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小说红与黑读书心得参考范本
司汤达是善于从爱情中反映重大社会问题的文学大师。于连的两次爱情都与时代风云紧密相连，这是当时阶级角逐的一种表现形式，他对德·雷纳尔夫人后来的确也产生了真正的感情，但开始是出于小市民对权贵的报复心理。因此，于连第一次占有德·雷纳尔夫人的手的时候，他感到的并不是爱情的幸福，而是拿破仑式的野心的胜利，是"狂欢"和"喜悦"，是报复心理的满足。 如果说于连对德·雷纳尔夫人的追求还有某些真挚情感的话，那么于连对玛蒂尔德小姐的爱情则纯属政治上的角逐，玛蒂尔德既有贵族少女的傲慢，任性的气质，又受到法国_的深刻影响。她认为，如果再有一次_，主宰社会的必定是像于连这样富于朝气的平民青年。同于连结成伉俪，既富于浪漫气息，又找到了有力的靠山。而于连则认为与玛蒂尔德小姐结婚可以爬上高位，青云直上，因此不惜去骗取她的爱情。
新人教版高中英语选修2Unit 1 Science and Scientists-Discovering useful structures教学设计
The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑体部分在句中作表语。2. 句1、2、3中的that在从句中不作成分，只起连接作用。 Step2: Review the basic components of predicative clauses1.Definition
新人教版高中英语选修2Unit 4 Journey Across a Vast Land教学设计
当孩子们由父母陪同时，他们才被允许进入这个运动场。3．过去分词(短语)作状语时的几种特殊情况(1)过去分词(短语)在句中作时间、条件、原因、让步状语时，相当于对应的时间、条件、原因及让步状语从句。Seen from the top of the mountain (＝When it is seen from the top of the mountain), the whole town looks more beautiful.从山顶上看，整个城市看起来更美了。Given ten more minutes (＝If we are given ten more minutes), we will finish the work perfectly.如果多给十分钟，我们会完美地完成这项工作。Greatly touched by his words (＝Because she was greatly touched by his words), she was full of tears.由于被他的话深深地感动，她满眼泪花。Warned of the storm (＝Though they were warned of the storm), the farmers were still working on the farm.尽管被警告了风暴的到来，但农民们仍在农场干活。(2)过去分词(短语)在句中作伴随、方式等状语时，可改为句子的并列谓语或改为并列分句。The teacher came into the room, followed by two students (＝and was followed by two students)．后面跟着两个学生，老师走进了房间。He spent the whole afternoon, accompanied by his mom(＝and was accompanied by his mom)．他由母亲陪着度过了一整个下午。
新人教版高中英语选修2Unit 1 Science and Scientists-Reading and thinking教学设计
Step 5： After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
新人教版高中英语选修2Unit 1 Science and Scientists-Using langauge教学设计
This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!
新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计
