Q4: What is the function of the International exploration ?Having astronauts from different countries on boardQ5: What can you learn from Para 4 ?China has made great achievements in exploring spaceQ6: What is the attitude to the space exploration ?SupportiveStep 6 Post reading---RetellPeople have always wanted to learn more about space. Before the mid-20th century, most people felt (1)_________ (travel) into space was an impossible dream. However, (2)____ the help of scientists, peoplesucceeded in realizing their dream (3) _________ (explore) space. On 4 October 1957, the Sputnik 1 satellite (4) ____________(launch) by the USSR. (5) ________________ scientists try to make sure nothing goes wrong, accidents can still happen. These disasters made everyone(6)___________(disappoint), but people still believe in the importance of (7) ________(carry) on space exploration. In 2003, China became the third country to (8)_____________ (independent) send humans into space. Then Shenzhou 6 and 7 completed (9)____ second manned orbit and the first Chinese spacewalk. In spite of the difficulties, scientists hope future (10)__________ (discovery) will not only enable us to understand the universe but also help us survive well into the future.Answers: 1. travelling 2. with 3. to explore 4. was launched 5. Although6. disappointed 7. carrying 8. independently 9. a 10. discoveriesStep 6 Post reading---Critical thinkingQ1: What do you think of the space exploration ? I think it is beneficial to us. Through further study of space, people will make full use of it in the future, such as the space experiments by Wang Yaping in Tian Gong 1.Q2: If you are determined to be an astronaut, what should you prepare at present ?First of all, I should study hard to get a related college degree. Besides, I must keep mental and physical healthy.Step 7. HomeworkTry to summarize the structure of the article by a mind map.
⑦在我看來, 探索太空是值得的。As far as I am concerned, it is worthwhile to explore the space.Step 10 Writing---draftRecently, students in our class have had heated a discussion on whether space is worth exploring. Students hold different ideas about it.30% of us think space exploration is not worthwhile. They think space is too far away from us and our daily life and is a waste of money. And the money spent on space exploration can be used to solve the earth’s problems such as starvation and pollution.On the other hand,70% think space is worth exploring because we have benefited a lot from it,such as using satellites for communication and weather forecast. What’s more,with further space research,we may solve the population problem by moving to other planets one day. Also,space research will enable us to find new sources to solve the problem of energy shortages on the earth.As far as I am concerned, it is worthwhile to explore the space. Not only can it promote the development of society but also enrich our life. Step 11 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1.Does the writer explain why he/she changed/wanted to change?2.Does the writer tell how the changes have improved or will improve his/her life?3.Is the text well-organised?4.Does the writer use words and expressions to show similarities and differences?5.Are there any grammar or spelling errors?6.Does the writer use correct punctuation?
另一方面,其余的人反對這個計劃,因為它可能會導(dǎo)致一些不好的影響。7.I hold the belief that space exploration not only enable us to understand how the universe began but also help us survived well into the future.我堅信探索太空不僅能夠使我們了解宇宙的起源而且能夠幫助我們更好地走進未來。8.I think we should spend more time and money exploring space so as to provide new and better solutions to people's shortterm and longterm problems.為了給人類的短期和長期問題提供更新和更好的解決方法,我認為我們應(yīng)該花更多的時間和金錢來探索太空。9.From my point of view,it is wrong of young people to depend on their telephones too much,which may do harm to both their physical and mental health.在我看來,年輕人過度依賴手機是不對的,因為它們可能會對他們的身心健康都有害。最近你班同學(xué)就“人類是否應(yīng)該進行宇宙探索”這個問題進行了激烈的討論。有人認為,探索宇宙不僅讓人類更好地了解宇宙的發(fā)展,還可以用來指導(dǎo)農(nóng)業(yè)生產(chǎn),以及把一些探索太空的高新技術(shù)用于現(xiàn)實生活;也有一些人認為探索太空花掉了大量的人力物力;影響了人們的生活水平。請你根據(jù)以下情況寫一篇報告并發(fā)表自己的觀點。注意:1.寫作內(nèi)容應(yīng)包括以上全部要點,可適當發(fā)揮,使上下文連貫;
