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新人教版高中英語(yǔ)選修2Unit 2 Learning about Language教學(xué)設(shè)計(jì)
The activity theme of this section is to design various activities around the key words in the first text. Therefore, the activities require students to pay attention to the spelling of words. On the other hand, let students grasp the meaning of words more accurately through sentences and short texts. This kind of teaching design also helps to improve the ability of using English thinking.1. Cultivating students' ability to use word formation to induce and memorize vocabulary, and the ability to use lexical chunks to express meaning.2. Guide the students to think independently and use the correct form of words to complete sentences3. Cultivate students' habit of using lexical chunks to express language completely, guide students to draw words in sentences quickly, pay attention to word collocation, so as to accumulate more authentic expressions4. Instruct students to create sentences with the chunks.1. Enable students to use the language points in the real situation or specific contexts flexibly and appropriately.2. Guiding the Ss to use unit topic words and the sentence patterns in a richer context.Step1: Think of a word that best fits each definition.1. to remember sth2.to accept, admit, or recognize sth or the truth/existence of sth3. the process of changing sth or yourself to suit a new situation4 .to make sb feel less worried or unhappy5. a strong desire to achieve sth
新人教版高中英語(yǔ)選修2Unit 3 Reading for writing教學(xué)設(shè)計(jì)
The theme of this part is to write an article about healthy diet. Through reading and writing activities, students can accumulate knowledge about healthy diet, deepen their understanding of the theme of healthy diet, and reflect on their own eating habits. This text describes the basic principles of healthy diet. The author uses data analysis, definition, comparison, examples and other methods. It also provides a demonstration of the use of conjunctions, which provides important information reference for students to complete the next collaborative task, writing skills, vivid language materials and expressions.1. Teach Ss to learn and skillfully use the new words learned from the text.2. Develop students’ ability to understand, extract and summarize information.3. Guide students to understand the theme of healthy diet and reflect on their own eating habits.4. To guide students to analyze and understand the reading discourse from the aspects of theme content, writing structure, language expression, etc., 5. Enable Ss to write in combination with relevant topics and opinions, and to talk about their eating habits.1. Guide students to analyze and understand the reading discourse from the aspects of theme content, writing structure, language expression, etc.2. Enable them to write in combination with relevant topics and opinions, and to talk about their eating habits.3. Guide the students to use the cohesive words correctly, strengthen the textual cohesion, and make the expression fluent and the thinking clear.Step1: Warming upbrainstorm some healthy eating habits.1.Eat slowly.2.Don’t eat too much fat or sugar.3.Eat healthy food.4.Have a balanced diet.Step2: Read the passage and then sum up the main idea of each paragraph.
新人教版高中英語(yǔ)選修2Unit 4 Reading for writing教學(xué)設(shè)計(jì)
假定你是英國(guó)的Jack，打算來(lái)中國(guó)旅行，請(qǐng)你給你的中國(guó)筆友李華寫一封信，要點(diǎn)如下：1．你的旅行計(jì)劃：北京→泰山→杭州；2．征求建議并詢問(wèn)他是否愿意充當(dāng)你的導(dǎo)游。注意：1.詞數(shù)80左右(開頭和結(jié)尾已給出，不計(jì)入總詞數(shù))；2．可以適當(dāng)增加細(xì)節(jié)，以使行文連貫。參考詞匯：故宮 the Forbidden City；泰山 Mount TaiDear Li Hua，I'm glad to tell you that 'm going to visit China.First，I am planning to visit Beijing，the capitalof China，where I am looking forward to enjoying the Great Wall，the Forbidden City and somebeautiful parks.Then I intend to go to visit Mount Tai in Shandong Province.I've heard that it is one ofthe most famous mountains in China and I can't wait to enjoy the amazing sunrise there.After that，I amalso going to Hangzhou.It is said that it is a beautiful modern city with breathtaking natural sights，among which the West Lake is a well- known tourist attraction.What do you think of my travel plan? Will you act as my guide? Hope to hear from you soon.
