，得估计值为3191.9≈3192，故③正确. 故选D.【点睛】回归直线方程中的ˆb 的大小和正负分别决定了单位增加量以及相关型的正负；相关系数2R 决定了相关性的强弱，越接近1相关性越强.6.已知直线0x y +=与圆22(1)()2x y b -+-=相切，则b =( )A. 3-B. 1C. 3-或1D.52【答案】C 【解析】 【分析】根据直线与圆相切，则圆心到直线的距离等于半径来求解.=∴|1|2b +=∴13b b ==-或 故选C.【点睛】本题考查直线与圆的位置关系中的相切，难度较易；注意相切时，圆心到直线的距离等于半径.7.已知31()3a =，133b =，13log 3c =，则( )A. a b c <<B. c b a <<C. c a b <<D. b c a <<【答案】C 【解析】 【分析】分析每个数的正负以及与中间值1的大小关系.【详解】因为311()()133a <<=，103331>=，1133log 3log 10<=，所以01,1,0a b c <<><，∴c a b <<，【点睛】指数、对数、幂的式子的大小比较，首先确定数的正负，其次确定数的大小（很多情况下都会和1作比较），在比较的过程中注意各函数单调性的使用. 8.已知,,a b c 为直线，,,αβγ平面，则下列说法正确的是( ) ①,a b αα⊥⊥，则//a b ②,αγβγ⊥⊥，则αβ⊥ ③//,//a b αα，则//a b ④//,//αγβγ，则//αβ A. ①②③ B. ②③④C. ①③D. ①④【答案】D 【解析】 【分析】①可根据线面垂直的性质定理判断；②③④可借助正方体进行判断.【详解】①由线面垂直的性质定理可知垂直同一平面的两条直线互相平行，故正确；②选取正方体的上下底面为αβ、以及一个侧面为γ，则//αβ，故错误；③选取正方体的上底面的对角线为a b 、，下底面为α，则//a b 不成立，故错误；④选取上下底面为αβ、，任意作一个平面平行上底面为γ，则有 //αβ成立，故正确.所以说法正确的有：①④. 故选D.【点睛】对于用符号语言描述的问题，最好能通过一个具体模型或者是能够画出相应的示意图，这样在判断的时候能更加直观. 9.函数2sin()y x ωϕ=+(0,||)2πωϕ><的图象（部分图象如图所示） ，则其解析式为( )A. ()2sin(2)6f x x π=+ B. ()2sin()6f x x π=+C. ()2sin(4)6f x x π=+D. ()2sin()6f x x π=-【答案】A【分析】（1）通过(0,1)以及ϕ的范围先确定ϕ的取值，再根据()f x 过点11(,0)12π计算ω的取值. 【详解】由2sin(0)1,||2πωϕϕϕ⋅+=<π,∴=6， 由111111242sin()0,,,002121261211k k Z T πωπϕωππωπωω⋅+=⋅+=∈>>∴<<=∴即2sin(2)6y x π=+，即为()f x 解析式.【点睛】根据三角函数的图象求解函数解析式时需要注意：（1）根据周期求解ω的值；（2）根据图象所过的特殊点求解ϕ的值；（3）根据图象的最值，确定A 的值.10.中国传统扇文化有着极其深厚的底蕴. 一般情况下，折扇可看作是从一个圆面中剪下的扇形制作而成，设扇形的面积为1S ，圆面中剩余部分的面积为2S ，当1S 与2S 的比值为51-时，扇面看上去形状较为美观，那么此时扇形的圆心角的弧度数为( )A. (35)π-B. 51)πC. 51)πD.(52)π【答案】A 【解析】 【分析】根据扇形与圆面积公式，可知面积比即为圆心角之比，再根据圆心角和的关系，求解出扇形的圆心角.【详解】1S 与2S 所在扇形圆心角的比即为它们的面积比， 设1S 与2S 所在扇形圆心角分别为,αβ，则αβ=，又2αβπ+=，解得(3απ=- 【点睛】本题考查圆与扇形的面积计算，难度较易.扇形的面积公式：21122S r lr α==，其中α是扇形圆心角的弧度数，l 是扇形的弧长.11.