
★教后記:歷史教學(xué)的最高目標(biāo)不是單純的記憶和培養(yǎng)能力,而是樹立正確的歷史觀,培養(yǎng)學(xué)生的歷史責(zé)任感。從這一點講,新課標(biāo)及新課標(biāo)教材給老師極大的發(fā)揮空間,擺脫了以往的“教教材”,真正實現(xiàn)了 “用教材教”,只有這樣,教師才不只是一個“備課”的“教書匠”,而是一名設(shè)計教學(xué)“設(shè)計師”,以教材為磚瓦,建造有自己獨特風(fēng)格的教育大廈。這是我設(shè)計教學(xué)的出發(fā)點。開放式的課堂需要思想開放的教師,但對教師的課堂駕馭能力要求更高,否則“一放就活,一活就亂”,只求課堂熱鬧,熱鬧過后,學(xué)生一無所獲,那么這樣的開放課堂依然是失敗的。開放式的課堂并不是任由學(xué)生說,教師必要的引導(dǎo)與客觀的評價尤為重要?!飭栴}解答⊙【學(xué)思之窗】請談?wù)?,火車機車的不斷改進,給國民經(jīng)濟發(fā)展、百姓生活帶來怎樣的影響?答案提示:運輸量大,有利于各地區(qū)的物資交流和勞動力流動,促進經(jīng)濟發(fā)展;交通便利快捷;機車內(nèi)部環(huán)境舒適,給百姓出行帶來方便。

設(shè)問:你怎么看待這個問題的?(這是達爾文沒有想到的,是有人利用了達爾文的學(xué)說,科學(xué)應(yīng)該與其區(qū)分開來,但是科學(xué)家在研究時,既要做到為追求真理不斷探索,又要有一定的人文精神,比如我們只有以人為本,才能找到解決當(dāng)今社會面臨的諸如環(huán)保、戰(zhàn)爭、饑荒等問題的途徑,才能構(gòu)建防止核物理技術(shù)、克隆技術(shù)、信息技術(shù)、生物技術(shù)、太空技術(shù)等可能對人類造成不可逆轉(zhuǎn)的破壞作用的思想基礎(chǔ)、決策機制和社會條件。更重要的是社會和國家應(yīng)該對此有足夠的認識,正因為此,所以現(xiàn)在當(dāng)一項科學(xué)發(fā)明出臺后,就會有一些法律出臺,限制其可能的非人道用途。但是這些影響應(yīng)不成為我們進行科學(xué)探究的阻礙。)(3)科學(xué)與宗教的斗爭設(shè)計意圖:再次引導(dǎo)學(xué)生認識,科學(xué)的探索永無止境,同時也再次認識宗教和科學(xué)理論產(chǎn)生的原因。材料1:1972年,美國加利福尼亞教育部竟明文規(guī)定,中學(xué)生物學(xué)課本除進化論外,必須還有神創(chuàng)論的內(nèi)容,而且兩者的頁數(shù)要各占一半。

【教學(xué)目標(biāo)與核心素養(yǎng)】1. Instruct students to get main facts by listening and motivate them to talk about the topics about how to prepare for the trip and make reservations by listening and ultimately can make travel arrangements and reservations. 2. Develop students’ sense of cooperative learning and individual thinking capability. 3. Develop students’ different listening skills to solve different listening comprehensive problems.4. Help students to understand how to use the structures “the present continuous tense (be doing) is used to express future plans.【教學(xué)重難點】1. Teach students how to focus on key words, not on single words or grammar.2. Prompt Ss to talk about the related topics, such as how to prepare for the trip and make a travel plan.【教學(xué)過程】Step 1: Listening and SpeakingLead inThe teacher is advised to talk with their students about the places that they want to travel most both at home and abroad: boys and girls, if you have a chance to travel around the world, where will you go? After their small talk, the teacher can move on by finishing the following listening task:Before travelling, what do we need to prepare for the trip?