新人教版高中英語(yǔ)選修2Unit 4 Using langauge-Listening教學(xué)設(shè)計(jì)
The theme of the listening section is " talking about scenery and culture along a journey."The part is designed to further lead the students to understand Canadian natural geography and social environment, and integrated into the cultural contrast by mentioning the long train journey from Beijing to Moscow routes. On this basis, the part activates students related travel experience, lets the student serial dialogue, guides the student to explore further the pleasure and meaning of the long journey, and Chinese and foreign cultural comparison.The part also provides a framework for the continuation of the dialogue, which is designed to provide a framework for students to successfully complete their oral expressions, and to incorporate an important trading strategy to end the dialogue naturally.1. Help students to understand and master some common English idioms in the context, and experience the expression effect of English idioms.2. Guide the students to understand the identity of different people in the listening context, and finish the dialogue according to their own experience.3. Instruct the students to use appropriate language to express surprise and curiosity about space and place in the dialogue, and master the oral strategy of ending the dialogue naturally.1. Instruct students to grasp the key information and important details of the dialogue.2. Instruct students to conduct a similar talk on the relevant topic.
新人教版高中英語(yǔ)選修2Unit 5 Learning about Language教學(xué)設(shè)計(jì)
The purpose of this section of vocabulary exercises is to consolidate the key words in the first part of the reading text, let the students write the words according to the English definition, and focus on the detection of the meaning and spelling of the new words. The teaching design includes use English definition to explain words, which is conducive to improving students' interest in vocabulary learning, cultivating their sense of English language and thinking in English, and making students willing to use this method to better grasp the meaning of words, expand their vocabulary, and improve their ability of vocabulary application. Besides, the design offers more context including sentences and short passage for students to practice words flexibly.1. Guide students to understand and consolidate the meaning and usage of the vocabulary in the context, 2. Guide the students to use the unit topic vocabulary in a richer context3. Let the students sort out and accumulate the accumulated vocabulary, establishes the semantic connection between the vocabulary,4. Enable students to understand and master the vocabulary more effectivelyGuiding the Ss to use unit topic words and the sentence patterns in a richer context.Step1: Read the passage about chemical burns and fill in the blanks with the correct forms of the words in the box.
新人教版高中英語(yǔ)選修2Unit 5 Reading and thinking教學(xué)設(shè)計(jì)