已知F 是抛物线24y x =的焦点，则过F 作倾斜角为60︒的直线分别交抛物线于,A B （A 在x 轴上方）两点，则||||AF BF 的值为( )B. 2C. 3D. 4【答案】C 【解析】 【分析】根据抛物线的焦半径的倾斜角和焦准距的表示形式将||||AF BF 表示出来，然后代入相应值计算即可.【详解】||1cos60p AF =-︒，||1cos60pBF =+︒∴||10.53||10.5AF BF +==-. 【点睛】焦点在x 轴上的抛物线，过抛物线的焦点倾斜角为θ的直线与抛物线交于,A B 两点，且||||AF BF >，则有||1cos p AF θ=-，||1cos p BF θ=+，22||sin pAB θ=. 12.已知函数1(0)()(0)xe xf x x -⎧-≤⎪=>，若存在0x R ∈ 使得00()(1)1f x m x --≤成立，则实数m 的取值范围为( ) A. (0,)+∞B. [1,0)(0,)-+∞ C. (,1][1,)-∞-+∞D.(,-∞-∞1](0,+)【答案】D 【解析】 【分析】数形结合去分析，先画出()f x 的图象，然后根据直线过(1,1)-将直线旋转，然后求解满足条件的m 取值范围.【详解】如图, 直线0(1)1y m x =--过定点(1,1)P -,m 为其斜率，0m >满足题意，当0m <时，考虑直线与函数1xy e -=-相切，此时000(1)11x x m x e m e --⎧--=-⎨=-⎩，解得010m x =-⎧⎨=⎩，此时直线与1x y e -=-的切点为(0,0)，∴1m ≤-也满足题意.选D【点睛】分段函数中的存在和恒成立问题，利用数形结合的思想去看问题会更加简便，尤其是直线与曲线的位置关系，这里需要注意：（1）直线过定点；（2）临界位置的切线问题. 二、填空题：本题共4小题． 13.已知1sincos225αα-=，则sin α=_____. 【答案】2425【解析】 【分析】将所给式子平方，找到sin α与sin cos22αα-的关系.【详解】1sincos225αα-=平方得242sin cos 2225αα= ∴24sin 25α=.【点睛】sin cos αα±与sin cos αα的关系：2(sin cos )12sin cos αααα±=±；14.设变量x ，y 满足约束条件03420x y x y x -≤⎧⎪+≤⎨⎪+≥⎩，则3z x y =-的最小值等于______．【答案】8- 【解析】 【分析】作出不等式组对应的平面区域，3z x y =-得1133y x z =-，利用数形结合即可的得到结论． 【详解】解：画出可行域如图，3z x y =-变形为1133y x z =-，过点(2,2)A --，z 取得最大值4， 过点(2,2)C -取得最小值8-． 故答案为：8-．【点睛】本题主要考查线性规划的应用，利用z 的几何意义，通过数形结合是解决本题的关键． 15.三棱锥P ABC -中，PA ⊥平面ABC ，AB AC ⊥,10PA =2,2AB AC ==，则三棱锥P ABC -的外接球的表面积为_____. 【答案】16π 【解析】 【分析】根据题设位置关系，可知以,,AB AC PA 为长、宽、高的长方体的外接球就是三棱锥P ABC -的外接球，根据这一特点进行计算.【详解】设外接球的半径为R ，则2222(2)16R PA AB AC =++= ∴16S π=【点睛】对于求解多条侧棱互相垂直的几何体的外接球，可考虑将该几何体放入正方体或者长方体内，这样更加方便计算出几何体外接球的半径. 16.已知△ABC 的内角,,A B C 的对边分别为,,a b c ，若(,)m b c a b =--,(sin ,sin sin )n C A B =+，且m n ⊥，则A =____;若△ABC 的面积为3ABC 的周长的最小值为_____.【答案】 (1). 3π(2). 