-
人教版高中歷史必修2第一次工業(yè)革命說課稿2篇
3、工業(yè)革命引起社會關(guān)系變化——形成兩大對立的工業(yè)資產(chǎn)階級和無產(chǎn)階級工業(yè)資產(chǎn)階級和工業(yè)無產(chǎn)階級成為社會的兩大階級。工業(yè)資產(chǎn)階級獲得更多的政治權(quán)利，各國通過改革，鞏固了資產(chǎn)階級的統(tǒng)治。 4、工業(yè)革命推動資產(chǎn)階級調(diào)整內(nèi)外政策——自由主義與殖民擴(kuò)張對內(nèi)，希望進(jìn)一步擺脫封建束縛，要求自由經(jīng)營、自由競爭和自由貿(mào)易。重商主義被自由放任政策所取代。對外，加快了殖民擴(kuò)張和殖民掠奪的步伐。三、世界市場的基本形成1、原因條件（1）工業(yè)革命的展開使世界貿(mào)易的范圍和規(guī)模迅速擴(kuò)大1840年前后，英國的大機(jī)器工業(yè)基本上取代了工場手工業(yè)，率先完成了工業(yè)革命，成為世界上第一個工業(yè)國家。之后，法國和美國等國也相繼完成工業(yè)革命。隨著工業(yè)革命的展開，資產(chǎn)階級竭力在全世界拓展市場，搶占原料產(chǎn)地，使世界貿(mào)易的范圍和規(guī)模迅速擴(kuò)大。
新人教版高中英語必修3Unit 1 Festivals and Celebrations教學(xué)設(shè)計(jì)二
1. Ss look at the picture and scan the passage to understand the main idea while teacher is giving the following questions to inspire Ss to think.*Where are those people?*What are they doing?*Why are they so excited?2. Ss complete the passage with the appropriate -ing form. Then discuss and check the answers with class.Answers: boring, interesting, taking, exciting, amazing3. The teacher raises questions for the students to discuss and encourages them to express their opinions.*Do you like La Tomatina? Why or why not?4. Each group representative reports the discussion result, the teacher gives feedback and the evaluation.Step 6 PracticeActivity 41. Ss complete the Ex 2 in Using structures.2. Check the answers after finishing the exercises.①The dragon boat races are the most exciting part of the Dragon Boat Festival.② The children were excited to go Easter egg hunting.③What an amazing performance! This is the best music festival I have ever been to.④We were amazed by her funny-looking hat.⑤His inspiring speech at the conference won the admiration/ favour of the audience.⑥This is a challenging game to test your memory and observation capabilities. 3. T asks Ss to finish Ex 3 and 4 in Using structures by themselves, then check the answers with class.Step 6 Homework1. Understand and master the functions and usage of the -ing form;2. Finish the other exercises in Using structures.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握動詞-ing形式作定語和表語的功能和意義；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否在理解文段內(nèi)容的基礎(chǔ)上，根據(jù)上下文語境和表達(dá)邏輯，能正確運(yùn)用動詞-ing形式描述節(jié)日慶典。3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否歸納和積累用于表達(dá)情緒的相關(guān)詞匯。
新人教版高中英語必修3Unit 2 Morals and Virtues教學(xué)設(shè)計(jì)二
Activity 41. Students complete the task of activity 4, then teachers and students check the answers. 2. The teacher organized the students to work together and asked them to use the tables and mind maps sorted out before to retold the important choices in Lin Qiaozhi's life and their resultsStep 5 Language points1. The teacher asks the students to read the text carefully, find out the core words and long and difficult sentences in the text and draw lines, understand the use of vocabulary, and analyze the structure of long and difficult sentences. 2. The teacher explains and summarizes the usage of core vocabulary and asks the students to take notes. 3. The teacher analyzes and explains the long and difficult sentences that the students don't understand, so that the students can understand them better. Step 6 Homework1. Read the text again, in-depth understanding of the text; 2. Master the use of core vocabulary and understand the long and difficult sentences. 3. Complete relevant exercises in the guide plan. 1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握閱讀文本中的新詞匯的意義與用法；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否結(jié)合文本特點(diǎn)總結(jié)林巧稚的人生原則和人格品質(zhì)特征；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否針對人生抉擇發(fā)表自己的看法；能否全面地、客觀地、理性地看待問題，進(jìn)而對道德和人性有更加深入的思考和理解。
新人教版高中英語必修3Unit 2 Morals and Virtues教學(xué)設(shè)計(jì)三