The theme of this activity is to learn the first aid knowledge of burns. Burns is common in life, but there are some misunderstandings in manual treatment. This activity provides students with correct first aid methods, so as not to take them for granted in an emergency. This section guides students to analyze the causes of scald and help students avoid such things. From the perspective of text structure and collaborative features, the text is expository. Expository, with explanation as the main way of expression, transmits knowledge and information to readers by analyzing concepts and elaborating examples. This text arranges the information in logical order, clearly presents three parts of the content through the subtitle, accurately describes the causes, types, characteristics and first aid measures of burns, and some paragraphs use topic sentences to summarize the main idea, and the level is very clear.1. Guide students to understand the causes, types, characteristics and first aid methods of burns, through reading2. Enhance students’ ability to deal withburnss and their awareness of burns prevention3. Enable students to improve the ability to judge the types of texts accurately and to master the characteristics and writing techniques of expository texts.Guide students to understand the causes, types, characteristics and first aid methods of burns, through readingStep1: Lead in by discussing the related topic:1. What first-aid techniques do you know of ?CPR; mouth to mouth artificial respiration; the Heimlich Manoeuvre
XX學(xué)年第一學(xué)期第8周國(guó)旗下講話稿：運(yùn)動(dòng)與生命同在。青春與快樂(lè)永存
敬愛的老師們，親愛的同學(xué)們：大家好，我是來(lái)自九年四班的葉佳蜜，今天我要演講的主題是運(yùn)動(dòng)與生命同在。青春與快樂(lè)永存。無(wú)論是過(guò)去，現(xiàn)在，還是將來(lái)，健康一直是人們追求的永恒主題。生命在于運(yùn)動(dòng)，人生短短幾十年，雖不長(zhǎng)，但要承擔(dān)的責(zé)任卻很重，要做的事情卻很多。健康的身體是多少人可望而不可得的夢(mèng)想。健康的健康是正處于青春期的我們意氣風(fēng)發(fā)的保證。只有擁有健康的身體才能讓我們的青春迸發(fā)出無(wú)限的激情和色彩。體育運(yùn)動(dòng)，多么驕傲，它讓生命之樹常青。生命給予運(yùn)動(dòng)以真實(shí)意義。每一細(xì)胞的組合，每一神經(jīng)的連動(dòng)，每一骨骼的存在，都穿起了運(yùn)動(dòng)的全部。生命，多么可貴，他讓運(yùn)動(dòng)的高峰迭起，生命，多么值得珍惜，它讓運(yùn)動(dòng)之火絢麗多姿。生命創(chuàng)造了運(yùn)動(dòng)，運(yùn)動(dòng)使青春快樂(lè)?？梢哉f(shuō)運(yùn)動(dòng)是非常重要的，自我校開創(chuàng)以來(lái)就非常注重體育運(yùn)動(dòng)。如自行車，柔道，還有最新的足球，小到日常的跑操，大道國(guó)家級(jí)的比賽，等等等等。
幼兒園中班數(shù)學(xué)教案：數(shù)字—我們的好朋友
2、從周圍生活中發(fā)現(xiàn)多種有趣的數(shù)字，初步了解數(shù)字在生活中的實(shí)際意義。 活動(dòng)準(zhǔn)備： 1、幼兒收集的有數(shù)字的物品； 2、電腦課件（打電話的情景） 3、英語(yǔ)兒歌 活動(dòng)過(guò)程： 一、英語(yǔ)兒歌引出?！ ?提問(wèn)：說(shuō)說(shuō)這首兒歌里有哪些數(shù)字？ 二、介紹生活中有數(shù)字的物品?！ ?你收集的材料上有哪些數(shù)字，它們有什么作用？ （在此進(jìn)行提升幼兒對(duì)數(shù)字的認(rèn)識(shí)，如：食品袋上的數(shù)字代表生產(chǎn)日期、保質(zhì)期；藥瓶上不僅有保質(zhì)期，而且還有劑量等。我們生活中處處有數(shù)字，數(shù)字用處很大。它可以表示順序、日期、時(shí)間等。如果沒(méi)有數(shù)字，生活就會(huì)變得亂糟糟，甚至還會(huì)出事故呢?。?。
幼兒園中班數(shù)學(xué)教案：5以內(nèi)的相鄰數(shù)
