1、2012 高考数学反证法与前面所讲的方法不同，反证法是属于“间接证明法”一类，是从反面的角度思考问题的证明方法，即：肯定题设而否定结论，从而导出矛盾推理而得。法国数学家阿达玛(Hadamard)对反证法的实质作过概括：“若肯定定理的假设而否定其结论，就会导致矛盾”。具体地讲，反证法就是从否定命题的结论入手，并把对命题结论的否定作为推理的已知条件，进行正确的逻辑推理，使之得到与已知条件、已知公理、定理、法则或者已经证明为正确的命题等相矛，矛盾的原因是假设不成立，所以肯定了命题的结论，从而使命题获得了证明。反证法所依据的是逻辑思维规律中的“矛盾律”和“排中律”。在同一思维过程中，两个互相矛盾的判断
2、不能同时都为真，至少有一个是假的，这就是逻辑思维中的“矛盾律”；两个互相矛盾的判断不能同时都假，简单地说“A 或者非 A”，这就是逻辑思维中的“排中律”。反证法在其证明过程中，得到矛盾的判断，根据“矛盾律”，这些矛盾的判断不能同时为真，必有一假，而已知条件、已知公理、定理、法则或者已经证明为正确的命题都是真的，所以“否定的结论”必为假。再根据“排中律”，结论与“否定的结论”这一对立的互相否定的判断不能同时为假，必有一真，于是我们得到原结论必为真。所以反证法是以逻辑思维的基本规律和理论为依据的，反证法是可信的。反证法的证题模式可以简要的概括我为“否定推理否定”。即从否定结论开始，经过正确无误的推
3、理导致逻辑矛盾，达到新的否定，可以认为反证法的基本思想就是“否定之否定”。应用反证法证明的主要三步是：否定结论 推导出矛盾 结论成立。实施的具体步骤是：第一步，反设：作出与求证结论相反的假设；第二步，归谬：将反设作为条件，并由此通过一系列的正确推理导出矛盾；第三步，结论：说明反设不成立，从而肯定原命题成立。在应用反证法证题时，一定要用到“反设”进行推理，否则就不是反证法。用反证法证题时，如果欲证明的命题的方面情况只有一种，那么只要将这种情况驳倒了就可以，这种反证法又叫“归谬法”；如果结论的方面情况有多种，那么必须将所有的反面情况一一驳倒，才能推断原结论成立，这种证法又叫“穷举法”。在数学解题中
4、经常使用反证法，牛顿曾经说过：“反证法是数学家最精当的武器之一”。一般来讲，反证法常用来证明的题型有：命题的结论以“否定形式”、“至少”或“至多”、“唯一”、“无限”形式出现的命题；或者否定结论更明显。具体、简单的命题；或者直接证明难以下手的命题，改变其思维方向，从结论入手进行反面思考，问题可能解决得十分干脆。、再现性题组：1.已知函数 f(x)在其定义域内是减函数，则方程 f(x)0 _。A.至多一个实根 B.至少一个实根 C.一个实根 D.无实根2.已知 aab ab B. ab aba C. aba ab D. ab ab a22 223.已知 l，a ，b ，若 a、b 为异面直线，则
5、_。A. a、b 都与 l 相交 B. a、b 中至少一条与 l 相交C. a、b 中至多有一条与 l 相交 D. a、b 都与 l 相交4. 四面体顶点和各棱的中点共 10 个，在其中取 4 个不共面的点，不同的取法有_。(97 年全国理)A. 150 种 B. 147 种 C. 144 种 D. 141 种【简解】1 小题：从结论入手，假设四个选择项逐一成立，导出其中三个与特例矛盾，选 A；2 小题：采用“特殊值法”，取 a1、b0.5，选 D；3 小题：从逐一假设选择项成立着手分析，选 B；4 小题：分析清楚结论的几种情况，列式是：C C 436,选 D。1046、示范性题组：例 1.