Step 3 Meaning1. 過去將來時表示從過去某一時間來看將要發(fā)生的動作或存在的狀態(tài), 常用在賓語從句中。一般由“would/should +動詞原形”構(gòu)成。She hoped that they would meet again someday. 她希望將來有一天他們能再見面。2. was/were going to+動詞原形: 表示過去將要發(fā)生或很有可能發(fā)生的動作, 常用于口語中, 表示預(yù)言、意圖或者打算等。He was going to start work the following week. 他打算下星期開始工作。3. was/were about to do: 常用來表示即將發(fā)生的動作, “剛要/正要做……”。注意該結(jié)構(gòu)不與任何時間狀語連用。I felt that something terrible was about to happen. 我感到某種可怕的事情即將發(fā)生。4.was/were to do: 表示“曾計劃做某事”, 如果表示“本來計劃做某事, 動作沒實現(xiàn)”, 則需用 “was/were to have done”。She said she was to have told me about the accident. 她說她本來想告訴我關(guān)于事故的事。5.Start, go, come, leave, see, meet等動詞的過去進行時: 表示就過去某一時刻而言即將發(fā)生的動作。She was coming later. 她隨后就來。I had just put on my overcoat and was leaving to visit a friend of mine. 我剛穿上外套要去看我的一個朋友。
4. A:We’d like to have someone to say a word at the beginning to welcome the group.B:↙Who?A:We thought that you or Dr.Johnson might do it.B用降調(diào)說Who,其意思是問,對方想讓誰在開場時致歡迎詞。Step 6 Pronunciation---Practice1. Listen to the short conversation and mark the intonation with ↗, ↙ or ↙, ↗. Then discuss with a partner what they intend to convey by using different intonation.Owner: You know what ?↗ It’s a million-pound bank note↙.Waiter 1: Really ?↗(question)Waiter 2: Really !↙(unbelievable and surprised)Waiter 3: Really ?!↙↗(first question then surprised)2. Listen to the conversations. Underline the parts that are stressed and mark the intonation. Then talk about the implied meanings of the responses with different intonations. Listen again and repeat.1) Henry: It’s a nice suit.Owner: Oh, it’s perfect!↙(The intonation means it is very suitable for Henry.)2) Henry: Well, that’s very kind of you.Owner: Kind, sir ?↗(what you said is not right) No, it’s kind of you. You must come whenever you want and have whatever you like. Just having you sit here is a great honour !!↙(welcome you to come again)3)Henry:Well, to be honest, I have none. Oliver:(happily) What luck!(excited) Brother↗, what luck!↙(It means “Didn’t you hear it?”)Henry: Well, it may seem lucky to you but not to me!↗(angry) If this is your idea of some kind of joke, I don’t think it’s very funny. Now if you’ll excuse me, I ought to be on my way.↙(If so, I would leave.)Roderick: Please don’t go↙...(hope Henry can wait for a moment)Part B Viewing and Talking---Describe people’s changing attitudes in a film clipStep 1 Before-listening---Tell the filmYou are going to watch part of the film The Million Pound Bank Note. Look at these photos and guess what happens in the film.
Step 4: Listen again and decide if the following statements are true (T) or false (F).1 It was the first time Chen Liyan's story was reported. T口 F口2 Chen found 10,000 yuan in a small plastic bag in Taiyuan railway station口 F口3 Wang Zheng apologized to Chen because he couldn't offer her more money. T口 F口4 Chen took out a large loan to cure her daughter, T口 F口5 Wang set up a fundraising website for Chen's daughter after Chen told him about her situation. T口 F口Step 5:After listening, discuss the questions.1 What kind of person do you think Chen Liyan is?Chen Liyan is generous and honest because she returned a large sum of money to the owner.2 Did Chen return the money because she didn't need it?No. She returned the money because it was the right thing to do. Evidence for this is that she refused to accept the reward money because she felt that it had not been earned. 3 Is it common for people to do what Chen did?It depends on the culture. In some countries it is quite common to return money that has been found. In other countries, people believe "Finders are keepers!" 4 How did Wang Zheng feel about the return of his money?He must have been very happy and relieved to have gotten his money back. We know this because he thanked Chen repeatedly and even offered her a reward.5 Why did Ma Dongbao tell Wang about Chen's family?He must have had great sympathy for Chen and her daughter and wanted to help them.'We know this because he arranged help for them. 6 How did the news reporter feel about Chen's actions?The news reporter felt that it showed that money wasn't the most important thing in life. We know this because the reporter told us that this is what Chen believes. and then said, “that's a great attitude to take."
