考点跟踪训练42 词汇运用

教学资料范本【2020最新】人教版中考英语考点跟踪突破：42阅读理解1含答案编辑：__________________时间：__________________(一)(20xx，天津)My grandfather Jack is 96 years old，and he has had an interesting life..He has travelled a lot in his life in the Far East..He visited the Taj Mahal in India and the Pyramids in Egypt..He hunted (狩猎) lions in Africa，and rode a camel in the Sahara Desert..He says the most beautiful place he has travelled to is Kathmandu in Nepal..Jack has married twice..His first wife died when she was 32..He met his second wife Maria while he was cycling round France..They have been married for 50 years，and they have lived happily in a small village since they got married..Jack says that he has never been ill in his life..The secret of good health，according to my grandfather，is exercise..He goes swimming every morning..He has done this since he was a boy..He also has a glass of wine every night！Perhaps that is his secret!1．What kind of life has Jack lived?A．A short life.. B．An interesting life..C．A lonely life.. D．A poor life..2．Which of the following does Jack think is the most beautiful place?A．Kathmandu.. B．The Pyramids..C．The Sahara Desert.. D．Taj Mahal..3．How many times has Jack married?A．Once.. B．Twice..C．Three times.. D．Four times..4．Where did Jack meet Maria?A．In India.. B．In Nepal..C．In France.. D．In Egypt..5．What does Jack do every night?A．He has a glass of wine.. B．He goes swimming..C．He hunts lions.. D．He rides a camel..(二)(20xx，聊城)My name is Sam..I joined a club called “passing help”last month..Now let me tell you why I joined it..One evening this May, on my way home my old car broke down(出故障)．It was 25 miles from my home..I wanted to get a ride(搭便车), but there was no car.. It was also hard to take a taxi.. I decided to take a bus home..I went to a bus stop nearby..After a while, a bus came, but it did not go to my town..the bus driver was a young woman..She was kind and she told me which bus I should take..I waited there for about thirty minutes，but no bus came..At last a car came to me and a woman came out of the car ..She was just the bus driver..“”she said , “Get in my car and I will take you back to your home..”“It is a long way..”I said..“”she said，“Let's go..”On the way，she told me a story.. A few days ago，there wasn't gas(汽油)in her car.. An old man drove her up to a gas station and then back to her car..When we got to my home，I wanted to give her some money to thank her，but she didn't accept her..“I only want to help others and do something nice for somebody..Pass it along.. ” she said..6．What happened to Sam one evening this May?A．He lost his way..B．His car broke down..C．He was hurt in an accident..D．He couldn't reach the gas station..7．Sam didn't think of going home________that evening..A．by train B．by bus C．by car D．by taxi8．From the passage , we know that the young woman was________..A．a club boss B．a taxi driverC．a bus driver D．a gas station worker9．The young woman wanted Sam to ________..A．give her some moneyB．get on her busC．take her to her houseD．help others just as she did10．The best title (题目)of the passage is ________..A．A kind old man B．Getting a rideC．Passing help D．A broken car(三)(20xx，河北)“Homestay is a form of study abroad program..It allows the visitor to rent a room from a local (当地的) family to better understand the local lifestyle..It also helps to improve the visitor's language ability，”said a teacher during a school meeting last term..“Students who wish to learn more about foreign cultures or to get foreign experience should join this kind of holiday..I am sure you won't be disappointed (失望的)．”After this special meeting，I always thought about this kind of st month，I had a chance at last to go on such a holiday with some of my schoolmates and we went to London，a place where I had wanted to go since years ago..As we were still young，we had a group leader who planned things for us and looked after us..After we got to London，we went to stay with different families..I was lucky that my host family (寄宿家庭) was a white couple who had a daughter about my age..They treated me as a daughter of their family during my stay there..They were interested in me and I learnt a lot of things from them，too..­seeing trip to different places of interest like the Big Ben，the London Bridge，and the Buckingham Palace..We would go back to our own homes after the activities..The holiday was a valuable experience for me..I enjoyed every minute of it..Yet，time really flew fast..Three weeks later，we had to leave “home” for Hong Kong..11．In the “homestay”program，a visitor can ________..A．learn more about holidaysB．understand his culture betterC．improve the language abilityD．take part in foreign meetings12．The writer had wanted to visit London since ________..A．last month B．years agoC．the special meeting D．her stay abroad13．The group leader should ________..A．make plans for the familyB．take care of the studentsC．stay with different familiesD．rent rooms to the students14．The writer's host family ________..A．was very kind to herB．went sight­seeing with herC．had two white daughtersD．was interested in her activities15．From the passage，we know that the writer ________ in London..A．wished to stay a little longerB．spent three weeks in her homeC．had classes in many interesting placesD．helped the teacher take the students in a car(四)(20xx，河南)Cause and effect is one way to explain things that happen around us..Many things happen because something caused or influenced them to happen..Sometimes it is hard to look at a cause and find out what causes the effect..It may help you to start with the effect and use your reasoning (推理的) skills..Think about all the things you know that could be reasons for the effect you can see..For example，you may see someone putting on a heavy jacket..This is the effect..To look for a cause，think to yourself，“What would make someone put on a heavy jacket？”Maybe the person is going outside into very cold weather..Maybe the person works in the penguin pen (企鹅圈养地) at Sea World..Maybe the person is going to visit an ice skating rink where the air is kept very cold..All of these things could be a cause for putting on a heavy jacket..Now，think about a second example..The effect is a boy named Abi has to go to the head teacher's office..What are the possible causes？Maybe he bullied (欺负) anotherstudent..Maybe he is just being picked up early..Maybe he is being given a prize!Here is another example for you to think about its cause and effect..Cait，13，was trying to fall asleep when her 8­year­old brother，Doug，came into her room..He looked around a bit，but seemed really out of it..Then Doug went back into the hallway and stood there looking straight up at the hall light for quite a while..Little brothers can be very strange，but this was really much too strange..Cait didn't know what to do..Just then，Cait's father appeared and explained that Doug was sleepwalking..What's the cause and effect，could you tell?16．According to the second paragraph，which of the following is an effect?A．Someone puts on a heavy jacket..B．Someone works in the penguin pen..C．Someone will go outside into cold weather..D．Someone will go to visit an ice skating rink..17．Abi has to go to the head teacher's office..Which of the following isn't the possible cause?A．He bullied another student..B．He is going shopping..C．he is being picked up early..D．He is being given a prize..18．What was Doug doing when his sister Cait tried to fall asleep?A．He was going outside..B．He was reading a story..C．He was sleepwalking..D．He was looking for his dad..19．Which of the following is cause and effect?A．Tony got up and had a glass of water..B．We came home and found him sleeping..C．The ball was lost and a window was broken..D．Tim was late again and his teacher got angry..20．What is the best title for the text?A．Truth and lies B．Work and sleepC．Cause and effect D．Life and dreams(五)Ask any student which subject he or she hates most..9 out of 10 students will answer “math”Jenny Sanders，a high school student in California，asks，“”For example，imagine you are a cook and must serve dinner to 100 guests..How should you divide your resources so that you can get the job done most efficiently (高效地)？In situations like this，the ability to think logically will get you to a reasonable answer and solve your problem..21．According to the passage，which subject do students always learn in different grades at school?A．Chinese.. B．Math.. C．Geography..22．What does Jenny Sanders think of learning math?A．Interesting.. B．Boring.. C．Useless..23．Which of the following is TRUE according to the passage?A．90% of the students hate learning math..C．Math can do calculations and store information..24．What does the underlined word “resources” mean in the passage?A．科目 B．效率 C．资源25．What does the writer want to tell us?A．Math is just learning to add and subtract numbers..B．Math can be good for both our body and our mind..C．Math helps us think logically and solve problems..(六)Fifty­It seems that Barbie has lost her magic among older girls..“For younger girls，playing with a Barbie is much fun..But when you get older，you want something smarter and more modern，”says Vera Shepherd，a shop assistant in a New York toy store..Mattel is planning big celebrations for Barbie's 53rd birthday..Fashion designers from all over the world havebeen called to make new dresses for Barbie..How long will Barbie stay popular in the world of toy dolls？It is hard to say，but 53 is surely not the age to retire(退休)．26．Barbie's family name is________..A．Roberts B．Millicent C．Shepherd D．Bratz27．Barbie's trouble is that ________..A．it wears heavy makeup and miniskirtsB．other dolls are more popular with little girlsC．other dolls are trying to beat her in the market28．Girls can do the following in the first Barbie Shop in Shanghai except________..A．going shopping B．taking photosC．drinking juice29．What's the meaning of the underlined words “fashion designers”in the passage?A．珠宝设计师B．发型设计师C．服装设计师30．What is the best title of the passage?A．First Barbie Shop in ShanghaiB．Barbie's Past and PresentC．Barbie's 53rd Birthday Party第42讲阅读理解(一)中考热身1～5..CABDD解题技法【例1】1.. A 2..C 3..D 4..C 5..B活学活用1．B 2..C 3..A 4..D 5..A实战强化(一)1～5..DADBC(二)6～10..CBBAC(三)11～15..ACDDC(四)16～20..AADBD(五)21～25..BCACD。

