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20以內(nèi)的不退位減法教案教學(xué)設(shè)計(jì)
教學(xué)目標(biāo)：1．引導(dǎo)幼兒參與學(xué)習(xí)活動(dòng)，經(jīng)歷十幾減幾計(jì)算方法的探索與算理的建構(gòu)過(guò)程。2．根據(jù) 11 至 20 各數(shù)的組成，掌握 20 以內(nèi)不進(jìn)位加法和不進(jìn)位減法的計(jì)算方法。教學(xué)重點(diǎn)：十幾減幾（不退位）的計(jì)算。教學(xué)過(guò)程：一、復(fù)習(xí)導(dǎo)入復(fù)習(xí)10以內(nèi)的數(shù)的組合，11～20各數(shù)的組成。1.碰球游戲?qū)耄瑥?fù)習(xí)10的分解組合2.老師分別出示數(shù)字卡片：14、17、12、11。幼兒說(shuō)數(shù)的組成。
中班美術(shù)手工活動(dòng)教學(xué)教案設(shè)計(jì)《小小插花瓶》
佛山石灣陶瓷發(fā)展歷史悠久，為了讓幼兒感受這張靚麗的歷史“名片”的魅力，了解石灣陶瓷栩栩如生的形象和一道道制作工序，在幼兒自己動(dòng)手制作的過(guò)程中掌握簡(jiǎn)單的制作方法，體驗(yàn)成功感并領(lǐng)略石灣陶瓷的藝術(shù)美。
《珍愛(ài)生命遠(yuǎn)離毒品》教學(xué)設(shè)計(jì)教案
教學(xué)目標(biāo)：1、使學(xué)生了解什么是毒品，毒品的種類，認(rèn)識(shí)吸毒行為，認(rèn)清毒品的危害性。2、通過(guò)圖文、吸毒而造成的悲慘事件，教育學(xué)生自覺(jué)遠(yuǎn)離毒品，提高拒毒防毒意識(shí)和能力。3、讓學(xué)生認(rèn)識(shí)吸毒成癮的途徑；認(rèn)識(shí)吸毒成癮的原因，如何預(yù)防。懂得“珍愛(ài)生命，拒絕毒品”，培養(yǎng)禁毒意識(shí)，遵紀(jì)守法，抵制毒品，增強(qiáng)與毒品違法犯罪作斗爭(zhēng)的自覺(jué)性。教學(xué)重點(diǎn)：知道什么是毒品，吸毒的危害，如何提高抵制毒品的能力。
新人教版高中英語(yǔ)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(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握動(dòng)詞-ing形式作定語(yǔ)和表語(yǔ)的功能和意義；2、通過(guò)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(yǔ)境和表達(dá)邏輯，能正確運(yùn)用動(dòng)詞-ing形式描述節(jié)日慶典。3、通過(guò)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(yǔ)必修3Unit 1 Festivals and Celebrations教學(xué)設(shè)計(jì)一
本板塊的活動(dòng)主題是“談?wù)摴?jié)日活動(dòng)”（Talk about festival activities），主要是從貼近學(xué)生日常生活的角度來(lái)切入“節(jié)日”主題。學(xué)生會(huì)聽(tīng)到發(fā)生在三個(gè)國(guó)家不同節(jié)日?qǐng)鼍跋碌暮?jiǎn)短對(duì)話，對(duì)話中的人們正在參與或?qū)⒁H歷不同的慶?；顒?dòng)。隨著全球化的進(jìn)程加速，國(guó)際交流日益頻繁，無(wú)論是國(guó)人走出國(guó)門(mén)還是外國(guó)友人訪問(wèn)中國(guó)，都已成為司空見(jiàn)慣的事情。因此，該板塊所選取的三個(gè)典型節(jié)日?qǐng)鼍岸际菍儆诳缥幕浑H語(yǔ)境，不僅每組對(duì)話中的人物來(lái)自不同的文化背景，對(duì)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(yǔ)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(guò)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(guò)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(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否針對(duì)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(wèn)題，進(jìn)而對(duì)道德和人性有更加深入的思考和理解。
新人教版高中英語(yǔ)必修3Unit 2 Morals and Virtues教學(xué)設(shè)計(jì)三
The joke set her crying.這個(gè)玩笑使她哭起來(lái)。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(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生是否理解和掌握動(dòng)詞-ing形式作賓語(yǔ)補(bǔ)足語(yǔ)語(yǔ)和狀語(yǔ)語(yǔ)的功能和意義；2、通過(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否正確使用動(dòng)詞-ing形式描述人物的行為、動(dòng)作及其經(jīng)歷；3、通過(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否獨(dú)立完成練習(xí)冊(cè)和導(dǎo)學(xué)案中的相關(guān)練習(xí)。
新人教版高中英語(yǔ)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(yǔ)從句中的“關(guān)系代詞＋助動(dòng)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(guò)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(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否根據(jù)上下文語(yǔ)境或情景恢復(fù)句子中省略的成分，體會(huì)使用省略的效果；3、通過(guò)本節(jié)內(nèi)容學(xué)習(xí)，學(xué)生能否獨(dú)立完成練習(xí)冊(cè)和導(dǎo)學(xué)案中的相關(guān)練習(xí)。
新人教版高中英語(yǔ)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(guò)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(guò)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(xiě)作邏輯；3、通過(guò)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(huì)多元文化對(duì)美國(guó)的影響。
新人教版高中英語(yǔ)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.