The joke set her crying.這個玩笑使她哭起來。Step 5 ReadingActivity 31. Students read the small text in activity 3. The teacher provides several small questions to check whether students understand the content of the text and the ideographic function of the -ing form in the text.*Where are those people?*Why did Dr Bethune come to China?*How did he help the Chinese people during the war?*What did Chairman Mao Zedong say about him?2. Ss try to rewrite some sentences using the -ing form. Then check the answers. When checking the answers, the teacher can ask different students to read the rewritten sentences and give comments.Answers:1. he became very interested in medicine, deciding to become a doctor.2. …after hearing that many people were dying in the war.3. Helping to organise hospitals, he taught doctors and nurses, and showed people how to give first aid./ He helped to organise hospitals, teaching doctors and nurses, and showing people how to give first aid.4. …praising Dr Bethune as a hero to be remembered in China.Step 6 PracticeActivity 4Students complete grammar activities 2 and 3 on page 69 of the workbook.Step 6 Homework1. Understand and master the functions and usage of the -ing form;2. Finish the other exercises in Using structures.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握動詞-ing形式作賓語補(bǔ)足語語和狀語語的功能和意義；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否正確使用動詞-ing形式描述人物的行為、動作及其經(jīng)歷；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否獨(dú)立完成練習(xí)冊和導(dǎo)學(xué)案中的相關(guān)練習(xí)。
新人教版高中英語必修3Unit 2 Morals and virtues教學(xué)設(shè)計(jì)一
(2) students are divided into groups according to the requirements of activity 3. Each student shares a story of personal experience or hearing-witnessing kindness, and then selects the most touching story in the group and shares it with the whole class. Before the students share the story, the teacher can instruct them to use the words and sentence patterns in the box to express. For example, the words in the box can be classified:Time order: first of all, then, after that, later, finally logical relationship :so, however, although, butTeachers can also appropriately add some transitional language to enrich students' expression:Afterwards, afterwards, at last, in the end, eventuallySpatial order: next to, far from, on the left, in front ofOtherwise, nevertheless, as a result, therefore, furthermore, in addition, as well asSummary: in a word, in short, on the whole, to sum up, in briefStep 8 Homework1. Understand the definition of "moral dilemma" and establish a correct moral view;2. Accumulate vocabulary about attitudes and emotions in listening texts and use them to express your own views;3. Complete relevant exercises in the guide plan.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否理解理解“道德困境”的定義；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否通過說話人所表達(dá)的內(nèi)容、說話的語氣、語調(diào)等來判斷其態(tài)度和情緒；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否針對具體的道德困境發(fā)表自己的看法和見解，能否掌握聽力理訓(xùn)練中的聽力策略。
新人教版高中英語必修3Unit 3 Diverse Cultures教學(xué)設(shè)計(jì)一
Activity 81.Grasp the main idea of the listening.Listen to the tape and answer the following questions:Who are the two speakers in the listening? What is their relationship?What is the main idea of the first part of the listening? How about the second part?2.Complete the passage.Ask the students to quickly review the summaries of the two listening materials in activity 2. Then play the recording for the second time.Ask them to complete the passage and fill in the blanks.3.Play the recording again and ask the students to use the structure diagram to comb the information structure in the listening.(While listening, take notes. Capture key information quickly and accurately.)Step 8 Talking Activity 91.Focus on the listening text.Listen to the students and listen to the tape. Let them understand the attitudes of Wu Yue and Justin in the conversation.How does Wu Yue feel about Chinese minority cultures?What does Justin think of the Miao and Dong cultures?How do you know that?2.learn functional items that express concerns.Ask students to focus on the expressions listed in activity. 3.And try to analyze the meaning they convey, including praise (Super!).Agree (Exactly!)"(You're kidding.!)Tell me more about it. Tell me more about it.For example, "Yeah Sure." "Definitely!" "Certainly!" "No kidding!" "No wonder!" and so on.4.Ask the students to have conversations in small groups, acting as Jsim and his friends.Justin shares his travels in Guizhou with friends and his thoughts;Justin's friends should give appropriate feedback, express their interest in relevant information, and ask for information when necessary.In order to enrich the dialogue, teachers can expand and supplement the introduction of Miao, dong, Lusheng and Dong Dage.After the group practice, the teacher can choose several groups of students to show, and let the rest of the students listen carefully, after listening to the best performance of the group, and give at least two reasons.