活動(dòng)準(zhǔn)備： 1、森林背景圖，6張蘑菇房子圖片?！ ?2、1－6的大點(diǎn)卡和數(shù)卡一套?！ ?3、小猴、小兔頭飾各一個(gè)和老虎的圖片一張 4、幼兒數(shù)學(xué)操作板1個(gè)/人，1－6的點(diǎn)卡一套/人?！ ?5、標(biāo)有1—6的數(shù)字卡片，每個(gè)小朋友一張 6、故事《住賓館》?！ 』顒?dòng)過(guò)程： 一、開始部分：初步理解“鄰居”關(guān)系。 1、拍手游戲：“嘿嘿，ⅹⅹⅹ（小朋友名），我問(wèn)你，你的朋友在哪里？”“嘿嘿嘿，在這里！”（被問(wèn)的小朋友舉起旁邊小朋友的手。） 2、我們每個(gè)小朋友都有自己午休的小床，請(qǐng)你說(shuō)一說(shuō)自己的鄰居都有誰(shuí)，讓幼兒理解什么是鄰居。
中班數(shù)學(xué)教案：6以內(nèi)的物體按數(shù)量歸類
2、繼續(xù)學(xué)習(xí)正確目測(cè)6以內(nèi)的數(shù)群。 3、樂(lè)意主動(dòng)的講述自己的操作過(guò)程和結(jié)果?！ 』顒?dòng)準(zhǔn)備： 1、教具：分類底版，6以內(nèi)的實(shí)物卡片，相應(yīng)數(shù)量的數(shù)卡 2、學(xué)具：超市售貨員（分類底版，6以內(nèi)的各種實(shí)物卡片，相應(yīng)數(shù)（點(diǎn)）卡等），給一樣多的發(fā)花（不同排列形式的實(shí)物操作卡，雪花片），一樣多的放一起（6以內(nèi)不同排列形式的實(shí)物卡片） 活動(dòng)過(guò)程： 1、游戲?qū)?，了解游戲玩法? ?。?）出示分層式分類底版，各種球類實(shí)物卡。 教師：超市里有許多的球，讓我們看看有哪些球呢？它們各是幾個(gè)？你是怎么看出來(lái)的？引導(dǎo)幼兒用目測(cè)的方法數(shù)數(shù)，并能說(shuō)一說(shuō)自己數(shù)的方法。 ?。?）師幼共同討論整理“分層貨架”的規(guī)則：一樣多的球放在一起
中班數(shù)學(xué)教案：破譯密碼——感知數(shù)字5
教學(xué)目標(biāo)：1、通過(guò)游戲活動(dòng)，初步理解5的概念，認(rèn)識(shí)數(shù)字5。2、初步感受用不同方法來(lái)數(shù)數(shù)，并能按照一定的順序來(lái)排列數(shù)。3、激發(fā)幼兒學(xué)習(xí)數(shù)學(xué)的興趣，體驗(yàn)成功的喜悅，培養(yǎng)合作的意識(shí)。教學(xué)重點(diǎn)：通過(guò)游戲活動(dòng)，初步理解5的概念，認(rèn)識(shí)數(shù)字5。教學(xué)難點(diǎn)：初步理解5的概念。教學(xué)準(zhǔn)備：1、 自制保險(xiǎn)箱一個(gè)，神奇的盒子3個(gè)。2、 在信封的正反兩面分別貼有圖案和圓點(diǎn)個(gè)數(shù)一致的和不一致的各若干個(gè)，5個(gè)信封當(dāng)中裝有數(shù)字1、2、3、4、5，其他都是小小的數(shù)字5。3、 若干個(gè)小籮筐和一個(gè)大籮筐，若干糖果。4、 機(jī)器貓胸飾一個(gè)，《機(jī)器貓》的主題曲。教學(xué)過(guò)程：一、創(chuàng)設(shè)情境，導(dǎo)入新課。師：“小朋友們，你們看，這是誰(shuí)呀？（出示機(jī)器貓胸飾貼在黑板上）原來(lái)是機(jī)器貓小叮當(dāng)。今天它給我們小朋友出了個(gè)難題，這兒有個(gè)漂亮的保險(xiǎn)箱，里面裝著許多好東西，它讓我們來(lái)想辦法打開這個(gè)保險(xiǎn)箱，可這個(gè)保險(xiǎn)箱需要用密碼打開，而密碼藏在了這三個(gè)神奇的盒子里?！保ǔ鍪鞠渥优c三個(gè)神奇的盒子）
點(diǎn)到直線的距離公式教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
4.已知△ABC三個(gè)頂點(diǎn)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(diǎn)式得直線BC的方程為 ＝ ，即x－2y＋3＝0，由兩點(diǎn)間距離公式得|BC|＝ ，點(diǎn)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(guò)點(diǎn)P(0,2),且A(1,1),B(-3,1)兩點(diǎn)到直線l的距離相等,求直線l的方程.解:(方法一)∵點(diǎn)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(diǎn)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(guò)線段AB的中點(diǎn)時(shí),A,B兩點(diǎn)到直線l的距離相等.∵AB的中點(diǎn)是(-1,1),又直線l過(guò)點(diǎn)P(0,2),∴直線l的方程是x-y+2=0.當(dāng)直線l∥AB時(shí),A,B兩點(diǎn)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.
兩點(diǎn)間的距離公式教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
一、情境導(dǎo)學(xué)在一條筆直的公路同側(cè)有兩個(gè)大型小區(qū),現(xiàn)在計(jì)劃在公路上某處建一個(gè)公交站點(diǎn)C,以方便居住在兩個(gè)小區(qū)住戶的出行.如何選址能使站點(diǎn)到兩個(gè)小區(qū)的距離之和最小?二、探究新知問(wèn)題1.在數(shù)軸上已知兩點(diǎn)A、B，如何求A、B兩點(diǎn)間的距離？提示：|AB|＝|xA－xB|.問(wèn)題2：在平面直角坐標(biāo)系中能否利用數(shù)軸上兩點(diǎn)間的距離求出任意兩點(diǎn)間距離？探究.當(dāng)x1≠x2，y1≠y2時(shí)，|P1P2|＝？請(qǐng)簡(jiǎn)單說(shuō)明理由．提示：可以，構(gòu)造直角三角形利用勾股定理求解．答案：如圖，在Rt △P1QP2中，|P1P2|2＝|P1Q|2＋|QP2|2，所以|P1P2|＝?x2－x1?2＋?y2－y1?2.即兩點(diǎn)P1(x1，y1)，P2(x2，y2)間的距離|P1P2|＝?x2－x1?2＋?y2－y1?2.你還能用其它方法證明這個(gè)公式嗎？2．兩點(diǎn)間距離公式的理解(1)此公式與兩點(diǎn)的先后順序無(wú)關(guān)，也就是說(shuō)公式也可寫成|P1P2|＝?x2－x1?2＋?y2－y1?2.(2)當(dāng)直線P1P2平行于x軸時(shí)，|P1P2|＝|x2－x1|.當(dāng)直線P1P2平行于y軸時(shí)，|P1P2|＝|y2－y1|.