人教A版高中數(shù)學(xué)必修二有限樣本空間與隨機(jī)事件事件的關(guān)系和運(yùn)算教學(xué)設(shè)計(jì)
新知講授（一）——隨機(jī)試驗(yàn) 我們把對(duì)隨機(jī)現(xiàn)象的實(shí)現(xiàn)和對(duì)它的觀察稱為隨機(jī)試驗(yàn)，簡(jiǎn)稱試驗(yàn)，常用字母E表示。我們通常研究以下特點(diǎn)的隨機(jī)試驗(yàn)：（1）試驗(yàn)可以在相同條件下重復(fù)進(jìn)行；（2）試驗(yàn)的所有可能結(jié)果是明確可知的，并且不止一個(gè)；（3）每次試驗(yàn)總是恰好出現(xiàn)這些可能結(jié)果中的一個(gè)，但事先不確定出現(xiàn)哪個(gè)結(jié)果。新知講授（二）——樣本空間思考一：體育彩票搖獎(jiǎng)時(shí)，將10個(gè)質(zhì)地和大小完全相同、分別標(biāo)號(hào)0，1，2，...，9的球放入搖獎(jiǎng)器中，經(jīng)過(guò)充分?jǐn)嚢韬髶u出一個(gè)球，觀察這個(gè)球的號(hào)碼。這個(gè)隨機(jī)試驗(yàn)共有多少個(gè)可能結(jié)果？如何表示這些結(jié)果？根據(jù)球的號(hào)碼，共有10種可能結(jié)果。如果用m表示“搖出的球的號(hào)碼為m”這一結(jié)果，那么所有可能結(jié)果可用集合表示{0，1，2，3，4，5，6，7，8，9}.我們把隨機(jī)試驗(yàn)E的每個(gè)可能的基本結(jié)果稱為樣本點(diǎn)，全體樣本點(diǎn)的集合稱為試驗(yàn)E的樣本空間。
雙曲線的簡(jiǎn)單幾何性質(zhì)（1）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)
問(wèn)題導(dǎo)學(xué)類比橢圓幾何性質(zhì)的研究，你認(rèn)為應(yīng)該研究雙曲線x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，的哪些幾何性質(zhì)，如何研究這些性質(zhì)1、范圍利用雙曲線的方程求出它的范圍，由方程x^2/a^2 -y^2/b^2 =1可得x^2/a^2 =1+y^2/b^2 ≥1 于是，雙曲線上點(diǎn)的坐標(biāo)（ x ， y ）都適合不等式，x^2/a^2 ≥1，y∈R所以x≥a 或x≤-a; y∈R2、對(duì)稱性 x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，關(guān)于x軸、y軸和原點(diǎn)都是對(duì)稱。x軸、y軸是雙曲線的對(duì)稱軸，原點(diǎn)是對(duì)稱中心，又叫做雙曲線的中心。3、頂點(diǎn)（1）雙曲線與對(duì)稱軸的交點(diǎn)，叫做雙曲線的頂點(diǎn) .頂點(diǎn)是A_1 （-a,0）、A_2 （a,0），只有兩個(gè)。（2）如圖，線段A_1 A_2 叫做雙曲線的實(shí)軸，它的長(zhǎng)為2a,a叫做實(shí)半軸長(zhǎng)；線段B_1 B_2 叫做雙曲線的虛軸，它的長(zhǎng)為2b,b叫做雙曲線的虛半軸長(zhǎng)。（3）實(shí)軸與虛軸等長(zhǎng)的雙曲線叫等軸雙曲線4、漸近線（1）雙曲線x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，的漸近線方程為：y=±b/a x（2）利用漸近線可以較準(zhǔn)確的畫(huà)出雙曲線的草圖