新人教版高中英語必修3Unit 1 Festivals and Celebrations教學(xué)設(shè)計(jì)一
本板塊的活動主題是“談?wù)摴?jié)日活動”（Talk about festival activities），主要是從貼近學(xué)生日常生活的角度來切入“節(jié)日”主題。學(xué)生會聽到發(fā)生在三個國家不同節(jié)日場景下的簡短對話，對話中的人們正在參與或?qū)⒁H歷不同的慶祝活動。隨著全球化的進(jìn)程加速，國際交流日益頻繁，無論是國人走出國門還是外國友人訪問中國，都已成為司空見慣的事情。因此，該板塊所選取的三個典型節(jié)日場景都是屬于跨文化交際語境，不僅每組對話中的人物來自不同的文化背景，對話者的身份和關(guān)系也不盡相同。1. Master the new words related to holiday: the lantern, Carnival, costume, dress(sb)up, march, congratulation, congratulate, riddle, ceremony, samba, make - up, after all. 2. To understand the origin of major world festivals and the activities held to celebrate them and the significance of these activities;3. Improve listening comprehension and oral expression of the topic by listening and talking about traditional festivals around the world;4. Improve my understanding of the topic by watching pictures and videos about different traditional festivals around the world;5. Review the common assimilation phenomenon in English phonetics, can distinguish the assimilated phonemes in the natural language flow, and consciously use the assimilation skill in oral expression. Importance:1. Guide students to pay attention to the attitude of the speaker in the process of listening, and identify the relationship between the characters;2. Inspire students to use topic words to describe the festival activities based on their background knowledge. Difficulties:In the process of listening to the correct understanding of the speaker's attitude, accurately identify the relationship between the characters.
新人教版高中英語必修3Unit 1 Festivals and Celebrations教學(xué)設(shè)計(jì)三
*wide range of origins(= a great number of different origins, many kinds of origins)*It featured a parade and a great feast with music, dancing, and sports. (=A parade and a great feast with music, dancing, and sports were included as important parts of the Egyptian harvest festival.)*.. some traditions may fade away and others may be established.(= Some traditions may disappear gradually, while other new traditions may come into being.）Step 6 Practice(1) Listen and follow the tape.The teacher may remind the students to pay attention to the meaning and usage of the black words in the context, so as to prepare for the completion of the blanks in activity 5 and vocabulary exercises in the exercise book.(2) Students complete the text of activity 5 by themselves.The teacher needs to remind the students to fill in the blanks with the correct form of the vocabulary they have learned in the text.Students exchange their answers with their partners, and then teachers and students check their answers.(3)Finish the Ex in Activity 5 of students’ book.Step 7 Homework1. Read the text again, in-depth understanding of the text;2. Discuss the origin of festivals, the historical changes of related customs, the influence of commercial society on festivals and the connotation and essential meaning of festivals.3. Complete relevant exercises in the guide plan.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握閱讀文本中的新詞匯的意義與用法；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否結(jié)合文本特點(diǎn)快速而準(zhǔn)確地找到主題句；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否理清論說文的語篇結(jié)構(gòu)和文本邏輯，了解節(jié)日風(fēng)俗發(fā)展與變遷，感悟節(jié)日的內(nèi)涵與意義。
