1.2應(yīng)用舉例(約4課時)

1.1正弦定理和余弦定理(約3課時)

3．重視加強意識和數(shù)學(xué)實踐能力

學(xué)數(shù)學(xué)的最終目的是應(yīng)用數(shù)學(xué)，而如今比較突出的兩個問題是，學(xué)生應(yīng)用數(shù)學(xué)的意識不強，創(chuàng)造能力較弱。學(xué)生往往不能把實際問題抽象成數(shù)學(xué)問題，不能把所學(xué)的數(shù)學(xué)知識應(yīng)用到實際問題中去，對所學(xué)數(shù)學(xué)知識的實際背景了解不多，雖然學(xué)生機械地模仿一些常見數(shù)學(xué)問題解法的能力較強，但當(dāng)面臨一種新的問題時卻辦法不多，對于諸如觀察、分析、歸納、類比、抽象、概括、猜想等發(fā)現(xiàn)問題、解決問題的科學(xué)思維方法了解不夠。針對這些實際情況，本章重視從實際問題出發(fā)，引入數(shù)學(xué)課題，最后把數(shù)學(xué)知識應(yīng)用于實際問題。

1．?dāng)?shù)學(xué)思想方法的重要性

數(shù)學(xué)思想方法的教學(xué)是中學(xué)數(shù)學(xué)教學(xué)中的重要組成部分，有利于學(xué)生加深數(shù)學(xué)知識的理解和掌握。

本章重視與內(nèi)容密切相關(guān)的數(shù)學(xué)思想方法的教學(xué)，并且在提出問題、思考解決問題的策略等方面對學(xué)生進行具體示范、引導(dǎo)。本章的兩個主要數(shù)學(xué)結(jié)論是正弦定理和余弦定理，它們都是關(guān)于三角形的邊角關(guān)系的結(jié)論。在初中，學(xué)生已經(jīng)學(xué)習(xí)了相關(guān)邊角關(guān)系的定性的知識，就是“在任意三角形中有大邊對大角，小邊對小角”，“如果已知兩個三角形的兩條對應(yīng)邊及其所夾的角相等,那么這兩個三角形全”等。

教科書在引入正弦定理內(nèi)容時，讓學(xué)生從已有的幾何知識出發(fā)，提出探究性問題：“在任意三角形中有大邊對大角，小邊對小角的邊角關(guān)系.我們是否能得到這個邊、角的關(guān)系準(zhǔn)確量化的表示呢?”，在引入余弦定理內(nèi)容時，提出探究性問題“如果已知三角形的兩條邊及其所夾的角,根據(jù)三角形全等的判定方法，這個三角形是大小、形狀完全確定的三角形.我們?nèi)匀粡牧炕慕嵌葋硌芯窟@個問題，也就是研究如何從已知的兩邊和它們的夾角計算出三角形的另一邊和兩個角的問題�！痹O(shè)置這些問題，都是為了加強數(shù)學(xué)思想方法的教學(xué)。

本章的中心內(nèi)容是如何解三角形，正弦定理和余弦定理是解三角形的工具，最后落實在解三角形的應(yīng)用上。通過本章學(xué)習(xí)，學(xué)生應(yīng)當(dāng)達到以下學(xué)習(xí)目標(biāo)：

(1)通過對任意三角形邊長和角度關(guān)系的探索，掌握正弦定理、余弦定理，并能解決一些簡單的三角形度量問題。

(2)能夠熟練運用正弦定理、余弦定理等知識和方法解決一些與測量和幾何計算有關(guān)的生活實際問題。

B、C、D，應(yīng)選A．

[說明]　 此例題用多種方法求解選項，指出3種選擇題的技巧．

∴應(yīng)選D

x軸交點中在原點右邊最接近原點的交點，而在原點左邊與x軸交點中最

的圖象．

∴選D

[說明]　 y=Asin(ωx+j)(A＞0，ω＞0)x∈R的圖象可由y=sinx的圖象經(jīng)下列各種順序變換得到的．

(1)先平移，后伸縮：

①把y=sinx的圖象向左(j＞0)或向右(j＜0)沿x軸方向平移|j|個單位；(相位變換)