1. 表示時間。Hearing these stories, I’m skeptical about the place. = When I heard these stories. . . 2. 表示原因。Not knowing his address, I can’t send this book to him. = Because/Since/As I don’t know his address. . . 3. 表示結(jié)果。His father died, leaving him a lot of money. =. . . and left him a lot of money4. 表示條件。Going straight down the road, you will find the department store. = If you go straight down the road. . . 5. 表示讓步。Being tired, they went on working. =Although they were tired. . . 6. 表示行為方式、伴隨情況或補充說明。He lay on the grass, staring at the sky for a long time. =. . . and stared at the sky for a long time注意:非謂語動詞作狀語時, 如所提供的動詞不能和句子中的主語保持一致, 動詞-ing形式必須有自己的邏輯主語, 通常由名詞或代詞來擔(dān)任, 這就是獨立主格結(jié)構(gòu)。The last bus having gone, we had to walk home. (having gone的邏輯主語是the last bus, 而不是we)Weather permitting, the football match will be played on Friday. (permitting的邏輯主語是time, 而不是the football match)Step 7 Practice1. ________(study) hard, you are sure to get first prize. 2. People use plastic in their daily life, _______(leave) large amounts of waste. 3. ________(work) hard at your lessons, you are to succeed. 4. The old man, ____________(work) abroad for twenty years, is on the way back to his motherland. 5. ______________(finish) his homework, he was playing on the playground. Answers: 1. Studying 2. leaving 3. Working 4.having worked 5. Having finishedStep 8 HomeworkFinish the homework on Page 22.

Example:One day, a poor boy who was trying to pay his way through school by sending newspapers door to door found that he only had one dime(一角)left. He was so hungry that he decided to beg for a meal at the next house.However, he lost his nerve when a lovely young woman opened the door. Instead of a meal he asked for a drink of water. She thought he looked hungry so she brought him a large glass of milk. He drank it slowly, and then asked, “How much do I owe you?” “You don’t owe me anything,” she replied, “Mother has taught me never to accept pay for a kindness.” “Then I thank you from the bottom of my heart.” With these words, Howard Kelly left that house.Years later the woman became badly ill and was finally sent to the hospital in a big city. Dr. Howard Kelly, now famous, was called in. When he heard the name of the town she came from, a strange light filled his eyes. Dressed in his doctor’s clothes, Dr. Kelly went into her room and recognized her at once. From that day on, he gave special attention to her, and decided to do his best to save her life.At last the woman was saved. Dr. Kelly asked the business office to pass the final bill to him. He looked at it and then wrote something on the side. The bill was sent to the woman’s room. She was afraid to open it because she was sure that it would take the rest of her life to pay for it off. Finally she looked, and the note on the side of the bill caught her attention. She read these words: “Paid in full with a glass of milk, Dr. Howard Kelly.” Tear of joy flooded her eyes.

The topic of this part is “Learn to make choices in life”.The Listening & Speaking & Talking part aims at the moral dilemmas, and this part is about making choices in life. The heroin is Lin Qiaozhi, a famous medical scientist, made a great contribution to our country’s medical care. Most importantly, her life experience can inspire our students whether in studying or the development of career. she had moral dilemmas and life choices, which are similar to the students who will step into society. Besides, Lin has quite good virtues like kindness, self-improvement, insistence, job-loving , generosity and responsibility, which is worth being learned.Concretely, this article is a biography about Lin Qiaozhi. The article tells her whole life according the timeline, among which the life choices is emphasized. For example, whether married or chased her dream, returned home or stayed abroad, family or public, her choices all reflected her faith, spirit, responsibility and devotion.1. Fast reading to get the detailed information about Lin Qiaozhi; careful reading to do the deductive information.2. Learn the reading skills--deductive judgement according the context.3. Study the structure features and language features. 4. Communicate about Lin’s life choices and reflect their own life choices.1. Learn the reading skills--deductive judgement according the context.2. Study the structure features and language features.3. Communicate about Lin’s life choices and reflect their own life choices.Step 1 Lead in---Small talkWhat are some important life choices?Importance choices: university study, jobs and marriage partners. Because they can determine our future.

1. 這個寓言是一個關(guān)于一位國王古寓言。 The fable is an old fable about a king.2.作者用這個故事讓讀者對于社區(qū)的問題負有個人責(zé)任的必要印象深刻。The author used the story to impress upon readers with the need to take personal responsibility for problems in the community.3. 這個故事十分成功的實現(xiàn)了它的目的。The story was quite successful in achieving its purpose.Step 7 WritingPlease write a review of the story according the outline above.The fable is an old fable about a king who thought his people are lazy, so he put a large stone in the middle of the road and hides and waited to see if anyone will try to move it.The author used this story to impress upon readers with the need to take personal responsibility for problems in the community. The story was quite successful in achieving its purpose, and I liked it because it had a clear moral.However, while the moral of the story is clear, the actions of the king seemed pointless to me, because none of the characters in the story learnt anything. For this reason, I think there are better stories that can be used to impress upon people with the need for personal responsibility.Step 8 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Does the writer give a short description of the story ?2. Does the description include the most important details of the story ?3. Does the writer give his or her opinion about the character or their actions ?4. Is the review well-organised ? 5. Does the writer use the -ing form as the adverbial correctly in the writing ?6. Are there any grammar, spelling, or punctuation errors ?Step 9 HomeworkPut up your revised draft in the classroom or read it to your class.

