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人教A版高中數(shù)學(xué)必修一二次函數(shù)與一元二次方程、不等式教學(xué)設(shè)計（2）
三個“二次”即一元二次函數(shù)、一元二次方程、一元二次不等式是高中數(shù)學(xué)的重要內(nèi)容，具有豐富的內(nèi)涵和密切的聯(lián)系，同時也是研究包含二次曲線在內(nèi)的許多內(nèi)容的工具 高考試題中近一半的試題與這三個“二次”問題有關(guān) 本節(jié)主要是幫助考生理解三者之間的區(qū)別及聯(lián)系，掌握函數(shù)、方程及不等式的思想和方法。課程目標(biāo)1. 通過探索，使學(xué)生理解二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系。2. 使學(xué)生能夠運用二次函數(shù)及其圖像，性質(zhì)解決實際問題． 3. 滲透數(shù)形結(jié)合思想，進(jìn)一步培養(yǎng)學(xué)生綜合解題能力。數(shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象：一元二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系；2.邏輯推理：一元二次不等式恒成立問題；3.數(shù)學(xué)運算：解一元二次不等式；4.數(shù)據(jù)分析：一元二次不等式解決實際問題；5.數(shù)學(xué)建模：運用數(shù)形結(jié)合的思想，逐步滲透一元二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系。
大班下學(xué)期國旗下講話
幼兒園新學(xué)期國旗下幼兒講話稿 親愛的小朋友們：大家早上好!暑假結(jié)束了，新年過去了，我們又長大了一歲，重新回到幼兒園，見到了老師和小朋友們，你們高興嗎?今天是我們新學(xué)期的第一次國旗下講話，首先，我希望小朋友們時時記住：我們是中國人!我們親愛的祖國，在地球上已經(jīng)存在了很長很長時間，創(chuàng)造了很多很多“好寶貝”，比如：四大發(fā)明、比如中華文明等等，為全世界做出了很大很大的貢獻(xiàn)。所以，我們應(yīng)該因為“我是中國人”而感到高興，感到自豪!鮮艷的五星紅旗代表著我們可愛的祖國，所以我們每個星期一都要準(zhǔn)時參加升旗禮，響亮地唱國歌!能不能做到?那么升國旗的時候應(yīng)該怎么做呢?請小朋友們認(rèn)真聽哦，在升國旗的時候不要做小動作，眼睛要看著國旗，手不要放在口袋里，不和小朋友們交談。唱國歌時聲音要洪亮。第二，我要說在過去的一年里，我們靖城中心幼兒園全體老師為了小朋友的成長，付出了很多很多，而小朋友在過去的一年里也學(xué)到了很多很多，我們都知道了怎么樣做是有禮貌，怎么樣做是守紀(jì)律，也知道了應(yīng)該怎樣來愛我們的幼兒園，愛我們的老師、同伴等等。新的學(xué)期開始了，我們能不能比以前做得更好呢?我相信，長大一歲的寶寶一定更懂事、更努力，也會做得更好!
高中學(xué)生會主席國旗下講話
為大家收集整理了《高中學(xué)生會主席國旗下講話范文》供大家參考，希望對大家有所幫助！??！敬愛的老師們，親愛的同學(xué)們：大家早上好！我是鄖陽中學(xué)新一屆學(xué)生會主席，來自高二班的張彥陽。首先，我代表新一屆學(xué)生會向給予我們關(guān)懷和信任的老師們表示衷心的感謝，向給予我們支持和幫助的全體同學(xué)表示深深的謝意，向給予我們鼓勵、寄予我們厚望的上一屆學(xué)生會全體成員表示崇高的敬意，謝謝你們！今天，我懷著十分激動的心情進(jìn)行國旗下演講。作為新一屆學(xué)生會主席，我深知自己身上的擔(dān)子不輕，權(quán)力越大，責(zé)任越大，但是有如此優(yōu)秀精英們組成的團(tuán)隊，讓我對未來的工作滿懷信心。我將會以百分之兩百的工作熱情去擔(dān)當(dāng)起這份重任，克服困難，迎接挑戰(zhàn)，努力實現(xiàn)我競選中所設(shè)想的那樣：將這一屆學(xué)生會打造成最為輝煌的一屆，名留校史！
第九周國旗下講話稿：愛班教育