兩條平行線間的距離教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
一、情境導(dǎo)學(xué)前面我們已經(jīng)得到了兩點(diǎn)間的距離公式，點(diǎn)到直線的距離公式，關(guān)于平面上的距離問(wèn)題，兩條直線間的距離也是值得研究的。思考1：立定跳遠(yuǎn)測(cè)量的什么距離？A.兩平行線的距離 B.點(diǎn)到直線的距離 C. 點(diǎn)到點(diǎn)的距離二、探究新知思考2：已知兩條平行直線l_1,l_2的方程，如何求l_1 〖與l〗_2間的距離？根據(jù)兩條平行直線間距離的含義，在直線l_1上取任一點(diǎn)P（x_0,y_0 ），,點(diǎn)P（x_0,y_0 ）到直線l_2的距離就是直線l_1與直線l_2間的距離，這樣求兩條平行線間的距離就轉(zhuǎn)化為求點(diǎn)到直線的距離。兩條平行直線間的距離1. 定義：夾在兩平行線間的__________的長(zhǎng).公垂線段2. 圖示： 3. 求法：轉(zhuǎn)化為點(diǎn)到直線的距離.1．原點(diǎn)到直線x＋2y－5＝0的距離是( )A．2 B．3 C．2 D．5D [d＝|－5|12＋22＝5.選D.]
兩直線的交點(diǎn)坐標(biāo)教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
1.直線2x+y+8=0和直線x+y-1=0的交點(diǎn)坐標(biāo)是( )A.(-9,-10) B.(-9,10) C.(9,10) D.(9,-10)解析:解方程組{■(2x+y+8=0"," @x+y"-" 1=0"," )┤得{■(x="-" 9"," @y=10"," )┤即交點(diǎn)坐標(biāo)是(-9,10).答案:B 2.直線2x+3y-k=0和直線x-ky+12=0的交點(diǎn)在x軸上,則k的值為( )A.-24 B.24 C.6 D.± 6解析:∵直線2x+3y-k=0和直線x-ky+12=0的交點(diǎn)在x軸上,可設(shè)交點(diǎn)坐標(biāo)為(a,0),∴{■(2a"-" k=0"," @a+12=0"," )┤解得{■(a="-" 12"," @k="-" 24"," )┤故選A.答案:A 3.已知直線l1:ax+y-6=0與l2:x+(a-2)y+a-1=0相交于點(diǎn)P,若l1⊥l2,則點(diǎn)P的坐標(biāo)為 . 解析:∵直線l1:ax+y-6=0與l2:x+(a-2)y+a-1=0相交于點(diǎn)P,且l1⊥l2,∴a×1+1×(a-2)=0,解得a=1,聯(lián)立方程{■(x+y"-" 6=0"," @x"-" y=0"," )┤易得x=3,y=3,∴點(diǎn)P的坐標(biāo)為(3,3).答案:(3,3) 4.求證:不論m為何值,直線(m-1)x+(2m-1)y=m-5都通過(guò)一定點(diǎn). 證明:將原方程按m的降冪排列,整理得(x+2y-1)m-(x+y-5)=0,此式對(duì)于m的任意實(shí)數(shù)值都成立,根據(jù)恒等式的要求,m的一次項(xiàng)系數(shù)與常數(shù)項(xiàng)均等于零,故有{■(x+2y"-" 1=0"," @x+y"-" 5=0"," )┤解得{■(x=9"," @y="-" 4"." )┤