(周期變換)

③把所有各點縱坐標(biāo)伸長(A＞1)或縮短(0＜A＜1)到原來的A倍，橫坐標(biāo)不變(振幅變換)

(2)先伸縮，后平移

①把y=sinx圖象上各點的橫坐標(biāo)縮短(ω＞1)或伸長(0＜ω＜1)到原

(相位變換)

③把所有各點縱坐標(biāo)伸長(A＞1)或縮短(0＜A＜1)到原來的A倍橫坐標(biāo)不變(振幅變換)

再把橫坐標(biāo)縮小到原來的一半，縱坐標(biāo)擴大到原來的4倍，則所得的圖象的解析式是　　 [　　 ]

∴選A．

[例17]　 方程sin2x=sinx在區(qū)間(0，2π)內(nèi)解的個數(shù)是

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 [　　 ]

A．1　　　　　 B．2　　　　　　 C．3　　　　　　　 D．4

[分析]　 本題有兩類解法

(1)求出方程在(0，2π)內(nèi)的所有解，再數(shù)其解的個數(shù)．而決定選項，對于選擇題，此法一般不用．

(2)在同一坐標(biāo)系中作出函數(shù)y=sin2x和y=sinx的圖象，如圖2-18所示．

它們在(0，2π)內(nèi)交點個數(shù)，即為所求方程解的個數(shù)，從而應(yīng)選C．

它體現(xiàn)了數(shù)、形的結(jié)合．

[例18]　 設(shè)函數(shù)f(x)是定義在R上的周期為3的奇函數(shù)，且f(1)=2，則f(5)=____

解：∵f(x)是奇函數(shù)，且f(1)=2，∴f(-1)=-2

又∵f(x)是周期為3的函數(shù)．　 ∴f(3+x)=f(x)

∴f(-1+3)=f(-1)=-2　 即f(2)=-2

f(2+3)=f(2)=-2　 即f(5)=-2

[例19]　 有一塊扇形鐵板，半徑為R，圓心角為60°，從這個扇形中切割下一個內(nèi)接矩形，即矩形的各個頂點都在扇形的半徑或弧上，求這個內(nèi)接矩形的最大面積．

[分析]　 本題入手要解決好兩個問題．

(1)內(nèi)接矩形的放置有兩種情況，如圖2-19所示，應(yīng)該分別予以處理．

(2)求最大值問題這里應(yīng)構(gòu)造函數(shù)，怎么選擇便于以此表達矩形面積的自變量．

解：如圖2-19(1)設(shè)∠FOA=θ，則FG＝Rsinθ

又設(shè)矩形EFGH的面積為S，那么

又∵0°＜θ＜60°，故當(dāng)cos(2θ－60°)＝1，即θ=30′時，

如圖2-19 (2)，設(shè)∠FOA＝θ，則EF＝2Rsin(30°-θ)，在△OFG中，∠OGF＝150°

設(shè)矩形的面積為S．

那么S＝EFFG＝4R²sinθsin(30°-θ)

＝2R²［cos(2θ-30°)－cos30°]

又∵0＜θ＜30°，故當(dāng)cos(2θ-30°)＝1

作出三角函數(shù)線，如圖2-17

MP=sinθ，OM=cosθ，BS=ctgθ

通過觀察和度量得MP＜OM＜BS

從而有sinθ＜cosθ＜ctgθ

∴應(yīng)選A

∴cosθ＞sinθ

從而可剔除B、D．

再由sinθ＜ctgθ，故可剔除C

故選A

故選A．

每次寫作前問自己四個問題：這篇文章的體裁格式是怎樣的？主體時態(tài)用什么時態(tài)？人稱用第幾人稱？可以分幾段，之間用什么過渡詞、連接詞？帶著這四個問題去審題，搞清楚文章的主要內(nèi)容，然后列出提綱。最后豐富自己的提綱就可以了。