新人教版高中英語必修3Unit 3 Diverse Cultures教學(xué)設(shè)計(jì)三
The price is the same as(the price was)before the war.價(jià)格與戰(zhàn)前相同。(4)定語從句中的“關(guān)系代詞＋助動詞be”可以省略。The ticket(that/which was)booked by his sister has been sent to him.他妹妹訂的那張票已送到了他那里。Step 5 PracticeActivity 3(1) Guide students to complete the four activities in the Using Structures part of exercise book, in which activities 1 and 2 focus on ellipsis in dialogue answers, activity 3 focus on signs and headlines, two typical situations where ellipsis is used, and activity 4 focus on ellipsis in diary, an informal style.(2) Combine the examples in the above activities, ask students to summarize the omitted situations in groups, and make their own summary into a poster, and post it on the class wall after class to share with the class.(This step should give full play to the subjectivity of students, and teachers should encourage students to conclude different ellipsis phenomena according to their own understanding, they can conclude according to the different parts omitted in the sentence.)Step 6 Homework1. Understand and master the usages of ellipsis;2. Finish the other exercises in Using structures of Workbook.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握省略的用法；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否根據(jù)上下文語境或情景恢復(fù)句子中省略的成分，體會使用省略的效果；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否獨(dú)立完成練習(xí)冊和導(dǎo)學(xué)案中的相關(guān)練習(xí)。
新人教版高中英語必修3Unit 3 Diverse Cultures教學(xué)設(shè)計(jì)二
(2)Consolidate key vocabulary.Ask the students to complete the exercises of activity 6 by themselves. Then ask them to check the answers with their partners.(The first language:Damage of the 1906 San Francisco earthquake and fire.A second language: Yunnan - one of the most diverse provinces in China).Step 5 Language points1. The teacher asks the students to read the text carefully, find out the more words and long and difficult sentences in the text and draw lines, understand the use of vocabulary, and analyze the structure of long and difficult sentences.2. The teacher explains and summarizes the usage of core vocabulary and asks the students to take notes.3. The teacher analyzes and explains the long and difficult sentences that the students don't understand, so that the students can understand them better.Step 6 Homework1. Read the text again, in-depth understanding of the text;2. Master the use of core vocabulary and understand the long and difficult sentences.3. Complete relevant exercises in the guide plan.1、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握閱讀文本中的新詞匯的意義與用法；2、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否結(jié)合文本特點(diǎn)了解文章的結(jié)構(gòu)和作者的寫作邏輯；3、通過本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否了解舊金山的城市風(fēng)貌、文化特色，以及加利福尼亞州的歷史，體會多元文化對美國的影響。
高中語文人教版必修二《歸園田居》說課稿
一、說教材本節(jié)課選自于人教版語文必修二第二單元詩三首中的一首詩歌，它是陶淵明歸隱后的作品。寫的是田園之樂，實(shí)際表明的是作者不愿與世俗同流合污的心聲，甘愿守著自己的拙志回歸田園。學(xué)習(xí)該詩，有助于學(xué)生了解山水田園詩的特點(diǎn)，感受者作者不同流俗的高尚情操，同時可以培養(yǎng)學(xué)生初步的鑒賞古典詩歌的能力。
高中語文人教版必修三《動物游戲之謎》說課稿
科學(xué)是人類認(rèn)識世界的重要工具，閱讀科普說明文不僅可以啟迪心智，了解更多知識。而且更夠激發(fā)學(xué)生對科學(xué)的興趣。學(xué)習(xí)這些文章要注重學(xué)生科學(xué)精神的培養(yǎng)，關(guān)注科學(xué)探索的過程，感受科學(xué)家在科學(xué)探索中表現(xiàn)的人格魅力。我們知道一些科學(xué)家就是因?yàn)殚喿x了相關(guān)的科普文章才對某一學(xué)科產(chǎn)生興趣，從而走上成功之路的。我們在講解的時候可以跟學(xué)生列舉一些例子，讓學(xué)生認(rèn)識到一篇好的科普文章的重大意義。
