設(shè)計(jì)意圖:通過設(shè)疑、討論及學(xué)生的親身體驗(yàn)與教師的引導(dǎo),得到描述圓周運(yùn)動(dòng)快慢的兩個(gè)物理量,也就成功的打破了學(xué)生在認(rèn)識(shí)上的思維障礙,突破了物理概念教學(xué)的難點(diǎn)。在解決線速度和角速度的問題之后,我將引領(lǐng)學(xué)生學(xué)習(xí)勻速圓周運(yùn)動(dòng)的概念以及勻速圓周運(yùn)動(dòng)中線速度、角速度的特點(diǎn)。并引出勻速圓周運(yùn)動(dòng)中周期、轉(zhuǎn)速的知識(shí)。為了加深學(xué)生對(duì)線速度、角速度與半徑關(guān)系的認(rèn)識(shí),我設(shè)計(jì)了第三個(gè)學(xué)生體驗(yàn)活動(dòng):四名學(xué)生以我為圓心做圓周運(yùn)動(dòng),四名學(xué)生始終并列,這時(shí)里圈同學(xué)走動(dòng)不急不慢,而外圈同學(xué)則要小跑。通過學(xué)生的活動(dòng),不難發(fā)現(xiàn)在角速度相同的情況下,半徑越大的線速度也越大。定性的得到了線速度、角速度與半徑的關(guān)系。接下來讓學(xué)生利用所學(xué)知識(shí)推導(dǎo)線速度、角速度與半徑的關(guān)系。設(shè)計(jì)意圖:這樣就通過設(shè)疑、學(xué)生猜想、體驗(yàn)、推導(dǎo)的方式得到了結(jié)論,突破了本節(jié)課的難點(diǎn)即線速度、角速度與半徑的關(guān)系。
3、馬克思主義的三大思想來源之一——空想社會(huì)主義理論,教師可以采用多媒體技術(shù)、投放幻燈片、人物圖片等資料進(jìn)行處理。這樣既能增強(qiáng)課堂的趣味性,激發(fā)學(xué)生的興趣,也容易讓學(xué)生理解什么是“空想社會(huì)主義”??梢苑謩e投放圣西門的實(shí)業(yè)制度、傅立葉的“法朗吉”和歐文的“新和諧公社”等資料加深學(xué)生的理解。為了充分發(fā)揮學(xué)生的學(xué)習(xí)主體性地位,還可以利用教材中“學(xué)習(xí)思考”的問題設(shè)計(jì):為什么說圣西門等思想家提出的設(shè)想是空想的?讓學(xué)生在教師提供的材料中探究答案。至于馬克思主義的另兩大思想來源:德意志古典哲學(xué)、英國古典政治經(jīng)濟(jì)學(xué)可以簡單處理。而馬克思、恩格斯為無產(chǎn)階級(jí)革命事業(yè)奮斗的事跡以及馬恩兩人的友誼是可以稍加擴(kuò)長的部分,教師可事先布置學(xué)生任務(wù),讓學(xué)生通過網(wǎng)絡(luò)或者書籍去查找相關(guān)知識(shí),也或者由教師在課堂上補(bǔ)充相關(guān)資料,調(diào)節(jié)課堂氣氛。
(2)多媒體展示:消費(fèi)者們反映iPhone4的500萬像素太不給力,3,5英寸的屏幕太小,促使蘋果公司給新一代iPhone裝上了一顆800萬像素的攝像頭4,0英寸的屏幕等,發(fā)展到最新的一代iPhone6plus已經(jīng)達(dá)到5.5英寸。師:新一代iphone更新的驅(qū)動(dòng)力是什么呢?其實(shí)新產(chǎn)品的升級(jí)對(duì)于蘋果公司來說經(jīng)費(fèi)投入不小但是不經(jīng)過升級(jí)換代產(chǎn)品就不能滿足消費(fèi)者的新的消費(fèi)要求,所以消費(fèi)者的反應(yīng)客觀上促進(jìn)了iphone的升級(jí)換代——消費(fèi)對(duì)生產(chǎn)的調(diào)整與升級(jí)起著導(dǎo)向作用(3)多媒體展示:隨著網(wǎng)購迅猛的發(fā)展,快遞、倉儲(chǔ)業(yè)務(wù)等也出現(xiàn)爆發(fā)式增長。這一現(xiàn)象說明了什么?(舉例:iPhone在全球市場(chǎng)的火熱,“殼”文化產(chǎn)業(yè)第一個(gè)進(jìn)入人們的視線,隨著時(shí)間的發(fā)展,外殼的產(chǎn)業(yè)飛速蓬勃的發(fā)展著)結(jié)論:一個(gè)新的消費(fèi)熱點(diǎn)的出現(xiàn)往往能帶動(dòng)一個(gè)或多個(gè)產(chǎn)業(yè)的出現(xiàn)和成長。消費(fèi)所形成的新的需求對(duì)生產(chǎn)的調(diào)整和升級(jí)起著導(dǎo)向作用,需求的數(shù)量和質(zhì)量調(diào)節(jié)供給的數(shù)量和質(zhì)量。