第四份資料

單項選擇[1] 第一節(jié)　單項填空(共15小題；每小題1分，滿分15分) 從A、B、C、D四個選項中，選出可以填入空白處的最佳選項。 21.-Do you know Uncle Tom is crazy about gardening? 　 　 -Sure. He ____ his flowers in the garden now. A. may be watering　 　 B. must be watering C. could look after　 　D. ought to watch 22.____ the temperature falling so rapidly, we couldn't go on with the experience. A. Since　 　B. With　 　 C. As　 　 D. For 23. I'd love ___ to your party last Sunday if not because of the unexpected guests. A. to go　 　B. going　 　 C. having gone　 　D.to have gone 24. -Will you two go to the show tomorrow? -No. We're going to a lecture, or at least I'm planning ____. A. it　B. to　 　C. that　 　D. so 25. The rescue team ______to help but failed to get there in time. A. had wanted　B. have planned C. were expecting　D. hoped 26.1 haven't got a single ______from Aunt Mary since I last saw her. A. advice　B. news　C. message　D. information 27.-Is it Pro. King that will give the lecture on radiation? -I can't __ I know it for sure. A. say　 　 B. tell　 　C. speak　 　　D. talk 28. "No, no ", he whispered,____ talking to himself. A. while　 　B. even if　 　 C. as if　 　 D. when 29. - Any phone call for me? -Yes.____ telephoned 10 minutes ago. A. A Doctor Simpson　 　B. The certain doctor C. The Tim Smith　 　 D. A Simpson Doctor 30. ____ is mentioned above, the number of the cattle here has been limited to 200. A. It　B. Which　 　 C. That　 　 D. As 31. -Would you please give him the paper the moment he ____? -No problem. A. arrives　 　 B. appearing　C. came　 　D. reaches 32.I wonder ____ we can solve this hard problem. A. what else　 　B. how else　C. that　 　 D. as if 33.- Excuse me, can you tell me the way to the bank? -Oh, that's ____, it's either the second or the third road on the left. A. the difficult one　 　B. a hard one C. an easy one　 　D. the very one 34. The newly-founded company is faced with lots of trouble, ____ the financial problem ia not the worst. A. which　B. of which　C. to whom　 　D. with which 35. To his surprise, his new play well ____ by the public in China, met a cold welcome abroad. A. received　 　B. accepted　 　C. accepting D. receiving

單項選擇[2] 第一節(jié)　單項填空(共15小題；每小題1分，滿分15分) 從A、B、C、D四個選項中，選出可以填入空白處的最佳選項。 21.- ____ at the new school? -Fine, I've got used to the life there and I've made some friends. A. How are you　B. How are you doing C. Are you getting on well　D. How do you do 22. -Mary has a very low opinion of George. -It can' t be any worse than ____ of her. A. he　B. his　 　 C. him　 　 D. he does 23. I'll be home late, but please don't stay ____ for me. A. up　 　 B. in　 　 C. over　 　 　D. on 24.- What are you going to do next? -To write a science story about outer space ___ by Science and Technology Press. A. published　 　　B. being published C. to be published　 　 D. publishing 25. -How do you like the film? -There was nothing special--- it was only ____. A. average　 　　B. usual　 　 C. normal　 　D. common 26. In salad bars the waiter does not bring you salad. You have to____ yourself, usually to as much as you want. A. bring　 　B. serve　C. help D. supply 27. Our TV sets sell well, but ten years ago no one could have imagined such a big share in the market that they ____. A. were having　 　B. had had　 　C. were to have　D. had 28. Let us suppose that you are in____ position of____ parent. Would you allow your child to do such a thing? A. a; a　 　 B. a; the　 　C. the; a　 　D. the; the 29.- He has to finish the experiment today. He must be in the lab,____? -That s quite possible. A. mustn't he　B. won't he　C. doesn't he　 　D. isn't he 30. However, at times this balance in nature is disturbed, ____ a number of possibly unforeseen effects. A. lying in　 　 B. calling in C. taking in　D. resulting in 31. I wrote to my parents once a week,____ I was too busy with my teaching work. A. it　B. unless　 　C. when　 　 D. as 32. -Where will you start your work after graduation? -Mmm, it's not been decided yet. I ____ continue my study for a higher degree. A. need　 　B. must　 　C. would　 　 D. might 33. The truth, Sir, is that the old man____ across the street when my car hit him. A. was to walk B. had been walkingC. walked D. was walking 34. So many uses have been discovered for this wood ____ the supply of white pine is becoming smaller and smaller. A. then B. what　 　 C. that　 　D. which 35.-You seemed to have been impressed by his songs. -Well, not exactly so. It was his way of singing____ his voice that really impressed me. A. rather than　B. as well as　 　C. but also D. together with