You have no excuse for not going.你没有理由不去。He was punished for not having finished his homework.他因未完成作业而受到惩罚。2．动词ing形式复合结构由物主代词或人称代词宾格、名词所有格或普通格加动词ing，即“sb./sb.'s＋doing”构成。动词ing形式的复合结构实际上是给动词ing形式加了一个逻辑主语。动词ing形式的复合结构有四种形式：①形容词性物主代词＋动词ing②名词所有格＋动词ing③代词宾格＋动词ing④名词＋动词ingHer coming to help encouraged all of us.她来帮忙鼓舞了我们所有人。The baby was made awake by the door suddenly shutting.这个婴儿被突然的关门声吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做饭的样子吗？无生命名词无论是作主语还是作宾语都不能用第②种形式。Tom's winning first prize last year impressed me a lot.汤姆去年得了一等奖使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克现在离开吗？Excuse me for my not coming on time．很抱歉我没能按时来。His father's being ill made him worried.他父亲病了，他很担心。We are looking forward to the singer's/the singer to give us a concert.我们盼望着这位歌手来给我们举办一场演唱会。
新人教版高中英语选修2Unit 1 Science and Scientists-Learning about Language教学设计
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention，the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys： 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
人教版高中政治选修3美国的联邦制教案
3、联邦制的弊端：（1）、效率不高：（2）、集团分享权力，维护资产阶级的利益，不顾人民要求。在美国实行联邦制的二百多年问，联邦制的弊端也显露无遗。美国联邦制的最大问题是效率不高，联邦政府与州政府之间相互扯皮、推诿，各州政府之间各自为政。全国性资产阶级利益集团与地方性资产阶级利益集团分享权力，对于广大人民群众的要求，资产阶级则利用国家结构形式的特点相互推卸责任。当大多数资产阶级利益集团意见接近时，联邦制既能保护州的灵活性，又能保证中央的权威；当资产阶级利益集团之间矛盾重重时，联邦制就处于低效运转之中。相关链接：1954年，美国最高法院在一项判决中宣布，公立学校实行种族隔离、拒绝黑人入学是违反宪法的。这一裁决引起南方一些州的抵制，一些州竟以暴力阻止黑人进入公立学校。
人教版高中政治选修3国际组织概观教案
4、中国积极发展与区域性国际组织的关系。中国积极发展与区域性国际组织的关系。中国与欧盟建立了领导人年度会晤机制，致力于发展全面战略伙伴关系。中国重视与非洲国家的传统友谊，与非洲联盟团结合作。中国与阿拉伯国家联盟、石油输出国组织等发展中国家组建的国际组织发展友好关系，支持它们维护自身的正当权益，并与它们共同为建立公正合理的国际政治经济新秩序而努力。新中国与国际组织关系的历史演变大致经历了三个时期。从中华人民共和国建立初期到1971年：新中国被排斥在联合国等国际组织之外，为恢复在联合国的合法席位进行了不懈的斗争。从1 9 7 1年到改革开放前：中国恢复了在联合国的合法席位，并与大批国际组织建立、恢复了友好合作关系。改革开放以来：中国恢复了在世界银行和国际货币基金组织的席位，加入了世界贸易组织、亚太经合组织等经济组织。世界银行出资兴建的希望小学小结：4个主要特征：国际组织的四个主要特征即：①跨国性、②目的性、③组织性、④自主性。
人教版高中政治选修3美国的利益集团教案