1.通過對德國魯爾工業(yè)區(qū)、我國的遼中南工業(yè)區(qū)的案例分析和比較,讓學(xué)生理解傳統(tǒng)工業(yè)地域形成的主要區(qū)位條件和衰落的原因;2.結(jié)合魯爾工業(yè)區(qū)產(chǎn)生的環(huán)境污染等局面,理解工業(yè)生產(chǎn)活動對地理環(huán)境的影響,并探討綜合整治的措施;3.通過對意大利中部和東北部工業(yè)區(qū)、美國“硅谷”的案例分析和比較,讓學(xué)生理解新工業(yè)地域形成的主要區(qū)位條件和衰落的原因;4.結(jié)合新工業(yè)地域和地理環(huán)境的關(guān)系,加深學(xué)生對工業(yè)生產(chǎn)活動對地理環(huán)境的影響的理解。【教學(xué)重、難點及解決辦法】重點:分析工業(yè)區(qū)位因素,舉例說明工業(yè)地域的形成條件與發(fā)展特點難點:結(jié)合實例說明工業(yè)生產(chǎn)活動對地理環(huán)境的影響解決方法:比較歸納法 知識遷移應(yīng)用 案例分析法 自主學(xué)習(xí)與合作探究 【教學(xué)準(zhǔn)備】多媒體課件缺勤登記:

案例探究:環(huán)地中海地區(qū)農(nóng)業(yè)的變遷讓學(xué)生思考:此地哪些因素發(fā)生了變化,農(nóng)業(yè)生產(chǎn)方式進行了如何調(diào)整?效果如何?二、農(nóng)業(yè)地域的形成1、農(nóng)業(yè)地域的概念:由于以上各因素的共同影響,在一定的地域和一定的歷史條件下,形成了相應(yīng)的生產(chǎn)地區(qū),稱為農(nóng)業(yè)地域。農(nóng)業(yè)地域的類型主要有:種植業(yè)、畜牧業(yè)、混合農(nóng)業(yè)。(在這里分別給學(xué)生展示一些農(nóng)業(yè)生產(chǎn)類型的圖片,并簡單說明什么是種植業(yè)、什么是畜牧業(yè)、及什么是混合農(nóng)業(yè))案例探究:閱讀澳大利亞地混合農(nóng)業(yè)生產(chǎn)思考:(1)、澳大利亞農(nóng)業(yè)生產(chǎn)的特點是什么?(2)、澳大利亞混合農(nóng)業(yè)的分布在哪里?受哪些區(qū)位因素的影響?(3)澳大利亞混合農(nóng)業(yè)生產(chǎn)有哪些優(yōu)點?

生1:加強對綠色食品的宣傳和扶持力度。當(dāng)前的形勢迫切要求我們發(fā)展綠色食品,因為綠色食品是真正實現(xiàn)可持續(xù)發(fā)展的,做到了發(fā)展經(jīng)濟和環(huán)境保護相結(jié)合,而且有利于增進人民身體健康。但目前綠色食品在市場上難成氣候,主要是宣傳和扶持不夠。生2:綠色食品對環(huán)境、生長過程、加工過程以及運輸?shù)冗^程都有很嚴(yán)格的要求,很多環(huán)境相對優(yōu)良的地區(qū)都是邊遠落后地區(qū),必須給予政策上的扶持和優(yōu)惠,才能降低成本,市場發(fā)展前景才會更加廣闊?;顒优c探究對當(dāng)?shù)鼐G色食品市場情況作調(diào)查并初步分析。活動的實施過程:1.確定調(diào)查研究的目標(biāo)并制定調(diào)查研究的計劃。市場調(diào)查要深入廣大消費者,可以去市場上做調(diào)查,‘對象包括消費者和經(jīng)營者。形式可以是問卷,也可以是現(xiàn)場采訪。弄清楚被調(diào)查者對綠色食品的態(tài)度,是否了解食用綠色食品的意義,是否懂得鑒別綠色食品等。對象力求涉及各個年齡段,多種職業(yè)。2.對問卷調(diào)查進行整理、分析,得出結(jié)論。