單項選擇[3] 第一節(jié)　單項填空(共15小題；每小題1分，滿分15分) 從A、B、C、D四個選項中，選出可以填入空白處的最佳選項。 21. I smoke out of ____ habit, not for ____ pleasure; for I have been in the habit for twenty years. A. a; the　 　B. the; a　 　C. x; the　 　D. x; x 22. His job is to sell the ____ carvings in the ____ department of the company. A. wooden; sales　 　 B. wood; sales　 　 　 C. wood; sale　 　 　　D. wooden; sale 23. My father ____ my brother for driving but he wanted to pick ____ the knowledge of the computer during his spare time. A. advised; up　 　　B.persuaded; out　 　 　　C.intended; up　 　 　D.managed; out 24. -Whose advice do you think I should take? -_______. A.You speak　B.That's itC.It's up to you　D.You got it 25. ____ the youth ____ the rising sun at 8 or 9 o'clock am, Mao Zedong expressed his great hope for the young men. A. Comparing; withB. Compared; to C. Compared; with D. Comparing; to 26. Not far from the club, there was a girden, ____ owner seated in it playing bridge with his children every afternoon. A. whose　B. its　C. which　D. that 27. I haven' t seen Mary these past few days. I m afraid she ____ herself for some time. A. isn't feeling　 　　B. hasn' t been feeling　 　 C. hadn't been feeling　 　 D. wasn't feeling 28. Doing your homework is a sure way to improve yor test scores, and this is especially true ____ it comes to classroom tests. A. before　B. since　 　 C. when　 　D. after 29. A love marriage, however, does not necessarily ____ much sharing of interests and responsibilities. A. take over　 　B. result in　 　C. hold on　 　 D. keep to 30. The teacher came to the classroom and demanded ____ what had happened. A. his students to tell him　 　 　B. being told C. telling him　 　 　D. to be told 31. There were many students and teachers at the party yesterday. I looked for two seats to sit down with my friend, Tim, but there were ____. A. neither　 　B. nothing　 　 C. none　 　 　D. no 32. It is in Steven Spielberg' s first film, Jaws, ____ a big white shark attacks swimmers ____ are spending their holidays in a small village by the sea. A. where; who　 　B. which; that　 　 C. that; that　D. where; that 33. -What do you think of the dinner in Mr Brown's? -Oh, great! We have never had a better one. It's a dinner of twenty ____. A. drinks　 　 B. people　 　C. tables　 　D. courses 34. The captain ordered the crew to throw ____ the side of the ship all heavy guns and even stores in order to raise the boat in the water. A. on　 　 B. through　 　 C. across　 　 　D. over 35. Knowing how long the test would last, the students who finished ____ back and waited until the end of the exam. A. settle　 　　B. settled　 　 C. settling　 　 D. to settle