考点跟踪突破43 词汇运用一、用下面方框中单词的适当形式填入短文空格内，使短文意思正确、通顺(每词限用一次)。

A(2016，黄石)show，sad，write，difficult，since，courage，them，hard­working，at，becomeI like reading.I love many different kinds of books，because they not only openmy mind but also give me 1.courage.Up to now I have read a lot of books，such as magazines，novels and storybooks.Butone of the books that I like best is The Story of My Life.It was 2.written by Americanwriter Helen Keller in 1902.She was a blind，deaf and dumb person.In the book，she wrote that she had not been able to see，hear or speak 3.since she was one yearand seven months old.This unusual thing made her very 4.sad．Luckily，she met hergood teacher，Miss Sullivan 5.at the age of seven.Helen was getting happier everyday.Then，Miss Sullivan helped her learn how to write English words.At first，Miss Sullivan wrote some words on Helen's hands with her own fingers again andagain.Helen was a very 6.hard­working girl.She tried as much as possible to rememberwords.After that，she wrote many famous works.The Story of My Life is one of 7.them．The Story of My Life describes her hard struggle(奋斗)to 8.bceome a good writerand educationist of the world.It 9.shows us an important truth：Nothing is 10.difficult if you put your heartinto it! This is why I like it best.What about you?B(2015，营口)bring，all，because of，it，feel，she，touch，tour，please，but There was a young flower in the desert(沙漠)where all was dry and sad looking.Itwas growing by 1.itself ，enjoying every day and saying to the sun，“Whenshall I be grown up？” and the sun would say，“Be patient—each time I 2.touch you，you grow a little.” She was so 3.pleased because she would havea chance 4.to_bring beauty to this corner of sand and this is 5.all she wanted to do—bring a little bit of beauty to this world.One day two 6.tourists came by and stepped on her.She was going todie and she 7.felt so sad.Not because she was dying 8.but because shewould not have a chance to bring a little bit of beauty to this corner of the desert.The great spirit saw her，and was listening.Indeed(确实)，he said she shouldbe living.And he reached down and touched her and gave 9.her life.And she grew up to be a beautiful flower，and this corner of the desert becameso beautiful 10.because_of her.C(2015，陕西)sweet，plant，she，child，run，high，sit，feel，day，notice One day，I took my two kids to the local playground.As soon as we got there，my daughter 1.ran to the swing(秋千)and asked for a push.When I washelping my daughter.I 2.noticed another girl trying to make her own swing gohigh by herself.Her old grandmother was 3.sitting on the chair nearby andsmiled at me.I gave my daughter one big push and then walked towards the little girl.I askedif she wanted me to give 4.her a push.She smiled and said“Yes”．For thenext two hours.I pushed the swings，and played with my two 5.children andthe little girl.When we went home，I was very tired.But my heart was flying much6.higher than the swings.One day two years later，after a 7.day's work.I was a little tired.ButI needed to pick up my kids before going home.While I was waiting outside the schoolgate，a little girl came over and smiled 8.sweetly at me.She gave me a bighug(拥抱)before catching her school bus.As I watched her running away，I didn't9.feel tired anymore.In life，the love we give others will find its way back to us.It may travel fromheart to heart or it may blossom(开花)in the heart which it was 10.planted in.The love we share，the kindness we give，and the happiness we create will alwayscome back to us with a pleasant surprise.D(2015，梅州)either，make，signs，them，best，provide，who，sure，prevents，others If you visit the animal shelter(收容所)in Salinas，California，you'll see hugesigns that have a picture of a dog and a cat on them.These 1.signs are put in frontof the shelter to catch people's attention.The signs 2.make people interested inthe shelter and encouraged them to visit it and maybe even take a cat or a dog intotheir homes.Each year，the Salinas shelter accepts thousands of dogs and cats.The animalsare 3.either lost ones or are left by people who can't take care of 4.them.Of allthe animals，some of them are taken into new homes.Some 5.others are moved to other shelters.And，unluckily，some cannot be saved because they are too sick or are thoughtto be dangerous.Animal shelters 6.provide food，medicine，and safe places for animals.But theyare not the 7.best homes.The animals stay in small cages(笼子)．The people 8.whowork at shelters do their best to care for the animals，but the animals do not alwaysget the attention or exercise they need.To prevent animals from becoming homeless，pet owners should take good care oftheir pets.Most pet doctors also suggest people make 9.sure their pets have aspecial surgery(外科手术)．It 10.prevents animals from having more babies.And thatreduces(减少)the number of homeless animals.Eonly，fine，notice，enough，eye，thief，allow，follow，crowd，searchI want to buy a pair of sports shoes for a long time.I had spent months saving up the money to buy them and I finally had st Saturday my friend Jake wanted to buy a new CD，so we decided to go shopping together.We took the bus into town and it was very 2.crowded ，so we had to stand all the way.Jake and I were talking when I suddenly 3.noticed that my bag was open and my purse had gone！The bus had just stopped and there was a boy near me who was going quickly towards the door.We thought he had stolen my money so we got off the bus and 4.followed him.The boy started running and then Jake ran after him shouting “Stop！5.Thief ！”It was like a scene out of a film！A policeman saw what was going on and managed to get the boy.The embarrassing thing was that when the policeman 6.searched the boy，he didn't have my purse！He had probably thrown it away before he was caught.The boy said we had made a mistake and we shouldn't blame(指责)him for the stolen purse.He explained that he had 7.only started running because he was late for a meeting with friends.The policeman 8.allowed him to go and I felt really stupid.I don't know whether he stole my purse or not as there was no proof(证据)．I wish I hadn't been so careless and had kept an 9.eye on my bag!I've lost my front door key and 60 pounds.I'm really fed up.Jake offered to lend me the money to buy the sports shoes，but I don't think it's 10.fine to take it.It isn't his fault(过失)that I had my purse stolen!Ftell，well，need，since，be，he，letter，at，know，lookA car stopped outside the Cherry Hotel and a young man got out.Mrs.Smith said to the young man.“What can I do for you，sir？”“Excuse me，”the young man said，“I am 1.looking for my uncle，Mr.White.He has been away from home 2.since two days ago.I think he is staying here.”“Yes，he is.”Mrs.Smith said，“But I'm afraid that he went back to London yesterday.”“Oh，dear，”said the young man，looking sad，“I went to his house，but I was 3.told by his children that he was going to stay here until the end of the week.”“Yes，” said Mrs.Smith.“He wanted to stay here the whole week，but yesterday someone called him saying that one of his friends 4.was ill.So he caught the train back to London to see the friend 5.at once.”“He should let me 6.know，” the young man said.“I wrote him a 7.letter，saying that I was coming.Well，he isn't her e.I won't wait any longer.”The young man thanked Mrs.Smith and went out.Mrs.Smith watched 8.him leave.When his car couldn't be seen，she called out，“You can come out now，Mr.White.He's gone.”Mr.White came out of the bedroom.“Many thanks，Mrs.Smith.”he said laughing.“You did very 9.well.The young man is my nephew(侄子)．When he 10.needs money，he will look for me everywhere.Next time he won't tell me by writing me a letter.”G(2015，天津)instrument，or，kind，smart，popular，encourage，around，work，hear，alsoIn the town of Lampang in northern Thailand，there is an unusual group ofmusicians.They play many different 1.kinds of music—everything from traditional Thai songs to music by Beethoven.Both children and adults love this group.What makes them so 2.popular？Is it their music？Their looks？Yes，it's both of the things，but it's 3.also something else：they're elephants.These musical elephants started at the TECC(泰国大象保护中心)in Lampang.The TECC protects elephants.It teaches people to understand and love them.And，like many zoos 4.around the world，the TECC encourages elephants to paint.Richard Lair 5.works for the TECC.He loves his job there and knows a lot about elephants.He says some of the animals' paintings are very good.But，in fact，elephants 6.hear better than they see.And so he had an idea：if elephants are 7.smart and they have good hearing，maybe they can play music.To test his idea，Lair and a friend started the Thai Elephant Orchestra.During a performance(表演)，the elephants play a number of 8.instruments ，including the drums and the xylophone(木琴)．But can elephants really make music properly？Yes，says Lair.They are very creative.Humans 9.encourage the animals to play，but the elephants make their own songs；they don't just copy their trainers 10.or other people.There are now CDs of the group's music which make money for the TECC.And the music these artists create is pretty amazing.Hbring，weigh，how，poor，with，however，if，they，sell，much In a town in France，there was a farmer who lived alone.Every day he 1.sold a pound of butter to his neighbor，who was a baker.One day the baker decided to weigh the butter to see 2.if he was getting a pound.After he weighed it，he found thathe wasn't.The baker then took the farmer to the judge(法官)．The judge wanted to know the farmer's ways to weigh the butter.The farmer replied，“I'm so 3.poor that I do not have enough money to buy anything to weigh it.4.However ，I do have a kind of scale(天平)．” The judge asked，“Then 5.how do you weigh the butter？” The farmer replied，“Before the baker started buying butter from me，I had bought bread from him.So now every time when I 6.bring home the bread from the baker，I put it on the scale and give him the butter of the same 7.weight.”We always get back what we give to others.Whenever you take action，ask yourself this question，“Am I honest？”Honesty or dishonesty can become a habit.Some dishonest people can lie 8.without a red face.Others lie so 9.much that they do not even know what the truth is any more.But who is it bad for? In fact，those who lie will hurt 10.themselves by their own dishonest behavior.I(2016，丹东)how，our，different，toy，pay，on，become，better，one，between，if，spendOur clothes will become small with our growth.Some books and 1.toys will be not used any more.2.How will you deal with these old things？Don't worry! Here'sa good way.Online shopping will help you.Online shopping is 3.becoming more and more popular now.We can bid (竞价)for the 4.different goods online，such as books，dolls，clothing and used cars.We can 5.spend less money on 6.better goods.Also，we can sell the things well through the Internet.There are many world online market places 7.on the Internet.8.If we want to buy or sell something online，we must become the member of one of them 9.first．Let's buy and sell things online.Let's enjoy 10.ourselves online.J(2016，乌鲁木齐)lose，worry，much，try，health，piece，hungry，know，advice，timeA lot of people wish to be slim(苗条)，but at the same time they are1.worried/worrying about their health.In fact，it is important for everyone to2.lose weight healthily，but how can you do it？Here’s some good3.advice．★ Drink plenty of water and eat a(n)4.healthy diet.If you feel like eating snacks(零食)，drink a glass of water first.If you are still5.hungry after 15 minutes，then it’s time for a light snack.6.Try to stay away from food with high calories(卡路里)，such as sweets and fast food.★ Do not eat 7.more than you can consume(消耗)．People get fat because they cannot consume all the calories that they get.So 8.to_know/knowing how many calories you really need is very important.★Take enough exercise.The “333” is good for you－exercise 3 9.times a week，for at least 30 minutes at a time，and your pulse rate(脉搏率) should be more than 130 after exercising.Keep the three 10.pieces of advice in mind and follow the advice.Then you’ll surely have a slim and strong body.。