思考:結(jié)合資料,看看“廣鋼”的搬遷還考慮到什么因素?主要從誰的角度去考慮?展示資料:廣鋼建于1958年,由于城市化進程的加快,原來地處偏僻的廣鋼一帶現(xiàn)已成鬧市,廣鋼因此給周邊帶來了許多不便,并屢被投訴,投訴的主要內(nèi)容是煙氣、粉塵超標(biāo)。近日,《珠三角環(huán)境保護規(guī)劃綱要(草案)》(以下簡稱《綱要》)正式提交省人大常委會審議,按照《綱要》要求,2010年前,廣東省將關(guān)、停、并、轉(zhuǎn)、遷位于城市中心區(qū)高能耗、重污染的工業(yè)企業(yè)。學(xué)生討論:環(huán)保要素、政策要素……從市民、政府等社會角度去考慮板書:2、環(huán)保要素 3、政策的變化小結(jié):影響工業(yè)區(qū)位選擇的因素很多,不同的工業(yè)區(qū)位選擇要考慮的主導(dǎo)因素可能是一個或幾個,應(yīng)因地制宜,具體分析。并且影響區(qū)位選擇的因素隨著社會的發(fā)展而變化;社會、環(huán)境需要對工業(yè)區(qū)位也有一定的影響力。所以工業(yè)區(qū)位選擇是復(fù)雜的,應(yīng)綜合考慮各種因素,以取得最大的經(jīng)濟、社會、環(huán)境綜合效益。學(xué)生活動:計算機模擬工業(yè)選址,看誰是最英明的決策者(通過實踐應(yīng)用讓學(xué)生感受到工業(yè)的區(qū)位選擇應(yīng)綜合考慮)

⑴ 原料、燃料對工業(yè)區(qū)位的影響逐漸減弱,市場對工業(yè)區(qū)位的影響逐漸加強; ⑵交通運輸條件對工業(yè)具有很大的吸引力,在沿海沿江港口、鐵路樞紐、高速公路沿線形成工業(yè)區(qū);⑶信息通信網(wǎng)絡(luò)的通達性作為工業(yè)區(qū)位的重要性越來越突出;⑷工業(yè)對勞動力技能的要求逐漸增強。再次顯示上表最后一項“各因素的發(fā)展變化”。由工業(yè)生產(chǎn)的一般過程中可以知道,工廠產(chǎn)出產(chǎn)品的同時,也產(chǎn)出廢氣、廢水、廢渣。這些廢棄物排入環(huán)境,會造成環(huán)境污染,危害人們的身體健康。隨著人們環(huán)境意識的增強,環(huán)境質(zhì)量已成為重要的區(qū)位因素。在工廠的區(qū)位選擇時,應(yīng)以不污染當(dāng)?shù)丨h(huán)境為佳,進行合理選擇。讀課本61頁圖4.6污染嚴(yán)重工業(yè)的區(qū)位選擇,思考以下問題:1、嚴(yán)重污染空氣的工廠布局時應(yīng)考慮那些因素?2、嚴(yán)重污染水源的工廠布局時應(yīng)考慮那些因素?3、對環(huán)境質(zhì)量要求高的工廠布局時應(yīng)考慮那些因素?教師解析:對這一部分知識需要強記。講解要注意盛行風(fēng)向,需結(jié)合必修一氣候一節(jié)將難點突破,可分中國大部分地區(qū)、西歐、印度半島等不同區(qū)域進行講解以加深印象。