（3）、各种利益集团内部很少有什么民主机制，大都为少数人所控制——从利益集团内部的管理机制看；广大群众常常对某些组织寄予期望，投人力量，但是他们的利益却往往得不到关注。（4）、利益集团为政府腐败提供了肥沃的土壤。利益集团的活动方式，在很大程度上是用金钱购买政治影响力，是一种滋养腐败的行为——从利益集团对政府的负面影响看。实际上，在国会议员、政府官员与利益集团之间，已经形成一种相互依赖的共生关系。3、利益集团机制的隐蔽性、欺骗性及其实质：美国政坛中的利益集团机制，是资产阶级控制国家机器的一种特殊形式，具有相当强的隐蔽性和欺骗性。表面上看，利益集团是所谓的“民意代表”，向政府反映各阶层、群体的观点和利益，实质上是资产阶级在“民意”的幌子下控制权力。
人教版高中政治选修3美国的三权分立教案
国会一直在政治生活中居于主导地位；到了当代，则是总统居于主导地位。由于司法机关无权直接支配社会力量和财富，相比之下，联邦法院力量向来较弱。第二次世界大战后，由于美国一直追逐全球霸权，美国总统的战争权力更加强化，向海外派遣军队的次数更加频繁。美国人民日益觉察到这种不断增长的“帝王般总统职位”可能带来的危险。2、三权分立制的本质——是一种资产阶级民主制度美国的三权分立制本质上是一种资产阶级民主制度。二百多年的历史经验表明，它有效地维护了美国资产阶级的统治。但是，广大劳动人民不可能在这种制度下享有真正的民主。虽然三大权力机关之间互相制约、平衡，却没有一个代表人民意志的权力机关，因而不可能实现人民群众的多数人统治。◇本框题小结：◇3个3种权力：3种权力即立法权、行政权和司法权；3个弊端：即三权分立原则的3 个弊端；3个中央政权机构即立法机关、行政机关和司法机关；◇2个原因：即确立三权分立原则的原因◇1个本质：即三权分立原则的本质
人教版高中政治选修3走进世界贸易组织教案
中国加人世贸组织承担的义务主要包括：进一步降低关税；取消非关税贸易壁垒；取消被禁止的出口补贴；开放国内市场，特别是服务市场；扩大对知识产权的保护范围；放宽和改善外资政策；增加贸易政策的透明度等。履行这些义务对中国提出了挑战。中国加入世贸组织后，享受多边、无条件、稳定的最惠国待遇和国民待遇；参与世贸组织各机构的所有会议；参与贸易政策审议，对贸易伙伴的贸易政策进行质询和监督；利用世贸组织的争端解决机制解决贸易纠纷；参与新一轮多边贸易谈判，制定多边贸易规则；享受发展中国家特有的权益。②意义：中国正充分行使这些权利，积极主动地参与、加强和发展多边贸易体制，推动建立公平、合理的国际经济新秩序，维护国家利益。相关链接：2005年7月．中国倡议的WTO小型部长级会议在大连召开，世贸组织总干事和三十多个成员的代表出席会议。
人教版高中数学选修3排列与排列数教学设计
4.有8种不同的菜种,任选4种种在不同土质的4块地里,有 种不同的种法. 解析:将4块不同土质的地看作4个不同的位置,从8种不同的菜种中任选4种种在4块不同土质的地里,则本题即为从8个不同元素中任选4个元素的排列问题,所以不同的种法共有A_8^4 =8×7×6×5=1 680(种).答案:1 6805.用1、2、3、4、5、6、7这7个数字组成没有重复数字的四位数.(1)这些四位数中偶数有多少个?能被5整除的有多少个?(2)这些四位数中大于6 500的有多少个?解:(1)偶数的个位数只能是2、4、6,有A_3^1种排法,其他位上有A_6^3种排法,由分步乘法计数原理,知共有四位偶数A_3^1·A_6^3=360(个);能被5整除的数个位必须是5,故有A_6^3=120(个).(2)最高位上是7时大于6 500,有A_6^3种,最高位上是6时,百位上只能是7或5,故有2×A_5^2种.由分类加法计数原理知,这些四位数中大于6 500的共有A_6^3+2×A_5^2=160(个).
人教版高中数学选修3超几何分布教学设计
探究新知问题1：已知100件产品中有8件次品，现从中采用有放回方式随机抽取4件．设抽取的4件产品中次品数为X，求随机变量X的分布列.（1）：采用有放回抽样，随机变量X服从二项分布吗？采用有放回抽样，则每次抽到次品的概率为0.08，且各次抽样的结果相互独立,此时X服从二项分布,即X～B(4，0.08).（2）：如果采用不放回抽样，抽取的4件产品中次品数X服从二项分布吗？若不服从，那么X的分布列是什么？不服从，根据古典概型求X的分布列.解：从100件产品中任取4件有 C_100^4 种不同的取法，从100件产品中任取4件，次品数X可能取0,1,2,3,4.恰有k件次品的取法有C_8^k C_92^(4-k)种.一般地，假设一批产品共有N件，其中有M件次品．从N件产品中随机抽取n件(不放回），用X表示抽取的n件产品中的次品数，则X的分布列为P(X＝k）＝CkM Cn－kN－M CnN ，k＝m，m＋1，m＋2，…，r.其中n，N，M∈N*，M≤N，n≤N，m＝max{0，n－N＋M}，r＝min{n，M}，则称随机变量X服从超几何分布．