敬愛的各位領(lǐng)導(dǎo)、老師，親愛的同學(xué)們：大家早上好!當(dāng)新的一天開始，鮮艷的五星紅旗冉冉升起，我內(nèi)心便充滿著對生活的感激，對長輩和同事的感恩，包含著我對六班的孩子們割舍不下深深的情誼!非常榮幸今天能站在國旗下講話。我今天講話的主題是：愛班教育。每一位翔宇學(xué)子進(jìn)校時都有屬于自己的班級。我們在場的每一位同學(xué)都不是一個完全獨立的學(xué)生而存在。我們生活在集體中，我們是集體中的一員。我們的一言一行不僅僅代表著個人，更代表著班級和學(xué)校。我們要用自己的言行舉止來提升班級的綜合素養(yǎng)和學(xué)校的綜合素養(yǎng)。而我們應(yīng)該如何來愛我們的班級呢？愛班就是在校園內(nèi)外見到師長記得喊老師好！不要因為自己的害羞而給老師留下一個不懂禮貌的背影。愛班就是真正做到不亂丟亂扔垃圾。讓我們每天走過的校園只留下四季變化的痕跡，而沒有垃圾的背影。愛班就是要求我們周一周五記得穿上校服。每天班級的清潔工作要按時完成，給大家營造一個干凈的舒適的學(xué)習(xí)環(huán)境。
在2022年商會第一屆理事會第四次擴(kuò)大會議上的講話范文
商會鄉(xiāng)賢的見面活動要繼續(xù)開展，不過方式方法有所改變，建議各縣市理事以上的領(lǐng)導(dǎo)帶頭出錢出力，1月3日副會長董時川自費設(shè)宴邀請在襄工作和生活的荊州籍洪湖人士，開展了一次見面會。我同監(jiān)事會主席余光輝及秘書處相關(guān)人員參加，活動開展的很好，知名人士紛紛表示會大力支持商會工作，愿為商會的發(fā)展建言獻(xiàn)策，只要會員和鄉(xiāng)賢有什么訴求，他們均愿意在力所能及的范圍為會員和鄉(xiāng)賢做貢獻(xiàn)。建議其他縣市理事以上的領(lǐng)導(dǎo)積極效仿，出錢、出力；
《拿來主義》說課稿（一） 2022-2023學(xué)年統(tǒng)編版高中語文必修上冊
（三）說目標(biāo)鑒于以上學(xué)情分析，結(jié)合單元學(xué)習(xí)任務(wù)群——思辨性閱讀與表達(dá)的定位，確定本課教學(xué)目標(biāo)為通過設(shè)置任務(wù)情境，帶領(lǐng)學(xué)生在活動中認(rèn)識表達(dá)的有針對性、論述的層次邏輯性以及感受文章蘊含的批判力量。其中以表達(dá)的有針對性為教學(xué)重點，以論述的層次邏輯性為難點。（四）說理念根據(jù)課標(biāo)和教材特點，結(jié)合學(xué)情，授課將依托“學(xué)為中學(xué)理論”“建構(gòu)主義學(xué)習(xí)理論”和“最近發(fā)展區(qū)理論”等，積極開展閱讀與鑒賞、表達(dá)與交流、梳理與探究等語文實踐活動提升學(xué)生語文核心素養(yǎng)。三、教學(xué)實施（一）設(shè)定學(xué)習(xí)情境為引導(dǎo)廣大學(xué)生合理對待外來文化，學(xué)校辯論社擬設(shè)定辯題——如何正確對待外來文化展開辯論。有同學(xué)說堅決抵制外來文化（正方），也有同學(xué)說要積極吸收（反方）……那么如果你是其中一位辯手，你將在《拿來主義》中如何擷取素材呢？
在一季度經(jīng)營工作例會暨資金調(diào)度會上的講話（集團(tuán)公司）
同志們：今天我們召開集團(tuán)公司一季度經(jīng)營工作例會暨資金調(diào)度會，主要任務(wù)是總結(jié)分析集團(tuán)公司今年以來的經(jīng)濟(jì)運行情況，查擺存在的問題及不足，提出具體解決措施，研究部署下一階段工作，為今后各項工作的開展打下堅實基礎(chǔ)。剛才，各子公司分別匯報了今年以來的生產(chǎn)經(jīng)營情況，各分管領(lǐng)導(dǎo)也針對各子公司存在問題提出了具體的意見，很有針對性和指導(dǎo)性，大家回去之后要認(rèn)真貫徹落實。針對此次會議內(nèi)容，我再提幾點意見：一、鉚足干勁、奮力沖刺，力爭完成第一季度經(jīng)營指標(biāo)*－*月份，集團(tuán)公司實現(xiàn)營業(yè)收入*億元，完成年度計劃的*％，同比下降*％；利潤總額*億元，完成年度計劃的*％，同比增長*％；歸母凈利潤*億元，完成年度計劃的*％，同比增長*％；資產(chǎn)總額*億元，較年初下降*％；資產(chǎn)負(fù)債率*％，較年初下降*個百分點。從經(jīng)營數(shù)據(jù)來看，集團(tuán)公司想要完成第一季度的經(jīng)營指標(biāo)以及全年的經(jīng)營指標(biāo)，任務(wù)還是比較艱巨的。比如利潤方面**板塊占比很高，如果單靠貿(mào)易和生產(chǎn)，是沒辦法實現(xiàn)利潤目標(biāo)的，大家要看到核心問題所在。時間也過得很快，轉(zhuǎn)眼間*月份已經(jīng)過了一周了，我們一定要增強緊迫感和危機(jī)感，鉚足干勁，加足馬力，奮力沖刺，抱著分秒必爭的決心和毅力去干，才有可能完成好年初制定的任務(wù)目標(biāo)。
在財稅金融工作暨一季度經(jīng)濟(jì)運行調(diào)度會上的講話