? Could you offer me some kind of work here?? I don’t want your charity, I just want an honest job.? Careless: I landed in Britain by accident.Step 7:Consolidation.? Find Henry? Roderick and Oliver were I .making a bet when they saw Henry, a poor young man. ? Know Henry? About a month ago, Henry was sailing and later he found himself carried out to sea by a strong wind. Fortunately, he 2.was spotted by a ship. And it was the ship that brought him to 3.England? Offer money to Henry ? Oliver and Roderick gave Henry a letter and told him that there was money in it. They 4.persuaded him to accept it, and made him 5.promise that it wouldn't be opened until 2 o'clock.Step 8:Language pointsa large amount of: a large quantity of; a great deal ofe.g. They bought a large amount of furniture before they moved their new house.make a bet: make an arrangement to risk money, etc. on an event of which the result is doubtful.e.g. We made a bet on the result of the match.permit sb to do something: allow somebody to do somethinge.g. My mother doesn’t permit me to ride in the street after it rained.by accident: as a result of chancee.g. I only found it by accident.stare at: look at somebody or something with the eyes wide open in a fixed gaze( in astonishment, wonder, fear, etc)to be honest: to tell you the truth; to be franke.g. To be honest, I don’t think we have a chance of winning.Step7 Homework:What do you think will happen to Henry? Will the bank-note help him or get him into trouble?
Everybody wants to get wealth.In today’s material world,making money or becoming wealthy symbolizes a person’s success and capability. Many people just make every effort, pay any price to attain greater wealth. With money,they can buy nice, large apartments in nice neighborhood. With money they can own luxurious cars. Wealth seems to bring all happiness in life.But is wealth the only road to happiness? Not really. There are many things in the world, which are beyond the means of money, such as friendship, love, health and knowledge. People are so preoccupied with struggling for money that they have no time or would not take the time to form or maintain friendship. What happiness can they feel living as lonely miserable creatures without love or friends in the world even if they accumulate tremendous wealth?In my opinion, people can’t do anything without money, but money is not everything. What money will bring you depends on your personal belief and goal in life. If you are kind enough to help others, especially the poor, money is a good thing to you. With it, you can do much more for the benefit of people and your country, and it will add to your own happiness. If you want money just for your own needs, you’ll never be satisfied or happy. In a word,you should have money spent for more people. Only then can money be the source of your happiness.Step 8 Homework4 students in a group, one acts Roderick, one Oliver, one servant and the fourth one acts Henry Adams, then listen to the tape, pay more attention to the difference between American English and British English in pronunciation, stress, tone.
2. 您能看到, 我頭發(fā)太長了。You can see that my hair is much too long.3. 無論什么時候, 只要您想回來就回來。Please come back whenever you want.4. 您僅有很少的頭發(fā)要理! You only have too little hair to cut !5. 為您服務(wù)是我的榮幸!It is my honour to serve you!Step 9 Writing(Henry is walking down the street when he sees a sign for a place that cuts hair. He decides to have it cut. )H=Henry B=BarberH: Good afternoon, I’d like to have my hair cut, if I may. (The barber looks at Henry’s hair and continues cutting another man’s hair. ) Er, I’d really like a haircut. As you can see it’s much too long. B: (in a rude manner) Yes, I can see that. Indeed, I can. H: Fine, well, I’ll have a seat then. (He sits in one of the barber’s chairs. The barber turns to look at Henry. )B: It’s quite expensive here, you know! Are you sure you can afford it?H: Yes. I think so. (After his hair is cut, the barber tells Henry how much he must pay. Henry shows the barber the bank note. )B: Why Mr. . . (looks shocked)H: Adams. Henry Adams. I’m sorry. I don’t have any change. B: Please don’t worry! (wearing a big smile) Nothing to worry about! Nothing at all! Please come back whenever you want, even if you only have too little hair to cut! It will be my honour to serve you!Step 10 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Are all the elements of a play included and in good order ?2. Do the character use suitable language ?3. Are the stage directions clear and useful ?4. Is the plot clear and exciting enough ?