6 【解析】【分析】先根据向量垂直得出边角关系，然后利用正、余弦定理求解A的值；根据面积以及在余弦定理，利用基本不等式，从而得到周长的最小值（注意取等号条件）.【详解】由m n ⊥得(,)(sin ,sin sin )()sin ()(sin sin )0m n b c a b C A B b c C a b A B ⋅=--⋅+=-+-+=()()()0b c c a b a b -+-+=得222a b c bc =+-,∴2221cos 22b c a A bc +-==∴3A π=；1sin 2S bc A ==4bc =又222224a b c bc b c =+-=+-所以6a b c b c ++=+（当且仅当2b c ==时等号成立） 【点睛】（1）1122(,),(,)a x y bx y ==，若a b ⊥垂直，则有：12120x x y y +=；（2）222(0,0)a b ab a b +≥>>取等号的条件是：a b =.三、解答题：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：17.已知数列{}n a 中，12a =，1122n n n a a ++=+，设2nn na b =. （Ⅰ）求证：数列{}n b 是等差数列； （Ⅱ）求数列11{}n n b b +的前n 项和n S . 【答案】（Ⅰ）见证明；（Ⅱ）111n S n =-+ 【解析】 【分析】（1）证明1n n b b c --=（c 为常数）即可；（2）将11n n b b +采用裂项的方式先拆开，然后利用裂项相消的求和方法求解n S .【详解】（Ⅰ）证明：当2n ≥时，111121222n n n n n n n n n a a a a b b ------=-== 11b =，所以{}n b 是以为1首项，为1公差的等差数列.（Ⅱ）由（Ⅰ）可知，n b n =，所以+11111n n b b n n =-+，所以1111111122311n S n n n =-+-++-=-++. 【点睛】常见的裂项相消形式： （1）111(1)1n n n n =-++；（2=（3）1111()(21)(21)22121n n n n =--+-+； （4）112311(31)(31)3131n n n n n ++=-----. 18.环保部门要对所有的新车模型进行广泛测试，以确定它的行车里程的等级，下表是对100辆新车模型在一个耗油单位内行车里程（单位：公里）的测试结果．（1）做出上述测试结果的频率分布直方图，并指出其中位数落在哪一组；（2）用分层抽样的方法从行车里程在区间[)38,40与[)40,42的新车模型中任取5辆，并从这5辆中随机抽取2辆，求其中恰有一个新车模型行车里程在[)40,42内的概率． 【答案】（1）图见解析；中位数在区间[)36,38 （2）35【解析】 【分析】(1)由频率分布表可画出频率分布直方图，由图可求出中位数所在区间．(2)由题意，设从[38，40)中选取的车辆为A ，B ，C ，从[40，42)中选取的车辆为a ，b ，利用列举法从这5辆车中抽取2辆，其中恰有一个新车模型行车里程在[40，42)内的概率． 【详解】（1）由题意可画出频率分布直方图如图所示：由图可知，中位数在区间[)36,38．（2）由题意，设从[)38,40中选取的车辆为A ，B ，C ， 从[)40,42中选取的车辆为a ，b ，则从这5辆车中抽取2辆的所有情况有10种，分别为AB ，AC ，Aa ，Ab ，BC ，Ba ，Bb ，Ca ，Cb ，ab ，其中符合条件的有6种，Aa ，Ab ，Ba ，Bb ，Ca ，Cb ，所以所求事件的概率为35. 【点睛】本题考查概率与统计的相关知识，考查频率分布直方图、古典概型、列举法等基础知识，考查运算求解能力，属于基础题．19.在三棱柱111ABC A B C -中，平面ABC 、平面1ACC A 、平面11BCC B 两两垂直.（Ⅰ）求证：1,,CA CB CC 两两垂直；（Ⅱ）若1CA CB CC a ===，求三棱锥11B A BC -的体积. 