精讲精练17 2017—2019年高考真题精讲精练
精讲精练13 2017—2019年高考真题精讲精练
高考真题精讲精练：训练步骤：1、先花十八分钟做完这三篇阅读理解。
2、再仔细阅读做题思维过程及试题分析和阅读技巧点拨。
3、然后翻译的文章要仔细研读并做到精通文章原意而且最好是能脱口而出。
2018阅读全国卷三阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项。
AWelcome to Holker Hall & GardensVisitor InformationHow to Get to HolkerBy Car: Follow brown signs an A590 from JB6, M6. Approximale travel times: Windermere - 20 minutes, Kendal - 25 minutes, Lancaster - 45 minutes, Manchester - 1 hour 30 minutes.By Rail: The nearest station is Cark-in-Cartmel with trains to Carnforth, Lancaster Preston for connections to major cities & airports.Opening TimesSunday-Friday (closed on Saturday)11:00 am-4:00pm, 30 March-2nd November.Admission ChargesSpecial EventsProducers: Market 13th AprilJoin us to taste a variety of fresh local food and drinks. Meet the producers and get some excellent recipe ideas.Holker Garden Festival 30th MayThe event celebrate its 22nd anniversary with a great show of the very best of gardening, making it one of themost popular events in gardening.National Garden Day 28th AugustHolker once again opens its gardens in aid of the disadvantaged. For just a small donation you can take a tour with our garden guide.Winter Market 8th NovemberThis is an event for all the family. Wander among a variety of shops selling gifts while enjoying a live music show and nice street entertainment.21. How long does it probably take a tourist to drive to Holker from Manchester?A. 20 minutes.B. 25 minutes.C. 45 minutes.D. 90 minutes.22. How much should a member of a tour group pay to visit to Hall & Cardens?A. £12.00.B. £9.00.C. £8.0D. £5.5023. Which event will you go to if you want to see a live music show?A. Producers’ Market.B. Holker Garden Festival.C. National Garden Day.D. Winter Market.BCities usually have a good reason for being where they are, like a nearby port or river. People settle in these places because they are easy to get to and naturally suited to communications and trade. New York City, for example, is near a large harbour at the mouth of the Hudson River. Over 300 years its population grew gradually from 800 people to 8 million. But not all cities develop slowly over a long period of time. Boom towns grow from nothing almost overnight. In 1896, Dawson, Canada, was unmapped wilderness (荒野). But gold was discovered there in 1897, and two years later, it was one of the largest cities in the West, with a population of 30,000.Dawson did not have any of the natural conveniences of cities like London or Paris. People went there for gold. They travelled over snow-covered mountains and sailed hundreds of miles up icy rivers. The path to Dawson was covered with thirty feet of wet snow that could fall without warming. An avalanche (雪崩) once closed the path, killing 63 people. For many who made it to Dawson, however, the rewards were worth the difficult trip. Of the first 20,000 people who dug for gold, 4,000 got rich. About 100 of these stayed rich men for the rest of their lives.But no matter how rich they were, Dawson was never comfortable. Necessities like food and wood were very expensive. But soon, the gold that Dawson depended on had all been found. The city was crowded withdisappointed people with no interest in settling down, and when they heard there were new gold discoveries in Alaska, they left Dawson City as quickly as they had come. Today, people still come and go --- to see where the Canadian gold rush happened. Tourism is now the chief industry of Dawson City --- its present population is 762.24. What attracted the early settlers to New York City?A. Its business culture.B. Its small population.C. Its geographical position.D. Its favourable climate.25. What do we know about those who first dug for gold in Dawson?A. Two-thirds of them stayed there.B. One out of five people got rich.C. Almost everyone gave up.D. Half of them died.26. What was the main reason for many people to leave Dawson?A. They found the city too crowded.B. They wanted to try their luck elsewhere.C. They were unable to stand the winter.D. They were short of food.27. What is the text mainly about?A. The rise and fall of a city.B. The gold rush in Canada.C. Journeys into the wilderness.D. Tourism in Dawson.CWhile famous foreign architects are invited to lead the designs of landmark buildings in China such as the new CCTV tower and the National Center for the Performing Arts, many excellent Chinese architects are making great efforts to take the center stage.Their efforts have been proven fruitful. Wang Shu, a 49-year-old Chinese architect, won the 2012 Pritzker Architecture Prize --- which is often referred to as the Nobel Prize in architecture --- on February 28. He is the first Chinese citizen to win this award.Wang serves as head of the Architecture Department at the China Academy of Art (CAA). His office is located at the Xiangshan campus (校园) of the university in Hangzhou, Zhejiang Province. Many buildings on the campus are his original creations.The style of the campus is quite different from that of most Chinese universities. Many visitors were amazed by the complex architectural space and abundant building types. The curves (曲线) of the buildings perfectlymatch the rise and fall of hills, forming a unique view.Wang collected more than 7 million abandoned bricks of different ages. He asked the workers to use traditional techniques to make the bricks into walls, roofs and corridors. This creation attracted a lot of attention thanks to its mixture of modern and traditional Chinese elements (元素).Wang’s works show a deep understanding of modern architecture and a good knowledge of traditions. Through such a balance, he had created a new type of Chinese architecture, said Tadao Ando, the winner of the 1995 Pritzker Prize.Wang believes traditions should not be sealed in glass boxes at museums. “That is only evidence that traditions once existed,” he said.“Many Chinese people have a misunderstanding of traditions. They think tradition means old things from the past. In fact, tradition also refers to the things that have been developing and that are still being created,” he said.“Today, many Chinese people are learning Western styles and theories rather than focusing on Chinese traditions. Many people tend to talk about traditions without knowing what they really are,” said Wang.The study of traditions should be combined with practice. Otherwise, the recreation of traditions would be artificial and empty, he said.28. Wang’s winning of the prize means that Chinese architects are ___________.A. following the latest world trendB. getting international recognitionC. working harder than ever beforeD. relying on foreign architects29. What impressed visitors to the CAA Xiangshan campus most?A. Its hilly environment.B. Its large size.C. Its unique style.D. Its diverse functions.30. What made Wang’s architectural design a success?A. The mixture of different shapes.B. The balance of East and West.C. The use of popular techniques.D. The harmony of old and new.31. What should we do about Chinese traditions according to Wang?A. Spread them to the world.B. Preserve them at museums.C. Teach them in universities.D. Recreate them in practice.现在来看A篇文章的解题思路和技巧点拨：像这样的信息查找题根本不用看文章内容，利用审关键词——》文中定位——》比对定选十二字方针原则来做题，这样可以节约做题时间，提高做题效率。
2017年新课标全国卷古诗鉴赏题——精讲精练,各个击破!
晚归山居 刘沧 寥落霜空木叶稀，初行郊野思依依。 深秋频忆故乡事，日暮独寻荒径归。 山影暗随云水动，钟声潜入远烟微。 娟娟唯有西林月，不惜清光照竹扉。 8．这首诗的颈联与王维《山居秋暝》的颔联“明月松间照，清泉 石上流”相比，在写景角度上有何相同点？在意境上有何区别？ 请简要分析。（5分） ①在写景角度上，二者都从视觉、听觉的角度描写了景物。（1 分）刘诗颈联从视觉角度描写“山影”，从听觉角度表现“钟 声”。王诗颔联从视觉角度描写“明月”，从视觉、听觉角度描 写“清泉”。（1分）②在意境上，刘诗颈联描写了山影投映溪 水，随波暗涌，古寺钟声悠长，又随远烟逝去，意境幽暗空寂。 （2分）而王诗颔联描写了一场秋雨后，只见皎洁的月光透过松 枝星星点点洒落下来,又闻泉水淙淙流泻于山石之间，意境幽清 明净。（1分）
表达了诗人凄凉孤寂、思乡的感情。（2分） “鸿雁”是书信的代称,“不闻鸿雁信”表达思乡而不得消息的苦 恼；“鹧鸪”叫声常有凄切思念之意,它的啼叫也勾起词人的故 旧之思； “落花”含有悲情的意思，借“落花”进一步表达出词人内心的凄 凉和孤寂。（4分，每个意象分析1分。）
春 尽 韩偓 惜春连日醉昏昏，醒后衣裳见酒痕。 细水浮花归别涧，断云含雨入孤村。 人闲易有芳时恨，地迥难招自古魂。 惭愧流莺相厚意，清晨犹为到西园。 【注】①韩偓官至翰林学士承旨，但后遭排挤，被贬淮州，后因避难投靠节度使 王审知。当时朱全忠弑帝，建立梁期，王审知接受梁的封号，韩偓离开王审 知定居于闽南泉州。诗作于此时。②招魂，语出《楚辞•招魂》，原指祈祷死 者复生的一种宗教仪式，这里只是一般地用作招致魂魄。 9．这首诗的后两联表达了作者什么样的情感？请简要分析。（ 6分）