一）充分肯定財稅金融工作取得的成績。面對國際國內(nèi)經(jīng)濟(jì)下行的復(fù)雜形勢和不利因素影響，全縣各級各部門特別是財稅金融部門的廣大干部職工緊抓組織收入不放松，認(rèn)真落實財稅金融政策，狠抓增收節(jié)支，深化財稅金融改革，信貸投放加速增長，全力服務(wù)經(jīng)濟(jì)社會發(fā)展，較好地完成了全年工作任務(wù)。X年全縣地區(qū)生產(chǎn)總值完成X億元，同比增長X%，固定資產(chǎn)投資增長X%；財政總收入達(dá)到X億元；工業(yè)總產(chǎn)值達(dá)到X億元；社會消費品零售總額達(dá)到X億元，同比增長X%；城鎮(zhèn)居民人均可支配收入達(dá)到X萬元，同比增長X%，農(nóng)村居民人均可支配收入達(dá)到X元，同比增長X%，公共財政預(yù)算收入增速全州排在第X位，稅收收入在全省X個非經(jīng)濟(jì)強縣的排位第X位。
關(guān)于開展扣好人生第一?？圩踊顒有牡皿w會八篇
自打我上小學(xué)，媽媽就讓我養(yǎng)成堅強、獨立的性格，自己的事自己做?！ ∧鞘且粋€飄著毛毛細(xì)雨的早晨，我早早地出門去買早餐。對于平常吃慣了面包牛奶的媽媽，我多么想給她一個驚喜——為她買一碗熱騰騰的面。我買完面便匆匆往回趕?！ ∥倚∨苤蠘?，希望快點把這個驚喜帶給媽媽。突然，我的腳下打了個滑，不但我自己摔了個狗啃泥，而且連滾燙的面也潑灑了我一手。我被燙得哇哇大哭，哭聲引來了媽媽，我哭喪著臉對媽媽訴苦，滿以為會得到一點同情與憐愛，可媽媽只是簡單地交代了幾句，便又遞給我錢，讓我重新去買一份。我大為震驚：媽媽怎么那么狠心呀?何況我又是個女孩，她居然都不安慰我一下，我到底是不是她親生的?我忍著疼痛和怒火接過媽媽給我的錢，又去買了一碗面。
2023年XX區(qū)委農(nóng)村工作領(lǐng)導(dǎo)小組第一次會議上的講話
同志們：剛才，會議審議了《XXXX》等重要文件，今年“三農(nóng)”工作目標(biāo)任務(wù)已明確（一產(chǎn)增加值增速XX％、農(nóng)民人均可支配收入增速XX％），要細(xì)化制定我區(qū)年度鄉(xiāng)村振興工作方案，按照“清單制＋責(zé)任制＋時限制”將任務(wù)分解到鎮(zhèn)（街）、細(xì)化到部門。回首2022年，面對疫情沖擊、高溫干旱等多重考驗，全區(qū)上下堅持把“三農(nóng)”工作作為全區(qū)工作的重中之重，以愿拼敢拼能拼會拼的精氣神，牢牢守住“三農(nóng)”基本盤，全力以赴抓產(chǎn)業(yè)、攻項目、促振興，順利抱回幾個沉甸甸的牌子，成績來之不易，這是市委、市政府堅強領(lǐng)導(dǎo)的結(jié)果，也是全區(qū)“三農(nóng)”干部埋頭苦干、拼搏實干的成果。在此，我代表區(qū)委、區(qū)政府向大家的辛勤付出，表示衷心的感謝！在肯定成績的同時，我們也要清醒地認(rèn)識到“三農(nóng)”工作的短板和差距，例如，糧食單產(chǎn)較低、產(chǎn)業(yè)鏈條不長、農(nóng)產(chǎn)品品牌較少、部分涉農(nóng)項目推進(jìn)緩慢。針對問題，區(qū)級各部門、各鎮(zhèn)（街道）要堅持“缺什么補什么、什么問題突出就解決什么問題”，把該謀的大事謀在前，把該做的工作做到位，認(rèn)真落實中央和省委、市委農(nóng)村工作會議決策部署，落實落細(xì)中央和省市1號文件各項措施，全面推進(jìn)鄉(xiāng)村振興，加快農(nóng)業(yè)農(nóng)村現(xiàn)代化步伐。下面，我再強調(diào)5點意見。
關(guān)于做有責(zé)任心的中學(xué)生國旗下講話
做有責(zé)任心的中學(xué)生在從事一定工作的人應(yīng)當(dāng)具備的品質(zhì)中，責(zé)任感，是那樣樸素而又十分可貴。忍著病痛走訪貧苦百姓的焦裕祿，迎著洪水探訪災(zāi)情的張鳴歧，以微薄收入供養(yǎng)藏族孤兒的孔繁森……縷述先進(jìn)人物的思想和事跡，無不具備一個共同的特點，就是對國家、對人民、對事業(yè)有著高度的責(zé)任感。“不患無策，只怕無心?！币粋€人的學(xué)識、能力、才華很重要，但缺乏責(zé)任感、責(zé)任意識和責(zé)任心，就不堪大用。即使小用，也令人擔(dān)心。責(zé)任感反映一個人的精神境界。有責(zé)任感的人，突出的優(yōu)點是他們絕不是個人中心主義者，他人的、集體的、國家的利益總是先于自己的利益。責(zé)任感反映一個人的思想品德，在“天下熙熙，皆為利來；天下攘攘，皆為利往”的喧囂中，有責(zé)任感的人淡泊的是名利。他們的價值觀是在幫助別人獲得幸福中得到滿足，而他們自己卻少有索求，因而責(zé)任感總是和顧全大局、助人為樂、謙遜禮讓等優(yōu)良品德聯(lián)系在一起。責(zé)任感是國民素質(zhì)的一個重要方面。