人教版高中數(shù)學(xué)選擇性必修二變化率問(wèn)題教學(xué)設(shè)計(jì)
導(dǎo)語(yǔ)在必修第一冊(cè)中，我們研究了函數(shù)的單調(diào)性，并利用函數(shù)單調(diào)性等知識(shí)，定性的研究了一次函數(shù)、指數(shù)函數(shù)、對(duì)數(shù)函數(shù)增長(zhǎng)速度的差異，知道“對(duì)數(shù)增長(zhǎng)” 是越來(lái)越慢的，“指數(shù)爆炸” 比“直線上升” 快得多，進(jìn)一步的能否精確定量的刻畫變化速度的快慢呢，下面我們就來(lái)研究這個(gè)問(wèn)題。新知探究問(wèn)題1 高臺(tái)跳水運(yùn)動(dòng)員的速度高臺(tái)跳水運(yùn)動(dòng)中，運(yùn)動(dòng)員在運(yùn)動(dòng)過(guò)程中的重心相對(duì)于水面的高度h(單位：m)與起跳后的時(shí)間t(單位：s)存在函數(shù)關(guān)系h(t)＝－4.9t2＋4.8t＋11.如何描述用運(yùn)動(dòng)員從起跳到入水的過(guò)程中運(yùn)動(dòng)的快慢程度呢？直覺(jué)告訴我們，運(yùn)動(dòng)員從起跳到入水的過(guò)程中，在上升階段運(yùn)動(dòng)的越來(lái)越慢，在下降階段運(yùn)動(dòng)的越來(lái)越快，我們可以把整個(gè)運(yùn)動(dòng)時(shí)間段分成許多小段，用運(yùn)動(dòng)員在每段時(shí)間內(nèi)的平均速度v ?近似的描述它的運(yùn)動(dòng)狀態(tài)。
圓的標(biāo)準(zhǔn)方程教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
(1)幾何法它是利用圖形的幾何性質(zhì),如圓的性質(zhì)等,直接求出圓的圓心和半徑,代入圓的標(biāo)準(zhǔn)方程,從而得到圓的標(biāo)準(zhǔn)方程.(2)待定系數(shù)法由三個(gè)獨(dú)立條件得到三個(gè)方程,解方程組以得到圓的標(biāo)準(zhǔn)方程中三個(gè)參數(shù),從而確定圓的標(biāo)準(zhǔn)方程.它是求圓的方程最常用的方法,一般步驟是:①設(shè)——設(shè)所求圓的方程為(x-a)2+(y-b)2=r2;②列——由已知條件,建立關(guān)于a,b,r的方程組;③解——解方程組,求出a,b,r;④代——將a,b,r代入所設(shè)方程,得所求圓的方程.跟蹤訓(xùn)練1．已知△ABC的三個(gè)頂點(diǎn)坐標(biāo)分別為A(0,5)，B(1，－2)，C(－3，－4)，求該三角形的外接圓的方程．[解] 法一：設(shè)所求圓的標(biāo)準(zhǔn)方程為(x－a)2＋(y－b)2＝r2.因?yàn)锳(0,5)，B(1,－2)，C(－3,－4)都在圓上，所以它們的坐標(biāo)都滿足圓的標(biāo)準(zhǔn)方程，于是有?0－a?2＋?5－b?2＝r2，?1－a?2＋?－2－b?2＝r2，?－3－a?2＋?－4－b?2＝r2.解得a＝－3，b＝1，r＝5.故所求圓的標(biāo)準(zhǔn)方程是(x＋3)2＋(y－1)2＝25.