人教版高中数学选修3二项式定理教学设计
二项式定理形式上的特点(1)二项展开式有n+1项,而不是n项.(2)二项式系数都是C_n^k(k=0,1,2,…,n),它与二项展开式中某一项的系数不一定相等.(3)二项展开式中的二项式系数的和等于2n,即C_n^0+C_n^1+C_n^2+…+C_n^n=2n.(4)在排列方式上,按照字母a的降幂排列,从第一项起,次数由n次逐项减少1次直到0次,同时字母b按升幂排列,次数由0次逐项增加1次直到n次.1．判断(正确的打“√”，错误的打“×”)(1)(a＋b)n展开式中共有n项． ( )(2)在公式中，交换a，b的顺序对各项没有影响． ( )(3)Cknan－kbk是(a＋b)n展开式中的第k项． ( )(4)(a－b)n与(a＋b)n的二项式展开式的二项式系数相同． ( )[解析] (1)× 因为(a＋b)n展开式中共有n＋1项．(2)× 因为二项式的第k＋1项Cknan－kbk和(b＋a)n的展开式的第k＋1项Cknbn－kak是不同的，其中的a，b是不能随便交换的．(3)× 因为Cknan－kbk是(a＋b)n展开式中的第k＋1项．(4)√ 因为(a－b)n与(a＋b)n的二项式展开式的二项式系数都是Crn.[答案] (1)× (2)× (3)× (4)√
人教版高中数学选修3全概率公式教学设计
2.某小组有20名射手，其中1，2，3，4级射手分别为2，6，9，3名.又若选1，2，3，4级射手参加比赛，则在比赛中射中目标的概率分别为0.85，0.64，0.45，0.32，今随机选一人参加比赛，则该小组比赛中射中目标的概率为________. 【解析】设B表示“该小组比赛中射中目标”，Ai(i=1，2，3，4)表示“选i级射手参加比赛”，则P(B)= P(Ai)P(B|Ai)= 2/20×0.85+ 6/20 ×0.64+ 9/20×0.45+ 3/20×0.32=0.527 5.答案：0.527 53.两批相同的产品各有12件和10件，每批产品中各有1件废品，现在先从第1批产品中任取1件放入第2批中，然后从第2批中任取1件，则取到废品的概率为________. 【解析】设A表示“取到废品”，B表示“从第1批中取到废品”，有P(B)= 112，P(A|B)= 2/11 ，P(A| )= 1/11所以P(A)=P(B)P(A|B)+P( )P(A| )4．有一批同一型号的产品，已知其中由一厂生产的占 30%, 二厂生产的占 50% , 三厂生产的占 20%, 又知这三个厂的产品次品率分别为2% , 1%, 1%，问从这批产品中任取一件是次品的概率是多少？
人教版高中数学选修3条件概率教学设计
(2)方法一:第一次取到一件不合格品,还剩下99件产品,其中有4件不合格品,95件合格品,于是第二次又取到不合格品的概率为4/99,由于这是一个条件概率,所以P(B|A)=4/99.方法二:根据条件概率的定义,先求出事件A,B同时发生的概率P(AB)=(C_5^2)/(C_100^2 )=1/495,所以P(B|A)=(P"(" AB")" )/(P"(" A")" )=(1/495)/(5/100)=4/99.6.在某次考试中,要从20道题中随机地抽出6道题,若考生至少答对其中的4道题即可通过;若至少答对其中5道题就获得优秀.已知某考生能答对其中10道题,并且知道他在这次考试中已经通过,求他获得优秀成绩的概率.解:设事件A为“该考生6道题全答对”,事件B为“该考生答对了其中5道题而另一道答错”,事件C为“该考生答对了其中4道题而另2道题答错”,事件D为“该考生在这次考试中通过”,事件E为“该考生在这次考试中获得优秀”,则A,B,C两两互斥,且D=A∪B∪C,E=A∪B,由古典概型的概率公式及加法公式可知P(D)=P(A∪B∪C)=P(A)+P(B)+P(C)=(C_10^6)/(C_20^6 )+(C_10^5 C_10^1)/(C_20^6 )+(C_10^4 C_10^2)/(C_20^6 )=(12" " 180)/(C_20^6 ),P(E|D)=P(A∪B|D)=P(A|D)+P(B|D)=(P"(" A")" )/(P"(" D")" )+(P"(" B")" )/(P"(" D")" )=(210/(C_20^6 ))/((12" " 180)/(C_20^6 ))+((2" " 520)/(C_20^6 ))/((12" " 180)/(C_20^6 ))=13/58,即所求概率为13/58.