考点跟踪突破40 词汇运用一、根据句意及所给的首字母或汉语提示完成以下单词。

A(2021，凉山)1．Christmas is in December，the t w elfth month of the year.2．The dish my mom is cooking smells nice，I can't wait to eat it.3．Country is a traditional kind of music from the southern (南方) states of America.4．Would you mind lending (借) me your eraser？I can't find mine.5．After hearing the bad news，my parents didn't talk and they finished the rest of their dinner in silence (沉默)．B(2021，黄石)1．It is w indy now.I'm afraid it is going to rain soon.2．Being afraid that Tim is lonely，his mom wants to have a second baby to play with him.4．It might seem more difficult to speak politely than directly，not hurting others.5．We can get information in many kinds of ways such as reading newspapers，watching TV and surfing the Internet.C(2021，泰安)1．The last bus has already gone.I'm afraid we have no choice/chance but to take a taxi.2．—Wow！You've got so many skirts.—But none of them are in fashion now.3．As a translator，understanding the true meaning that people want to express is very important.4．The traditional Chinese culture will be helpful/useful (有帮助的) for our future if we can learn more.D(2021，百色)1．In my hometown，it is very hot in July (七月)．2．I hardly (几乎不) heard what you said.Can you say it again?3．We can borro w (借) books from the library.4．The Youjiang River runs through/across (穿过) the city of Baise.5．Kate doesn't like this one.Please show her another (另一个)．6．There are 25 students in our art club.They are sixteen girls and nine boys.7．Sally is from the USA，she is an American．8．China has the largest population in the world.It's about 1.4 billion.10．Hello，everyone.Let me introduce my new teacher to you.二、根据句子意思，用括号中所给汉语提示或英语单词的适当形式完成以下单词。