【例3】本例中“p是q的充分不必要條件”改為“p是q的必要不充分條件”,其他條件不變,試求m的取值范圍.【答案】見解析【解析】由x2-8x-20≤0得-2≤x≤10,由x2-2x+1-m2≤0(m>0)得1-m≤x≤1+m(m>0)因?yàn)閜是q的必要不充分條件,所以q?p,且p?/q.則{x|1-m≤x≤1+m,m>0}?{x|-2≤x≤10}所以m>01-m≥-21+m≤10,解得0<m≤3.即m的取值范圍是(0,3].解題技巧:(利用充分、必要、充分必要條件的關(guān)系求參數(shù)范圍)(1)化簡p、q兩命題,(2)根據(jù)p與q的關(guān)系(充分、必要、充要條件)轉(zhuǎn)化為集合間的關(guān)系,(3)利用集合間的關(guān)系建立不等關(guān)系,(4)求解參數(shù)范圍.跟蹤訓(xùn)練三3.已知P={x|a-4<x<a+4},Q={x|1<x<3},“x∈P”是“x∈Q”的必要條件,求實(shí)數(shù)a的取值范圍.【答案】見解析【解析】因?yàn)椤皒∈P”是x∈Q的必要條件,所以Q?P.所以a-4≤1a+4≥3解得-1≤a≤5即a的取值范圍是[-1,5].五、課堂小結(jié)讓學(xué)生總結(jié)本節(jié)課所學(xué)主要知識(shí)及解題技巧
本課是高中數(shù)學(xué)第一章第4節(jié),充要條件是中學(xué)數(shù)學(xué)中最重要的數(shù)學(xué)概念之一, 它主要討論了命題的條件與結(jié)論之間的邏輯關(guān)系,目的是為今后的數(shù)學(xué)學(xué)習(xí)特別是數(shù)學(xué)推理的學(xué)習(xí)打下基礎(chǔ)。從學(xué)生學(xué)習(xí)的角度看,與舊教材相比,教學(xué)時(shí)間的前置,造成學(xué)生在學(xué)習(xí)充要條件這一概念時(shí)的知識(shí)儲(chǔ)備不夠豐富,邏輯思維能力的訓(xùn)練不夠充分,這也為教師的教學(xué)帶來一定的困難.“充要條件”這一節(jié)介紹了充分條件,必要條件和充要條件三個(gè)概念,由于這些概念比較抽象,中學(xué)生不易理解,用它們?nèi)ソ鉀Q具體問題則更為困難,因此”充要條件”的教學(xué)成為中學(xué)數(shù)學(xué)的難點(diǎn)之一,而必要條件的定義又是本節(jié)內(nèi)容的難點(diǎn).A.正確理解充分不必要條件、必要不充分條件、充要條件的概念;B.會(huì)判斷命題的充分條件、必要條件、充要條件.C.通過學(xué)習(xí),使學(xué)生明白對(duì)條件的判定應(yīng)該歸結(jié)為判斷命題的真假.D.在觀察和思考中,在解題和證明題中,培養(yǎng)學(xué)生思維能力的嚴(yán)密性品質(zhì).
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.
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.
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.
另一方面,其余的人反對(duì)這個(gè)計(jì)劃,因?yàn)樗赡軙?huì)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(jiān)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(shí)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(duì)的,因?yàn)樗鼈兛赡軙?huì)對(duì)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(gè)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(shí)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(qǐng)你根據(jù)以下情況寫一篇報(bào)告并發(fā)表自己的觀點(diǎn)。注意:1.寫作內(nèi)容應(yīng)包括以上全部要點(diǎn),可適當(dāng)發(fā)揮,使上下文連貫;
【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!
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(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.
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(shí),|P1P2|=?請(qǐng)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(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(shí),|P1P2|=|x2-x1|.當(dāng)直線P1P2平行于y軸時(shí),|P1P2|=|y2-y1|.