【參考范文】Narrator:(Henry is smiling as he leaves the restaurant. As he is walking down the street, he sees a sign for a place that cuts hair. He decides to get it cut. )H=Henry;B=Barber;R=rude manH:Good afternoon, I'd like to get a cut, if I may. (The barber looks at Henry's hair and continues cutting another man's hair. )Er, I'd really like a haircut. As you can see it's much too long. B:(in a rude manner) Yes, I can see that. Indeed, I can. H:Fine, well I'll have a seat then. (He sits in one of the barber's chairs. The barber turns to look at Henry. )B:It's quite expensive here, you know!Are you sure you can afford it?H:Yes. I think so. (In comes the rude man. )R:Hey you there. I need a haircut quickly. Can you do me straightaway?B:All right, then, get in the chair and I'll see what I can do. R:Thank you. (sits down in one of the barber's chairs)H:Excuse me, but I was here first. Aren't you going to do my hair first?B:This man's in a hurry. H:Well so am I!I insist that you cut my hair first. B:OK, but I'll have to be quick. This gentleman is waiting. H:Thank you. (They both become quiet. After his hair is cut, the barber tells Henry how much he must pay. Henry shows the barber the bank note. )B:Why, Mr . . . (looks shocked)H:Adams. Henry Adams. I'm sorry, I don't have any change. R:You're that Mr Adams! Well,I'm glad I waited or I might never have known it was you. B:Why, Mr Adams, please don't worry!(wearing a big smile) Nothing to worry about!Nothing at all!Please come back any time, even if you only need too little hairs cut!It will be my honour to serve you!