小學(xué)美術(shù)人教版一年級上冊《第5課五彩的煙花》教學(xué)設(shè)計模板說課稿
2學(xué)情分析一年級學(xué)生對美術(shù)的興趣很高，對五顏六色的物體特別感興趣，孩子們課前做的準(zhǔn)備很好。3重點難點1.節(jié)日里煙花的畫法。2.油畫棒和水彩顏料相結(jié)合的涂色技巧。教學(xué)活動活動1【活動】教案第5課五彩的煙花
新人教版高中英語必修3Unit 1 Festivals and Celebrations-Reading for Writing教學(xué)設(shè)計一
The topic of this part is “Write about your festival experience”.During the Listening and Speaking and Talking, students are just asked to say out their festival experiences such as the Spring Festival, Mid-autumn Day, but this part students will be asked to write down their own festival experiences. During the reading part, it introduces the Naadam Festival in Inner Mongolia Autonomous Region, which can give students a good example to imitate. Students not only learn the festival, but touch and feel the Inner Mongolian’s character, the spirit and cultural atmosphere, which can help students form the cultural awareness and learn to enjoy and value the diversity of Chinese culture.Concretely, the dairy tells the experience that the author spent the Naadam Festival in Inner Mongolia Autonomous Region with his/her friend. The structure is clear. In the opening paragraph, it introduces the topic of the Naadam Festival and the whole feeling. Then it introduces the items of the festival like the ceremony, wrestling and horse racing. Finally, it summarizes this experience. Because this part is a travel journal, we must guide students pay more attention to these details: 1. use the first person. 2. use the past tense to tell the past thing and use the present or future tense to describe the scenery. 3. use the timeline to tell the development. 4. be careful for the author’s psychology, emotion and feeling, etc.1. Read quickly to get main idea; read carefully to get the detailed information about Naadam Festival.2. Learn the structure of the reading article and language.3. Write an article about a festival experience4. Learn to use the psychology, emotions and feeling in the writing.1. Write an article about a festival experience.2. Use the structure of the reading article and language.