考点跟踪突破40 词汇运用一、用下面方框中单词的适当形式填入短文空格内，使短文意思正确、通顺(每词限用一次)。

A(2015，北海)friend，others，teach，you，too，different，rule，what，spend，adult Young people and older people don't always agree with each other.They sometimes have 1.different ideas about work and life.But in one special program in New York State，adults and teenagers live together in a 2.friendly way.Each summer 200 teenagers and 50 3.adults live and work together for eight weeks as a group.Everyone works several hours each day.Some teenagers work in the forest or on the farms.Some learn to make things like tables and chairs and build houses.The adults 4.teach them these skills.There are several free hours every weekday.Weekends are free，5.too.During the free hours，some of the teenagers learn photo taking or painting.6.Others sit around and talk or sing.Each teenager chooses his own way to 7.spend his free time.When people live together，rules are necessary，In this program the teenagers and the adults make the rules together.If someone breaks a 8.rule，the problem is brought to the whole group.They talk about it and ask，“How did it happen? 9.What should we do about it？”One of the teenagers says about his experience，“ 10.You stop thinking only about yourself.You learn to think about the group.”B(2015，营口)bring，all，because of，it，feel，she，touch，tour，please，but There was a young flower in the desert(沙漠)where all was dry and sad looking.It was growing by 1.itself，enjoying every day and saying to the sun，“When shall I be grown up？” and the sun would say，“Be patient—each time I 2.touch you，you grow a little.” She was so 3.pleased because she would have a chance 4.to_bring beauty to this corner of sand and this is 5.all she wanted to do—bring a little bit of beauty to this world.One day two 6.tourists came by and stepped on her.She was going to die and she 7.felt so sad.Not because she was dying 8.but because she would not have a chance to bring a little bit of beauty to this corner of the desert.The great spirit saw her，and was listening.Indeed(确实)，he said she should be living.And he reached down and touched her and gave 9.her life.And she grew up to be a beautiful flower，and this corner of the desert became so beautiful 10.because_of her.C(2015，陕西)sweet，plant，she，child，run，high，sit，feel，day，notice One day，I took my two kids to the local playground.As soon as we got there，my daughter 1.ran to the swing(秋千)and asked for a push.When I was helping my daughter.I 2._noticed another girl trying to make her own swing go high by herself.Her old grandmother was 3.sitting on the chair nearby and smiled at me.I gave my daughter one big push and then walked towards the little girl.I asked if she wanted me to give 4.her a push.She smiled and said“Yes”．For the next two hours.I pushed the swings，and played with my two 5.children and the little girl.When we went home，I was very tired.But my heart was flying much 6.higher than the swings.One day two years later，after a 7.day's work.I was a little tired.But I needed to pick up my kids before going home.While I was waiting outside the school gate，a little girl came over and smiled 8.sweetly at me.She gave me a big hug(拥抱)before catching her school bus.As I watched her running away，I didn't 9.feel tired anymore.In life，the love we give others will find its way back to us.It may travel from heart to heart or it may blossom(开花)in the heart which it was 10.planted in.The love we share，the kindness we give，and the happiness we create will always come back to us with a pleasant surprise.D(2015，梅州)either，make，signs，them，best，provide，who，sure，prevents，others If you visit the animal shelter(收容所)in Salinas，California，you'll see huge signs that have a picture of a dog and a cat on them.These 1.signs are put in front of the shelter to catch people's attention.The signs 2.make people interested in the shelter and encouraged them to visit it and maybe even take a cat or a dog into their homes.Each year，the Salinas shelter accepts thousands of dogs and cats.The animals are 3.either lost ones or are left by people who can't take care of 4.them.Of all the animals，some of them are taken into new homes.Some 5.others are moved to other shelters.And，unluckily，some cannot be saved because they are too sick or are thought to be dangerous.Animal shelters 6.provide food，medicine，and safe places for animals.But they are not the 7.best homes.The animals stay in small cages(笼子)．The people 8.who work at shelters do their best to care for the animals，but the animals do not always get the attention or exercise they need.To prevent animals from becoming homeless，pet owners should take good care of their pets.Most pet doctors also suggest people make 9.sure their pets have a special surgery(外科手术)．It 10.prevents animals from having more babies.And that reduces(减少)the number of homeless animals.Eonly，fine，notice，enough，eye，thief，allow，follow，crowd，searchI want to buy a pair of sports shoes for a long time.I had spent months saving up the money to buy them and I finally had st Saturday my friend Jake wanted to buy a new CD，so we decided to go shopping together.We took the bus into town and it was very 2.crowded，so we had to stand all the way.Jake and I were talking when I suddenly 3.noticed that my bag was open and my purse had gone！The bus had just stopped and there was a boy near me who was going quickly towards the door.We thought he had stolen my money so we got off the bus and 4.followed him.The boy started running and then Jake ran after himshouting “Stop！5.Thief！”It was like a scene out of a film！A policeman saw what was going on and managed to get the boy.The embarrassing thing was that when the policeman 6.searched the boy，he didn't have my purse！He had probably thrown it away before he was caught.The boy said we had made a mistake and we shouldn't blame(指责)him for the stolen purse.He explained that he had 7.only started running because he was late for a meeting with friends.The policeman 8._allowed him to go and I felt really stupid.I don't know whether he stole my purse or not as there was no proof(证据)．I wish I hadn't been so careless and had kept an 9.eye on my bag!I've lost my front door key and 60 pounds.I'm really fed up.Jake offered to lend me the money to buy the sports shoes，but I don't think it's 10.fine to take it.It isn't his fault(过失)that I had my purse stolen!Ftell，well，need，since，be，he，letter，at，know，lookA car stopped outside the Cherry Hotel and a young man got out.Mrs.Smith said to the young m an.“What can I do for you，sir？”“Excuse me，”the young man said，“I am 1.looking for my uncle，Mr.White.He has been away from home 2.since two days ago.I think he is staying here.”“Yes，he is.”Mrs.Smith said，“But I'm afraid that he went back to London yesterday.”“Oh，dear，”said the young man，looking sad，“I went to his house，but I was 3.told by his children that he was going to stay here until the end of the week.”“Yes，” said Mrs.Smith.“He wanted to stay here the whole week，but yesterday someone called him saying that one of his friends 4.was ill.So he caught the train back to London to see the friend 5.at once.”“He should let me 6.know，” the young man said.“I wrote him a 7.letter，saying that I was coming.Well，he isn't here.I won't wait any longer.”The young man thanked Mrs.Smith and went out.Mrs.Smith watched 8.him leave.When his car couldn't be seen，she called out，“You can come out now，Mr.White.He's gone.”Mr.White came out of the bedroom.“Many thanks，Mrs.Smith.”he said laughing.“You did very 9.well.The young man is my nephew(侄子)．When he 10.needs money，he will look for me everywhere.Next time he won't tell me by writing me a letter.”G(2015，天津)instrument，or，kind，smart，popular，encourage，around，work，hear，alsoIn the town of Lampang in northern Thailand，there is an unusual group of musicians.They play many different 1.kinds of music—everything from traditional Thai songs to music by Beethoven.Both children and adults love this group.What makes them so 2.popular？Is it their music？Their looks？Yes，it's both of the things，but it's 3.also something else：they're elephants.These musical elephants started at the TECC(泰国大象保护中心)in Lampang.The TECC protects elephants.It teaches people to understand and love them.And，like many zoos 4.around the world，the TECC encourages elephants to paint.Richard Lair 5.works for the TECC.He loves his job there and knows a lotabout elephants.He says some of the animals' paintings are very good.But，in fact，elephants 6.hear better than they see.And so he had an idea：if elephants are 7.smart and they have good hearing，maybe they can play music.To test his idea，Lair and a friend started the Thai Elephant Orchestra.During a performance(表演)，the elephants play a number of 8.instruments，including the drums and the xylophone(木琴)．But can elephants really make music properly？Yes，says Lair.They are very creative.Humans 9.encourage the animals to play，but the elephants make their own songs；they don't just copy their trainers 10.or other people.There are now CDs of the group's music which make money for the TECC.And the music these artists create is pretty amazing.Hbring，weigh，how，poor，with，however，if，they，sell，much In a town in France，there was a farmer who lived alone.Every day he 1.solda pound of butter to his neighbor，who was a baker.One day the baker decided to weigh the butter to see 2._if he was getting a pound.After he weighed it，he found thathe wasn't.The baker then took the farmer to the judge(法官)．The judge wanted to know the farmer's ways to weigh the butter.The farmer replied，“I'm so 3.poor that I do not have enough money to buy anything to weigh it.4.However，I do have a kind of scale(天平)．” The judge asked，“Then 5.howdo you weigh the butter？” The farmer replied，“Before the baker started buying butter from me，I had bought bread from him.So now every time when I 6.bring home the bread from the baker，I put it on the scale and give him the butter of the same 7.weight.”We always get back what we give to others.Whenever you take action，ask yourself this question，“Am I honest？”Honesty or dishonesty can become a habit.Some dishonest people can lie 8.without a red face.Others lie so 9.much that they do not even know what the truth is any more.But who is it bad for? In fact，those who lie will hurt 10.themselves by their own dishonest behavior.I(2015，德阳)she，tourist，because，everything，hungry，arrive，delicious，buy，with，carefulLast summer was Ann's trip to Russia.She was very excited.But when she 1.arrivedat the hotel，she found that her Russian money wasn't in her handbag.She looked forit 2.carefully in all her bags，but she couldn't find it.She had only a ten­pound note 3.with her.She found a place to change her English money.On her way back to the hotel，Ann 4.bought some cheese，some bread and some oranges.She told the manager that she didn't eat Russian food except for breakfast，5.because she knew the priceof the hotels included breakfast.Others visited places of great interest in Russia，but Ann always said she wasn't well.In fact her holiday wasn't bad，except that she was always 6.hungry．After all，a piece of fruit for lunch，and bread and cheese for supper isn't enough… especially not for two weeks.On the last day of her holiday，Jane，one of the 7._tourists asked Ann why she never ate with them in the hotel restaurants.The food was 8.delicious．Ann told her all about her money problem.Jane looked at 9.her for a moment，and then said，“But didn't you know the price of this hotel includes 10.everything？”。