【答案】（Ⅰ）见证明；（Ⅱ）316a 【解析】 【分析】（1）通过辅助线以及根据面面垂直的性质定理可证1,,CA CB CC 中任意一条直线垂直于另外两条直线构成的平面，即垂直于另外两条直线；（2）采用替换顶点的方式计算体积，计算出高和底面积即可计算体积. 【详解】（Ⅰ）证明：在ABC ∆内取一点P ，作,PD AC PE BC ⊥⊥，因为平面ABC ⊥平面11ACC A ，其交线为AC ，所以PD ⊥平面11ACC A ，1PD CC ⊥， 同理1PE CC ⊥，所以1CC ⊥平面ABC ，11,CC AC CC BC ⊥⊥， 同理AC BC ⊥，故1,,CC AC BC 两两垂直.（Ⅱ）由（Ⅰ）可知，三棱锥11A BCB -的高为11A C a =，1211122BCB S BC BB a ∆=⋅=，所以三棱锥11B A BC -的体积为316a . 【点睛】（1）面面垂直的性质定理：两个平面垂直，一个平面内垂直于交线的直线与另一个平面垂直；（2）计算棱锥的体积时，有时候可考虑采用替换顶点的方式去简化计算.a 20.已知点(1,0),(1,0)M N -，若点(,)P x y 满足||||4PM PN +=. （Ⅰ）求点P 的轨迹方程；（Ⅱ）过点(Q 的直线l 与（Ⅰ）中曲线相交于,A B 两点，O 为坐标原点， 求△AOB 面积的最大值及此时直线l 的方程.【答案】（Ⅰ）22143x y +=；（Ⅱ）AOB ∆面积的最大值为，此时直线l 的方程为3x y =±. 【解析】 【分析】（1）根据椭圆的定义求解轨迹方程；（2）设出直线方程后，采用1||2AB d ⨯⨯（d 表示原点到直线AB 的距离）表示面积，最后利用基本不等式求解最值.【详解】解：（Ⅰ）由定义法可得，P 点的轨迹为椭圆且24a =，1c =.因此椭圆的方程为22143x y +=.（Ⅱ）设直线l的方程为x ty =-与椭圆22143x y +=交于点11(,)A x y ，22(,)B x y ，联立直线与椭圆的方程消去x可得22(34)30t y +--=，即12234y y t +=+，122334y y t -=+. AOB ∆面积可表示为1211||||22AOB S OQ y y =⋅-=△2216223434t t ===++u =，则1u ≥，上式可化为26633u u u u=++≤当且仅当u=t = 因此AOB ∆l的方程为x y =-【点睛】常见的利用定义法求解曲线的轨迹方程问题：（1）已知点(,0),(,0)M c N c -，若点(,)P x y 满足||||2PM PN a +=且22a c >，则P 的轨迹是椭圆；（2）已知点(,0),(,0)M c N c -，若点(,)P x y 满足||||||2PM PN a -=且22a c <，则P 的轨迹是双曲线. 21.设函数1()ln x f x x x+=+. （Ⅰ）求函数()f x 的极值；（Ⅱ）若(0,1)x ∈时，不等式1ln 2(1)xx a x +<--恒成立，求实数a 的取值范围.【答案】（Ⅰ）()2f x =极小值，无极大值；（Ⅱ）01a <≤ 【解析】 【分析】（1）求导后，求解导函数零点，并用列表法分析极值；（2）对所给不等式进行变形，将ln x 分离出来便于求导，同时构造新函数2(1)()ln (01)1a x g x x x x -=-<<+，分析(0,1)x ∈时，()0>g x 恒成立时a 的范围.【详解】解：（Ⅰ）令21()0x f x x-'==，1x =()= (1)2f x f ∴=极小值，无极大值；（II ）由题意可知，0a >，则原不等式等价于2(1)ln 01a x x x -->+，令2(1)()ln (01)1a x g x x x x -=-<<+，22((24)1)()(1)x a x g x x x -+-+'=+，①当01a <≤时，2(24)10x a x +-+≥，()0g x '≤，()g x 在(0,1)上单调递减，()(1)0g x g >=，成立；②当1a >时，2000(0,1),(24)10x x a x ∃∈+-+=，使得当0(0,)x x ∈时，()0g x '<，()g x 单调递减，当0(,1)x x ∈时，()0g x '>，()g x 单调递增，故当0(,1)x x ∈时，()(1)0g x g <=，不成立；综上所述，01a <≤.