①伤春惜春之情。“芳时恨”表现了作者的心惜春之情。 ②年华迟暮，有志难骋的沉痛：芳时春尽，人生老去，诗人却只能“闲”置一隅， 其苦闷沉痛可知。 ③孤身独处，苦无知音的寂寞：诗人地处偏僻，非但亲朋息迹，古人魂魄也难招 致，唯有“流莺相厚”，更见其寂寞之感。
高考必考语法精讲精练专题四：介词 含解析
高考必考语法精讲精练语法专题四：介词介词又叫前置词，是一种虚词。
它是高考必考点之一。
《2017年普通高等学校招生全国统一考试大纲》附录语法项目表中对介词考查列了一项：介词和介词短语。
介词在句子中不能单独使用，只能与名词、代词等构成介词短语，在句中作状语、后置定语、表语和补语等。
2015年高考全国卷Ⅰ第66题（语法填空）考查了介词短语by car乘汽车；第74题（短文改错）考查了介词短语with the developmentof随着......的发展。
2016年高考全国卷Ⅰ第64题（语法填空）考查了介词短语go back to回到；第78题（短文改错）考查了介词短语dream of梦想。
2017年高考全国卷Ⅰ第61题（语法填空）考查了介词as表示“作为”；第68题（语法填空）考查了介词by后面接v-ing；第80题考查了介词短语in the middle of里的介词of。
I.介词分类：III.高考英语短文改错及语法填空考点分析及训练·介词考点规律分析：短文改错对介词的考查主要涉及在及物动词后接宾语时误加介词和在不及物动词后接宾语时漏加介词、可直接用作状语的副词短语前误加介词、介词与其他词的常用搭配、常用介词的基本用法、习语中的介词用法等。
语法填空主要涉及介词的选择。
介词单句改错之真题训练：1. Bill insisted in staying near the car.2. Suddenly we caught sight at a car and some men.3. When I have free time I go a long walk.4.When they came down the police were angry to them.5. Most people can quickly get for help from a doctor or go to a hospital since they are ill.6. …and some books, for example, books for history, science, cooking and gardening are also popular.7. I never knew about a ride down a river could be so exciting.8. It was very kind for them to meet me at the railway station.9. In fact, they are planning to visit China in next year.10. We practise for three times every week.11.We must keep in mind that we play for the team instead ourselves.12. Unfortunately, there are too many people among my family.13. I was happy with any programme but the others spent a lot time arguing…14. Thanks very much on inviting me to your birthday party on Sunday.15. So I’m really sorry that I won’t be able to come in this time.16. …but we do not seem to get much time to talk about together.17. For instance, on one night he played strong and loud music till four o’clock in the morning.18.I was so tired that I fell asleep at the moment my head touched the pillow.19. His parents asked him to spend in more time preparing for the college entrance examination.20.I feel sorry to him.21.Because so much viewing, children may not develop the habit of reading and the ability to enjoy themselves.22. On one year the average child will see 25,000 television commercials…23. The main problem was in that I always thought in Chinese…24. I’m sure they will laugh to me and see me as a fool. So I feel unhappy every day.25. You can find all kinds information in just a few minutes on the Internet.26. But I have spent lots my money, …27. …you will probably want to join in the Stamp Collectors’ Club…28. We have a lot on common and have a lot to talk about.介词单句改错之模拟训练：1. We must serve for the people heart and soul.2. I followed the man for a while, and saw him enter into the bank.3. Soon the nurse married with my friend Jim.4. I took a great many of photographs in the mountains.5. In English class, we often talk each other in English.6. Don’t talk. What the man says is well worth listening.7. The chair looks hard, but it is comfortable to sit.8. She was very kind and insisted lending her car to us.9. I asked to her what she would be doing on Saturday.10. Are you glad to be going to back to school?11. On his way to home, he met one of his old friends Jack.12. Please close the door at next time you come in.13. Thousands of people go to the seaside in every year.14. We can finish the work either this week or in next week.15. We walked down the stairs instead taking the elevator.16. We could not have heard them because the noise from the river.17. Don’t be angry to me for not having written—I was really too busy.18. I’ve read a lot books about a nimals.19. He invited us to dinner, which was very kind for him.20. I knew that there was no hope on the moment I saw him.21. Don’t go by plane. It’s a lot of more expensive.22. Except milk and cheese, we all need vegetables.23. On my way back, I called at Mr Smith at his office.介词单句改错之提升训练：1. His father has been ill on bed for two years.2. During the summer vacation, he worked in the farm.3. He is very fond of football and he is in the school football team.4. I have made rapid progress under the help of my teacher.5. Don’t read under the strong light.6. The killer ran away to the direction of Beijing.7. He lives on No.124. Wuyi Road.8. He is very angry to his son for his failing in the exam.9. He hit me on the face.10. He is strict to me in my work.11. The bottle is filled of the gas.12. London stands to the Thames.13. His mother took pride of his great achievements.14. There are two windows on the wall.15. On the way home, I found I had lost the key of the door.16. We are trying to find the answer of the problem.17. You are required to write your story with your own words.18. With what language did she make the speech?19. He is the cleverest in all the students.20. At a clear night, he went out in search of the gold.21. He had an English party at Christmas Eve.22. Women should be equal with men.23. He is blind on both his eyes.24. Uncle Tom is famous as his skill in cooking.25. He will come back after five weeks.26. He said that he had met us many years ago.27. He is the tallest between the four of us.28. I called on my uncle’s last night.29. It is very clever for a dog to save its owner.30. You should be beware to dangers.介词单句语法填空之真题训练：1．That young man is honest，cooperative，always there when you need his help. ______short，he’s reliable.2．In addition ________ the school，the village has a clinic，which was also built with government support.3．The dictionary is of date：many words have been added to the language since it was published. 4．My connection with pandas goes back ________ my days on a TV show in the mid－1980s. 5.My uncle says that he never dreams _______becoming rich in a short period of time.6．Most of us are more focused_______our tasks in the morning than we are later in the day.7.Are you interested ________ becoming a musician and getting a recording contract(合同)?8.Five years ago, when I taught art at a school in Seattle, I used Tinkertoys as a test ________ the beginning of a term to find out something about my students.9.Chopsticks are not used everywhere in Asia.In India, for example, most people traditionally eat________their hands.10.Now I am leaving home __________ college.At last, I will be on my own, but I still want to have my parents to turn to whenever I need help.11.In high school, I became curious ________ the computer, and built my first website.12.Find an issue you are interested in and learn more.V olunteer or, if you can, contribute a little money ________a cause.13.The mother continued to care for the young panda________more than two years.14.Parents should actively urge their children to take advantage________the opportunity to join sports teams.15.Shelly－Ann is a little woman ________ a big smile.She has mental toughness that did not come about by chance.16.The Scottish girl ________ blue eyes won the first prize in the Fifth Chinese Speech Contest.17.Jane is in a hurry because the train to the airport leaves ________ half an hour.18.Human life is regarded as part of nature and, as such, the only way for us to survive is to live ________ harmony with nature.19.The whole team count ________ Cristiano Ronaldo, and he seldom lets them down.20.Many of the things we now benefit from would not be around but ________ Thomas Edison.21.Have you ever heard of the trees that are homes ________ animals both on land and sea?22.Most people work because it's unavoidable._______ contrast, there are some people who actually enjoy work.23.We tend to have a better memory for things that excite our senses or appeal _____our emotions than for straight facts.24.These comments came in response_____ specific questions often asked by local newsmen.25.This meeting room is a non-smoking area.I would like to warn you _____ advance that if you smoked here you would be fined.学习札记：_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ ____________________________________________________________参考答案及解析介词单句改错之真题训练：1.in 改为on，insist on 为固定搭配2.at 改为of，catch sight of是习语，意为“看见”3.go 后加for，go for a walk 是习语4.to 改为with，要表示对某人生气，英语习惯上用be angry with sb5.去掉for，因其前的get 是及物动词6.books for 改为books on，此处的on 意为“关于”7.去掉about 或将about 改为that，因动词knew 后可直接跟宾语从句，无需用介词8.for 改为of，注意句型It’s kind of sb to do sth9.去掉in，在由next, this, last 等构成的时间短语中，一般可直接用作时间状语，无需加in, on, at 这样的介词10.去掉for，在表示频率的名词前通常不加介词11.instead 后加of，instead of 为复合介词，在此表示“而不是”12.among 改为in，in my family 意为“在我家里”13.a lot 后加of，因a lot 不能直接修饰名词14.on 改为for，thanks for doing sth 意为“因某事而感谢某人”15.去掉in，因this time 可直接用作状语16.去掉about，因about 后没有接宾语，about 属多余17.去掉on，因one night 可直接用作状语18.去掉at，the moment 在此用作连词，相当于as soon as19.去掉in，spend 是及物动词，其后可直接跟名词作宾语20.to 改为for，be / feel sorry for sb 意为“为某人感到难过”21.Because 后加of，因so much viewing 相当于名词22.On 改为In，意为“在一年中”23.去掉that 前的in，was 后是一个以that 引导的宾语从句，in 是多余的24.to 改为at，laugh at 意为“嘲笑”25.kinds 后加of，a kind of 意为“一种……”，all kinds of…意为“各种各样的……”26.lots后加of，lots / a lot后不能接名词；后接名词时，要用lots of…，a lot of…27.去掉in，表示“参加，加入”某个组织，join 后不要再加介词in；表示“参加”某项活动时，才加in28.on 改为in，因为have sth in common 是固定搭配，意为“有共同的……”介词单句改错之模拟训练：1. 去掉for，serve 表示“为……服务”，是及物动词，后接宾语时无需用介词。