單項選擇[4] 第一節(jié)　單項填空(共15小題；每小題1分，滿分15分) 從A、B、C、D四個選項中，選出可以填入空白處的最佳選項。 21. What ______ public is concerned about is whether medical workers and scientists will be able to find for this new disease in a short time. A.不填;不填　B.不填;the　 　 C. the;不填　 　D.the;a 22._____ good, these cookies sell well. A.Smelled　 　 B. Smelling　C. Being smelled D. To smell 23.-Haven't I told you that I like the beef well done? -Yes, but I _____ it longer than I usually do. A. was cooking B.will cook　C. cooked D. had cooked 24. We' ve published large quantities of books. This year___ we've published three million. A. only　 　　B. just　 　 　C. alone　 　　D. merely 25. He ______. It's a shame my mobile phone was power-off. A. ought to call me　B. could have called me　 C. may be calling me　 　D.might call me 26.-Since you can't find a better job, why don't you stick to the present one? 　 　 -Well,_____. A.I believe not　 　　B.I don't care C. Never mind　 　 D. I might as well 27.The wedding party is to be held on May 18,_____ is, ten days_____ today. A. which; fromB.that;except C.that;from　D.as;since 28.You don't have to share the umbrellas. I'll give you one_____. A.every B.each　 　C.all　D.both 29.-Tom, keep your_____ on your studies. 　 　 - Sure, mum. I'll keep that in_____. A. mind;mind　B.heart;headC. brain; mind D.heart;brain 30.According to the Ministry of Health, by May 1, 2003, the total SARS deaths on the Chinese mainland_____to 170. A.has come　 　B. had reached　C.increased　 　D. had climbed 31. The door opened and in _____. A. he came　B. came he　C. did he come D. did Mr Smith come 32. After months of voyage, Columbus arrived in_____ later proved a new continent. A.where　B. what　C.which　 　 D.that 33._____ I toured Zhang Jiajie, I was deeply impressed with its beautiful scenery. A.For the fust time　 　B. At first　 　 C.It was the first time　 　 　D. The first time 34._____ private cars are bringing us convenience, they may also cause more traffic accidents and pollution. A.While　 　 B.As　 　 　C.If　 　 　 D.Since 35. Having ended the major combat (主戰(zhàn)), President Bush_____ rebuilding Iraq. A. started out B. went all out　C. turned to　D. went on

單項選擇[5] 第一節(jié)　單項填空(共15小題；每小題1分，滿分15分) 從A、B、C、D四個選項中，選出可以填入空白處的最佳選項。 21. ---Good morning. Grand Hotel. 　 　---Hello, I'd like to book a room for the nights of the 18th and 19th. A. What can I do for you?　B. Just a minute, please. C. What's the matter?　D. At your service. 22. You’d better choose someone______ you think ____ kind and friendly to help you. A. whom; to beB. who; is C. that; is　 　D. which; to be 23. Readers can __quite well without knowing the exact meaning of each word. A. get along B. get over C. get in　D. get through 24. The first textbooks written for teaching English as a foreign language ____ in the 16th century. A. came about　B. came out C. came along　D. came up 25. I shall always ____ your friendship greatly for friendship is more important than money. A. value B. pay high respect C. respect　 　D. store 26. Later they discovered, ____ was news to him, that Pamela was the headmaster’s daughter. A. that　 　 B. which　 　C. what　 　D. who 27. Was it in this very room ____ he made up his mind ____ he should break away from his family? A. that; which　B. which; that C. which; which D. that; that 28. Tim Bemers-Lee is generally considered ____ the World Wide Web, on which all the information is shared by all. A.to have founded B.having foundedC. founding D. to found 29. ____has been said before, it is not easy to learn a foreign language. A. As　 　B. It　 　　C. What　 　　D. As it 30. The employee must have been dismissed by the employer last month, ____ he? A. haven't　 　　B. hasn't　 　C. didn't　 　 D. wasn't 31.---I didn't go to work yesterday because my car broke down. 　---You ____ mine. I wasn't using it then. A. might borrow B. could have borrowed C. must have borrowed　 　 D. ought to borrow 32. I admired my classmate Lisa very much. ____ her prettiness, she was smart and helpful. A. Except for　B. But for　C. Apart from　D. In spite of 33. I haven’t seen her ____ the time ____ she had the accident. A. for; that　B. since; when　 　C. since; as　D. for; when 34. ---I'm going to Guilin next week. Do you have anything ____ there? 　---No, but thank you all the same. A. to be taken　B. to take　 　C. taking　 　　D. taken 35. The ____ is that the new machine will arrive tomorrow. A. chance　 　　B. luck　 　 　 C. happening　 　 D. accident