【点睛】根据不等式恒成立求解参数范围的问题常用的方法：（1）分类讨论法（所给不等式进行适当变形，利用参数的临界值进行分析）； （2）参变分离法（构造新的函数，将函数的取值与参数结合在一起）.（二）选考题：请考生在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.在平面直角坐标系xOy 中，直线l的参数方程为12x y ⎧=⎪⎪⎨⎪=⎪⎩（t 为参数），以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，圆C 的极坐标方程为24cos 3ρρθ-=. （Ⅰ）求直线l 的普通方程和圆C 的直角坐标方程；（Ⅱ）直线l 与圆C 交于,A B 两点，点(1,2)P ，求||||PA PB ⋅的值.【答案】（Ⅰ）直线l 的普通方程为30x y +-=，圆C 的直角坐标方程为22430x y x +--=.（Ⅱ）2 【解析】 【分析】（1）求直线l 的普通方程，消去参数t 即可；求圆的直角坐标方程利用cos sin x y ρθρθ=⎧⎨=⎩互化即可.（2）根据直线所过定点，利用直线参数方程中t 的几何意义求解||||PA PB ⋅的值. 【详解】解：（Ⅰ）直线l 的普通方程为30x y +-=， 圆C 的直角坐标方程为22430x y x +--=. （Ⅱ）联立直线l 的参数方程与圆C的直角坐标方程可得22(1)(2)4(1)30++---=，化简可得220t +-=. 则12||||||2PA PB t t ⋅==.【点睛】（1）直角坐标和极坐标互化公式：cos sin x y ρθρθ=⎧⎨=⎩；（2）直线过定点P ，与圆锥曲线的交点为A B 、，利用直线参数方程中t 的几何意义求解：||||||AB PA PB 、，则有12||||AB t t =-，12||||||PA PB t t =.23.已知函数()|3||1|f x x x =+-- . （Ⅰ）解关于x 的不等式()1f x x +≥ ；（Ⅱ）若函数()f x 的最大值为M ，设0,0a b >>，且(1)(1)a b M ++=，求+a b 的最小值. 【答案】（Ⅰ）(,5][1,3]-∞--；（Ⅱ）最小值为2 【解析】 【分析】（1）采用零点分段的方法解不等式；（2）计算出()f x 的最大值，再利用基本不等式求解+a b 的最小值.【详解】（Ⅰ）由题意(3)(1),34,3()(3)(1),3122,31(3)(1),14,1x x x x f x x x x x x x x x x ----<--<-⎧⎧⎪⎪=+---≤≤=+-≤≤⎨⎨⎪⎪+-->>⎩⎩当3x <-时，41x -+≥，可得5x ≤-，即5x ≤-.当31x -≤≤时，221x x ++≥，可得1x ≥-，即11x -≤≤. 当1x >时，41x +≥，可得3x ≤，即13x <≤. 综上，不等式()1f x x +≥的解集为(,5][1,3]-∞--.（Ⅱ）由（Ⅰ）可得函数()f x 的最大值4M =，且14ab a b +++=， 即23()()2a b a b ab +-+=≤，当且仅当a b =时“=”成立， 可得2(2)16a b ++≥，即2a b +≥，因此+a b 的最小值为2.【点睛】（1）解绝对值不等式，最常用的方法就是零点分段：考虑每个绝对值等于零时x 的值，再逐段分析；（2）注意利用||||||x a x b a b -+-≥-，||||||x a x b a b ---≤-求解最值.。