高考数学总复习考点知识讲解与提升练习专题42 数列中的构造问题数列中的构造问题是历年高考的一个热点内容，主、客观题均可出现，一般通过构造新的数列求数列的通项公式．题型一形如a n＋1＝pa n＋f(n)型命题点1a n＋1＝pa n＋q(p≠0,1，q≠0)例1(1)数列{a n}满足a n＝4a n－1＋3(n≥2)且a1＝0，则a2024等于()A．22023－1 B．42023－1 C．22023＋1 D．42023＋1答案B解析∵a n＝4a n－1＋3(n≥2)，∴a n＋1＝4(a n－1＋1)(n≥2)，∴{a n＋1}是以1为首项，4为公比的等比数列，则a n＋1＝4n－1.∴a n＝4n－1－1，∴a2024＝42023－1.(2)已知数列{a n}的首项a1＝1，且1an＋1＝3an＋2，则数列{a n}的通项公式为__________．答案a n＝1 2·3n－1－1解析∵1a n＋1＝3an＋2，等式两边同时加1整理得1an＋1＋1＝3⎝⎛⎭⎪⎫1an＋1，又∵a 1＝1，∴1a 1＋1＝2，∴⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n ＋1是首项为2，公比为3的等比数列．∴1a n＋1＝2·3n －1，∴a n ＝12·3n －1－1.命题点2a n ＋1＝pa n ＋qn ＋c (p ≠0,1，q ≠0)例2已知数列{a n }满足a n ＋1＝2a n －n ＋1(n ∈N *)，a 1＝3，求数列{a n }的通项公式． 解∵a n ＋1＝2a n －n ＋1， ∴a n ＋1－(n ＋1)＝2(a n －n )， ∴a n ＋1－(n ＋1)a n －n＝2，∴数列{a n －n }是以a 1－1＝2为首项，2为公比的等比数列， ∴a n －n ＝2·2n －1＝2n ， ∴a n ＝2n ＋n .命题点3a n ＋1＝pa n ＋q n (p ≠0,1，q ≠0,1)例3(1)已知数列{a n }中，a 1＝3，a n ＋1＝3a n ＋2·3n ＋1，n ∈N *.则数列{a n }的通项公式为() A ．a n ＝(2n ＋1)·3n B ．a n ＝(n －1)·2n C ．a n ＝(2n －1)·3n D ．a n ＝(n ＋1)·2n 答案C解析由a n ＋1＝3a n ＋2·3n ＋1得a n ＋13n ＋1＝a n 3n ＋2·3n ＋13n ＋1， ∴a n ＋13n ＋1－a n3n ＝2，即数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫a n 3n 是首项为1，公差为2的等差数列，∴a n3n ＝2n －1，故a n ＝(2n －1)·3n .(2)在数列{a n }中，a 1＝1，且满足a n ＋1＝6a n ＋3n ，则a n ＝________. 答案6n3－3n －1解析将已知a n ＋1＝6a n ＋3n 的两边同乘13n ＋1，得a n ＋13n ＋1＝2·a n 3n ＋13，令b n ＝a n3n ，则b n ＋1＝2b n ＋13，利用命题点1的方法知b n ＝2n 3－13，则a n ＝6n3－3n －1.思维升华跟踪训练1(1)在数列{a n }中，a 1＝1，a n ＋1＝2a n ＋2n .则数列{a n }的通项公式a n 等于() A ．n ·2n －1 B ．n ·2n C ．(n －1)·2n D ．(n ＋1)·2n 答案A解析由a n ＋1＝2a n ＋2n 得a n ＋12n＝a n 2n －1＋1，设b n ＝a n 2n －1，则b n ＋1＝b n ＋1，又b 1＝1，∴{b n }是首项为1，公差为1的等差数列． ∴b n ＝n ， ∴a n ＝n ·2n －1.(2)(2023·黄山模拟)已知数列{a n }满足a 1＝1，(2＋a n )·(1－a n ＋1)＝2，设⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 的前n 项和为S n，则a2023(S2023＋2023)的值为()A．22023－2 B．22023－1 C．2 D．1 答案C解析(2＋a n)(1－a n＋1)＝2，则a n＋1＝a na n ＋2，即1an＋1＝2an＋1，得1an＋1＋1＝2⎝⎛⎭⎪⎫1an＋1，故⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1an＋1是以2为首项，2为公比的等比数列，1an＋1＝2n，1an＝2n－1，a n＝12n－1，S2023＋2023＝2＋22＋…＋22023＝22024－2，∴a2023(S2023＋2023)＝2.(3)已知数列{a n}满足a n＋1＝2a n＋n，a1＝2，则a n＝________.答案2n＋1－n－1解析令a n＋1＋x(n＋1)＋y＝2(a n＋xn＋y)，即a n＋1＝2a n＋xn＋y－x，与原等式比较得，x＝y＝1，所以an＋1＋(n＋1)＋1an＋n＋1＝2，所以数列{a n＋n＋1}是以a1＋1＋1＝4为首项，2为公比的等比数列，所以a n＋n＋1＝4×2n－1，即a n＝2n＋1－n－1. 题型二相邻项的差为特殊数列(形如a n＋1＝pa n＋qa n－1)例4(1)已知数列{a n}满足：a1＝a2＝2，a n＝3a n－1＋4a n－2(n≥3)，则a9＋a10等于() A．47 B．48 C．49 D．410答案C解析由题意得a1＋a2＝4，由a n＝3a n－1＋4a n－2(n≥3)，得a n ＋a n －1＝4(a n －1＋a n －2)， 即a n ＋a n －1a n －1＋a n －2＝4(n ≥3)，所以数列{a n ＋a n ＋1}是首项为4，公比为4的等比数列，所以a 9＋a 10＝49.(2)已知数列{a n }满足a 1＝1，a 2＝2，且a n ＋1＝2a n ＋3a n －1(n ≥2，n ∈N *)．则数列{a n }的通项公式为a n ＝________. 答案3n －(－1)n4解析方法一因为a n ＋1＝2a n ＋3a n －1(n ≥2，n ∈N *)， 设b n ＝a n ＋1＋a n ，所以b n b n －1＝a n ＋1＋a n a n ＋a n －1＝3(a n ＋a n －1)a n ＋a n －1＝3，又因为b 1＝a 2＋a 1＝3，所以{b n }是以首项为3，公比为3的等比数列． 所以b n ＝a n ＋1＋a n ＝3×3n －1＝3n ， 从而a n ＋13n ＋1＋13·a n 3n ＝13， 不妨令c n ＝a n 3n ，即c n ＋1＋13c n ＝13，故c n ＋1－14＝－13⎝ ⎛⎭⎪⎫c n －14，即c n ＋1－14c n －14＝－13，又因为c 1－14＝a 13－14＝112，所以数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫c n －14是首项为112，公比为－13的等比数列，故c n －14＝112×⎝ ⎛⎭⎪⎫－13n －1＝a n 3n －14，从而a n ＝3n －(－1)n4.方法二因为方程x 2＝2x ＋3的两根为－1,3， 可设a n ＝c 1·(－1)n －1＋c 2·3n －1， 由a 1＝1，a 2＝2， 解得c 1＝14，c 2＝34，所以a n ＝3n －(－1)n4.思维升华可以化为a n ＋1－x 1a n ＝x 2(a n －x 1a n －1)，其中x 1，x 2是方程x 2－px －q ＝0的两个根，若1是方程的根，则直接构造数列{a n －a n －1}，若1不是方程的根，则需要构造两个数列，采取消元的方法求数列{a n }．跟踪训练2若x ＝1是函数f (x )＝a n ＋1x 4－a n x 3－a n ＋2x ＋1(n ∈N *)的极值点，数列{a n }满足a 1＝1，a 2＝3，则数列{a n }的通项公式a n ＝________. 答案3n －1解析f ′(x )＝4a n ＋1x 3－3a n x 2－a n ＋2，∴f ′(1)＝4a n ＋1－3a n －a n ＋2＝0，即a n ＋2－a n ＋1＝3(a n ＋1－a n )，∴数列{a n ＋1－a n }是首项为2，公比为3的等比数列， ∴a n ＋1－a n ＝2×3n －1，则a n ＝a n －a n －1＋a n －1－a n －2＋…＋a 2－a 1＋a 1＝2×3n －2＋…＋2×30＋1＝3n －1.题型三倒数为特殊数列⎝ ⎛⎭⎪⎫形如a n ＋1＝pa n ra n ＋s 型 例5(1)已知数列{a n }满足a 1＝1，a n ＋1＝a n 4a n ＋1(n ∈N *)，则满足a n >137的n 的最大取值为()A ．7B ．8C ．9D ．10 答案C 解析因为a n ＋1＝a n 4a n ＋1，所以1a n ＋1＝4＋1a n ，所以1a n ＋1－1a n ＝4，又1a 1＝1，所以数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 是以1为首项，4为公差的等差数列．所以1a n ＝1＋4(n －1)＝4n －3，所以a n ＝14n －3，由a n >137，即14n －3>137，即0<4n －3<37，解得34<n <10，因为n 为正整数，所以n 的最大取值为9.(2)(多选)数列{a n }满足a n ＋1＝a n 1＋2a n(n ∈N *)，a 1＝1，则下列结论正确的是()A.2a 10＝1a 3＋1a 17B.1{2}na 是等比数列C ．(2n －1)a n ＝1D ．3a 5a 17＝a 49 答案ABC解析由a n ＋1＝a n1＋2a n ，可得1a n ＋1＝1＋2a na n ＝1a n ＋2，所以1a n ＋1－1a n ＝2，且1a 1＝1，所以数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 是等差数列，且该数列的首项为1，公差为2，所以1a n＝1＋2(n －1)＝2n －1，则(2n －1)a n ＝1，其中n ∈N *，故C 对；1111112=22n n nna a a a ++-＝22＝4，所以数列1{2}na 是等比数列，故B 对；由等差中项的性质可得2a 10＝1a 3＋1a 17，故A 对；由上可知a n ＝12n －1，则3a 5a 17＝3×12×5－1×12×17－1＝199，a 49＝12×49－1＝197，所以3a 5a 17≠a 49，故D 错． 