一、說教材(一)、教材內(nèi)容《古代中國的發(fā)明和發(fā)現(xiàn)》是人教版高中歷史必修三第三單元第一課內(nèi)容,本課教材主要從五個方面的典型事例向?qū)W生介紹了古代中國幾千年的科技成就。本課一方面展示了古代中國人民的勤勞智慧以及對世界文明發(fā)展作出的巨大貢獻,另一方面也提出了一個重大問題引起學(xué)生的思考,即造成中國科技在近代落后的原因是什么。此外、本課在教材中具有承上啟下的地位和作用,前承中國傳統(tǒng)文化主流思想,后啟現(xiàn)代中國科學(xué)技術(shù)的發(fā)展。根據(jù)課標要求和教材內(nèi)容,我將本課的三維目標確定如下:(三)教學(xué)目標(1)知識與能力:掌握中國古代科技進步的基礎(chǔ)知識,特別是四大發(fā)明。認識古代中國四大發(fā)明對世界文明發(fā)展的貢獻,以及取得重大成就的原因。⑵過程與方法:通過指導(dǎo)學(xué)生課前閱讀課本,在課堂上進行問題探究、實驗體驗以及歷史比較,學(xué)會總結(jié)歸納。
四、說教學(xué)過程:1、導(dǎo)入新課:以視頻形式導(dǎo)入新課,說明環(huán)境問題產(chǎn)生原因,引出人地關(guān)系的重要性2、新課講授:學(xué)習(xí)主題一:過去——人地關(guān)系的歷史回顧以動畫形式展現(xiàn)人地關(guān)系思想的發(fā)展,激發(fā)學(xué)生學(xué)習(xí)本專題的興趣,歸納人與自然關(guān)系的演變過程。學(xué)習(xí)主題二:現(xiàn)狀——直面環(huán)境問題以人類與環(huán)境關(guān)系模式圖說明環(huán)境問題產(chǎn)生的原因,人地關(guān)系實質(zhì);以因果聯(lián)系框圖培養(yǎng)學(xué)生判讀方法,了解人口、資源與環(huán)境三者之間的關(guān)系;通過閱讀課文,了解環(huán)境問題的類型及其空間差異的表現(xiàn);以圖表了解不同國家和地區(qū)環(huán)境問題在空間軸上的表現(xiàn);以《京都議定書》為引子說明保護環(huán)境是全人類的共同使命學(xué)習(xí)主題三:未來——可持續(xù)發(fā)展展示“可持續(xù)發(fā)展示意圖”理解可持續(xù)發(fā)展內(nèi)涵、原則
【教學(xué)目標】知識與技能:理解環(huán)境承載力與環(huán)境人口容量的含義、兩者的關(guān)系以及環(huán)境人口容量的影響因素;理解人口合理容量的含義,影響因素并掌握保持人口合理容量的做法;結(jié)合中國國情提出適合中國保持合理人口容量的措施過程與方法:通過問題探究及案例分析理解環(huán)境承載力與環(huán)境人口容量的關(guān)系及影響因素;通過問題探討掌握保持人口合理容量的措施。情感態(tài)度與價值觀:樹立并強化學(xué)生的可持續(xù)發(fā)展觀念,科學(xué)發(fā)展觀。激發(fā)學(xué)生愛國情感更多地關(guān)注國家國情,樹立主人翁意識保護地球強大祖國?!窘虒W(xué)重點】環(huán)境人口容量的內(nèi)涵以及影響因素人口合理容量的影響因素以及措施【教學(xué)難點】環(huán)境人口容量的內(nèi)涵以及影響因素人口合理容量的影響因素以及措施二、說教法【教學(xué)方法】案例分析、問題探究、歸納總結(jié)
本節(jié)課我分成兩個課時A首先我會在在ppt上放幾張關(guān)于區(qū)域的圖,讓學(xué)生思考什么是區(qū)域,區(qū)域有什么特征。其次我會在在書上畫出區(qū)域的定義,在給與解釋說明,再在書上畫出區(qū)域的四個特征,讓同學(xué)小組討論哪些區(qū)域是有界的,哪些區(qū)域是無界的,從而加深同學(xué)們對區(qū)域的理解。B在ppt上放出長江三角洲和松嫩平原,不同風(fēng)土人情由此導(dǎo)入下一個知識點:不同區(qū)域由于地理環(huán)境的差異,人們的生產(chǎn)特點有許多的不同,發(fā)展方式也存在差異,然后讓學(xué)生思考長江三角洲和松嫩平原有什么差異,各自給區(qū)域環(huán)境發(fā)展帶來什么影響,啟發(fā)學(xué)生從氣候等方向思考,然后用表格的方式給不同因素歸類(歸位自然和社會經(jīng)濟兩大類)再啟發(fā)同學(xué)們從兩大類分別討論對農(nóng)業(yè)與工業(yè)發(fā)展的影響,最后再用表格的形式分類表達C然后給同學(xué)們幾個問題,鞏固同學(xué)課堂所學(xué),最后留下一個問題課后解決:除了今天講的因素外還有哪些因素對區(qū)域發(fā)展產(chǎn)生影響?