拋物線的簡(jiǎn)單幾何性質(zhì)（1）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)
問(wèn)題導(dǎo)學(xué)類比用方程研究橢圓雙曲線幾何性質(zhì)的過(guò)程與方法，y2 = 2px (p＞0)你認(rèn)為應(yīng)研究拋物線的哪些幾何性質(zhì)，如何研究這些性質(zhì)？1. 范圍拋物線 y2 = 2px (p＞0) 在 y 軸的右側(cè)，開(kāi)口向右，這條拋物線上的任意一點(diǎn)M 的坐標(biāo) (x, y) 的橫坐標(biāo)滿足不等式 x ≥ 0；當(dāng)x 的值增大時(shí)，|y| 也增大，這說(shuō)明拋物線向右上方和右下方無(wú)限延伸．拋物線是無(wú)界曲線．2. 對(duì)稱性觀察圖象，不難發(fā)現(xiàn)，拋物線 y2 = 2px (p＞0)關(guān)于 x 軸對(duì)稱，我們把拋物線的對(duì)稱軸叫做拋物線的軸．拋物線只有一條對(duì)稱軸． 3. 頂點(diǎn)拋物線和它軸的交點(diǎn)叫做拋物線的頂點(diǎn).拋物線的頂點(diǎn)坐標(biāo)是坐標(biāo)原點(diǎn) (0, 0) ．4. 離心率拋物線上的點(diǎn)M 到焦點(diǎn)的距離和它到準(zhǔn)線的距離的比，叫做拋物線的離心率. 用 e 表示，e = 1．探究如果拋物線的標(biāo)準(zhǔn)方程是〖 y〗^2=-2px(p>0), ②〖 x〗^2=2py(p>0), ③〖 x〗^2=-2py(p>0), ④
拋物線的簡(jiǎn)單幾何性質(zhì)（2）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)
二、直線與拋物線的位置關(guān)系設(shè)直線l:y=kx+m,拋物線:y2=2px(p>0),將直線方程與拋物線方程聯(lián)立整理成關(guān)于x的方程k2x2+2(km-p)x+m2=0.(1)若k≠0,當(dāng)Δ>0時(shí),直線與拋物線相交,有兩個(gè)交點(diǎn);當(dāng)Δ=0時(shí),直線與拋物線相切,有一個(gè)切點(diǎn);當(dāng)Δ<0時(shí),直線與拋物線相離,沒(méi)有公共點(diǎn).(2)若k=0,直線與拋物線有一個(gè)交點(diǎn),此時(shí)直線平行于拋物線的對(duì)稱軸或與對(duì)稱軸重合.因此直線與拋物線有一個(gè)公共點(diǎn)是直線與拋物線相切的必要不充分條件.二、典例解析例5.過(guò)拋物線焦點(diǎn)F的直線交拋物線于A、B兩點(diǎn)，通過(guò)點(diǎn)A和拋物線頂點(diǎn)的直線交拋物線的準(zhǔn)線于點(diǎn)D，求證：直線DB平行于拋物線的對(duì)稱軸．【分析】設(shè)拋物線的標(biāo)準(zhǔn)方程為：y2＝2px（p＞0）．設(shè)A（x1，y1），B（x2，y2）．直線OA的方程為： ＝ ＝ ，可得yD＝ ．設(shè)直線AB的方程為：my＝x﹣ ，與拋物線的方程聯(lián)立化為y2﹣2pm﹣p2＝0，
拋物線及其標(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)