新人教版高中英語必修3Unit 4 Space Exploration-Listening&Speaking&Talking教學(xué)設(shè)計一
Listening and Speaking introduces the topic of “talking about how to become an astronaut”. This period is aimed to inform students some details about the requirements of being an astronaut. Students can be motivated and inspired by the astronauts. Teachers ought to encourage students to learn from them and let them aim high and dream big.Listening and Talking introduces the theme of "talk about life in space". This part also informs students more details about life in space and can inspire students to be curious about this job. 1. Guide students to listen for numbers concerning dates, years and ages etc2. Cultivate students' ability to talk about how to become an astronaut and life in space ; 3. Instruct students to use functional sentences of the dialogue such as “ first of all, I am not sure, so what might be .. I guess.. I wonder…I am curious…)appropriately.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to guess the meaning of words in listening; discuss with their peers how to become a qualified astronaut and describe the life in space.Part 1: Listening and SpeakingStep 1: Lead inPredictionThe teacher can ask students to predict what the listening text is about by looking at the pictures.About how to become an astronaut./the requirements of an astronautStep 2: Then, play the radio which is about an interview a. And after finishing listening for the first time, the students need to solve the following tasks.
新人教版高中英語必修3Unit 4 Space Exploration-Reading and Thinking教學(xué)設(shè)計一
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.
新人教版高中英語必修3Unit 4 Space Exploration-Reading For Writing教學(xué)設(shè)計一
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(jìn)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(rèn)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(jī)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(jìn)行宇宙探索”這個問題進(jìn)行了激烈的討論。有人認(rèn)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(rèn)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(dāng)發(fā)揮，使上下文連貫；
新人教版高中英語必修3Unit 5 The Value of Money-Reading and Thinking教學(xué)設(shè)計一
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.
新人教版高中英語必修3Unit 5 the value of money-Reading For Writing教學(xué)設(shè)計一
【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!
空間向量基本定理教學(xué)設(shè)計人教A版高中數(shù)學(xué)選擇性必修第一冊
反思感悟用基底表示空間向量的解題策略1.空間中,任一向量都可以用一個基底表示,且只要基底確定,則表示形式是唯一的.2.用基底表示空間向量時,一般要結(jié)合圖形,運用向量加法、減法的平行四邊形法則、三角形法則,以及數(shù)乘向量的運算法則,逐步向基向量過渡,直至全部用基向量表示.3.在空間幾何體中選擇基底時,通常選取公共起點最集中的向量或關(guān)系最明確的向量作為基底,例如,在正方體、長方體、平行六面體、四面體中,一般選用從同一頂點出發(fā)的三條棱所對應(yīng)的向量作為基底.例2.在棱長為2的正方體ABCD-A1B1C1D1中,E,F分別是DD1,BD的中點,點G在棱CD上,且CG=1/3 CD(1)證明:EF⊥B1C;(2)求EF與C1G所成角的余弦值.思路分析選擇一個空間基底,將(EF) ?,(B_1 C) ?,(C_1 G) ?用基向量表示.(1)證明(EF) ?·(B_1 C) ?=0即可;(2)求(EF) ?與(C_1 G) ?夾角的余弦值即可.(1)證明:設(shè)(DA) ?=i,(DC) ?=j,(DD_1 ) ?=k,則{i,j,k}構(gòu)成空間的一個正交基底.
點到直線的距離公式教學(xué)設(shè)計人教A版高中數(shù)學(xué)選擇性必修第一冊
4.已知△ABC三個頂點坐標(biāo)A(－1,3)，B(－3,0)，C(1,2)，求△ABC的面積S.【解析】由直線方程的兩點式得直線BC的方程為 ＝ ，即x－2y＋3＝0，由兩點間距離公式得|BC|＝ ，點A到BC的距離為d，即為BC邊上的高，d＝ ，所以S＝ |BC|·d＝ ×2 × ＝4，即△ABC的面積為4.5.已知直線l經(jīng)過點P(0,2),且A(1,1),B(-3,1)兩點到直線l的距離相等,求直線l的方程.解:(方法一)∵點A(1,1)與B(-3,1)到y(tǒng)軸的距離不相等,∴直線l的斜率存在,設(shè)為k.又直線l在y軸上的截距為2,則直線l的方程為y=kx+2,即kx-y+2=0.由點A(1,1)與B(-3,1)到直線l的距離相等,∴直線l的方程是y=2或x-y+2=0.得("|" k"-" 1+2"|" )/√(k^2+1)=("|-" 3k"-" 1+2"|" )/√(k^2+1),解得k=0或k=1.(方法二)當(dāng)直線l過線段AB的中點時,A,B兩點到直線l的距離相等.∵AB的中點是(-1,1),又直線l過點P(0,2),∴直線l的方程是x-y+2=0.當(dāng)直線l∥AB時,A,B兩點到直線l的距離相等.∵直線AB的斜率為0,∴直線l的斜率為0,∴直線l的方程為y=2.綜上所述,滿足條件的直線l的方程是x-y+2=0或y=2.