【情感態(tài)度及價值觀】 通過創(chuàng)設(shè)探究情境,展示典型顯示案例激發(fā)思考,與學(xué)生共同感受當前區(qū)域經(jīng)濟一體化與經(jīng)濟全球化浪潮的沖擊,以及當前我國、我省發(fā)展的機遇、成就和危機,培養(yǎng)學(xué)生的時代感和使命感。五、重點難點【重點】1、產(chǎn)業(yè)轉(zhuǎn)移的影響因素2、產(chǎn)業(yè)轉(zhuǎn)移對區(qū)域地理環(huán)境的影響【難點】1、如何從圖文材料中分析出影響產(chǎn)業(yè)轉(zhuǎn)移的主要因素2、產(chǎn)業(yè)轉(zhuǎn)移對產(chǎn)業(yè)遷出區(qū)和移入?yún)^(qū)的不同影響六、教學(xué)方法1、材料分析法。提供分層次的問題與材料,并進行方法指導(dǎo),學(xué)生通過思考和討論自行分析發(fā)現(xiàn)知識、構(gòu)建知識。使不同層次的學(xué)生均有發(fā)展。這是本節(jié)設(shè)計主要采用的教學(xué)方法。2、合作探究法3、多媒體教學(xué)法七、 教學(xué)過程(一) 引入 :假如某同學(xué)買彩票中大獎,想投資生產(chǎn)面臨幾項選擇1、投資高端智能手機制造還是普通服裝廠?2、廠址選擇在濮陽市還是南樂縣?
師我國河流眾多,長江流域、黃河流域、珠江流域等正在繼續(xù)開發(fā),出示“長江流域示意圖”,請同學(xué)們借鑒今天所學(xué)的分析方法,分析長江流域發(fā)展的自然地理條件。(學(xué)生相互交流、討論)生略。師長江干流全長6300余千米,發(fā)源于青藏高原,流經(jīng)青、藏、滇、川、渝、鄂、湘、贛、皖、蘇、滬,奔入東海。水域遼闊,總面積達180萬平方千米,流經(jīng)我國半壁河山。水量汪洋壯闊,多年平均入海近10000億立方米。流域內(nèi)總?cè)丝?、耕地各約占全國的35%,工農(nóng)業(yè)總產(chǎn)值占全國的40%~50%,歷來是中華民族繁衍的沃土。流域經(jīng)過我國三大階梯,流經(jīng)青藏高原、橫斷山脈、四川盆地、云貴高原、長江中下游平原等地形區(qū)。流域內(nèi)水系發(fā)達、眾多,以亞熱帶季風(fēng)氣候為主,氣候溫暖濕潤,降水量豐富,河流水量大,水能資源、森林資源、礦產(chǎn)資源豐富,長江干流自古以來就是我國東西航運的大動脈,溝通內(nèi)地和沿海的廣大地區(qū),干支流通航里程約占全國內(nèi)河航道總里程的2/3,形成了一個縱橫廣闊的水運網(wǎng),被譽為“黃金水道”。
指導(dǎo)學(xué)生閱讀圖3.8,讓同學(xué)們討論山西省三類工業(yè)發(fā)展變化的情況??梢钥闯觯删驑I(yè)占工業(yè)增加值的比重在1985~1995年間有所上升,但在1995~2000年下降,且下降速度很快。原料工業(yè)始終在增加,且有越來越快的趨勢。加工工業(yè)1985~1995年間比重下降,到2000年幾乎停滯不前。這說明山西省雖然實現(xiàn)了產(chǎn)業(yè)結(jié)構(gòu)的升級,但還是限于初級加工階段,工業(yè)發(fā)展水平還不高。山西省只是一個能源大省,并不是一個工業(yè)大省,更不是經(jīng)濟強省,山西省的改革還有很長的路要走。(參考資料)《急需調(diào)整產(chǎn)業(yè)結(jié)構(gòu)的山西經(jīng)濟》(山西日報1999年11月25日)山西能源的綜合利用是一個正在發(fā)展完善的過程,教學(xué)中教師可以結(jié)合目前存在的一些問題和困境展開討論,引導(dǎo)學(xué)生深入探究。(例如屢屢發(fā)生的礦難,以及背后隱藏的“官煤勾結(jié)”問題,這些都是目前各種媒體關(guān)注的焦點,相關(guān)的新聞報道,教師在課前應(yīng)該專門搜集一些,或者讓有條件上網(wǎng)的學(xué)生自己去搜集,使得課堂教學(xué)更加貼近現(xiàn)實生活。)