高考必考语法精讲精练专题十二：非谓语动词(含解析)
高考必考语法精讲精练语法专题十二：非谓语动词非谓语动词是高考必考点，《2017年一般高等学校招生全国统一考试大纲》附录语法项目表中对非谓语动词列了三项：动词不定式、动名词和分词（包括现在分词和过去分词）。
动词不定式一、动词不定式的形式二、动词不定式的用法动词不定式可以充当谓语之外的全部句子成分，动词不定式可以带宾语或状语构成不定式短语，没有人称和数的改变，但有时态和语态的改变。
1．作主语（1）动词不定式作主语，一般表示详细的某次动作，谓语动词用单数形式。
例如：①To see is to believe.②To master English is of great importance.（2）不定式或不定式短语作主语时，常用it作形式主语，构成“It is + adj+for sb.+to do”结构,或It is +adj+for sth +to be done。
例如：①It is impossible for him to give up smoking.②It is not easy to find your way in the mountain.③It is difficult for the problem to be solved.④It is impossible for my question to be answered in his absence.2.作宾语（1）动词不定式作宾语时，常跟在某些及物动词后面，常见的有：agree，dare，decide，expect，help，hope，learn，manage，offer，pretend，promise，refuse，want, intend, fail, wish, choose等。
例如：①I mean to go there at once.②We must learn to tell friends from enemies.（2）不定式短语作宾语时，假如还带有宾语补足语，往往把不定式短语放在宾补之后，而用it 作形式宾语。
高考必考语法精讲精练专题二_代词版含解析
高考必考语法精讲精练语法专题二：代词代词是英语中非常重要的一类词，也是高考必考考点。
《2017年普通高等学校招生全国统一考试大纲》附录语法项目表中对代词考查列了六项：①人称代词②物主代词③反身代词④指示代词⑤不定代词⑥疑问代词。
2015年高考全国卷Ⅰ第54题（完形填空）考查的是代词whoever、whatever、whichever 与whenever的辨析；第63题（语法填空）考查的是its的用法；第78题（短文改错）考查的是不定代词much与many的辨析，第80题（短文改错）考查的是your与our的辨析。
2016年高考全国卷Ⅰ第44题（完形填空）考查的是代词each，another，this与that 的辨析；第68题（语法填空）考查的是its的用法（给出代词it，根据题意须将其变为its）；第71题（短文改错）考查的是关系代词that与which的辨析；第79题（短文改错）考查的是our与his的辨析。
2017高考全国卷Ⅰ第70题考查的是关系代词which引导非限制性定语从句。
I.代词种类：II.人称代词、物主代词及反身代词对应关系表：III.不定代词用法注意点：1. one, some与any:1) one可以泛指任何人，也可特指，复数为ones。
some多用于肯定句，any多用于疑问句和否定句。
One should learn to think of others.Have you any bookmarks? No, I don’t have any bookmarks.I have some questions to ask.2) some可用于疑问句中，表示盼望得到肯定的答复，或者表示建议，请求等。
Would you like some bananas?Could you give me some money?3) some 和any修饰可数名词单数时，some表示某个，any表示任何一个。
精讲精练15 2017—2019年高考真题精讲精练
高考真题精讲精练：训练步骤：1、先花十八分钟做完这三篇阅读理解。
2、再仔细阅读做题思维过程及试题分析和阅读技巧点拨。
3、然后翻译的文章要仔细研读并做到精通文章原意而且最好是能脱口而出。
2017阅读全国卷一阅读下列短文，从每题所给的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。
APacific Science Center Guide◆Visit Pacific Science Center’sStoreDon’t forget to stop by Pacific Science Center’s Store while you are here to pick up a wonderful science activity or remember your visit. The store is located (位于) upstairs in Building 3 right next to the Laster Dome.◆HungryOur exhibits will feed your mind but what about your body? Our café offers a complete menu of lunch and snack options, in addition to seasonal specials. The café is located upstairs in Building 1 and is open daily until one hour before Pacific Science Center closes.◆Rental InformationLockers are available to store any belongings during your visit. The lockers are located in Building 1 near the Information Desk and in Building 3. Pushchairs and wheelchairs are available to rent at the Information Desk and Denny Way entrance. ID required.◆S upport Pacific Science CenterSince 1962 Pacific Science Center has been inspiring a passion (热情) for discovery and lifelong learning in science, math and technology. Today Pacific Science Center serves more than 1.3 million people a year and beings inquiry-based science education to classrooms and community events all over Washington State. It’s an amazing accomplishment and one we cａn not achiｅve without generous support from individuals, corporations, and other social organizations. visit to find various ways you can support Pacific Science Center.21. Where can you buy a souvenir at Pacific Science Center?A. In Building 1.B. In Building 3.C. At the last Dome.D. At the Denny Way entrance.22. What does PacificScience Center do for schools?A. Train Science teachers.B. Disncie science books.C. Inspire scientific research.D. Take science to the classroom.23. What is the purpose of the last part of the text?A. To encourage donations.B. To advertise coming events.C. To introduce special exhibits.D. To tell about the Center’s history.BI work with Volunteers for Wildlife, a rescue and education organization at Bailey Arboretum in Locust Valley. Trying to help injured, displaced or sick creatures can be heartbreaking; survival is never certain. However, when it works, it is simply beautiful.I got a rescue call from a woman in Muttontown. She had found a young owl (猫头鹰) on the ground. When I arrived, I saw a 2-to 3-week-old owl. It had already been placed in a carrier for safety.I examined the chick (雏鸟) and it seemed fine. If I could locate the nest, I might have been able to put it back, but no luck. My next work was to construct a nest and anchor it in a tree.The homeowner was very helpful. A wire basket was found. I put some pine branches into the basket to make this nest safe and comfortable. I placed the chick in the nest, and it quickly calmed down.Now all that was needed were the parents, but they were absent. I gave the homeowner a recording of the hunger screams of owl chicks. These advertise the presence of chicks to adults; they might also encourage our chick to start calling as well. I gave the owner as much information as possible and headed home to see what news the night might bring.A nervous night to be sure, but sometimes the spirits of nature smile on us all! The homeowner called to say that the parents had responded to the recordings. I drove over and saw the chick in the nest looking healthy and active. And it was accompanied in the nest by the greatest sight of all --- LUNCH! The parents had done their duty and would probably continue to do so.24. What is unavoidable in the author’s rescue work according to paragraph 1?A. Efforts made in vain.B. Getting injured in his work.C. Feeling uncertain about his future.D. Creatures forced out of their homes.25. Why was the author called to Muttontown?A. To rescue a woman.B. To take care of a woman.C. To look at a baby owl.D. To cure a young owl.26. What made the chick calm down?A. A new nest.B. Some food.C. A recording.D. Its parents.27. How would the author feel about the outcome of the event?A. It’s unexpected.B.It’s beautiful.C.It’s humorous.D.It’s discouraging.CSome of the world’s most famous musicians recently gathered in Paris and New Orleans to celebrate the first annual International Jazz Day. UNESCO (United Nations Educational, Scientific and Cultural Organization) recently set April 30 as a day to raise awareness of jazz music, its significance, and its potential as a unifying (联合) voice across cultures.Despite the celebrations, though, in the U.S. the jazz audience continues to shrink and grow older, and the music has failed to connect with younger generations.It’s Jason Moran’s job to help change that. As the Kennedy Center’s artistic adviser for jazz, Moran hopes to widen the audience for jazz, make the music more accessible, and preserve its history and culture.