本節(jié)課選自《2019人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)》第二章《直線和圓的方程》，本節(jié)課主要學(xué)習(xí)拋物線及其標(biāo)準(zhǔn)方程在經(jīng)歷了橢圓和雙曲線的學(xué)習(xí)后再學(xué)習(xí)拋物線，是在學(xué)生原有認(rèn)知的基礎(chǔ)上從幾何與代數(shù)兩 個(gè)角度去認(rèn)識(shí)拋物線.教材在拋物線的定義這個(gè)內(nèi)容的安排上是：先從直觀上認(rèn)識(shí)拋物線，再?gòu)漠?huà)法中提煉出拋物線的幾何特征，由此抽象概括出拋物線的定義，最后是拋物線定義的簡(jiǎn)單應(yīng)用.這樣的安排不僅體現(xiàn)出《課程標(biāo)準(zhǔn)》中要求通過(guò)豐富的實(shí)例展開(kāi)教學(xué)的理念，而且符合學(xué)生從具體到抽象的認(rèn)知規(guī)律，有利于學(xué)生對(duì)概念的學(xué)習(xí)和理解.坐標(biāo)法的教學(xué)貫穿了整個(gè)“圓錐曲線方程”一章，是學(xué)生應(yīng)重點(diǎn)掌握的基本數(shù)學(xué)方法 運(yùn)動(dòng)變化和對(duì)立統(tǒng)一的思想觀點(diǎn)在這節(jié)知識(shí)中得到了突出體現(xiàn)，我們必須充分利用好這部分教材進(jìn)行教學(xué)
雙曲線的簡(jiǎn)單幾何性質(zhì)（2）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)
二、典例解析例4．如圖，雙曲線型冷卻塔的外形，是雙曲線的一部分，已知塔的總高度為137.5m，塔頂直徑為90m，塔的最小直徑(喉部直徑)為60m，喉部標(biāo)高112.5m，試建立適當(dāng)?shù)淖鴺?biāo)系，求出此雙曲線的標(biāo)準(zhǔn)方程（精確到1m）解:設(shè)雙曲線的標(biāo)準(zhǔn)方程為 ，如圖所示：為喉部直徑，故 ，故雙曲線方程為 .而 的橫坐標(biāo)為塔頂直徑的一半即 ，其縱坐標(biāo)為塔的總高度與喉部標(biāo)高的差即 ，故 ，故 ，所以 ，故雙曲線方程為 .例5．已知點(diǎn) 到定點(diǎn) 的距離和它到定直線l: 的距離的比是 ，則點(diǎn) 的軌跡方程為?解：設(shè)點(diǎn) ，由題知, ，即 .整理得： .請(qǐng)你將例5與橢圓一節(jié)中的例6比較，你有什么發(fā)現(xiàn)？例6、 過(guò)雙曲線 的右焦點(diǎn)F2,傾斜角為30度的直線交雙曲線于A,B兩點(diǎn),求|AB|.分析:求弦長(zhǎng)問(wèn)題有兩種方法:法一:如果交點(diǎn)坐標(biāo)易求,可直接用兩點(diǎn)間距離公式代入求弦長(zhǎng);法二:但有時(shí)為了簡(jiǎn)化計(jì)算,常設(shè)而不求,運(yùn)用韋達(dá)定理來(lái)處理.解：由雙曲線的方程得，兩焦點(diǎn)分別為F1(-3,0),F2(3,0).因?yàn)橹本€AB的傾斜角是30°，且直線經(jīng)過(guò)右焦點(diǎn)F2，所以，直線AB的方程為
雙曲線及其標(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)
∵在△EFP中,|EF|=2c,EF上的高為點(diǎn)P的縱坐標(biāo),∴S△EFP=4/3c2=12,∴c=3,即P點(diǎn)坐標(biāo)為(5,4).由兩點(diǎn)間的距離公式|PE|=√("(" 5+3")" ^2+4^2 )=4√5,|PF|=√("(" 5"-" 3")" ^2+4^2 )=2√5,∴a=√5.又b2=c2-a2=4,故所求雙曲線的方程為x^2/5-y^2/4=1.5.求適合下列條件的雙曲線的標(biāo)準(zhǔn)方程.