思维升华两边同时取倒数转化为1a n ＋1＝s p ·1a n ＋r p的形式，化归为b n ＋1＝pb n ＋q 型，求出1a n的表达式，再求a n .跟踪训练3已知函数f (x )＝x 3x ＋1，数列{a n }满足a 1＝1，a n ＋1＝f (a n )(n ∈N *)，则数列{a n }的通项公式为____________． 答案a n ＝13n －2(n ∈N *) 解析由已知得，a n ＋1＝a n 3a n ＋1，∴1a n ＋1＝1a n＋3，即1a n ＋1－1a n＝3，∴数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 是首项为1a 1＝1，公差为d ＝3的等差数列，∴1a n＝1＋(n －1)×3＝3n －2.故a n ＝13n －2(n ∈N *)．课时精练1．已知数列{a n }满足a 1＝2，a n ＋1＝2a n ＋1，则a 4的值为() A ．15 B ．23 C ．32 D ．42 答案B解析因为a n ＋1＝2a n ＋1，所以a n＋1＋1＝2(a n＋1)，所以{a n＋1}是以3为首项，2为公比的等比数列，所以a n＋1＝3·2n－1，所以a n＝3·2n－1－1，a4＝23.2．在数列{a n}中，a1＝5，且满足an＋12n－5－2＝an2n－7，则数列{a n}的通项公式为()A．2n－3B．2n－7C．(2n－3)(2n－7) D．2n－5 答案C解析因为a n＋12n－5－2＝an2n－7，所以an＋12n－5－an2n－7＝2，又a12－7＝－1，所以数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫an2n－7是以－1为首项，公差为2的等差数列，所以an2n－7＝－1＋2(n－1)＝2n－3，所以a n＝(2n－3)(2n－7)．3．已知数列{a n}满足：a1＝1，且a n＋1－2a n＝n－1，其中n∈N*，则数列{a n}的通项公式为()A．a n＝2n－n B．a n＝2n＋nC．a n＝3n－1D．a n＝3n＋1答案A解析由题设，a n＋1＋(n＋1)＝2(a n＋n)，而a1＋1＝2，∴{a n＋n}是首项、公比均为2的等比数列，故a n＋n＝2n，即a n ＝2n －n .4．已知数列{a n }满足a 2＝14，a n －a n ＋1＝3a n a n ＋1，则数列的通项公式a n 等于()A.13n －2B.13n ＋2C ．3n －2D ．3n ＋2 答案A解析∵a n －a n ＋1＝3a n a n ＋1，a 2＝14，∴a 1－a 2＝3a 1a 2， 即a 1－14＝34a 1，解得a 1＝1. 由题意知a n ≠0， 由a n －a n ＋1＝3a n a n ＋1得1a n ＋1－1a n＝3，又1a 1＝1，∴数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 是以1为首项，3为公差的等差数列，∴1a n＝1＋3(n －1)＝3n －2，则a n ＝13n －2.5．在数列{a n }中，若a 1＝3，a n ＋1＝a 2n ，则a n 等于() A ．2n －1 B.3n －1 C ．132n － D ．123n －答案D解析由a 1＝3，a n ＋1＝a 2n 知a n >0，对a n ＋1＝a 2n 两边取以3为底的对数得，log 3a n ＋1＝2log 3a n ，则数列{log 3a n }是以log 3a 1＝1为首项，2为公比的等比数列， 则log 3a n ＝1·2n －1＝2n －1，即a n ＝123n －.6．设数列{a n }满足a 1＝1，a n ＝－a n －1＋2n (n ≥2)，则数列的通项公式a n 等于() A.13·2n ＋13 B.13·2n＋13·(－1)n C.2n ＋13＋13 D.2n ＋13＋13·(－1)n 答案D解析∵a n －1＋a n ＝2n ，两边同时除以2n得，a n 2n ＋12·a n －12n －1＝1.令c n ＝a n2n ，则c n ＝－12c n －1＋1.两边同时加上－23得c n －23＝－12·⎝⎛⎭⎪⎫c n －1－23.∴数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫c n－23是以c 1－23为首项，－12为公比的等比数列，∴c n －23＝⎝ ⎛⎭⎪⎫c 1－23·⎝ ⎛⎭⎪⎫－12n －1＝13·⎝ ⎛⎭⎪⎫－12n ，∴c n ＝23＋13·⎝ ⎛⎭⎪⎫－12n，∴a n ＝2n·c n ＝2n ＋13＋13·(－1)n .7．(多选)已知数列{a n }满足a 1＝1，a n ＋1＝a n 2＋3a n(n ∈N *)，则下列结论正确的是()A.⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n ＋3为等差数列 B ．{a n }的通项公式为a n ＝12n －1－3C ．{a n }为递减数列 D.⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 的前n 项和T n ＝2n ＋2－3n －4答案CD 解析因为a n ＋1＝a n 2＋3a n，所以1a n ＋1＝2＋3a na n＝2a n＋3，所以1a n ＋1＋3＝2⎝ ⎛⎭⎪⎫1a n ＋3， 且1a 1＋3＝4≠0，所以⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n ＋3是以4为首项，2为公比的等比数列，即1a n＋3＝4×2n －1，所以1a n＝2n ＋1－3，可得a n ＝12n ＋1－3， 故选项A ，B 错误； 因为1a n＝2n ＋1－3单调递增，所以a n ＝12n ＋1－3单调递减， 即{a n }为递减数列，故选项C 正确；⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 的前n 项和T n ＝(22－3)＋(23－3)＋…＋(2n ＋1－3)＝(22＋23＋…＋2n ＋1)－3n＝22×1－2n1－2－3n ＝2n ＋2－3n －4，故选项D 正确．8．将一些数排成如图所示的倒三角形，其中第一行各数依次为1,2,3，…，2023，从第二行起，每一个数都等于它“肩上”的两个数之和，最后一行只有一个数M ，则M 等于()A ．2023×22020B ．2024×22021C ．2023×22021D ．2024×22022 答案B解析记第n 行的第一个数为a n ，则a 1＝1，a 2＝3＝2a 1＋1，a 3＝8＝2a 2＋2，a 4＝20＝2a 3＋4，…，a n ＝2a n －1＋2n －2，∴a n 2n －2＝a n －12n －3＋1，即⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫a n 2n －2是以a 12－1＝2为首项，1为公差的等差数列．∴a n 2n －2＝2＋(n －1)×1＝n ＋1，∴a n ＝(n ＋1)×2n －2.又每行比上一行的数字少1个， ∴最后一行为第2023行， ∴M ＝a 2023＝2024×22021.9．已知数列{a n }满足a 1＝32，a n ＋1＝3a n a n ＋3，若c n ＝3n a n ，则c n ＝____________.答案(n ＋1)3n －1解析因为a 1＝32，a n ＋1＝3a na n ＋3，所以1a n ＋1＝a n ＋33a n ＝13＋1a n， 即1a n ＋1－1a n ＝13， 所以数列⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫1a n 是首项为1a 1＝23，公差为13的等差数列，所以1a n ＝23＋13(n －1)＝n ＋13，则c n ＝3na n＝(n ＋1)3n －1.10．已知数列{a n }满足a n ＋1＝3a n －2a n －1(n ≥2，n ∈N *)，且a 1＝0，a 6＝124，则a 2＝________. 答案4解析由a n ＋1＝3a n －2a n －1(n ≥2，n ∈N *)可得a n ＋1－a n ＝2(a n －a n －1)， 若a n －a n －1＝0，则a 6＝a 5＝…＝a 1，与题中条件矛盾，故a n －a n －1≠0， 所以a n ＋1－a na n －a n －1＝2，即数列{a n ＋1－a n }是以a 2－a 1为首项，2为公比的等比数列，所以a n ＋1－a n ＝a 2·2n －1，所以a 6－a 1＝a 2－a 1＋a 3－a 2＋a 4－a 3＋a 5－a 4＋a 6－a 5＝a 2·20＋a 2·21＋a 2·22＋a 2·23＋a 2·24＝31a 2＝124，所以a 2＝4.11．在数列{a n }中，a 1＝1，且满足a n ＋1＝3a n ＋2n ，则a n ＝________. 答案52·3n －1－n －12解析∵a n ＋1＝3a n ＋2n ①，∴a n ＝3a n －1＋2(n －1)(n ≥2)，两式相减得，a n ＋1－a n ＝3(a n －a n －1)＋2，令b n ＝a n ＋1－a n ，则b n ＝3b n －1＋2(n ≥2)，利用求a n ＋1＝pa n ＋q 的方法知，b n ＝5·3n －1－1，即a n ＋1－a n ＝5·3n －1－1②，再利用累加法知，a n ＝52·3n－1－n－12⎝⎛⎭⎪⎫或联立①②解出a n＝52·3n－1－n－12.12．英国著名物理学家牛顿用“作切线”的方法求函数零点时，给出的“牛顿数列”在航空航天中应用广泛，若数列{x n}满足x n＋1＝x n－f(xn)f′(xn)，则称数列{x n}为牛顿数列．如果函数f(x)＝2x2－8，数列{x n}为牛顿数列，设a n＝ln xn＋2xn－2，且a1＝1，x n>2.数列{a n}的前n项和为S n，则S n＝________. 答案2n－1解析∵f(x)＝2x2－8，∴f′(x)＝4x，又∵x n＋1＝x n－f(xn)f′(xn)＝x n－2x2n－84x n＝x2n＋42x n，∴x n＋1＋2＝(x n＋2)22x n，x n＋1－2＝(x n－2)22x n，∴xn＋1＋2xn＋1－2＝⎝⎛⎭⎪⎫x n＋2xn－22，又x n>2，∴ln xn＋1＋2xn＋1－2＝ln⎝⎛⎭⎪⎫x n＋2xn－22＝2lnxn＋2xn－2，又a n＝ln xn＋2xn－2，且a1＝1，∴a n＋1＝2a n，∴数列{a n}是首项为1，公比为2的等比数列，∴{a n}的前n项和S n＝1×(1－2n)1－2＝2n－1.。