“Jazz seems like it’s not really a part of the American appetite,” Moran tells National Public Radio’s reporter Neal Conan. “What I’m hoping to accomplish is that my generation and younger start to reconsider and understand that jazz is not black and write anymore. It’s actually color, and it’s actually digital.”Moran says one of the problems with jazz today is that the entertainment aspect of the music has been lost. “The music can’t be presented today the way it was in 1908 or 1958. It has to continue to move, because the way the world works is not the same,” says Moran.Last year, Moran worked on a project that arranged Fats Waller’s music for a dance party, “Just to kind of put it back in the mind that Waller is dance music as much as it is concert music,” says Moran. “For me, it’s the recontextualization. In music, where does the emotion (情感) lie? Are we, as humans, gaining any insight (感悟) on how to talk about ourselves and how something as abstract as a Charlie Parker record gets us into a dialogue about our emotions and our thoughts? Sometimes we lose sight that the music has a wider context,” says Moran, “so I want to continue those dialogues. Those are the things I want to foster.”28．Why did UNESCO set April 30 as International Jazz Day?A．To remember the birth of jazz.B．To protect cultural diversity.C．To encourage people to study music.D．To recognize the value of jazz.29．What does the underlined word “that” in paragraph 3 refer to?A．Jazz becoming more accessible.B．The production of jazz growing faster.C．Jazz being less popular with the young.D．The jazz audience becoming larger.30．What can we infer about Moran’s opinion on jazz?A．It will disappear gradually.B．It remains black and white.C．It should keep up with the times.D．It changes every 50 years.31．Which of the following can be the best title for the text?A．Exploring the Future of Jazz.B．The Rise and Fall of Jazz.C．The Story of a Jazz Musician.D．Celebrating the Jazz Day.下面我们来看看A篇文章的思维过程解析和解题技巧点拨：往往A篇都是信息查找题，因此可以直接做题以节约时间提高做题效率。
高考必考语法精讲精练专题五：形容词和副词-Word版含解析
高考必考语法精讲精练语法专题五：形容词与副词形容词、副词是特别重要的词，是高考必考内容。
《2017年一般高等学校招生全国统一考试大纲》附录语法项目表中对形容词和副词考查都列了两项：①形容词（比较级和最高级）②副词（比较级和最高级）。
纵观历年高考试题，试题中出现的考点主要有：形容词和副词的语义辨析，形容词与副词的相互转换，形容词和副词的等级。
2015年高考全国卷Ⅰ第69题（语法填空）考查了形容词regular变成副词regularly；第76题（短文改错）考查了副词seriously变成形容词serious。
此外，完形填空中第44、第48、第50、第53、第57和第60题都是考查形容词或副词在详细语境中的词义。
2016年高考全国卷Ⅰ第63题（语法填空）考查了形容词official变为副词officially；第75题考查了形容词honest变为名词honesty。
此外，完型填空第52题还考查了quiet、still、away与calm 的辨析。
2017年高考全国卷Ⅰ第66题（语法填空）考查了形容词bad变成比较级worse；第69题（语法填空）考查了care变成形容词careful；第78题（短文改错）考查了副词late变成later；第79题（短文改错）考查了副词suddenly改为形容词sudden。
此外，完型填空第54、第58和60题都是考查形容词或副词在详细语境中的词义。
I.形容词、副词的等级(一)形容词/副词的比较级和最高级构成2.3.形容词、副词递减的比较等级的构成★★在形容词、副词前加less和least，表示“较不”和“最不”:interesting好玩的less interesting较无趣的least interesting最无趣的important重要的less important较不重要的least important最不重要的★★有些形容词可以加er及est或前面加上more / most来形成比较级和最高级polite –politer 或more polite – politest 或most polite ，这类词还有quiet，handsome，pleasant，common，exact等. II.高考英语短文改错及语法填空考点分析及训练·形容词与副词考点规律分析：短文改错对形容词与副词的考查主要涉及形容词和副词比较等级的误用(尤其是在本身已是比较级的词前误加more)、形容词与副词的混用(如修饰动词时误用形容词或修饰名词时误用副词)等，另外，用作表语时该用形容词的却误用了名词、简短副词(如in, down 等)的误加与漏用、涉及形容词搭配的as…as 结构、how 与what 的混用等也是常考的考点。
备战2017高考数学(精讲+精练+精析)专题9.2圆与点、线、圆的位置关系试题理(含解析)
专题9.2 圆与点、线、圆位置关系【三年高考】1. 【2021高考新课标2理数】圆2228130x y x y +--+=圆心到直线10ax y +-=距离为1，那么a=〔 〕〔A 〕43- 〔B 〕34- 〔C 〔D 〕2【答案】A2．【2021高考新课标3理数】直线l ：30mx y m ++=与圆2212x y +=交于,A B 两点，过,A B分别做l 垂线与x 轴交于,C D 两点，假设AB =那么||CD =__________________. 【答案】4【解析】因为||AB =，且圆半径为所以圆心(0,0)到直线30mx y m ++=距离为，那么由，解得，代入直线l 方程，得，所以直线l 倾斜角为30︒，由平面几何知识知在梯形ABDC 中，．3．【2021高考江苏卷】如图，在平面直角坐标系xOy 中，以M 为圆心圆22:1214600M x y x y +--+=及其上一点(2,4)A〔1〕设圆N 与x 轴相切，与圆M 外切，且圆心N 在直线6x =上，求圆N 标准方程；〔2〕设平行于OA 直线l 与圆M 相交于,B C 两点，且BC OA =,求直线l 方程；〔3〕设点(,0)T t 满足：存在圆M 上两点P 与Q ,使得,TA TP TQ +=,求实数t 取值范围。
(3)设()()1122,,Q ,.P x y x y 因为()()2,4,,0,A T t TA TP TQ +=,所以 ……① 因为点Q 在圆M 上，所以()()22226725.x y -+-= …….②将①代入②，得()()22114325x t y --+-=.于是点()11,P x y 既在圆M 上，又在圆()()224325x t y -++-=⎡⎤⎣⎦上，从而圆()()226725x y -+-=与圆()()224325x t y -++-=⎡⎤⎣⎦有公共点，所以()()2255463755,t -≤+-+-≤+⎡⎤⎣⎦ 解得22212221t -≤≤+.因此，实数t 取值范围是2221,2221⎡⎤-+⎣⎦.4．【2021 高考重庆，理8】直线l ：x +ay -1=0〔a ∈R 〕是圆C ：224210x y x y +--+=A 〔-4，a 〕作圆C 一条切线，切点为B ，那么|AB |= 〔 〕A 、2B 、42C 、6D 、210 【答案】C【解析】圆C 标准方程为22(2)(1)4x y -+-=，圆心为(2,1)C ，半径为2r =，因此2110a +⨯-=，1a =-，即(4,1)A --，2222(42)(11)46AB AC r =-=--+---=.选C .5.【2021 高考广东，理5】平行于直线且与圆相切直线方程是〔 〕A ．或 B. 或012=++y x 522=+y x 052=+-y x 052=--y x 052=++y x 052=-+y xC. 或D. 或 【答案】．6.【2021 高考山东，理9】一条光线从点()2,3--射出，经y 轴反射后与圆()()22321x y ++-=相切，那么反射光线所在直线斜率为〔 〕〔A 〕53-或35- 〔B 〕32- 或23- 〔C 〕54-或45- 〔D 〕43-或34- 【答案】D【解析】由光反射原理知，反射光线反向延长线必过点()2,3- ，设反射光线所在直线斜率为k ，那么反身光线所在直线方程为：()32y k x +=- ，即：230kx y k ---=.又因为光线与圆相切，()()22321x y ++-= 所以， ,整理：21225120k k ++= ，解得： ，或 ,应选D ． 7.【2021 高考广东，理20】过原点动直线与圆相交于不同两点，．〔1〕求圆圆心坐标；〔2〕求线段中点轨迹方程； 〔3〕是否存在实数，使得直线与曲线只有一个交点：假设存在，求出取值范围；假设不存在，说明理由．052=+-y x 052=--y x 052=++y x 052=-+y x D l 221:650C xy x A B 1C AB M C k :(4)L yk x C k8．【2021高考江苏卷第9题】在平面直角坐标系xoy 中，直线230x y +-=被22(2)(1)4x y -++=圆截得弦长为 .【答案】LDxyOC E F8．【2021全国2高考理第16题】设点M 〔0x ,1〕，假设在圆O:221x y +=上存在点N ，使得∠OMN=45°，那么0x 取值范围是________. 【答案】[1,1]-【解析】由题意知：直线MN 与圆O 有公共点即可，即圆心O 到直线MN 距离小于等于1即可，如图，过OA ⊥MN ，垂足为A ，在Rt OMA ∆中，因为∠OMN=45，所以||||sin 45OA OM ==， 解得||2OM ≤，因为点M 〔0x ,1〕，所以20||12OM x =+≤，解得011x -≤≤，故0x 取值范围是9．【2021四川高考理第14题】设m R ∈，过定点A 动直线0x my +=与过定点B 动直线30mx y m --+=交于点(,)P x y ，那么||||PA PB ⋅最大值是 . 【答案】10．【2021重庆高考理第13题】直线02=-+y ax 与圆心为C 圆()()4122=-+-a y x 相交于B A ，两点，且ABC ∆为等边三角形，那么实数=a _________. 【答案】415【解析】7由题设圆心到直线20ax y --=3415a =所以答案应填：41511．【2021高考湖北卷理第12题】直线1:l y x a =+与2:l y x b =+将单位圆22:1C x y +=分成长度相等四段弧，那么22a b += .【答案】2【解析】8依题意，设1l 与单位圆相交于B A ,两点，那么∠90=AOB °.如图，当1,1-==b a 时满足题意，所以222=+b a .12．【2021大纲高考理第15题】直线1l 与2l 是圆222x y +=两条切线，假设1l 与2l 交点为()1,3，那么1l 与2l 夹角正切值等于 . 【答案】43．【三年高考命题回忆】纵观前三年各地高考试题, 对圆与点、直线、圆位置关系这局部考察，主要考察点与圆位置关系、直线与圆位置关系、圆与圆位置关系，从题型来看，高考中一般以选择题与填空形式考察，难度较低，局部省份会与其他圆锥曲线局部结合起来，综合考察．【2021年高考复习建议与高考命题预测】由前三年高考命题形式可以看出 , 直线与圆是两个根本图形，对它们研究，既可以从几何角度来探索它们位置关系，又可以从方程角度来解决一些度量问题，表达用代数方法研究几何问题思想，同时又是研究圆锥曲线根底，所以对这局部内容复习要倍加关注．对直线与圆位置关系考察．一般会涉及弦长、距离计算与圆切线问题与直线与圆位置关系判定，还可能会考察轨迹问题与与圆有关最值问题，其中渗透数形结合思想与转化与化归思想运用．圆与圆位置关系考察，属于简单题，主要涉及位置关系判定与长度问题．预测2021年直线与圆位置关系可能涉及，新课标卷可能会出一道选择题，也有可能出一道解答题. 【2021年高考考点定位】高考对圆与直线、圆位置关系考察有三种主要形式：一是考察直线与圆位置关系；二是考察圆切线问题；三是与圆有关弦长问题；四是考察圆与圆位置关系；五是考察与圆有关最值问题；六是考察与圆有关轨迹问题，注意几何法在解题中重大作用．【考点1】点、直线、圆与圆位置关系 【备考知识梳理】1．直线0=++C By Ax 与圆222)()(r b y a x =-+-位置关系有三种：〔1〕假设，0<∆⇔⇔>相离r d ；〔2〕0=∆⇔⇔=相切r d ；〔3〕0>∆⇔⇔<相交r d ．还可以利用直线方程与圆方程联立方程组⎩⎨⎧=++++=++022F Ey Dx y x C By Ax 求解，通过解个数来判断：〔1〕当方程组有2个公共解时〔直线与圆有2个交点〕，直线与圆相交；〔2〕当方程组有且只有1个公共解时〔直线与圆只有1个交点〕，直线与圆相切；〔3〕当方程组没有公共解时〔直线与圆没有交点〕，直线与圆相离；即：将直线方程代入圆方程得到一元二次方程，设它判别式为Δ，圆心C 到直线l 距离为d,那么直线与圆位置关系满足以下关系：相切⇔d=r ⇔Δ＝0；相交⇔d<r ⇔Δ>0；相离⇔d>r ⇔Δ<0．2. 两圆位置关系判定方法：设两圆圆心分别为O 1，O 2，半径分别为r 1，r 2，d O O =21． 条公切线外离421⇔⇔+>r r d ；条公切线外切321⇔⇔+=r r d ；条公切线相交22121⇔⇔+<<-r r d r r ；条公切线内切121⇔⇔-=r r d ；无公切线内含⇔⇔-<<210r r d ；判断两个圆位置关系也可以通过联立方程组判断公共解个数来解决 【规律方法技巧】1.直线与圆位置关系问题，既可以用几何判断，也可以用代数判断，通常利用几何判断较为简洁，即圆心到直线距离d 与圆半径r 比拟．2.点与圆位置关系判断，只需将点坐标代入圆方程左边，当左边大于右边时，点在圆外；当左边小于右边时，点在园内；当左边等于右边时，点在圆上． 3．圆与圆位置关系判定，既可以利用圆心距与两圆半径与差比拟，也可以利用两圆公切线条数来判定，两圆相切注意分内切或外切讨论．4. 假设两圆相交，那么两圆公共弦所在直线方程可由两圆方程作差得到． 【考点针对训练】1. 【2021届湖北省八校高三二联】圆C 方程为()()22210x y r r -+=>，假设p ：13r ≤≤；q ：圆C 上至多有3个点到直线3+30x y -=距离为1，那么p 是q 〔 〕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】A2. 【2021届陕西省安康市高三第三次联考】圆M 与圆22255:33N x y r ⎛⎫⎛⎫-++= ⎪ ⎪⎝⎭⎝⎭关于直线y x =对称, 且点在圆M 上. 〔1〕判断圆M 与圆N 位置关系；〔2〕设P 为圆M 上任意一点, 与PB 不共线,PG 为APB ∠平分线, 且交AB 于G .求证：PBG ∆与APG ∆面积之比为定值.【解析】〔1〕圆N 圆心关于直线y x =对称点为22255416,,3339M r MD ⎛⎫⎛⎫-∴==-= ⎪ ⎪⎝⎭⎝⎭,∴圆M 方程为225516339x y ⎛⎫⎛⎫++-= ⎪ ⎪⎝⎭⎝⎭,22101010282,3333MN r ⎛⎫⎛⎫=+=>= ⎪ ⎪⎝⎭⎝⎭∴圆M 与圆N 相离.〔2〕设()00,P x y ,那么()()222220000051654113933PA x y x x x ⎛⎫⎛⎫=++-=-+++=- ⎪ ⎪⎝⎭⎝⎭, ()()2222200000516516113933PB x y y x x ⎛⎫⎛⎫=-+-=-++-=- ⎪ ⎪⎝⎭⎝⎭,224,2,PB PB G PA PA ∴=∴=为APB ∠角平分线上一点,G ∴ 到PA 与PB 距离相等, 为定值.【考点2】圆切线问题 【备考知识梳理】过切点与圆心直线垂直于切线，即圆心到直线距离等于半径 【规律方法技巧】1.直线与圆相切判定以及与切线有关参数问题都可以利用圆心到切线距离等于半径列方程判断或求解；涉及切线长问题，可以利用勾股定理求．2.对于圆切线问题，尤其是圆外一点引圆切线，易无视切线斜率k 不存在情形．3. 圆切线问题处理要抓住圆心到直线距离等于半径建立关系解决问题． 【考点针对训练】1. 【2021年河南省八市重点高中质检】过点(3,1)作圆222(1)x y r -+=切线有且只有一条，那么该切线方程为〔 〕A ．250x y +-=B ．270x y +-=C ．250x y --=D ．270x y --= 【答案】B2. 【2021届陕西师大附中高三下第十次模拟】从圆222210x x y y -+-+=外一点()3,2P 向这个圆作两条切线，那么两切线夹角余弦值为〔 〕A ．0B ．12C ．32D ． 35【答案】D【考点3】弦长问题 【备考知识梳理】 求圆弦长常用方法(1)几何法：设圆半径为r ，弦心距为d ，弦长为l l ，那么. (2)代数方法：运用根与系数关系及弦长公式：2221212121|x -x |=1[()4]k k x x x x +++-注意：常用几何法研究圆弦有关问题． 【规律方法技巧】处理直线与圆弦长问题时多用几何法，即弦长一半、弦心距、半径构成直角三角形．【考点针对训练】1. 【2021届山东省济宁市高三下第三次模拟】圆22:(1)(3)2C x y -+-=被直线3y x b =+所截得线段长度等于2，那么b 等于〔 〕A ．5±B ．10±C ．25±D ．