圓的一般方程教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
情境導(dǎo)學(xué)前面我們已討論了圓的標(biāo)準(zhǔn)方程為(x-a)2+(y-b)2=r2,現(xiàn)將其展開可得：x2+y2-2ax-2bx+a2+b2-r2=0.可見,任何一個(gè)圓的方程都可以變形x2+y2+Dx+Ey+F=0的形式.請(qǐng)大家思考一下,形如x2+y2+Dx+Ey+F=0的方程表示的曲線是不是圓?下面我們來(lái)探討這一方面的問(wèn)題.探究新知例如,對(duì)于方程x^2+y^2-2x-4y+6=0,對(duì)其進(jìn)行配方，得〖(x-1)〗^2+(〖y-2)〗^2=-1,因?yàn)槿我庖稽c(diǎn)的坐標(biāo) (x,y) 都不滿足這個(gè)方程，所以這個(gè)方程不表示任何圖形，所以形如x2+y2+Dx+Ey+F=0的方程不一定能通過(guò)恒等變換為圓的標(biāo)準(zhǔn)方程，這表明形如x2+y2+Dx+Ey+F=0的方程不一定是圓的方程.一、圓的一般方程（1）當(dāng)D2+E2-4F>0時(shí),方程x2+y2+Dx+Ey+F=0表示以(-D/2,-E/2)為圓心,1/2 √(D^2+E^2 "-" 4F)為半徑的圓,將方程x2+y2+Dx+Ey+F=0，配方可得〖(x+D/2)〗^2+(〖y+E/2)〗^2=(D^2+E^2-4F)/4（2）當(dāng)D2+E2-4F=0時(shí),方程x2+y2+Dx+Ey+F=0，表示一個(gè)點(diǎn)(-D/2,-E/2)（3）當(dāng)D2+E2-4F0);
人教版高中數(shù)學(xué)選修3離散型隨機(jī)變量及其分布列(1)教學(xué)設(shè)計(jì)
4.寫出下列隨機(jī)變量可能取的值，并說(shuō)明隨機(jī)變量所取的值表示的隨機(jī)試驗(yàn)的結(jié)果．(1)一個(gè)袋中裝有8個(gè)紅球，3個(gè)白球，從中任取5個(gè)球，其中所含白球的個(gè)數(shù)為X.(2)一個(gè)袋中有5個(gè)同樣大小的黑球，編號(hào)為1,2,3,4,5，從中任取3個(gè)球，取出的球的最大號(hào)碼記為X.(3). 在本例(1)條件下，規(guī)定取出一個(gè)紅球贏2元，而每取出一個(gè)白球輸1元，以ξ表示贏得的錢數(shù)，結(jié)果如何？[解] (1)X可取0,1,2,3.X＝0表示取5個(gè)球全是紅球；X＝1表示取1個(gè)白球，4個(gè)紅球；X＝2表示取2個(gè)白球，3個(gè)紅球；X＝3表示取3個(gè)白球，2個(gè)紅球．(2)X可取3,4,5.X＝3表示取出的球編號(hào)為1,2,3；X＝4表示取出的球編號(hào)為1,2,4；1,3,4或2,3,4.X＝5表示取出的球編號(hào)為1,2,5；1,3,5；1,4,5；2,3,5；2,4,5或3,4,5.(3) ξ＝10表示取5個(gè)球全是紅球；ξ＝7表示取1個(gè)白球，4個(gè)紅球；ξ＝4表示取2個(gè)白球，3個(gè)紅球；ξ＝1表示取3個(gè)白球，2個(gè)紅球．
直線的點(diǎn)斜式方程教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
【答案】B [由直線方程知直線斜率為3，令x＝0可得在y軸上的截距為y＝－3.故選B.]3．已知直線l1過(guò)點(diǎn)P(2,1)且與直線l2：y＝x＋1垂直，則l1的點(diǎn)斜式方程為________．【答案】y－1＝－(x－2) [直線l2的斜率k2＝1，故l1的斜率為－1，所以l1的點(diǎn)斜式方程為y－1＝－(x－2)．]4．已知兩條直線y＝ax－2和y＝(2－a)x＋1互相平行，則a＝________. 【答案】1 [由題意得a＝2－a，解得a＝1.]5.無(wú)論k取何值,直線y-2=k(x+1)所過(guò)的定點(diǎn)是 . 【答案】(-1,2)6．直線l經(jīng)過(guò)點(diǎn)P(3,4)，它的傾斜角是直線y＝3x＋3的傾斜角的2倍，求直線l的點(diǎn)斜式方程．【答案】直線y＝3x＋3的斜率k＝3，則其傾斜角α＝60°，所以直線l的傾斜角為120°.以直線l的斜率為k′＝tan 120°＝－3.所以直線l的點(diǎn)斜式方程為y－4＝－3(x－3)．