(1)兩個(gè)焦點(diǎn)的坐標(biāo)分別是(-5,0),(5,0),雙曲線上的點(diǎn)與兩焦點(diǎn)的距離之差的絕對(duì)值等于8;(2)以橢圓x^2/8+y^2/5=1長(zhǎng)軸的端點(diǎn)為焦點(diǎn),且經(jīng)過(guò)點(diǎn)(3,√10);(3)a=b,經(jīng)過(guò)點(diǎn)(3,-1).解:(1)由雙曲線的定義知,2a=8,所以a=4,又知焦點(diǎn)在x軸上,且c=5,所以b2=c2-a2=25-16=9,所以雙曲線的標(biāo)準(zhǔn)方程為x^2/16-y^2/9=1.(2)由題意得,雙曲線的焦點(diǎn)在x軸上,且c=2√2.設(shè)雙曲線的標(biāo)準(zhǔn)方程為x^2/a^2 -y^2/b^2 =1(a>0,b>0),則有a2+b2=c2=8,9/a^2 -10/b^2 =1,解得a2=3,b2=5.故所求雙曲線的標(biāo)準(zhǔn)方程為x^2/3-y^2/5=1.(3)當(dāng)焦點(diǎn)在x軸上時(shí),可設(shè)雙曲線方程為x2-y2=a2,將點(diǎn)(3,-1)代入,得32-(-1)2=a2,所以a2=b2=8.因此,所求的雙曲線的標(biāo)準(zhǔn)方程為x^2/8-y^2/8=1.當(dāng)焦點(diǎn)在y軸上時(shí),可設(shè)雙曲線方程為y2-x2=a2,將點(diǎn)(3,-1)代入,得(-1)2-32=a2,a2=-8,不可能,所以焦點(diǎn)不可能在y軸上.綜上,所求雙曲線的標(biāo)準(zhǔn)方程為x^2/8-y^2/8=1.
橢圓的簡(jiǎn)單幾何性質(zhì)（1）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.判斷 (1)橢圓x^2/a^2 +y^2/b^2 =1(a>b>0)的長(zhǎng)軸長(zhǎng)是a. ( )(2)若橢圓的對(duì)稱軸為坐標(biāo)軸,長(zhǎng)軸長(zhǎng)與短軸長(zhǎng)分別為10,8,則橢圓的方程為x^2/25+y^2/16=1. ( )(3)設(shè)F為橢圓x^2/a^2 +y^2/b^2 =1(a>b>0)的一個(gè)焦點(diǎn),M為其上任一點(diǎn),則|MF|的最大值為a+c(c為橢圓的半焦距). ( )答案:(1)× (2)× (3)√ 2.已知橢圓C:x^2/a^2 +y^2/4=1的一個(gè)焦點(diǎn)為(2,0),則C的離心率為( )A.1/3 B.1/2 C.√2/2 D.(2√2)/3解析:∵a2=4+22=8,∴a=2√2.∴e=c/a=2/(2√2)=√2/2.故選C.答案:C 三、典例解析例1已知橢圓C1:x^2/100+y^2/64=1,設(shè)橢圓C2與橢圓C1的長(zhǎng)軸長(zhǎng)、短軸長(zhǎng)分別相等,且橢圓C2的焦點(diǎn)在y軸上.(1)求橢圓C1的半長(zhǎng)軸長(zhǎng)、半短軸長(zhǎng)、焦點(diǎn)坐標(biāo)及離心率;(2)寫(xiě)出橢圓C2的方程,并研究其性質(zhì).解:(1)由橢圓C1:x^2/100+y^2/64=1,可得其半長(zhǎng)軸長(zhǎng)為10,半短軸長(zhǎng)為8,焦點(diǎn)坐標(biāo)為(6,0),(-6,0),離心率e=3/5.(2)橢圓C2:y^2/100+x^2/64=1.性質(zhì)如下:①范圍:-8≤x≤8且-10≤y≤10;②對(duì)稱性:關(guān)于x軸、y軸、原點(diǎn)對(duì)稱;③頂點(diǎn):長(zhǎng)軸端點(diǎn)(0,10),(0,-10),短軸端點(diǎn)(-8,0),(8,0);④焦點(diǎn):(0,6),(0,-6);⑤離心率:e=3/5.