30±【答案】B【解析】因圆心到直线3y x b =+距离是,半弦长为1,故,解之得10±=b ,应选B.2. 【2021届广州省惠州市高三第一次调研】圆22(2)(2)x y a ++-=截直线20x y ++=所得弦长为6，那么实数a 值为〔 〕A ．8B ．11C ．14D ．17【答案】B【解析】圆22(2)(2)x y a ++-=，圆心()2,2-，半径a ．故弦心距．再由弦长公式可得2911a =+=；应选B ．【考点4】与圆有关最值问题【备考知识梳理】与圆有关最值问题也是命题热点内容，它着重考察数形结合与转化思想.归纳起来常见命题角度有：1斜率型最值问题； 2截距型最值问题； 3距离型最值问题；【规律方法技巧】解决与圆有关最值问题关键在于能正确认识所给问题含义，明确几何意义，结合几何图形数形结合法求解与圆有关最值问题：(1)形如t ＝y －b x －a形式最值问题，可转化为动直线斜率最值问题； (2)形如t ＝ax ＋by 形式最值问题，可转化为动直线截距最值问题；(3)形如t ＝(x －a )2＋(y －b )2形式最值问题，可转化为动点到定点距离最值问题．【考点针对训练】1. 【2021届广州省惠州市高三第一次调研】设,m n R ∈，假设直线:10l mx ny +-=与x 轴相交于点A ，与y 轴相交于点B ，且与圆224x y += 相交所得弦长为2，O 为坐标原点，那么AOB ∆面积最小值为 .【答案】32．【2021届河南省洛阳市高三考前练习二】点(,)P x y 是直线40kx y ++=〔0k >〕上一动点，,PA PB 是圆22:20C x y y +-=两条切线，,A B 为切点，假设四边形PACB 最小面积是2，那么k 值为________.【答案】2【解析】先求圆半径，四边形PACB 最小面积是2，转化为三角形PBC 面积是1，求出切线长，再求PC 距离也就是圆心到直线距离，可解k 值．圆22:20C x y y +-=圆心〔0，1〕，半径是r=1，由圆性质知：2PBC PACB S S =四边形，四边形PACB 最小面积是2，〔d 是切线长〕，∴2d =最小值，圆心到直线距离就是PC222125,021k k k =+=>∴=+，.【考点5】与圆有关轨迹问题 【备考知识梳理】求与圆有关轨迹问题时，根据题设条件不同常采用以下做法(1)直接法：直接根据题目提供条件列出方程．(2)定义法：根据圆、直线等定义列方程．(3)几何法：利用圆与圆几何性质列方程．(4)代入法：找到要求点与点关系，代入点满足关系式等．【规律方法技巧】利用圆定义或者探讨曲线上点坐标满足方程，从而得到动点运动轨迹为圆，进而利用圆相关性质解题．【考点针对训练】1．【2021届海南师范大学附属中学高三临考】过点)3,0(F 且与直线03=+y 相切动圆圆心轨迹方程为〔 〕A ．y x 122=B ．x y 122-=C ．x y 122=D ．y x 122-=【答案】A2．【2021届湖北襄阳五中高三5月二模】定圆22:(3)16,M x y +=动圆N 过点(3,0)F 且与圆M 相切,记圆心N 轨迹为.E〔1〕求轨迹E 方程；〔2〕设点,,A B C 在E 上运动，A 与B 关于原点对称，且AC BC =,当ABC ∆面积最小时，求直线AB 方程．【应试技巧点拨】1．解决直线与圆综合问题时，一方面，要注意运用解析几何根本思想方法(即几何问题代数化)，把它转化为代数问题；另一方面，由于直线与圆与平面几何联系得非常严密，因此，准确地作出图形，并充分挖掘几何图形中所隐含条件，利用几何知识使问题较为简捷地得到解决．2．直线与圆中三个定理：切线性质定理，切线长定理，垂径定理；两个公式：点到直线距离公式及弦长公式，其核心都是转化到与圆心、半径关系上，这是解决直线与圆根本思路.对于多元问题，也可先确定主元，如此题以P为主元，提醒P在两个圆上运动，从而转化为两个圆有交点这一位置关系，这也是解决直线与圆问题一个思路，即将问题转化为直线与圆、圆与圆位置关系.3．直线与圆位置关系由圆心到直线距离d 与半径r 关系确定，d r =相切；d r <相交，此时半弦长、弦心距、半径构成直角三角形；d r >用圆几何性质，特别是半弦长、弦心距、半径构成直角三角形，满足勾股定理．圆切线问题一般利用d r =求解，但要注意切线斜率不存在情形，与圆有关最值，范围问题要注意数形结合思想运用．直线与圆中常见最值问题：①圆外一点与圆上任一点距离最值．②直线与圆相离，圆上任一点到直线距离最值．③过圆内一定点直线被圆截得弦长最值．④直线与圆相离，过直线上一点作圆切线，切线长最小值问题．⑤两圆相离，两圆上点距离最值.二年模拟1. 【2021届陕西省黄陵中学高三下第六次模拟】,a b 为正实数，直线0x y a ++=与圆()()2212x b y -+-=相切，那么最小值是〔 〕A ．2B ．4C ．6D ．8【答案】B2. 【2021届山东省临沂十八中高三三模】圆C:228150x y x +-+=，直线2y kx =+上至少存在一点P ，使得以点P 为圆心，半径为1圆与圆C 有公共点，那么k 最小值是〔 〕A ．43- B ．54- C ．35-D ．53- 【答案】A【解析】圆C:22(4)1x y -+=，由题意得1111CP -≤≤+,即圆C 到直线2y kx =+距离不大于2，因此2min 2|42|4423400331k k k k k k +≤⇒+≤⇒-≤≤⇒=-+，选A. 3. 【2021届山东省潍坊一中高三下三轮冲刺】假设直线y kx =与圆22(2)1x y -+=两个交点关于直线20x y b ++=对称，那么,k b 值分别为〔 〕A ．B ．C ．D ．【答案】A【解析】由题知两直线互相垂直,可得斜率积为1-,那么, 又圆上两点关于直径对称即直线20x y b ++=过圆心()2,0点,可得4b =-.故此题选A.4. 【2021届宁夏六盘山高中高三四模】圆方程为()2214x y +-=，假设过点直线l 与此圆交于A,B 两点，圆心为C ，那么当ACB ∠最小时，直线l 方程为〔 〕 A ．0324=--y x B ．022=-+y x C ．0324=-+y xD ．220x y -+=【答案】A5. 【2021届四川南充高中高三4月模拟三】圆方程为2260x y x +-=，过点()1,2该圆所有弦中，最短弦长为〔 〕A ．12B ．1C ．2D ．4【答案】C【解析】圆圆心坐标为)0,3(，半径为3，最短弦长为2])02()31[(32222=-+--，应选C.6. 【2021届福建省泉州五中高三最后一卷】设,m n R ∈，假设直线()()1120m x n y +++-=与圆()()22111x y -+-=相切，那么m n +取值范围是〔 〕A ．13,13⎡⎤-+⎣⎦B ．(),1313,⎤⎡-∞-++∞⎦⎣C ．222,222⎡⎤-+⎣⎦D ．(),222222,⎤⎡-∞-++∞⎦⎣【答案】D7. 【2021届江苏省清江中学高三考前一周模拟】如果直线()21400,0ax by a b -+=>>与函数()()110,1x f x m m m +=+>≠图象恒过同一个定点，且该定点始终落在圆()()221225x a y b -+++-=内部或圆上，那么b a 取值范围为 ．【答案】【解析】由题意知()()110,1x f x m m m +=+>≠图象定点(1,2)-，又直线()21400,0ax by a b -+=>>过定点(1,2)-，所以7+=a b ①，又定点(1,2)-在圆()()221225x a y b -+++-=内部或圆上，所以2225+≤a b ②，由①②解得34≤≤a ，，77341,43-⎡⎤∴==-∈⎢⎥⎣⎦b a a a a ．所以答案应填：．8. 【2021届山东省临沂十八中高三三模】点()2,1A --，()1,5B -，点P 是圆C:()()22214x y -+-=上动点，那么∆PAB 面积最大值与最小值之差为 ．【答案】10【解析】由于底边AB 为定值，所以当点P 到直线AB 距离最大值与最小值时，∆PAB 面积取最大值与最小值，因此∆PAB 面积最大值与最小值之差为1[(d r)(d r)]AB 2510.2r AB +--⋅=⋅=⨯= 9．【2021届四川省成都市高中毕业班摸底测试】圆22:2410C x y x y +--+=上存在两点关于直线:10l x my ++=对称，经过点(,)M m m 作圆C 切线，切点为P ，那么MP =_____________.【答案】310. 【2021届福建省厦门市高三5月月考】点F 为抛物线2:4E x y =焦点，直线l 为准线，C 为抛物线上一点〔C 在第一象限〕，以点C 为圆心，||CF 为半径圆与y 轴交于,D F 两点，且CDF ∆为正三角形.〔1〕求圆C 方程；〔2〕设P 为l 上任意一点，过P 作抛物线24x y =切线，切点为,A B ，判断直线AB 与圆C 位置关系.【解析】〔1〕由(0,1)F ，设圆C 半径为r ，因为EFC ∆为正三角形，，因为点C 在抛物线24x y =上，得，即2316160r r -+=，解得：4r =或，所以圆C 方程为221:(23)(3)16C x y -+-=或22223116:()()339C x y -+-=. 〔2〕方法一：因为准线l 为1y =-，设1122(,1),(,),(,)P t A x y B x y -，因为，所以，11(,)A x y 为切点切线方程为：，，即，因为切线过(,1)P t -，得，同理可得，所以直线AB 方程为，即220tx y -+=，圆心1(23,3)C ，14r =，1C 到直线距离，可得22124(23)1604t d t -+-=≤+，所以23t =-时，14d =，直线AB 与圆1C 相切，23t ≠-时，14d <，直线AB 与圆1C AB 与圆1C 相交或相切.同理可证，直线AB 与圆2C AB 与圆1C 、2C 相交或相切.〔注：因为直线AB 过定点(0,1)F ，且斜率，因为(0,1)F 在圆1C 、2C 上，所以直线AB 与圆1C 、2C 相交或相切，这样答扣1分〕11.【2021 届甘肃省天水市一中高三第五次高考模拟考试】过平面区域内一点P 作圆22:1O x y +=两条切线，切点分别为,A B ，记APB α∠=，那么当α最小时cos α值为〔 〕A．10B ．1920C ．910D ．12 【答案】C【解析】根据题意可知，当点P 距离圆心越远时，APB ∠越小，所以当点P 距离圆心最远时，即点P 落在(4,2)--处时角α到达最小，此时，所以219cos 12sin 121010αα=-=-=，应选C ． 12.【2021 届浙江省嘉兴市高三下学期教学测试一】直线:cos sin 2()l x y R ααα⋅+⋅=∈，圆22:2cos 2sin 0C x y x y θθ++⋅+⋅=()R θ∈，那么直线l 与圆C 位置关系是A ．相交B ．相切C ．相离D ．与,αθ相关【答案】D【解析】()()1sin cos sin 2cos 22222=-+-=⋅+⋅++θθθθy x y x y x ，所以圆圆心坐标为()θθsin ,cos --半径为1，那么直线到圆心距离为()2cos d αθ==+-[]3,1∈，所以直线l 与圆C 位置关系是相切或相离，故应选D.13. 【2021 届四川省雅安市高三第三次诊断性考试】直线l ：50x ky --=与圆O :2210x y +=交于A 、B 两点且0OA OB ⋅=，那么k =〔 〕A ．2B ．2± C． D【答案】B【解析】将5x ky 代入2210x y +=得22(1)10150k y ky ．由0OA OB ⋅=得12120x x y y ，即212121212210(5)(5)0,(1)5()250,155()250,21k ky ky y y k y y k y y k k k ．14.【2021 届黑龙江省哈尔滨九中高三第三次高考模拟】直线2:,:21+==x y l x y l 与圆C 02222=--+ny mx y x 四个交点把圆C 分成四条弧长相等，那么=mA ．0或1B ．0或1-C ．1-D ．1【答案】B15.【2021 届山东省日照市高三校际联合检测〔二模〕】在平面直角坐标系xOy 中，设直线2y x =-+与圆()2220x y r r +=>交于A,B 两点，O 为坐标原点，假设圆上一点C 满足，那么r=______. 10拓展试题以及解析1. 假设圆C ：224x y +=上点到直线l ：y x a =+最小距离为2，那么a =〔 〕A ．22B ．42C ．22±D ．42±【答案】 D【解析】由题意，知圆心到直线l 距离为4，那么，解得42a =±，应选D ．【入选理由】此题考察圆方程，点到直线距离，直线与圆位置关系等根底知识，意在考察学生分析问题能力与计算能力．此题是一个常规题，难度不大，应选此题.2.自圆C ：22(3)(4)4x y -++=外一点(,)P x y 引该圆一条切线，切点为Q ，切线长度等于点P 到原点O 长，那么点P 轨迹方程为〔 〕A ．86210x y --=B ．86210x y +-=C ．68210x y +-=D ．68210x y --=【答案】D【解析】由切线性质知PQ CQ ⊥，所以222PQ PC QC =-，那么由PQ PO =，得，2222(3)(4)4x y x y -++-=+，化简得68210x y --=，即点P 轨迹方程，应选D ，【入选理由】此题考察了此题考察直线与圆位置关系、点到直线距离等根底知识，意在考察学生分析问题，解决问题能力，逻辑思维能力、转化能力，以及运算能力．此题由切线问题转化为直角三角形问题，由勾股定理建立方程，可得轨迹，此题构思比拟巧，确是一个好题，应选此题.3.直线:22l mx ny +=与圆O ：221x y +=交于A 、B 两点，假设AOB ∆为直角三角形，那么点(,)M m n 到点(2,0)P -、(20)Q ，距离之与〔 〕【答案】D【入选理由】此题考察了此题考察直线被圆所截弦长以及椭圆定义等根底知识，意在考察学生分析问题，解决问题能力，数形结合思想，以及运算能力．此题由条件确定动点(,)M m n 轨迹是一个椭圆，由椭圆定义即可得距离之与，此题构思比拟巧，确是一个好题，应选此题.4.在平面直角坐标系xOy 中，点(3,0)A ，动点P 满足2PA PO =，动点(3,45)()Q a a a +∈R ，那么线段PQ 长度最小值为_______. 【答案】15【解析】设(,)P x y ，那么由2PA PO =得222222(3)4()(1)4x y x y x y -+=+⇒++=，即动点P 在圆上运动，因为(3,45)()Q a a a +∈R ，因此动点Q 在直线43150x y -+=上运动，所以线段PQ 长度最小值为|415|12.55-+-= 【入选理由】此题考察了此题考察圆轨迹方程，直线轨迹方程，直线与圆位置关系等根底知识，意在考察学生分析问题，解决问题能力，数形结合思想，以及运算能力．此题由条件确定动点P 轨迹是一个圆，动点Q 轨迹是43150x y -+=，问题转化为圆上一点到直线距离最小值，此题构思比拟巧，确是一个好题，应选此题.5.圆)0(:222>=+r r y x C 经过点)3,1(．〔Ⅰ〕求圆C 方程；〔Ⅱ〕是否存在经过点)1,1(-直线l ，它与圆C 相交于A 、B 两个不同点，且满足关系 0=•OB OAO (为坐标原点)，如果存在，求出直线l 方程；如果不存在，请说明理由．【入选理由】此题考察了此题考察直线与圆位置关系、求圆方程，求直线方程，探索性问题等根底知识，意在考察学生分析问题，解决问题能力，数形结合思想运用与函数与方程思想与根本运算能力．此题是圆探索性问题，作为圆，高考也出过大题，因此圆解答题也应加强训练，应选此题.。
高考必考语法精讲精练专题九：定语从句-Word版含解析
高考必考语法精讲精练语法专题九：定语从句定语从句是比较重要的语法项目。
《2017年一般高等学校招生全国统一考试大纲》附录语法项目表中将定语从句列为必考项。
全国卷新课标Ⅰ对定语从句的考查一般在语法填空和短文改错中，主要考查定语从句引导词的用法。
2015年高考全国卷Ⅰ第64题（语法填空）考查了定语从句引导词that/which。
2016年高考全国卷Ⅰ第65题（语法填空）考查了定语从句的引导词when。
2017年高考全国卷Ⅰ第70题（语法填空）考查了定语从句的引导词which。
基本概念：定语从句:在复合句中修饰名词或代词、充当定语的句子叫定语从句。
因其功能相当于形容词，所以又称为形容词性从句。
先行词:被定语从句所修饰的名词或代词。
关系词:引导定语从句的词，也叫引导词。
分为关系代词（who，whom，that，which，whose ,as）和关系副词(where，when，why)。
关系词要在定语从句中作某个成分，如主语、宾语、状语等。
限制性定语从句：对先行词起修饰限定作用的定语从句。
非限制性定语从句：对先行词或主句起补充说明作用的定语从句，通常引导词和先行词之间用逗号隔开。
关系词及其意义：关系代词和关系副词功能有三个：①用来引导定语从句，在先行词和定语从句之间起纽带作用，使二者联系起来。
②关系代词和关系副词可作定语从句的一个成分。
关系代词可作主语、宾语、定语；关系副词可作状语。
③关系代词和关系副词在从句中代替在他前面的先行词。
一、关系代词引导的定语从句1．who 指人，在定语从句中作主语。
①The boys who are playing football are from Class One.②Yesterday I helped an old man who had lost his way.③ That is the teacher who teaches us physics.2．whom 指人，在定语从句中做宾语，常可省略。
2017-2019年高考真题数学(文)分项汇编_专题19 不等式选讲