(2)l的傾斜角為90°,即l平行于y軸,所以m+1=2m,得m=1.延伸探究1 本例條件不變,試求直線l的傾斜角為銳角時(shí)實(shí)數(shù)m的取值范圍.解:由題意知(m"-" 1"-" 1)/(m+1"-" 2m)>0,解得1<m<2.延伸探究2 若將本例中的“N(2m,1)”改為“N(3m,2m)”,其他條件不變,結(jié)果如何?解:(1)由題意知(m"-" 1"-" 2m)/(m+1"-" 3m)=1,解得m=2.(2)由題意知m+1=3m,解得m=1/2.直線斜率的計(jì)算方法(1)判斷兩點(diǎn)的橫坐標(biāo)是否相等,若相等,則直線的斜率不存在.(2)若兩點(diǎn)的橫坐標(biāo)不相等,則可以用斜率公式k=(y_2 "-" y_1)/(x_2 "-" x_1 )(其中x1≠x2)進(jìn)行計(jì)算.金題典例 光線從點(diǎn)A(2,1)射到y(tǒng)軸上的點(diǎn)Q,經(jīng)y軸反射后過點(diǎn)B(4,3),試求點(diǎn)Q的坐標(biāo)及入射光線的斜率.解:(方法1)設(shè)Q(0,y),則由題意得kQA=-kQB.∵kQA=(1"-" y)/2,kQB=(3"-" y)/4,∴(1"-" y)/2=-(3"-" y)/4.解得y=5/3,即點(diǎn)Q的坐標(biāo)為 0,5/3 ,∴k入=kQA=(1"-" y)/2=-1/3.(方法2)設(shè)Q(0,y),如圖,點(diǎn)B(4,3)關(guān)于y軸的對(duì)稱點(diǎn)為B'(-4,3), kAB'=(1"-" 3)/(2+4)=-1/3,由題意得,A、Q、B'三點(diǎn)共線.從而入射光線的斜率為kAQ=kAB'=-1/3.所以,有(1"-" y)/2=(1"-" 3)/(2+4),解得y=5/3,點(diǎn)Q的坐標(biāo)為(0,5/3).
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(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"." )┤
(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.
【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.無論k取何值,直線y-2=k(x+1)所過的定點(diǎn)是 . 【答案】(-1,2)6.直線l經(jīng)過點(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).
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.
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(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.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.]
解析:①過原點(diǎn)時(shí),直線方程為y=-34x.②直線不過原點(diǎn)時(shí),可設(shè)其方程為xa+ya=1,∴4a+-3a=1,∴a=1.∴直線方程為x+y-1=0.所以這樣的直線有2條,選B.答案:B4.若點(diǎn)P(3,m)在過點(diǎn)A(2,-1),B(-3,4)的直線上,則m= . 解析:由兩點(diǎn)式方程得,過A,B兩點(diǎn)的直線方程為(y"-(-" 1")" )/(4"-(-" 1")" )=(x"-" 2)/("-" 3"-" 2),即x+y-1=0.又點(diǎn)P(3,m)在直線AB上,所以3+m-1=0,得m=-2.答案:-2 5.直線ax+by=1(ab≠0)與兩坐標(biāo)軸圍成的三角形的面積是 . 解析:直線在兩坐標(biāo)軸上的截距分別為1/a 與 1/b,所以直線與坐標(biāo)軸圍成的三角形面積為1/(2"|" ab"|" ).答案:1/(2"|" ab"|" )6.已知三角形的三個(gè)頂點(diǎn)A(0,4),B(-2,6),C(-8,0).(1)求三角形三邊所在直線的方程;(2)求AC邊上的垂直平分線的方程.解析(1)直線AB的方程為y-46-4=x-0-2-0,整理得x+y-4=0;直線BC的方程為y-06-0=x+8-2+8,整理得x-y+8=0;由截距式可知,直線AC的方程為x-8+y4=1,整理得x-2y+8=0.(2)線段AC的中點(diǎn)為D(-4,2),直線AC的斜率為12,則AC邊上的垂直平分線的斜率為-2,所以AC邊的垂直平分線的方程為y-2=-2(x+4),整理得2x+y+6=0.
【課件展示】《秦朝中央集權(quán)制度的建立》《教材簡析》《教學(xué)目標(biāo)》《教法簡介》《教學(xué)過程設(shè)計(jì)及特色簡述》【師】本節(jié)內(nèi)容以秦代政治體制和官僚系統(tǒng)的建立為核心內(nèi)容,主要包括秦朝中央集權(quán)制的建立的背景、建立過程及影響。本節(jié)內(nèi)容在整個(gè)單元中起到承前啟后的作用,在整個(gè)模塊中也有相當(dāng)重要的地位。讓學(xué)生了解中國古代中央集權(quán)政治體制的初建對(duì)于理解我國古代政治制度的發(fā)展乃至我們今天的政治體制是十分必要的。 本堂課我采用多媒體和講授法及歷史辯論法相結(jié)合,通過巧妙設(shè)計(jì)問題情境,調(diào)動(dòng)學(xué)生的學(xué)習(xí)積極性,使學(xué)生主動(dòng)學(xué)習(xí),探究思考。教師引導(dǎo)和組織學(xué)生采取小組討論、情景體驗(yàn)等方式,達(dá)到教學(xué)目標(biāo)。 本節(jié)內(nèi)容分三個(gè)部分,下面首先看秦朝中央集權(quán)制度建立的前提即秦的統(tǒng)一
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