2019-2020年中考英语总复习考点跟踪突破42词语运用（含答案）根据短文内容，用方框内所给词或短语的适当形式填空，使短文内容完整。

(每词或短语限用一次)(一)(xx，大连)many，classroom，good，a few，get，family，ill，stop，hear of，haveHope for the futureLiu Sanzi is an eight­year­old boy from a village in Hunan Province.His parents want him to drop out of school.It's important for him to work on their farm because there are seven people in Liu's 1.family and they are very poor.Li Yinming is 14 and from Zhangxian in Gansu Province.He 2.stopped going to school a few years ago.His parents have been 3.ill and he has to look after them.Many children like Li Yinming and Liu Sanzi can't 4.get an education because their families are poor.Now they can go to school with the help of Project Hope.In the last 15 years，this project 5.has raised money and paid for the education of 2.5 million poor students in the countryside.People in China and abroad have given 2.2 billion yuan.With this money，Project Hope has built 6.many schools and libraries.It has also trained teachers and it has sent students to high schools.Last year Shen，a boy from Shanxi Province，went to a school with no electricity and only 7.a_few books.But this year he's at a new school with big 8.classrooms and lots of books.Project Hope paid for it.Most people in China have 9.heard_of Project Hope and have given money.But 40 million children from poor families still need help.Because of Project Hope，thousands of children have 10.better` lives.Perhaps we should all ask：What can we do for Project Hope？How can we help?(二)(xx，营口)find，smile，machine，on，be，however，say，good，so，work Some puters and other 11.machines will be able to remember you by looking at your eyes.The program 12.works because everyone's eyes are different.13.So in the future you won't have to remember a number when you want to use a machine or take money out ofbank.You'll just have to look at the machine and it will be able to tell who you 14.are．The eye­recognition (识别) program is already being tested in shops and banks in theUSA，Britain，Spain，Italy and Turkey.Soon，this technology will take the place of all other ways of 15.finding out whom people are.16.However，scientists are working on other systems.Machines will soon be able to know you from the shape of your face or hand or even your smell.We already have machines that can tell who you are from your voice or the mark made by your finger.Eye-recognition is 17.better than other kinds because your eyes don't change as you get older，or get dirty like hands or fingers.And even twins have different eyes，so the program can be up to 94% correct，depending 18.on how good the technology is.Some programs may only be right 51% of the time.In Britain，it was found that 91% of people who had tried it 19.said that they liked the idea of eye-recognition.In the future your puter will be looking atyou in the eye.So 20.smile．(三)(xx，阜新)we，read，also，learn，to，watch，by，use，and，book，for，like Reading is very important for us in our life.It is very interesting and eful．It's the key 22.to school success.We can not only learn a lot of knowledge but 23.also open our mind 24.by reading.What's more，reading can make /ourselves happy and smart.However，some of us don't have a good habit of 26.reading．They would rather spend their free time listening to music，surfing the Internet，27.watching TV and so on.So，I would 28.like to suggest that we should read more books，especially some good 29.books．The more，the better.Let's start reading now.The more we read，the more we will 30.learn．And let it bee a part of our life.(四)(xx，辽阳)until，happy，nothing，different，cook，still，same，moment，next，what，angry，timeA man was worried these days.He found there was something wrong with his wife.So he went to a docor，“I think my wife is going to be deaf.31.What can I do to help her？”The doctor thought for a 32.moment and said，“Well，try to test her hearing.Stand a little far from her and ask her a question.If she doesn't answer，then move a little closer and ask her the 33.same question again.Keep doing this 34.until she answers.That way we can know how bad the problem is.”When the man got home，her wife 35.was_cooking in the kitchen.He stood far away and asked，“Tina，what's for dinner？”He didn't hear any answer.So he moved closer，“Tina，what's for dinner？”There was 36.still no answer.He moved closer and closer.And he asked the question again and again.But 37.nothing happened.At last，he just stood 38.next to his wife.His wife looked up and said 39.angrily，“I have answered you for ten 40.times．I said we would have fish.”(五)(xx，泸州)tea，time，way，also，ideas，meals，country，thing，usually，when Tea is a popular drink around the world.But tea does not mean the same 41.thing to everyone.In different countries people have different 42.ideas about drinking tea.In China，for example，tea is always served 43.when people get together.The Chinese drink it at any 44.time of the day at home or in teahouse.They prefer their tea with nothing else in it.Tea is also important in Japan.The Japanese have a special way of serving 45.tea．It isvery old and full of meaning.Everything must be done in a special 46.way．There is even a special room for it in Japan.Another tea­drinking 47.country is England.In England，the late afternoon is “teatime”．Almost everyone has a cup of tea at that time.The English people ually make tea in a teapot and drink it with milk and sugar.They 49.also eat cakes，cookies and little sandwiches at teatime.In the United States people drink tea mostly for breakfast or after 50.meals．Americans usually use tea-bags to make their tea.Tea-bags are faster and easier than making tea in teapots.In summer，many Americans drink cold tea—“iced tea”．(六)(xx，成都)check，China，difficult，easy，farm，forget，little，many，other，peace，amazing，seriousLook at the picture，what do you see？51.Amazingly，some people say it's an old man，while others say it's a young woman and an old 52.farmer．It is a problem with manyanswers.Why?When you look at a problem from different views，you get different answers.Just turn it in your mind 53.a_little bit，and you may see it in a pletely new way.Some people only form an idea in their mind “A problem has only one answer，and all the 54.others are wrong.”Some even laugh at the different answers others e up with.Well，they're wrong！If people only believed in one answer，we might still think the world is square (方形的)!What's one plus one？That's easy，two！Right？Well，that's one right answer，but not the only answer.You might think of 11，or some 55.Chinese characters like “二”or “十”！What's a mom plus a dad？Y ou might think of two people，or a man and a woman，or a whole family！So，even the 56.easiest questions can have many answers.Of course，some problems do only have one answer.If each of the questions in a mathtest had 57.more than one answer，it would be quite a problem for teachers 58.to_check．Look at things in different ways，face your life with a 59.peaceful mind，and you'll see a pletely different world.After reading my article，if I ask you again：“What do you see in this picture？”，will you still give the same answer now？I'm sure this picture will be 60.unforgettable to you.(七)(xx，黔南)sa v e，fast，from，call，one，w atch，great，make，rice，you Dear Cindy，How are you？I had a great time last Monday，June 2th，xx.It was a traditional Chinesefestival 61.called Dragon Boat Festival that day.This festival is in memory of Qu Yuan，one of the 62.greatest Chinese poets.He killedhimself by jumping into the Miluo River on May 5th of the lunar calender (阴历)，278BC.People there rowed the boats 63.to_save him.But it was too late.They were very sad and then threw 64.rice into the river to feed the fishes so that they would stay away from his body.65．From then on，every year on this day，people enjoy 66.making Zongzi which is made of rice with meat，eggs and so on.In the past we ate it only 67.once a year，but now we regard it as our daily food.We can have it any time we like.Have you ever 68.watched the dragon boat race on TV？It is another important part ofthis festival.Several teams row their dragon-shaped boats as 69.fast as they can.The first team to reach the finish line wins.If you have a plan to visit China next year，would 70.you like to spend this festival with us?Best wishes!Yours，Shen B ?:30851 7883 碃22006 55F6 嗶37102 90EE 郮^29065 7189 熉27641 6BF9 毹27279 6A8F 檏&33530 82FA 苺。