③在薩斯索羅地區(qū)集聚的相關(guān)企業(yè)和服務(wù)性機構(gòu)有哪些?④薩斯索羅瓷磚工業(yè)小區(qū)的生產(chǎn)—銷售—服務(wù)網(wǎng)絡(luò)中支撐企業(yè)、輔助性企業(yè)、服務(wù)性企業(yè)、服務(wù)性機構(gòu)有哪些?學(xué)生回答問題后教師小結(jié):意大利的新工業(yè)區(qū),以中小企業(yè)集聚的工業(yè)小區(qū)為獨特的發(fā)展模式。工業(yè)小區(qū)的優(yōu)勢是有助于加強專業(yè)化,提高生產(chǎn)效率,降低生產(chǎn)成本,增強在市場上的競爭力。完成課本70頁活動:1. 比較溫州鄉(xiāng)鎮(zhèn)企業(yè)與意大利新工業(yè)區(qū)的發(fā)展有什么異同(相同:有大批廉價勞動力,企業(yè)規(guī)模小,以輕工業(yè)為主,企業(yè)生產(chǎn)高度專業(yè)化,資本集中程度低。不同:最大的不同是意大利工業(yè)小區(qū)密切聯(lián)系協(xié)作,共同形成巨型企業(yè),溫州雖生產(chǎn)同種產(chǎn)品,但是聯(lián)系協(xié)作不如意,形成多家企業(yè)競爭局面,規(guī)模效應(yīng)大減。)2. 溫州鄉(xiāng)鎮(zhèn)企業(yè)的發(fā)展有哪些些問題?你能為其解決這些問題提出合理化的建議嗎?(加大技術(shù)投入,企業(yè)間聯(lián)系協(xié)作,杜絕惡性競爭等)

2.音響生產(chǎn)的工業(yè)集聚有哪些優(yōu)勢?點撥:可以加強各企業(yè)間的信息交流和技術(shù)協(xié)作,降低中間產(chǎn)品的運輸費用和能源消耗,進而降低生產(chǎn)成本,提高生產(chǎn)效率和利潤,取得規(guī)模效益。3.根據(jù)惠州音響零件的來源百分比,說明惠州音響零件供應(yīng)廠家的地域分布有什么規(guī)律。點撥:距離遞減規(guī)律,距離惠州音響整機組裝廠越近的地區(qū)零件來源所占比例越高。三)工業(yè)地域工業(yè)聯(lián)系—--------- 工業(yè)集聚------------工業(yè)地域工業(yè)地域:工業(yè)集聚而形成的地域稱之為工業(yè)地域。1.工業(yè)地域形成的兩種情況⑴自發(fā)形成的工業(yè)地域: 以生產(chǎn)工序上的工業(yè)聯(lián)系為基礎(chǔ),以降低生產(chǎn)成本為目的。⑵規(guī)劃建設(shè)的工業(yè)地域:如我國許多地方的經(jīng)濟技術(shù)開發(fā)區(qū):①把生產(chǎn)上有投入 產(chǎn)出聯(lián)系密切的工廠布局在一起。②先建成基礎(chǔ)設(shè)施,再吸引投資者建廠,形成空間和信息共同利用的工業(yè)聯(lián)系。我國許多地方的經(jīng)濟技術(shù)開發(fā)區(qū),就是利用這一原理建成的。2.兩類不同性質(zhì)的工業(yè)地域

過渡:在實際生活中,城市內(nèi)部空間結(jié)構(gòu)并非完全按照這一經(jīng)濟規(guī)律呈現(xiàn),而是更具復(fù)雜性。這說明除了經(jīng)濟因素外,還有很多其他因素在起作用,請大家結(jié)合你的認識、圖2.9和案例1:紐約市的少數(shù)民族區(qū)談?wù)勀愕目捶ā#?)其他因素I.收入 —— 形成不同級別住宅區(qū)的常見原因。有能力支付昂貴租金和選擇最佳居住環(huán)境的人,其居住地往往形成高級住宅區(qū)。II.知名度 ——城市內(nèi)某些地區(qū)在歷史、文化或經(jīng)濟方面具有很高的聲譽,這往往會吸引更多新的住宅或商場建在該處,以提高其知名度。III.種族聚居區(qū)的形成 ——在有些城市的某一區(qū)域內(nèi),如果某個種族或宗教團體占優(yōu)勢,就可能形成種族聚居區(qū)。如紐約市的唐人街、哈林區(qū)、小意大利區(qū)等。IV歷史因素——城市的建筑物和街道設(shè)計可以維持久遠,早期的土地利用方式對日后的功能分區(qū)有著深遠的影響。3、城市內(nèi)部空間結(jié)構(gòu)的形成和變化