首先引導(dǎo)回顧細胞質(zhì)內(nèi)各個細胞器的分工協(xié)作、產(chǎn)生分泌蛋白的過程;同時思考:為什么這些細胞器可以這樣有條不紊的密切協(xié)作?這中間有沒有專門起協(xié)調(diào)和控制作用的部門?從而導(dǎo)入本節(jié)內(nèi)容。通過學(xué)生小組討論及師生共同分析“資料分析”中的4個實驗,總結(jié)出細胞核的功能,即細胞核是遺傳信息庫,控制細胞代謝和遺傳的功能。在此基礎(chǔ)上,向?qū)W生舉出克隆羊多莉的實例,加強理解。設(shè)問:那么細胞核為什么能成為細胞代謝和遺傳的控制中心?要弄清這個問題,我們必須從細胞核的結(jié)構(gòu)中尋找答案,從而引出細胞的結(jié)構(gòu)。在這部分,引導(dǎo)學(xué)生思考以下幾個問題:(1)細胞核能控制細胞的遺傳,說明其應(yīng)該有什么物質(zhì)?(2)含有DNA的結(jié)構(gòu)如線粒體、葉綠體,它們的外面都有什么相同的結(jié)構(gòu)?(3)細胞核能控制細胞,肯定能與外界聯(lián)系,如何能辦到?(4)學(xué)習(xí)RNA的分布時,RNA主要分布在細胞質(zhì),少量還分布在哪里呢?
二、典例解析例4. 用 10 000元購買某個理財產(chǎn)品一年.(1)若以月利率0.400%的復(fù)利計息,12個月能獲得多少利息(精確到1元)?(2)若以季度復(fù)利計息,存4個季度,則當每季度利率為多少時,按季結(jié)算的利息不少于按月結(jié)算的利息(精確到10^(-5))?分析:復(fù)利是指把前一期的利息與本金之和算作本金,再計算下一期的利息.所以若原始本金為a元,每期的利率為r ,則從第一期開始,各期的本利和a , a(1+r),a(1+r)^2…構(gòu)成等比數(shù)列.解:(1)設(shè)這筆錢存 n 個月以后的本利和組成一個數(shù)列{a_n },則{a_n }是等比數(shù)列,首項a_1=10^4 (1+0.400%),公比 q=1+0.400%,所以a_12=a_1 q^11 〖=10〗^4 (1+0.400%)^12≈10 490.7.所以,12個月后的利息為10 490.7-10^4≈491(元).解:(2)設(shè)季度利率為 r ,這筆錢存 n 個季度以后的本利和組成一個數(shù)列{b_n },則{b_n }也是一個等比數(shù)列,首項 b_1=10^4 (1+r),公比為1+r,于是 b_4=10^4 (1+r)^4.
二、典例解析例3.某公司購置了一臺價值為220萬元的設(shè)備,隨著設(shè)備在使用過程中老化,其價值會逐年減少.經(jīng)驗表明,每經(jīng)過一年其價值會減少d(d為正常數(shù))萬元.已知這臺設(shè)備的使用年限為10年,超過10年 ,它的價值將低于購進價值的5%,設(shè)備將報廢.請確定d的范圍.分析:該設(shè)備使用n年后的價值構(gòu)成數(shù)列{an},由題意可知,an=an-1-d (n≥2). 即:an-an-1=-d.所以{an}為公差為-d的等差數(shù)列.10年之內(nèi)(含10年),該設(shè)備的價值不小于(220×5%=)11萬元;10年后,該設(shè)備的價值需小于11萬元.利用{an}的通項公式列不等式求解.解:設(shè)使用n年后,這臺設(shè)備的價值為an萬元,則可得數(shù)列{an}.由已知條件,得an=an-1-d(n≥2).所以數(shù)列{an}是一個公差為-d的等差數(shù)列.因為a1=220-d,所以an=220-d+(n-1)(-d)=220-nd. 由題意,得a10≥11,a11<11. 即:{█("220-10d≥11" @"220-11d<11" )┤解得19<d≤20.9所以,d的求值范圍為19<d≤20.9