考点跟踪突破40词汇运用一、根据句意及汉语提示完成下列单词。

1．In the USA，people eat with _______ (刀) and forks.2．I left my book at home. May I borrow _______ (你的)?3．You must look at the traffic lights before you go ________ (穿过) the road.4．It rained ________ (大) on my way home yesterday afternoon.5．The ________ (越早) kids learn to be independent，the better it is for their future.6．The basketball match is ________ (值得) watching.7．We are supposed to ________ (鼓励) the young to read more books.8．Today is Mary's _________ birthday. We will go to her birthday party.9．It's good to have a __________ (健康的) eating habit.10．We shouldn't waste water. Instead，we should _______ (节约) it.11．The students are having a _________ (化学) class in the lab.12．Each different part of China has its own special forms of ________ (传统的) art.13．Parents always try to ________ (提供) a comfortable environment for their children. 14．Chinese clay art is famous because the clay pieces are so small but they look very ______ (真实的)．15．All my classmates went to the old people's home ________ (除了) Eric because he was ill.二、根据句意及首字母提示完成下列单词。

2019中考英语(人教新课件)：(42)词汇运用考点跟踪练习注意事项：认真阅读理解，结合历年的真题，总结经验，查找不足！重在审题，多思考，多理解！考点跟踪训练422.It’snoteasyforLindatoatnight.3.Jimfailedinthetestbecausehewaslastweekend.4.Chinesemedicineshouldbedevelopedallovertheworld.5.Ginawonthefirstprizeinthesingingcompetition.soshewenthome.答案：1.attention2.fallasleep3.stressedout4.traditional5.happily2.Imustleavehome,_orI’llbelateforwork.3.I’vetheGreatWallalot,butI’veneverbeenthere.4.It’sapitythathewon’tcometoyourbirthdaypartynextSaturday.5.Thelittlegirllookedattheunusuallytallman.答案：1.gettingreadyfor2.rightaway3.heardof4.beableto5.insurpriseheoutsideworldclosertopeople’shomes.SomepeoplesaytheworldisthanbeforebecauseofTV.What’sgoingonincountries?Howdopeopleliveinplacesfaraway?Isthereagoodsportsgamesomewh ere?What’slivinginthedeepest(最深的)partthesea?Ifyouwanttheseandotherkindsofquestions,justturntheTV.Youcanseealotandlearna lot.Ofcourse,peoplecanalsolearnthroughreadingortotheradio.ButwithTVtheycanlearn betterandmoreeasily.Why?Becausetheycanandwatch,too.alsohelpsustoopenourminds(思维).TVoftengivesnewideas.NewerandbetterwaysofdoingsomethingcanbeOnTV.答案：1.activities2.smaller3.other4.of5.toanswer6.on7.listening8.hear10.learned/learntiswidely1.inamodernsociety.Itisaverygoodmanner.Youshouldsay “Thankyou”2.othershelpyouorsaysomethingkindtoyou.Forexample:whensomeone3.thedoorforyou,wh ensomeonesaysyouhavedoneyourworkwell,whensomeonesaysyouhave4.aniceshirt,oryourc ity5.verybeautiful,youshouldsay“Thankyou”.“Thankyou”isusednotonlybetweenfriends,6.betweenparentsandchildren,brothersandsisters,husb andsandwives.“Excuseme”is7.shortpoliteusage.Weuseitasthesameas “Thankyou”.Whenyouhearsomeonesaysobehindyou,you’dgottoknowthatsomebodywantstowalkpastyouwithout8.you.Itisnotpolitetointerrupt(打断)otherswhiletheyare9..Ifyouwanttohaveawordwithoneofthem,pleasesay“Excuseme”10.,_andthenbegintotalk.Youshouldalsodosowhenyouwanttocoughormakeanyunpleasantn oisebeforeothers.Let’ssay“Thankyou”and“Excuseme”ontherightoccasion.答案：ed2.whenever3.opens4.bought5.is6.butalso7.another8.touching9.talking10.firstOncetherewasateacherwhotookallhisstudentsforsea.Whatmadethestudents1.wastha tallthecupsonthetablewere2..Eachofthemtookacupandstarted3.theirowntea,lookingat the4.cups.Theteachersaid:“Doyounoticeyour5.?Youarealllookingateachother’steacupsand6.ofyouevenenvy(羡慕)the7.cupsofothers.“Thenhewenton:“Iputthedifferentcupshereonpurpose!Lifeislike8.tea.Youallhavethesamethinginyou rcups—tea.Andyetyoucan’t9.enjoyitinyourenvyofanother’scup.Youforget10.yourownlifewhenyouenvysomeoneelse’slife.Sonow,tasteyourtea!Doesitmatterfromwhichcupitcomesfrom？”答案：1.surprised2.different3.drinking4.others’5.behavior6.some7.finer8.this9.really10.toenjoyI’mJohnWood,adoctoratafamousBostonhospital.Duringthefirsttwoyearsofhighschool,Ifo undbiologyvery1..Myreportcardsalwayssaidthingslike“muststudyharder”or “Johnshouldn’tchoosescience2..”Itwasreallyterriblefor3.whohadalwaysdreamedofbecomingadoctor.Ilostconfidence,so Ilefthighschoolatsixteenand4.workingatasupermarket.OneeveningIsawadocumentaryaboutAlbertEinstein.Accordingtothedocumentary,Ein steinhaddonereally5.atschool.IbegantothinkthatEinsteincould6.,_thenImayhaveacha nce,too.Ididn’twanttoleavemyjob,7.Idecidedtogotonightschooltofinishhighschool.Twoyearslater,I wenttoa8.university.I’veoftenthoughtIshouldcontactthe9.oftheEinsteindocumentaryand10.him.Asforthebiol ogyteacher,Imightcontacther,too,oneday—butnottothankher!答案及解析：1.difficult根据下文“成绩单总是写着’应努力学习’”可生物对作者来说很难。

考点跟踪突破42词汇运用一、根据句意及汉语提示写单词。

1．In order to search for the missing passengers in the MH370，two soldiers(军人) died.(2014，黄冈)2．Can you speak more slowly (慢)？I can't hear you clearly.(2014，毕节)3．Pass me the salt (盐)，please.I need it for my soup.(2014，兰州)4．It is well known that the Diaoyu Island belongs (属于) to China.5．Tom is_preparing (准备) for the final exam.Please be quiet!6．I made a lot of mistakes (错误) in this exam.7．You will fail in this exam unless (除非) you do it carefully.8．Thank you very much for inviting (邀请) me to your party.9．All of us were surprised (惊奇的) that such a little girl spoke English so well.10．Everyone else in my class was invited except (除了) me，and I don't know why.二、根据句意及首字母提示写单词。

11．I'm feeling hungry now.Where can I get something to eat？(2014，广州)12．He sold his old car for $5，000 yesterday.He wants to buy a new one.(2014，杭州) 13．You can borrow the books from the library，but you must return them in time.(2014，贺州)14．If you are far away from your parents for a long time，you will miss them.15．The boy is so clever that he can work out many difficult problems.16．Tom，your hands are really dirty．Go and wash them.17．Chinese people are supposed to shake hands when we meet for the first time.18．There is little time left.We have to walk quickly to get there on time.19．We must follow the teacher's instructions when we are in the lab.20．He has some trouble understanding what his teacher says because of his poor English.三、根据句意，用括号中所给单词的适当形式填空。