专题19不等式选讲1．【2019年高考全国Ⅰ卷文数】已知a ，b ，c 为正数，且满足abc =1．证明： （1）222111a b c a b c++≤++； （2）333()()()24a b b c c a +++≥++． 【答案】（1）见解析；（2）见解析．【解析】（1）因为2222222,2,2a b ab b c bc c a ac +≥+≥+≥，又1abc =，故有222111ab bc ca a b c ab bc ca abc a b c++++≥++==++．所以222111a b c a b c++≤++． （2）因为, , a b c 为正数且1abc =，故有333()()()a b b c c a +++++≥=3(+)(+)(+)a b b c a c3≥⨯⨯⨯=24．所以333()()()24a b b c c a +++++≥．【名师点睛】本题考查利用基本不等式进行不等式的证明问题，考查学生对于基本不等式的变形和应用能力，需要注意的是在利用基本不等式时需注意取等条件能否成立． 2．【2019年高考全国Ⅱ卷文数】已知()|||2|().f x x a x x x a =-+-- （1）当1a =时，求不等式()0f x <的解集； （2）若(,1)x ∈-∞时，()0f x <，求a 的取值范围． 【答案】（1）(,1)-∞；（2）[1,)+∞【解析】（1）当a =1时，()=|1| +|2|(1)f x x x x x ---．当1x <时，2()2(1)0f x x =--<；当1x ≥时，()0f x ≥．所以，不等式()0f x <的解集为(,1)-∞．（2）因为()=0f a ，所以1a ≥．当1a ≥，(,1)x ∈-∞时，()=() +(2)()=2()(1)<0f x a x x x x a a x x -----． 所以，a 的取值范围是[1,)+∞．【名师点睛】本题主要考查含绝对值的不等式，熟记分类讨论的方法求解即可，属于常考题型． 3．【2019年高考全国Ⅲ卷文数】设,,x y z ∈R ，且1x y z ++=．（1）求222(1)(1)(1)x y z -++++的最小值；（2）若2221(2)(1)()3x y z a -+-+-≥成立，证明：3a ≤-或1a ≥-． 【答案】（1）43；（2）见详解． 【解析】（1）由于2[(1)(1)(1)]x y z -++++222(1)(1)(1)2[(1)(1)(1)(1)(1)(1)]x y z x y y z z x =-+++++-++++++-2223(1)(1)(1)x y z ⎡⎤≤-++++⎣⎦，故由已知得2224(1)(1)(1)3x y z -++++≥， 当且仅当x =53，y =–13，13z =-时等号成立． 所以222(1)(1)(1)x y z -++++的最小值为43．（2）由于2[(2)(1)()]x y z a -+-+-222(2)(1)()2[(2)(1)(1)()()(2)]x y z a x y y z a z a x =-+-+-+--+--+--2223(2)(1)()x y z a ⎡⎤≤-+-+-⎣⎦，故由已知2222(2)(2)(1)()3a x y z a +-+-+-≥，当且仅当43a x -=，13a y -=，223a z -=时等号成立． 因此222(2)(1)()x y z a -+-+-的最小值为2(2)3a +．由题设知2(2)133a +≥，解得3a ≤-或1a ≥-．【名师点睛】两个问都是考查柯西不等式，属于柯西不等式的常见题型． 4．【2019年高考江苏卷数学】设x ∈R ，解不等式||+|2 1|>2x x -．【答案】1{|1}3x x x <->或．【解析】当x <0时，原不等式可化为122x x -+->，解得x <13-； 当0≤x ≤12时，原不等式可化为x +1–2x >2，即x <–1，无解； 当x >12时，原不等式可化为x +2x –1>2，解得x >1． 综上，原不等式的解集为1{|1}3x x x <->或．【名师点睛】本题主要考查解不等式等基础知识，考查运算求解和推理论证能力． 5．【2018年高考全国Ⅰ卷文数】已知()|1||1|f x x ax =+--． （1）当1a =时，求不等式()1f x >的解集；（2）若(0,1)x ∈时不等式()f x x >成立，求a 的取值范围． 【答案】（1）1{|}2x x >；（2）(0,2]．【解析】（1）当1a =时，()|1||1|f x x x =+--，即2,1,()2,11,2, 1.x f x x x x -≤-⎧⎪=-<<⎨⎪≥⎩故不等式()1f x >的解集为1{|}2x x >．（2）当(0,1)x ∈时|1||1|x ax x +-->成立等价于当(0,1)x ∈时|1|1ax -<成立． 若0a ≤，则当(0,1)x ∈时|1|1ax -≥； 若0a >，|1|1ax -<的解集为20x a <<，所以21a≥，故02a <≤． 综上，a 的取值范围为(0,2]．6．【2018年高考全国Ⅱ卷文数】设函数()5|||2|f x x a x =-+--． （1）当1a =时，求不等式()0f x ≥的解集；（2）若()1f x ≤，求a 的取值范围．【答案】（1）{|23}x x -≤≤；（2）(,6][2,)-∞-+∞．【解析】（1）当1a =时，24,1,()2,12,26, 2.x x f x x x x +≤-⎧⎪=-<≤⎨⎪-+>⎩可得()0f x ≥的解集为{|23}x x -≤≤． （2）()1f x ≤等价于|||2|4x a x ++-≥．而|||2||2|x a x a ++-≥+，且当2x =时等号成立．故()1f x ≤等价于|2|4a +≥． 由|2|4a +≥可得6a ≤-或2a ≥，所以a 的取值范围是(,6][2,)-∞-+∞． 7．【2018年高考全国Ⅲ卷文数】设函数()211f x x x =++-． （1）画出()y f x =的图像；（2）当[)0x +∞∈，，()f x ax b +≤，求a b +的最小值．【答案】（1）图像见解析；（2）a b +的最小值为5．【解析】（1）13,,21()2,1,23, 1.x x f x x x x x ⎧-<-⎪⎪⎪=+-≤<⎨⎪≥⎪⎪⎩()y f x =的图像如图所示．（2）由（1）知，()y f x =的图像与y 轴交点的纵坐标为2，且各部分所在直线斜率的最大值为3，故当且仅当3a ≥且2b ≥时，()f x ax b ≤+在[0,)+∞成立，因此a b +的最小值为5． 8．【2018年高考江苏卷数学】若x ，y ，z 为实数，且x +2y +2z =6，求222x y z ++的最小值． 【答案】222x y z ++的最小值为4．【解析】由柯西不等式，得2222222()(122)(22)x y z x y z ++++≥++． 因为22=6x y z ++，所以2224x y z ++≥， 当且仅当122x y z ==时，不等式取等号，此时244333x y z ===，，， 所以222x y z ++的最小值为4．9．【2017年高考全国Ⅰ卷文数】已知函数4)(2++-=ax x x f ，|1||1|)(-++=x x x g ． （1）当1=a 时，求不等式)()(x g x f ≥的解集；（2）若不等式)()(x g x f ≥的解集包含[–1，1]，求a 的取值范围．【答案】（1）{|1x x -≤≤；（2）[1,1]-． 【解析】（1）当1a =时，不等式()()f x g x ≥等价于2|1||1|40x x x x -+++--≤．① 当1x <-时，①式化为2340x x --≤，无解；当11x -≤≤时，①式化为220x x --≤，从而11x -≤≤；当1x >时，①式化为240x x +-≤，从而112x -+<≤． 所以()()f x g x ≥的解集为1{|1}2x x -+-≤≤． （2）当[1,1]x ∈-时，()2g x =．所以()()f x g x ≥的解集包含[1,1]-，等价于当[1,1]x ∈-时()2f x ≥．又()f x 在[1,1]-的最小值必为(1)f -与(1)f 之一，所以(1)2f -≥且(1)2f ≥，得11a -≤≤． 所以a 的取值范围为[1,1]-．【名师点睛】形如||||x a x b c -+-≥（或c ≤）型的不等式主要有两种解法：（1）分段讨论法：利用绝对值号内式子对应方程的根，将数轴分为(,]a -∞，(,]a b ，(,)b +∞（此处设a b <）三个部分，将每部分去掉绝对值号并分别列出对应的不等式求解，然后取各个不等式解集的并集． （2）图像法：作出函数1||||y x a x b =-+-和2y c =的图像，结合图像求解． 10．【2017年高考全国Ⅱ卷文数】已知330,0,2a b a b >>+=．证明：（1）55()()4a b a b ++≥； （2）2a b +≤．【答案】（1）证明略；（2）证明略．【解析】（1）()()556556a b a b a ab a b b ++=+++()()()2333344222244.a ba b ab a b ab a b =+-++=+-≥（2）因为()3322333a b a a b ab b +=+++()()()()232332432,4ab a b a b a b a b =+++≤+++=+所以()38a b +≤，因此2a b +≤．【名师点睛】利用基本不等式证明不等式是综合法证明不等式的一种情况，证明思路是从已证不等式和问题的已知条件出发，借助不等式的性质和有关定理，经过逐步的逻辑推理最后转化为需证问题．若不等式恒等变形之后与二次函数有关，可用配方法．11．【2017年高考全国Ⅲ卷文数】已知函数f （x ）=│x +1│–│x –2│．（1）求不等式f （x ）≥1的解集；（2）若不等式()2f x x x m ≥-+的解集非空，求m 的取值范围． 【答案】（1）{}1x x ≥；（2）54⎛⎤∞ ⎥⎝⎦-，【解析】（1）()31211232,x f x x ,x ,x -<-⎧⎪=--≤≤⎨⎪>⎩，当1x <-时，()1f x ≥无解；当12x -≤≤时，由()1f x ≥得，211x -≥，解得12x ≤≤； 当2x >时，由()1f x ≥解得2x >． 所以()1f x ≥的解集为{}1x x ≥．（2）由()2f x x x m ≥-+得212m x x x x ≤+---+，而2223551212244x x x x x x x x x ⎛⎫+---+≤++--+=-+≤ ⎪⎝⎭-，且当32x =时，25124x x x x +---+=． 故m 的取值范围为54⎛⎤∞ ⎥⎝⎦-，．【名师点睛】绝对值不等式的解法有三种：法一：利用绝对值不等式的几何意义求解，体现了数形结合的思想； 法二：利用“零点分段法”求解，体现了分类讨论的思想；法三：通过构造函数，利用函数的图象求解，体现了函数与方程的思想．12．【2017年高考江苏卷数学】已知,,,a b c d 为实数，且22224,16,a b c d +=+=证明：8.ac bd +≤【答案】见解析【解析】由柯西不等式可得22222()()()ac bd a b c d +≤++， 因为22224,16a b c d +=+=，所以2()64ac bd +≤， 因此8ac bd +≤．【名师点睛】柯西不等式的一般形式：设a 1，a 2，…，a n ，b 1，b 2，…，b n 为实数，则（22212n a a a +++）（22212n b b b +++）≥（a 1b 1＋a 2b 2＋…＋a n b n ）2，当且仅当b i ＝0或存在一个数k ，使a i ＝kb i （i ＝1，2，…，n ）时，等号成立．本题中，由柯西不等式可得22222()()()ac bd a b c d +≤++，代入即得结论．。
高考物理 必考17个实验精讲精练 专题09 测定金属的电阻率(含解析)-人教版高三全册物理试题
测定金属的电阻率一、知识点梳理 电阻定律S L R ρ=，其中ρ为电阻率，如此LRS =ρ，L 为导线长度，用刻度尺测量，S 为导线横截面积，42d S π=，d 为导线直径，用游标卡尺或螺旋测微器测量。
游标卡尺和螺旋测微器的结构、使用和读数游标卡尺：先读主尺，再读游标尺，然后相加。
游标尺的第几个格与主尺的某格对齐，如此用游标卡尺的准确度乘以几。
游标卡尺准确度一般有3种，即0.1mm(10个格的游标尺),0.05mm(20个格的游标尺),0.02mm(50个格的游标尺).游标卡尺不估读。
螺旋测微器：先读固定刻度，再可动刻度，然后相加。
螺旋测微器要估读。
电阻R 用伏安法测量。
1. 伏安法测电阻中电流表内接和外接电路电路图如下甲图，是电流表外接，乙图如此是电流表内接。
2.误差分析电流表外接时，电压表分流引起系统误差，测量值=VVR R RR +，为电阻R 与电压表内阻V R 的并联值，所以，测量值小于真实值。
电流表内接时，测量值为，为电阻与电流表内阻的串联值，所以，测量值大于真实值。
所以，当电阻小于小于电压表内阻时，是小电阻用电流表外接法，当电阻大于大于电流表内阻时，是大电阻，用电流表内接法。
3.怎样才算小电阻和大电阻呢？ 取，待测电阻R ，假设中R R <，如此为小电阻，用电流表外接法；假设中R R >，如此为大电阻，用电流表内接法。
关于伏安法测电阻实验中的电流表外接和内接的问题，是高考的重点和热点，也是学生学习中的难点，有的同学总有点似懂非懂、似是而非的感觉。
通过例题谈一谈测电阻实验中的电流表内接和电流表外接的问题。
二、例题和习题〔含近年来高考全国1、全国2、全国3、、某某、江苏省、海南等卷物理实验题〕 1. 〔2019年高考某某卷第9〔3〕题〕 现测定长金属丝的电阻率。
①某次用螺旋测微器测量金属丝直径的结果如下列图，其读数是______mm 。
固定刻度0，可动刻度0.200，答案为0.200mm②利用如下器材设计一个电路，尽量准确地测量一段金属丝的电阻。
备战2017高考英语(精讲+精练+精析)专题11 名词性从句试题(含解析)
专题11 名词性从句【2017年高考命题预测】高考研究名词性从句是英语中比较复杂的结构，既涉及词汇的用法，也涉及句法结构，是整个高中阶段英语学习的重点和难点之一。
在学习名词性从句时，应注意从以下几个方面入手：一是要熟悉句子的各种成分，尤其是主语、宾语、表语、同位语的特点。
二是要掌握引导名词性从句的连接代词、连接副词的分类及用法(that，if，whether的用法区别)；三是要注意名词性从句中的特殊情况(that的省略，语序问题，时态问题，语气问题)；四是要注意疑问连接词what，when，where等引导名词性从句不表示疑问的情况；五是要注意whoever，whichever，whatever，whenever，wherever等引导从句的用法。
特别需要注意的是要掌握it替代从句的用法。
【考点定位】2017考纲解读和近几年考点分布（1）考纲要求名词性从句是高考的热点，对于名词性从句考纲要求掌握以下内容：掌握主语从句、宾语从句、表语从句的基本用法，了解同位语从句的基本用法。
要求考生在复习备考中应该掌握名词性从句的基本用法；一些易混引导词的辨析；句子的语序、否定前移；名词性从句和定语从句、状语从句的辨析等。
（2）命题规律一、重点考查宾语从句，其次是同位语从句、表语从句和主语从句，通常考查引导这些从句的引导词的选择。
二、高考对名词性从句的考查仍将不会单纯考查其语法结构，而是将其融入一定的语境中来考查考生的实际综合运用能力。
【考点pk】名师考点透析考点1 主语从句特别提示(1)if不能引导主语从句。
(2)形式主语it替代主语从句。
常见的it替代主语从句的句式主要有以下几种：A．It+系动词+形容词+that从句。
如：It is quite clear that the whole project is doomed to failure．很清楚，整个计划注定要失败。
B．It+系动词+名词+that从句。
高考英语必考语法精讲精练专题一：名词 Word版含解析
高考必考语法精讲精练语法专题一：名词名词是英语中非常重要的一类词，也是高考必考内容之一。
《2017年普通高等学校招生全国统一考试大纲》附录语法项目表中对名词考查列了四项：①可数名词及其单复数②不可数名词③专有名词④名词所有格。
纵观历年高考试题，试题中出现的考点主要有：可数名词的单复数形式、名词的所有格的构成及应用、不可数名词的辨认、名词的功能、名词辨义、名词与其他词类之间的转换等。
2015年高考全国卷Ⅰ第65题（语法填空）考查的是可数名词单复数，括号里给出painting，结合题意要将其变成paintings；第77题（短文改错）考查的是不可数名词air，原文给出的是airs，要求考生将其改成air。
而在完形填空中，有7题（总共20小题）是考查名词词义以及对语境的理解。
2016年高考全国卷Ⅰ第61题（语法填空）考查的是词性转换，括号里给出的是动词attract，根据题意要将其改成名词attraction；第69题（语法填空）考查的是可数名词单复数，括号里给出day，结合题意要将其变成复数形式days；第74题考查的是词性转换，题目中给的是形容词honest，根据题意需要将其改为名词honesty。
而在完形填空中，有4题（总共20小题）是考查名词词义以及对语境的理解。
2017年高考全国卷Ⅰ第62题（语法填空）考查的是可数名词单复数，括号里给出effect，结合题意要将其变成effects，构成side effects（副作用）；第75题（短文改错）考查的是可数名词单复数，原句中给出的是word，结合题意要将其变成words。
而在完形填空中，有5题（总共20小题）是考查名词词义以及对语境的理解。
1. 规则可数名词的复数形式：一般在单数形式后面加-s或-es。
现将构成方法列表如下：III. 名词的所有格：名词在句中表示所有关系的语法形式叫做名词所有格。
所有格分三种：一是名词词尾加’s 构成，多表示有生命的东西；二是由介词of加名词构成，多表示无生命的东西；三是双重所有格。
备战2017高考数学(精讲+精练+精析)选做02矩阵试题(江苏版)(含解析)