橢圓的簡(jiǎn)單幾何性質(zhì)（2）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)
二、典例解析例5. 如圖，一種電影放映燈的反射鏡面是旋轉(zhuǎn)橢圓面（橢圓繞其對(duì)稱軸旋轉(zhuǎn)一周形成的曲面）的一部分。過(guò)對(duì)稱軸的截口 ABC是橢圓的一部分，燈絲位于橢圓的一個(gè)焦點(diǎn)F_1上，片門(mén)位另一個(gè)焦點(diǎn)F_2上，由橢圓一個(gè)焦點(diǎn)F_1 發(fā)出的光線，經(jīng)過(guò)旋轉(zhuǎn)橢圓面反射后集中到另一個(gè)橢圓焦點(diǎn)F_2，已知 〖BC⊥F_1 F〗_2，|F_1 B|=2.8cm, |F_1 F_2 |=4.5cm,試建立適當(dāng)?shù)钠矫嬷苯亲鴺?biāo)系，求截口ABC所在的橢圓方程(精確到0.1cm)典例解析解：建立如圖所示的平面直角坐標(biāo)系，設(shè)所求橢圓方程為x^2/a^2 +y^2/b^2 =1 (a>b>0) 在Rt ΔBF_1 F_2中,|F_2 B|= √(|F_1 B|^2+|F_1 F_2 |^2 )=√(〖2.8〗^2 〖+4.5〗^2 ) 有橢圓的性質(zhì) , |F_1 B|+|F_2 B|=2 a, 所以a=1/2(|F_1 B|+|F_2 B|)=1/2(2.8+√(〖2.8〗^2 〖+4.5〗^2 )) ≈4.1b= √(a^2 〖-c〗^2 ) ≈3.4所以所求橢圓方程為x^2/〖4.1〗^2 +y^2/〖3.4〗^2 =1 利用橢圓的幾何性質(zhì)求標(biāo)準(zhǔn)方程的思路1．利用橢圓的幾何性質(zhì)求橢圓的標(biāo)準(zhǔn)方程時(shí)，通常采用待定系數(shù)法，其步驟是：(1)確定焦點(diǎn)位置；(2)設(shè)出相應(yīng)橢圓的標(biāo)準(zhǔn)方程(對(duì)于焦點(diǎn)位置不確定的橢圓可能有兩種標(biāo)準(zhǔn)方程)；(3)根據(jù)已知條件構(gòu)造關(guān)于參數(shù)的關(guān)系式，利用方程(組)求參數(shù)，列方程(組)時(shí)常用的關(guān)系式有b2＝a2－c2等．
人教版高中數(shù)學(xué)選修3分類加法計(jì)數(shù)原理與分步乘法計(jì)數(shù)原理(1)教學(xué)設(shè)計(jì)
問(wèn)題1. 用一個(gè)大寫(xiě)的英文字母或一個(gè)阿拉伯?dāng)?shù)字給教室里的一個(gè)座位編號(hào)，總共能編出多少種不同的號(hào)碼？因?yàn)橛⑽淖帜腹灿?6個(gè)，阿拉伯?dāng)?shù)字共有10個(gè)，所以總共可以編出26+10=36種不同的號(hào)碼.問(wèn)題2.你能說(shuō)說(shuō)這個(gè)問(wèn)題的特征嗎？上述計(jì)數(shù)過(guò)程的基本環(huán)節(jié)是：（1）確定分類標(biāo)準(zhǔn)，根據(jù)問(wèn)題條件分為字母號(hào)碼和數(shù)字號(hào)碼兩類；（2）分別計(jì)算各類號(hào)碼的個(gè)數(shù)；（3）各類號(hào)碼的個(gè)數(shù)相加，得出所有號(hào)碼的個(gè)數(shù).你能舉出一些生活中類似的例子嗎？一般地，有如下分類加法計(jì)數(shù)原理：完成一件事，有兩類辦法. 在第1類辦法中有m種不同的方法，在第2類方法中有n種不同的方法，則完成這件事共有:N= m+n種不同的方法.二、典例解析例1.在填寫(xiě)高考志愿時(shí)，一名高中畢業(yè)生了解到，A,B兩所大學(xué)各有一些自己感興趣的強(qiáng)項(xiàng)專業(yè)，如表，