1、 前提條件:①環(huán)境幾乎一樣的平原地區(qū),人口分布均勻2、 ②區(qū)域的運輸條件一致,影響運輸?shù)奈┮灰蛩厥蔷嚯x。城市六邊形服務(wù)范圍形成過程。(理解)a.當(dāng)某一貨物的供應(yīng)點只有少數(shù)幾個時,為了避免競爭、獲取最大利潤,供應(yīng)點的距離不會太近,它們的服務(wù)范圍都是圓形的。 b.在利潤的吸引下,不斷有新的供應(yīng)點出現(xiàn),原有的服務(wù)范圍會因此而縮小。這時,該貨物的供應(yīng)處于飽和。每個供應(yīng)點的服務(wù)范圍仍是圓形的,并彼此相切c.如果每個供應(yīng)點的服務(wù)范圍都是圓形相切卻不重疊的話,圓與圓之間就會存在空白區(qū)。這里的消費者如果都選擇最近的供應(yīng)點來尋求服務(wù)的話,空白區(qū)又可以分割咸三部分,分別屬于三個離其最近的供應(yīng)點。[思考]①圖2.15中城市有幾個等級?②找出表示每一等級六邊形服務(wù)范圍的線條顏色?③敘述不同等級城市之間服務(wù)范圍及其相互關(guān)系?3、理論基礎(chǔ):德國南部城市4、意義:運用這種理論來指導(dǎo)區(qū)域規(guī)劃、城市建設(shè)和商業(yè)網(wǎng)點的布局。1、 應(yīng)用——“荷蘭圩田居民點的設(shè)置”。

學(xué)生探究案例:找出不同等級城市的數(shù)目與城鎮(zhèn)級別的關(guān)系、城鎮(zhèn)的分布與城鎮(zhèn)級別的關(guān)系并試著解釋原因。在此基礎(chǔ)上,指導(dǎo)學(xué)生一步步閱讀書上的閱讀材料,首先說明這是德國著名的經(jīng)濟地理學(xué)家克里斯泰勒對德國南部城市等級體系研究得出的中心地理論,他是在假設(shè)土壤肥力相等、資源分布均勻、沒有邊界的平原上,交通條件一致、消費者收入及需求一致、人們就近購買貨物和服務(wù)的情況下得出的理想模式。然后指導(dǎo)學(xué)生閱讀圖2.14下文字說明,理解城市六邊形服務(wù)范圍形成過程。指導(dǎo)學(xué)生讀圖2.15,找出圖中城市的等級、每一等級六邊形服務(wù)范圍并敘述不同等級城市之間服務(wù)范圍及其相互關(guān)系,從而得出不同等級城市的空間分布規(guī)律,六邊形服務(wù)范圍,層層嵌套的理論模式。給出荷蘭圩田空白圖,讓學(xué)生應(yīng)用上面的理論規(guī)劃設(shè)計居民點并說出理由,再和教材上的規(guī)劃進行對照。然后給出長三角地區(qū)城市分布圖和各城市人口數(shù),讓學(xué)生對這些城市進行分級,概括每一級城市的服務(wù)功能、統(tǒng)計每一等級城市的數(shù)目以及彼此間的平均距離,總結(jié)城市等級與服務(wù)范圍、空間分布的關(guān)系?

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(dāng)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

二、典例解析例10. 如圖,正方形ABCD 的邊長為5cm ,取正方形ABCD 各邊的中點E,F,G,H, 作第2個正方形 EFGH,然后再取正方形EFGH各邊的中點I,J,K,L,作第3個正方形IJKL ,依此方法一直繼續(xù)下去. (1) 求從正方形ABCD 開始,連續(xù)10個正方形的面積之和;(2) 如果這個作圖過程可以一直繼續(xù)下去,那么所有這些正方形的面積之和將趨近于多少?分析:可以利用數(shù)列表示各正方形的面積,根據(jù)條件可知,這是一個等比數(shù)列。解:設(shè)正方形的面積為a_1,后續(xù)各正方形的面積依次為a_2, a_(3, ) 〖…,a〗_n,…,則a_1=25,由于第k+1個正方形的頂點分別是第k個正方形各邊的中點,所以a_(k+1)=〖1/2 a〗_k,因此{a_n},是以25為首項,1/2為公比的等比數(shù)列.設(shè){a_n}的前項和為S_n(1)S_10=(25×[1-(1/2)^10 ] )/("1 " -1/2)=50×[1-(1/2)^10 ]=25575/512所以,前10個正方形的面積之和為25575/512cm^2.(2)當(dāng)無限增大時,無限趨近于所有正方形的面積和
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