人教A版高中數(shù)學(xué)必修二古典概型和概率的基本性質(zhì)教學(xué)設(shè)計(jì)
新知講授（一）——古典概型 對隨機(jī)事件發(fā)生可能性大小的度量（數(shù)值）稱為事件的概率。我們將具有以上兩個特征的試驗(yàn)稱為古典概型試驗(yàn)，其數(shù)學(xué)模型稱為古典概率模型，簡稱古典概型。即具有以下兩個特征：1、有限性：樣本空間的樣本點(diǎn)只有有限個；2、等可能性：每個樣本點(diǎn)發(fā)生的可能性相等。思考一：下面的隨機(jī)試驗(yàn)是不是古典概型？（1）一個班級中有18名男生、22名女生。采用抽簽的方式，從中隨機(jī)選擇一名學(xué)生，事件A=“抽到男生”（2）拋擲一枚質(zhì)地均勻的硬幣3次，事件B=“恰好一次正面朝上”（1）班級中共有40名學(xué)生，從中選擇一名學(xué)生，即樣本點(diǎn)是有限個；因?yàn)槭请S機(jī)選取的，所以選到每個學(xué)生的可能性都相等，因此這是一個古典概型。
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
4.已知△ABC三個頂點(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過線段AB的中點(diǎn)時,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過點(diǎn)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(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
一、情境導(dǎo)學(xué)在一條筆直的公路同側(cè)有兩個大型小區(qū),現(xiàn)在計(jì)劃在公路上某處建一個公交站點(diǎn)C,以方便居住在兩個小區(qū)住戶的出行.如何選址能使站點(diǎn)到兩個小區(qū)的距離之和最小?二、探究新知問題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，|P1P2|＝？請簡單說明理由．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)的先后順序無關(guān)，也就是說公式也可寫成|P1P2|＝?x2－x1?2＋?y2－y1?2.(2)當(dāng)直線P1P2平行于x軸時，|P1P2|＝|x2－x1|.當(dāng)直線P1P2平行于y軸時，|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
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.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
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"." )┤
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
(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)法由三個獨(dú)立條件得到三個方程,解方程組以得到圓的標(biāo)準(zhǔn)方程中三個參數(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
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,任何一個圓的方程都可以變形x2+y2+Dx+Ey+F=0的形式.請大家思考一下,形如x2+y2+Dx+Ey+F=0的方程表示的曲線是不是圓?下面我們來探討這一方面的問題.探究新知例如,對于方程x^2+y^2-2x-4y+6=0,對其進(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) 都不滿足這個方程，所以這個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,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,方程x2+y2+Dx+Ey+F=0，表示一個點(diǎn)(-D/2,-E/2)（3）當(dāng)D2+E2-4F0);
圓與圓的位置關(guān)系教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊
1.兩圓x2+y2-1=0和x2+y2-4x+2y-4=0的位置關(guān)系是( )A.內(nèi)切 B.相交 C.外切 D.外離解析:圓x2+y2-1=0表示以O(shè)1(0,0)點(diǎn)為圓心,以R1=1為半徑的圓.圓x2+y2-4x+2y-4=0表示以O(shè)2(2,-1)點(diǎn)為圓心,以R2=3為半徑的圓.∵|O1O2|=√5,∴R2-R1<|O1O2|<R2+R1,∴圓x2+y2-1=0和圓x2+y2-4x+2y-4=0相交.答案:B2.圓C1:x2+y2-12x-2y-13=0和圓C2:x2+y2+12x+16y-25=0的公共弦所在的直線方程是 . 解析:兩圓的方程相減得公共弦所在的直線方程為4x+3y-2=0.答案:4x+3y-2=03.半徑為6的圓與x軸相切,且與圓x2+(y-3)2=1內(nèi)切,則此圓的方程為( )A.(x-4)2+(y-6)2=16 B.(x±4)2+(y-6)2=16C.(x-4)2+(y-6)2=36 D.(x±4)2+(y-6)2=36解析:設(shè)所求圓心坐標(biāo)為(a,b),則|b|=6.由題意,得a2+(b-3)2=(6-1)2=25.若b=6,則a=±4;若b=-6,則a無解.故所求圓方程為(x±4)2+(y-6)2=36.答案:D4.若圓C1:x2+y2=4與圓C2:x2+y2-2ax+a2-1=0內(nèi)切,則a等于 . 解析:圓C1的圓心C1(0,0),半徑r1=2.圓C2可化為(x-a)2+y2=1,即圓心C2(a,0),半徑r2=1,若兩圓內(nèi)切,需|C1C2|=√(a^2+0^2 )=2-1=1.解得a=±1. 答案:±1 5. 已知兩個圓C1:x2+y2=4,C2:x2+y2-2x-4y+4=0,直線l:x+2y=0,求經(jīng)過C1和C2的交點(diǎn)且和l相切的圓的方程.解:設(shè)所求圓的方程為x2+y2+4-2x-4y+λ(x2+y2-4)=0,即(1+λ)x2+(1+λ)y2-2x-4y+4(1-λ)=0.所以圓心為 1/(1+λ),2/(1+λ) ,半徑為1/2 √((("-" 2)/(1+λ)) ^2+(("-" 4)/(1+λ)) ^2 "-" 16((1"-" λ)/(1+λ))),即|1/(1+λ)+4/(1+λ)|/√5=1/2 √((4+16"-" 16"(" 1"-" λ^2 ")" )/("(" 1+λ")" ^2 )).解得λ=±1,舍去λ=-1,圓x2+y2=4顯然不符合題意,故所求圓的方程為x2+y2-x-2y=0.