人教版高中数学选修3正态分布教学设计
3.某县农民月均收入服从N(500,202)的正态分布,则此县农民月均收入在500元到520元间人数的百分比约为 . 解析:因为月收入服从正态分布N(500,202),所以μ=500,σ=20,μ-σ=480,μ+σ=520.所以月均收入在[480,520]范围内的概率为0.683.由图像的对称性可知,此县农民月均收入在500到520元间人数的百分比约为34.15%.答案:34.15%4.某种零件的尺寸ξ(单位:cm)服从正态分布N(3,12),则不属于区间[1,5]这个尺寸范围的零件数约占总数的 . 解析:零件尺寸属于区间[μ-2σ,μ+2σ],即零件尺寸在[1,5]内取值的概率约为95.4%,故零件尺寸不属于区间[1,5]内的概率为1-95.4%=4.6%.答案:4.6%5. 设在一次数学考试中,某班学生的分数X~N(110,202),且知试卷满分150分,这个班的学生共54人,求这个班在这次数学考试中及格(即90分及90分以上)的人数和130分以上的人数.解:μ=110,σ=20,P(X≥90)=P(X-110≥-20)=P(X-μ≥-σ),∵P(X-μσ)≈2P(X-μ130)=P(X-110>20)=P(X-μ>σ),∴P(X-μσ)≈0.683+2P(X-μ>σ)=1,∴P(X-μ>σ)=0.158 5,即P(X>130)=0.158 5.∴54×0.158 5≈9(人),即130分以上的人数约为9人.
人教版高中政治选修3国家的本质教案
①含义：即国家管理形式，是国家政权的组织形式②政体的必要性和重要性A、行使职能B、维护其根本利益掌握国家政权的阶级为实现政治统治、行使社会管理职能，必然要采取某种形式组织政权机关。统治阶级为维护其根本利益，总是力求采用最有效的政权组织形式。3、国体与政体的关系（板书）（1）、政体的多样性（2）、国体与政体的关系①国体决定政体，并通过一定的政体来体现；政体体现国体，并服务于特定的国体。适当的政体能够巩固国体，不适当的政体会危害国体。补充：政体由国体决定并反映国体，国体是主要的方面。但是，政体也具有一定的独立性，影响它形成的因素主要有：历史条件、阶级力量对比、传统习惯、国际环境影响等。②专政政体国体与政体，即是国家制度中内容与形式两个方面(3)从国体、政体两个方面看民主制国家补充：专政即是主要依靠暴力实行的统治，它与民主相对立，属于国体的范畴，而专制则与法制相对立，属于政体的范畴。
人教版高中数学选修3组合与组合数教学设计
解析:因为减法和除法运算中交换两个数的位置对计算结果有影响,所以属于组合的有2个.答案:B2.若A_n^2=3C_(n"-" 1)^2,则n的值为( )A.4 B.5 C.6 D.7 解析:因为A_n^2=3C_(n"-" 1)^2,所以n(n-1)=(3"(" n"-" 1")(" n"-" 2")" )/2,解得n=6.故选C.答案:C 3.若集合A={a1,a2,a3,a4,a5},则集合A的子集中含有4个元素的子集共有 个. 解析:满足要求的子集中含有4个元素,由集合中元素的无序性,知其子集个数为C_5^4=5.答案:54.平面内有12个点,其中有4个点共线,此外再无任何3点共线,以这些点为顶点,可得多少个不同的三角形?解:(方法一)我们把从共线的4个点中取点的多少作为分类的标准:第1类,共线的4个点中有2个点作为三角形的顶点,共有C_4^2·C_8^1=48(个)不同的三角形;第2类,共线的4个点中有1个点作为三角形的顶点,共有C_4^1·C_8^2=112(个)不同的三角形;第3类,共线的4个点中没有点作为三角形的顶点,共有C_8^3=56(个)不同的三角形.由分类加法计数原理,不同的三角形共有48+112+56=216(个).(方法二 间接法)C_12^3-C_4^3=220-4=216(个).