专题2 矩 阵【三年高考】1．【2021年高考江苏】矩阵 矩阵B 逆矩阵 ，求矩阵AB . 【答案】 【解析】试题分析：先求逆矩阵逆： ，再根据矩阵运算求矩阵AB .试题解析：解：设，那么1110120102a b c d -⎡⎤-⎡⎤⎡⎤⎢⎥==⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦B B ， 即1110220122a c b d cd ⎡⎤--⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦⎣⎦， 故，解得，所以.因此，151121440210102⎡⎤⎡⎤⎢⎥⎡⎤⎢⎥==⎢⎥⎢⎥⎢⎥-⎣⎦⎢⎥-⎣⎦⎢⎥⎣⎦AB .【考点】逆矩阵，矩阵乘法【名师点睛】矩阵乘法及逆矩阵需明确运算法那么，实质是考察一种运算法那么：1||||,(||0)||||db a b ad bc cd c a --⎡⎤⎢⎥⎡⎤⎢⎥=⇒==-≠⎢⎥-⎢⎥⎣⎦⎢⎥⎣⎦，A A A A A A A a b e f ae bgaf bh c d g h ce dgcf dh ++⎡⎤⎡⎤⎡⎤=⎢⎥⎢⎥⎢⎥++⎣⎦⎣⎦⎣⎦，类似求矩阵特征值及特征向量也是如此.2．【2021 江苏高考，21】R y x ∈,，向量是矩阵属性特征值2-一个特征向量，矩阵A 以及它另一个特征值.【答案】,另一个特征值为1．【考点定位】矩阵运算，特征值与特征向量3．【2021江苏，理21B】[选修4-2：矩阵与变换]矩阵1211,121A Bx-⎡⎤⎡⎤==⎢⎥⎢⎥-⎣⎦⎣⎦，向量，,x y是实数，假设Aa Ba=，求x y+值.【答案】72．【解析】由题意得，解得.∴.4．【2021江苏，理21B】[选修4－2：矩阵与变换](本小题总分值10分)矩阵A＝，B＝，求矩阵A－1B. 【答案】．5．【2021江苏，理21B】[选修4－2：矩阵与变换]矩阵A逆矩阵，求矩阵A特征值．【答案】λ1＝－1，λ2＝4.．【解析】解：因为A－1A＝E，所以A＝(A－1)－1.因为，所以，于是矩阵A特征多项式为f(λ)＝＝λ2－3λ－4.令f(λ)＝0，解得A特征值λ1＝－1，λ2＝4.6．【2021江苏，理21B 】选修4-2：矩阵与变换 矩阵，向量．求向量α，使得2αβ=A 【答案】．【解析】解： =,设，由βα=2A 得,，从而，解得2,1=-=y x ，所以.【2021年高考命题预测】纵观近几年江苏高考试题，对矩阵考察，主要考察矩阵运算，矩阵变换，矩阵特征值与特征向量及二阶逆矩阵．题目难度一般为中、低档，着重考察利用根本概念、根底知识求解矩阵，高考对这局部要求不是太高，会进展矩阵乘法运算，会利用矩阵运算进展平面变换，会判断一个二阶矩阵有否逆矩阵及求得逆矩阵，会求矩阵特征值与特征向量，并用特征值与特征向量进展矩阵乘方运算．备考中应严格控制训练题难度．高考对这局部要求不是太高，高考中在附加题局部.预测2021年矩阵仍是考试重点．复习建议：在复习矩阵知识过程中，注意培养、强化与提高计算能力，逐步提升数学素养，提高分析解决综合问题能力.【2021年高考考点定位】高考对矩阵考察，主要考察矩阵运算，考察矩阵变换，考察矩阵特征值与特征向量及二阶逆矩阵运算． 【考点1】矩阵运算与矩阵变换 【备考知识梳理】 1．乘法规那么(1)行矩阵[a 11 a 12]与列矩阵⎣⎢⎡⎦⎥⎤b 11b 21乘法法那么： [a 11 a 12]⎣⎢⎡⎦⎥⎤b 11b 21＝[a 11b 11＋a 12b 21]．(2)二阶矩阵⎣⎢⎡⎦⎥⎤a 11 a 12a 21 a 22与列向量⎣⎢⎡⎦⎥⎤x 0y 0乘法规那么：⎣⎢⎡⎦⎥⎤a 11 a 12a 21 a 22⎣⎢⎡⎦⎥⎤x 0y 0＝⎣⎢⎡⎦⎥⎤a 11x 0＋a 12y 0a 21x 0＋a 22y 0. (3)两个二阶矩阵相乘结果仍然是一个二阶矩阵，其乘法法那么如下：⎣⎢⎡⎦⎥⎤a 11 a 12a 21 a 22⎣⎢⎡⎦⎥⎤b 11 b 12b 21 b 22＝⎣⎢⎡⎦⎥⎤a 11b 11＋a 12b 21 a 11b 12＋a 12b 22a 21b 11＋a 22b 21 a 21b 12＋a 22b 22. (4)两个二阶矩阵乘法满足结合律，但不满足交换律和消去律，即(AB )C ＝A (BC )． (5)A k A l＝Ak ＋l，(A k )l ＝A kl (其中k ，l ∈N *)．2．常见平面变换 (1)恒等变换：因为⎣⎢⎡⎦⎥⎤1 001⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤x y ，该变换把点(x ，y )变成(x ，y )，故矩阵⎣⎢⎡⎦⎥⎤1 001表示恒等变换．(2)反射变换：因为⎣⎢⎡⎦⎥⎤－1 0 0 1⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤－x y ，该变换把点(x ，y )变成(－x ，y )，故矩阵⎣⎢⎡⎦⎥⎤－1 0 0 1表示关于y 轴反射变换；类似地，⎣⎢⎡⎦⎥⎤1 00 －1，⎣⎢⎡⎦⎥⎤0， 11 0，⎣⎢⎡⎦⎥⎤0， －1－1 0分别表示关于x 轴、直线y ＝x 和直线y ＝－x 反射变换．(3)伸缩变换：因为⎣⎢⎡⎦⎥⎤1 00 k ⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤x ky ，该变换把点(x ，y )变成点(x ，ky )，在此变换中，点横坐标不变，纵坐标变成原来k 倍，故矩阵⎣⎢⎡⎦⎥⎤1， 00 k 表示y 轴方向上伸缩变换；类似地，矩阵⎣⎢⎡⎦⎥⎤s001可以用来表示水平伸缩变换．(4)旋转变换：把点A (x ，y )绕着坐标原点逆时针旋转α角变换，对应矩阵是⎣⎢⎡⎦⎥⎤cos α －sin αsin α cos α.(5)切变变换：⎣⎢⎡⎦⎥⎤1s 0 1⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤x ＋sy y 表示是沿x 轴切变变换．沿y 轴切变变换对应矩阵是⎣⎢⎡⎦⎥⎤1 0t1.(6)投影变换：⎣⎢⎡⎦⎥⎤1000⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤x 0，该变换把所有横坐标为x 点都映射到了点(x,0)上，因此矩阵⎣⎢⎡⎦⎥⎤1 000表示是x 轴上投影变换．类似地，⎣⎢⎡⎦⎥⎤0 00 1表示是y 轴上投影变换． 【规律方法技巧】1．待定系数法在平面变换中应用通过二阶矩阵与平面向量乘法求出变换前与变换后坐标之间变换公式，进而得到所求曲线(或点)，求解时应注意待定系数法应用．2．矩阵相等实质上是矩阵对应元素相等，表达了方程思想，要注意矩阵对应元素相等． 3．矩阵乘法只满足结合律，不满足交换律和消去律． 4．对于平面图形变换要分清是伸缩、反射、还是切变变换．5．伸缩、反射、切变变换这三种几何变换称为初等变换，对应变换矩阵为初等变换矩阵，由矩阵乘法可以看出，矩阵乘法对应于变换复合，一一对应平面变换都可以看作这三种初等变换一次或屡次复合． 6．在解决通过矩阵进展平面曲线变换时，变换矩阵可以通过待定系数法解决，在变换时一定要把变换前后变量区别清楚，防止混淆．7．曲线(或点)经过二阶矩阵变换后曲线(或点)求法，类似于平面解析几何中代入法求轨迹，此类问题关键是求对坐标之间变换公式． 8．注意两个易错点：〔1〕二阶矩阵乘法运算律中，易无视AB ≠BA ，AB ＝AC ⇒/ B ＝C ，但满足(AB )C ＝A (BC )．〔2〕易混淆绕原点逆时针旋转90°变换与绕原点顺时针旋转90°变换． 【考点针对训练】 1．求使等式⎣⎢⎡⎦⎥⎤2 435＝⎣⎢⎡⎦⎥⎤2 00 1M ⎣⎢⎡⎦⎥⎤1 00 －1成立矩阵M . 【答案】⎣⎢⎡⎦⎥⎤1 －23 －5.【解析】设M ＝⎣⎢⎡⎦⎥⎤mn p q ，那么⎣⎢⎡⎦⎥⎤2 435＝⎣⎢⎡⎦⎥⎤2 00 1M ⎣⎢⎡⎦⎥⎤1 00 －1＝⎣⎢⎡⎦⎥⎤2m －2n p －q ， 那么⎩⎪⎨⎪⎧ 2m ＝2，－2n ＝4，p ＝3，－q ＝5，⇒⎩⎪⎨⎪⎧m ＝1，n ＝－2，p ＝3，q ＝－5，即M ＝⎣⎢⎡⎦⎥⎤1 －23 －5.2，直线l ：ax ＋y ＝1在矩阵A ＝⎣⎢⎡⎦⎥⎤1201对应变换作用下变为直线l ′：x ＋by ＝1.(1)求实数a ，b 值；(2)假设点P (x 0，y 0)在直线l 上，且A ⎣⎢⎡⎦⎥⎤x 0y 0＝⎣⎢⎡⎦⎥⎤x 0y 0，求点P 坐标．【答案】〔1〕⎩⎪⎨⎪⎧a ＝1，b ＝－1.；〔2〕(1,0)．【考点2】矩阵特征值与特征向量 【备考知识梳理】 1．逆变换与逆矩阵(1)逆变换：设ρ是一个线性变换，如果存在线性变换σ，使得σρ＝ρσ＝1，那么称变换ρ可逆，并且称σ是ρ逆变换．(2)逆矩阵：设A 是一个二阶矩阵，如果存在二阶矩阵B ，使得BA ＝AB ＝E 2，那么称矩阵A 可逆，或称矩阵A 是可逆矩阵，并且称B 是A 逆矩阵．(3)逆矩阵性质性质①：设A 是一个二阶矩阵，如果A 是可逆，那么A 逆矩阵是唯一．性质②：设A ，B 是二阶矩阵，如果A ，B 都可逆，那么AB 也可逆，且(AB )－1＝B －1A －1.(4)定理：二阶矩阵A ＝⎣⎢⎡⎦⎥⎤ab cd 可逆，当且仅当det A ＝ad －bc ≠0.2．逆矩阵与二元一次方程组 (1)定理：如果关于变量x ，y二元一次方程组(线性方程组)⎩⎪⎨⎪⎧ax ＋by ＝e ，cx ＋dy ＝f 系数矩阵A ＝⎣⎢⎡⎦⎥⎤ab cd 可逆，那么该方程组有唯一解⎣⎢⎡⎦⎥⎤x y ＝⎣⎢⎡⎦⎥⎤ab cd －1⎣⎢⎡⎦⎥⎤e f .(2)推论：关于变量x ，y 二元一次方程组⎩⎪⎨⎪⎧ax ＋by ＝0，cx ＋dy ＝0.其中a ，b ，c ，d 是不全为零常数，有非零解充分必要条件是系数矩阵行列式⎪⎪⎪⎪⎪⎪ab cd ＝0.3．特征值和特征向量设矩阵A ＝⎣⎢⎡⎦⎥⎤ab cd ，如果存在数λ以及非零向量ξ，使得Aξ＝λξ，那么称λ是矩阵A 一个特征值，ξ是矩阵A 属于特征值λ一个特征向量． 4．特征向量性质设λ1，λ2是二阶矩阵A 两个不同特征值，ξ1，ξ2是矩阵A 分别属于特征值λ1，λ2特征向量，对于任意非零平面向量α，设α＝t 1ξ1＋t 2ξ2(t 1，t 2为实数)，那么对任意正整数n ，有A nα＝t 1λn1ξ1＋t 2λn2ξ2. 【规律方法技巧】 1．求逆矩阵常见方法 (1)待定系数法：设A 是一个二阶可逆矩阵⎣⎢⎡⎦⎥⎤ab cd ，AB ＝BA ＝E 2；(2)公式法：|A |＝⎪⎪⎪⎪⎪⎪a b c d ＝ad －bc ，有A －1＝⎣⎢⎢⎡⎦⎥⎥⎤d |A | －b |A |－c |A | a |A |，当且仅当|A |≠0；(3)从几何变换角度求解二阶矩阵逆矩阵； (4)利用逆矩阵性质(AB )－1＝B －1A －1. 2．求特征值和特征向量方法(1)矩阵M ＝⎣⎢⎡⎦⎥⎤ab cd 特征值λ满足(λ－a )(λ－d )－bc ＝0，属于λ特征向量a ＝⎣⎢⎡⎦⎥⎤x y 满足M ⎣⎢⎡⎦⎥⎤x y ＝λ⎣⎢⎡⎦⎥⎤x y . (2)求特征向量和特征值步骤：①解f (λ)＝⎪⎪⎪⎪⎪⎪λ－a －b －c λ－d ＝0得特征值；②解⎩⎪⎨⎪⎧λ－ax －by ＝0，－cx ＋λ－d y ＝0⇔(λ－a )x －by ＝0，取x ＝1或y ＝1，写出相应向量．3．注意3个易错点：〔1〕并不是每一个二阶矩阵都是可逆：矩阵A ＝⎣⎢⎡⎦⎥⎤a b cd 可逆充分必要条件是它对应行列式|A |满足|A |＝ad －bc ≠0，且A－1＝⎣⎢⎢⎡⎦⎥⎥⎤d |A |－b |A |－c |A | a |A |. 〔2〕不是每个矩阵都有特征值与特征向量，矩阵M ＝⎣⎢⎡⎦⎥⎤a b cd 有特征值λ充分必要条件是方程⎪⎪⎪⎪⎪⎪λ－a －b －c λ－d ＝0有解．〔3〕属于矩阵不同特征值特征向量不共线． 【考点针对训练】1．矩阵A ＝⎣⎢⎡⎦⎥⎤ 21－13将直线l ：x ＋y －1＝0变换成直线l ′.(1)求直线l ′方程；(2)判断矩阵A 是否可逆？假设可逆，求出矩阵A 逆矩阵A －1；假设不可逆，请说明理由．【答案】〔1〕l ′方程为4x ＋y －7＝0；〔2〕A－1＝⎣⎢⎢⎡⎦⎥⎥⎤37 －1717 27. 【解析】(1)在直线l 上任取一点P (x 0，y 0)，设它在矩阵A ＝⎣⎢⎡⎦⎥⎤2 1－1 3对应变换作用下变为Q (x ，y )．∵⎣⎢⎡⎦⎥⎤ 2 1－1 3⎣⎢⎡⎦⎥⎤x 0y 0＝⎣⎢⎡⎦⎥⎤x y ， ∴⎩⎪⎨⎪⎧x ＝2x 0＋y 0，y ＝－x 0＋3y 0，即⎩⎪⎨⎪⎧x 0＝3x －y7y 0＝x ＋2y7，又∵点P (x 0，y 0)在直线l ：x ＋y －1＝0上， ∴3x －y 7＋x ＋2y7－1＝0， 即直线l ′方程为4x ＋y －7＝0.(2)∵⎪⎪⎪⎪⎪⎪ 2 1－13≠0，∴矩阵A 可逆．设A －1＝⎣⎢⎡⎦⎥⎤a b cd ，∴AA －1＝⎣⎢⎡⎦⎥⎤1 001，∴⎩⎪⎨⎪⎧2a ＋c ＝1，2b ＋d ＝0，－a ＋3c ＝0，－b ＋3d ＝1，解之得⎩⎪⎪⎨⎪⎪⎧a ＝37，b ＝－17，c ＝17，d ＝27，∴A－1＝⎣⎢⎢⎡⎦⎥⎥⎤37 －1717 27. 2．矩阵M ＝⎣⎢⎡⎦⎥⎤4 －32 －1，向量α＝⎣⎢⎡⎦⎥⎤75.(1)求矩阵M 特征值及属于每个特征值一个特征向量； (2)求M 3α.【答案】〔1〕特征值λ1＝1一个特征向量为α1＝⎣⎢⎡⎦⎥⎤11，特征值λ2＝2一个特征向量为α2＝⎣⎢⎡⎦⎥⎤32.；〔2〕⎣⎢⎡⎦⎥⎤4933.【解析】(1)矩阵M 特征多项式为f (λ)＝⎪⎪⎪⎪⎪⎪λ－4 3－2 λ＋1＝λ2－3λ＋2，令f (λ)＝0，得λ1＝1，λ2＝2.当λ1＝1时，解方程组⎩⎪⎨⎪⎧－3x ＋3y ＝0，－2x ＋2y ＝0，得一个非零解⎩⎪⎨⎪⎧x ＝1，y ＝1.因此，矩阵M 属于特征值λ1＝1一个特征向量为α1＝⎣⎢⎡⎦⎥⎤11；当λ2＝2时，同理可得矩阵M 属于特征值λ2＝2一个特征向量为α2＝⎣⎢⎡⎦⎥⎤32.(2)设α＝m α1＋n α2，得⎩⎪⎨⎪⎧m ＋3n ＝7，m ＋2n ＝5，解得m ＝1，n ＝2.所以M 3α＝M 3(α1＋2α2)＝M 3α1＋2M 3α2＝λ31α1＋2λ32α2＝⎣⎢⎡⎦⎥⎤11＋2×23⎣⎢⎡⎦⎥⎤32＝⎣⎢⎡⎦⎥⎤4933.【两年模拟详解析】1．【江苏省扬州中学2021 —2021学年第二学期质量检测】矩阵 10120206A B -⎡⎤⎡⎤==⎢⎥⎢⎥⎣⎦⎣⎦，，求矩阵1.A B - 【答案】【解析】由逆矩阵公式得，再利用矩阵运算得2．【江苏省苏中三市〔南通、扬州、泰州〕2021届高三第二次调研测试数学试题】在平面直角坐标系xOy 中，设点()1,2A -在矩阵对应变换作用下得到点A '，将点()3,4B 绕点A '逆时针旋转90得到点B '，求点B '坐标．【答案】()1,4- 【解析】设(),B x y '， 依题意，由，得()1,2A '．那么()()2,2,1,2A B A B x y '''==--． 记旋转矩阵， 那么，即，解得， 所以点B '坐标为()1,4-．3．【南京市、盐城市2021届高三年级第二次模拟考试】a ，b 是实数，如果矩阵A ＝ 所对应变换T 把点(2，3)变成点(3，4)．〔1〕求a ，b 值．〔2〕假设矩阵A 逆矩阵为B ，求B 2． 【答案】〔1〕a ＝－1，b ＝5．〔2〕4．【江苏省南京市2021届高三年级第三次学情调研适应性测试数学】变换T 1是逆时针旋转2π角旋转变换，对应变换矩阵是M 1；变换T 2对应变换矩阵是M 2＝． 〔1〕点P (2，1)经过变换T 1得到点P'，求P'坐标；〔2〕求曲线y ＝x 2先经过变换T 1，再经过变换T 2所得曲线方程. 【答案】〔1〕P '(-1,2).〔2〕y －x ＝y 2. 【解析】(1)M 1＝，M 121⎡⎤⎢⎥⎣⎦＝12-⎡⎤⎢⎥⎣⎦．所以点P (2,1)在T 1作用下点P '坐标是P '(-1,2). (2)M ＝M 2·M 1＝，设x y ⎡⎤⎢⎥⎣⎦是变换后图象上任一点,与之对应变换前点是00x y ⎡⎤⎢⎥⎣⎦, 那么M 00x y ⎡⎤⎢⎥⎣⎦＝x y ⎡⎤⎢⎥⎣⎦,也就是 即所以,所求曲线方程是y －x ＝y 2.5．【南京市2021届高三年级第三次模拟考试】曲线C ：x 2＋2xy ＋2y 2＝1，矩阵A ＝所对应变换T 把曲线C 变成曲线C 1，求曲线C 1方程． 【答案】x 2＋y 2＝26．【苏锡常镇四市2021届高三教学情况调研〔二〕】变换T 把平面上点(34)-，，(5 0)，分别变换成(21)-，，(1 2)-，，试求变换T 对应矩阵M ．【答案】【解析】设，由题意，得35214012a b c d -⎡⎤⎡⎤⎡⎤=⎢⎥⎢⎥⎢⎥--⎣⎦⎣⎦⎣⎦， ∴ 解得1,513,202,51120a b c d ⎧=-⎪⎪⎪=-⎪⎨⎪=⎪⎪⎪=⎩. 即． 7．【江苏省苏北三市2021届高三最后一次模拟】矩阵，向量，计算5A a .【答案】8．【南通市2021届高三下学期第三次调研考试】在平面直角坐标系xOy 中，直线20x y +-=在矩阵对应变换作用下得到直线()0,x y b a b R +-=∈，求a b +值.【答案】4a b +=【解析】设(),P x y 是直线20x y +-=上一点，由，得()20x ay x y b +++-=即，由条件得，，解得，所以4a b +=9．【盐城市2021届高三年级第三次模拟考试】矩阵两个特征向量，，假设，求2βM . 【答案】42⎡⎤⎢⎥⎣⎦【解析】设矩阵M 特征向量1α对应特征值为1λ，特征向量2α对应特征值为2λ，那么由可解得：120,2,1m n λλ====，又1211022201βαα⎡⎤⎡⎤⎡⎤==+=+⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦， 所以2222121122104(2)242012M M βααλαλα⎡⎤⎡⎤⎡⎤=+=+=+=⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦. 10．【江苏省淮安市2021 届高三第五次模拟考试】矩阵A ＝，假设矩阵A 属于特征值－1一个特征向量为α1＝11⎡⎤⎢⎥-⎣⎦，属于特征值4 一个特征向量为α2＝32⎡⎤⎢⎥⎣⎦．求矩阵A ，并写出A 逆矩阵A －1． 【答案】，【解析】由矩阵A 属于特征值－1一个特征向量为α1＝11⎡⎤⎢⎥-⎣⎦可得， 11⎡⎤⎢⎥-⎣⎦＝，即a －b ＝－1；由矩阵A 属于特征值4一个特征向量为α2＝32⎡⎤⎢⎥⎣⎦， 可得32⎡⎤⎢⎥⎣⎦＝342⎡⎤⎢⎥⎣⎦，即3a +2b ＝12， 解得.即A ＝，所以A 逆矩阵A -1是 11．【江苏省扬州中学2021 届高三4月双周测】矩阵A ＝⎣⎢⎡⎦⎥⎤ 3 3 c d ，假设矩阵A 属于特征值6一个特征向量为α1＝⎣⎢⎡⎦⎥⎤11，属于特征值1一个特征向量为α2＝⎣⎢⎡⎦⎥⎤ 3－2 ．求矩阵A ，并写出A 逆矩阵． 【答案】A ＝⎣⎢⎡⎦⎥⎤ 3 3 2 4， A 逆矩阵是⎣⎢⎢⎡⎦⎥⎥⎤ 23 －12－13 12．12．【2021 年高考模拟(南通市数学学科基地命题)(3)】矩阵，其中,a b 均为实数，假设点(3,1)A -在矩阵M 变换作用下得到点(3,5)B ，求矩阵M 特征值.【答案】1,4-【解析】由条件可知，所以，那么3,2a b ==．矩阵特征多项式为223()(2)(1)(2)(3)3421f λλλλλλλ--==-----=----， 令()0f λ=,得两个特征值分别为121,4λλ=-=．13．【2021 年高考模拟(南通市数学学科基地命题)(2)】，求矩阵B ．【答案】【解析】设 那么1 0 1 22 2a b a c b d ⎡⎤⎡⎤=⎢⎥⎢⎥++⎣⎦⎣⎦B ，故4,4,3,3, 4 3.24,4, 4 221, 2.a ab b ac c bd d =-=-⎧⎧⎪⎪==-⎡⎤⎪⎪=⎨⎨⎢⎥+==-⎣⎦⎪⎪⎪⎪+=-=-⎩⎩解得故B 14．【泰州市2021 届高三第三次调研测试】在平面直角坐标系xOy 中，点A 〔0，0〕，B 〔2，0〕，C 〔1，2〕，矩阵，点A ，B ，C 在矩阵M 对应变换作用下得到点分别为A '，B '，C '，求△A B C '''面积．【答案】1【解析】因，，， 即1(00)(01)(2)2A B C '''--，，，，，． 故1212S A B ''=⨯⨯=． 15．【2021 年高考模拟(南通市数学学科基地命题)(2)】二阶矩阵M 有特征值1λ=-及对应一个特征向量，并且矩阵M 对应变换将点()1,1变换成()0,3-．〔1〕求矩阵M ；〔2〕向量，求5M α值．【答案】〔1〕；〔2〕.【解析】〔1〕设，那么，故 .，故 .联立以上方程组解得1,1,4,1a b c d ==-=-=，故.〔2〕由〔1〕知那么矩阵M 特征多项式为2211()(1)42341f λλλλλλ-==--=--- 令0)(=λf ，得矩阵M 另一个特征值为3.设矩阵M 另一个特征向量是，那么，解得20x y +=,故 .由12m n =+αe e ，得，得3,1m n == .∴5A α5551212(3)3()M M M =+=+e e e e 55551122112463()3(1)322480λλ--⎡⎤⎡⎤⎡⎤=+=⨯-+=⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦e e .拓展试题以及解析1． 矩阵10120206A B -⎡⎤⎡⎤==⎢⎥⎢⎥⎣⎦⎣⎦，，求矩阵1.A B - 【答案】1101212.1060302A B --⎡⎤--⎡⎤⎡⎤⎢⎥==⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦【入选理由】此题考察矩阵乘法运算，考察二阶逆矩阵求法，意在考察学生逻辑思维能力和运算求解能力.此题首先求出二阶逆矩阵1A -，再计算，像这种题型考察知识根底，目明确，是高考出题方向，应选此题.2．矩阵，假设矩阵A 属于特征值6一个特征向量为，属于特征值1一个特征向量为．求A 逆矩阵．【答案】【解析】由题意得，那么 ， 解得，即，所以.【入选理由】此题考察矩阵特征值与特征向量，此题通过特征值与特征向量概念求得矩阵A ，然后再求得逆矩阵，意在考察最根本运算求解能力，意在考察学生逻辑思维能力.符合江苏高考对选做题要求，应选此题.3．变换1T 是逆时针旋转2π旋转变换，对应变换矩阵是1M ；变换2T 对应用变换矩阵是．求函数2y x =图象依次在1T ，2T 变换作用下所得曲线方程．【答案】2y x y -=【入选理由】此题考察矩阵运算与平面变换之间关系，考察用矩阵运算表示平面变换，意在考察学生分析问题与解决问题能力，考察推理想象能力，考察运算求解能力，此题型考察知识根底，方法简单，是高考出题方向，应选此题.。
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高考真题精讲精练：训练步骤：1、先花十八分钟做完这三篇阅读理解。
2、再仔细阅读做题思维过程及试题分析和阅读技巧点拨。
3、然后翻译的文章要仔细研读并做到精通文章原意而且最好是能脱口而出。
2017阅读全国卷二阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳答案。
AIn the coming months, we are bringing together artists form all over the globe, to enjoy speaking Shakespeare’s plays in their own language, in our Globe, within the architecture Shakespeare wrote for. Please come and join us.National Theatre of China Beijing | ChineseThis great occasion (盛会) will be the National Theatre of China’s first visit to the UK. The company’s productions show the new face of 21st century Chinese theatre. This production of Shakespeare’s Richard III will be directed by the National’s Associate Director, Wang Xiaoying.Date & Time: Saturday 28 April, 2.30 pm & Sunday 29 April, 1.30 pm & 6.30 pmMarjanishvili Theatre Tbilisi | GeorgianOne of the most famous theatres in Georgia, the Marjanishvili, founded in 1928, appears regularly at theatre festivals all over the world. This new production of it is helmed（指导）by the company’s Artistic Director Levan Tsuladze.Date & Time: Friday 18 May, 2.30 pm & Saturday 19 May, 7.30 pmDeafinitely Theatre London | British Sign Language（BSL）By translating the rich and humorous text of Love’s Labour’s Lost into the physical language of BSL, Deafinitely Theatre creates a new interpretation of Shakespeare’s comedy and aims to build a bridge between deaf and hearing worlds by performing to both groups as one audience.Date & Time: Tuesday 22 May, 2.30 pm & Wednesday 23 May, 7.30 pmHabima National Theatre Tel Aviv | HebrewThe Habima is the centre of Hebrew-language theatre worldwide, Founded in Moscow after the 1905 revolution, the company eventually settled in Tel Aviv in the late 1920s. Since 1958, they have been recognised as the national theatre of Israel. This production of Shakespeare’s The Merchant of Venice marks their first visit to the UK.Date & Time: Monday 28 May, 7.30 & Tuesday 29 May, 7.30 pm21. Which play will be performed by the National Theatre of China?A.Richard Ⅲ.B.Lover’s Labour’s LostC.As You Like ItD.The Merchant of V enice22. What is special about Deafinitely Theatre?A. It has two groups of actorsB. It is the leading theatre in LondonC.It performs plays in BSLD. It is good at producing comedies23. When can you see a play in Hebrew?A. On Saturday 28 April.B. On Sunday 29 AprilC. On Tuesday 22 May.D. On Tuesday 29 MayBI first met Paul Newman in 1968, when George Roy Hill, the director of Butch Cassidy and the Sundance Kid, introduced us in New York City. When the studio didn’t want me for the film ---it wanted somebody as well-known as Paul --- he stood up for me. I don’t know how many people would have done that; they would have listened to their agents or the studio powers.The friendship that grew out of the experience of making that film and The Sting four years later had its root in the fact that although there was an age difference, we both came from a tradition of theater and live TV. We were respectful of craft（技艺）and focused on digging into the characters we were going to play. Both of us had the qualities and virtues that are typical of American actors: humorous, aggressive, and making fun of each other --- but always with an underlying affection. Those were also at the core（核心）of our relationship off the screen.We shared the belief that if you’re fortunate enough to have success, you should put something back - he with his Newman’s Own food and his Hole in the Wall camps for kids who are seriously ill, and me with Sundance and the institute and the festival. Paul and I didn’t see each other all that regularly, but sharing that brought us together. We supported each other financially and by showing up at events.I last saw him a few months ago. He’d been in and out of the hospital. He and I both knew what the deal was,and we didn’t talk about it. Ours was a relationship that didn’t need a lot of words.24. Why was the studio unwilling to give the role to author at first?A. Paul Newman wanted it.B. The studio powers didn’t like his agent.C. He wasn’t famous enough.D. The director recommended someone else.25. Why did Paul and the author have a lasting friendship?A. They were of the same age.B. They worked in the same theater.C. They were both good actors.D. They had similar characteristics.26. What does the underlined word “that” in paragraph 3 refer to?A. Their belief.B. Their care for children.C. Their success.D. Their support for each other.27. What is the author’s purpose in writing the test?A. To show his love of films.B. To remember a friend.C. To introduce a new movie.D. To share his acting experience.CTerrafugia Inc. said Monday that its new flying car has completed its first flight, bringing the company closer to its goal of selling the flying car within the next year. The vehicle-named the Transition –has two seats, four wheels and wings that fold up so it can be driven like a car. The Transition, which flew at 1,400 feet for eight minutes last month, can reach around 70 miles per hour on the road and 115 in the air. It flies using a 23-gallon tank of gas and bums 5 gallons per hour in the air. On the ground, it gets 35 miles per gallon.Around 100 people have already put down a $10,000 deposit to get a Transition when they go on sale, and those numbers will likely rise after Terrafugia introduces the Transition to the public later this week at the New York Auto Show. But don’t expect it to show up in too many driveways. It’s expected to cost $279,000. And it won’t help if you’re stuck in traffic. The car needs a runway.Inventors have been trying to make flying cars since the 1930s, according to Robert Mann, an airline industry expert. But Mann thinks Terrafugia has come closer than anyone to making the flying car a reality. The government has already permitted the company to use special materials to make it easier for the vehicle to fly. The Transition is now going through crash tests to make sure it meets federal safety standards.Mann said Terrafugia was helped by the Federal Aviation Administration’s decision five years ago to create a separate set of standards for light sport aircraft, which are lower than those pilots of larger planesTerrafugia says an owner would need to pass a test and complete 20 hours of flying time to be able to fly the Transition, a requirement pilots would find relatively easy to meet.28. What is the first paragraph mainly about?A. The basic data of the Transition.B. The advantages of flying cars.C. The potential market for flying cars. C. The designers of the Transition.29. Why is the Transition unlikely to show up in too many driveways?A. It causes traffic jams.B. It is difficult to operate.C. It is very expensive.D. It bums too much fuel.30. What is the government’s attitude to the development of the flying car?A. CautiousB. Favorable.C. Ambiguous.D. Disapproving.31. What is the best title for the text?A. Flying Car at Auto ShowB. The Transition’s First FlightC. Pilots’ Dream Coming TrueD. Flying Car Closer to Reality先来看A篇阅读理解的思维过程解析和技巧点拨：这类信息题直接做题以提高做题效率，缩短你做题时间。