6、如图，设 SA、SB 是圆锥 SO 的两条母线，O 是底面圆心，C 是 SB 上一点。求证：AC 与平面 SOB 不垂直。【分析】结论是“不垂直”，呈“否定性”，考虑使用反证法，即假设“垂直”后再导出矛盾后，再肯定“不垂直”。【证明】 假设 AC平面 SOB， 直线 SO 在平面 SOB 内， ACSO， SO底面圆 O， SOAB， SO平面 SAB， 平面 SAB底面圆 O，这显然出现矛盾，所以假设不成立。即 AC 与平面 SOB 不垂直。【注】否定性的问题常用反证法。例如证明异面直线，可以假设共面，再把假设作为已知条件推导出矛盾。例 2. 若下列方程：x 4ax4a30， x (a1)x
7、a 0, x 2ax2a0 至2222少有一个方程有实根。试求实数 a 的取值范围。【分析】 三个方程至少有一个方程有实根的反面情况仅有一种：三个方程均没有实根。先求出反面情况时 a 的范围，再所得范围的补集就是正面情况的答案。【解】 设三个方程均无实根，则有：,解得 ,即 CCthe weather is too coldDit is extremely short of water3 结构相似 取其一（有众多相同的词）一时装模特，在表演时，自己笑了，台下一片喝彩声. 她自感成功，下去向老板索奖. 谁知老板不仅没奖，反而把她炒了. 冤枉不？不冤枉！模特二字，特是幌子，模是目的. 模特表演是不
8、能笑的. 试想，模特一笑，只能显示模特本人的特色，谁还去看她身上的服装呢？所以，模特一笑，特在模掉！70. According to the study of Brown Medical School, _.A. more than 6 million Americans distrust doctorsB. only 1/10 of medical websites aim to make a profitC. about 1/10 of the websites surveyed are of high quality BCD. 72% of health websites offer i
9、ncomplete and faulty factsE.72. According to the text, Driver Alert _.A. aims to reduce tiredness-related accidents B. has gone through testing at laboratories C. aims to prevent drivers from sleeping ACD. has been on sale for 12 months69. When people suffer from Alzheimer”s disease, _. A. their fam
10、ilies and friends will suffer from the same disease B. their families and friends will experience mental sufferings ABC. they will certainly die in 8 to 10 years D. they will forget everybody but their spouses 16. The rapid-transit rail lines should _.A. develop as quickly as possible B. develop wit
11、h local economic development C. develop after local economic development D. develop with the construction industryBC4 相对、绝对项 取其一一群人到庙里上香，其中有一个聋子，还有一个小孩.上香完毕，发现小孩不见了.半天找不到影子后，大家来“问”这聋子.聋子把手一指，发现小孩藏在大钟底下，而且还在用手拍钟.大家奇怪，连我们都没有听见小孩拍钟的声音，聋子怎么听着了呢？其实，大伙把事情想错了，聋子哪里听到了钟声，只是凭着他的亮眼，发现大钟底下是藏小孩的好地方. 74According
12、to the passage, which of the following statements is TRUE?AMountaineering is a match between climbers.BMountaineering is similar to other sports in many ways. C 相对 D 绝对CClimbers work like a team when their lives may depend on a rope.DClimbers help each other in time of difficulty.52According to the
13、passage, the new treatment_Acan kill all the H1V viruses A 相对 B 绝对Bcannot get rid of the viruses completelyCcan double the number of disease - fighting cellsDcan reconstruct the patients immune system想了解更多满分秘诀，请立即购买张勇强编辑的 2012 高考英语阅读思维重现法则，尤其适合 100 分以上的高考生使用！强军英语高分密码真的有这么神奇吗？是！一点儿没错！效果是绝对的真实！作为一种标准化
14、考试，选择题本身是有很多缺陷的,这些缺陷就是暗示点，就是解题的突破口!吴军英语高分密码通过对历年真题的长时间的研究，对这些暗示点进行了全面、深入、细致的挖掘和整理,将其转化为超级解题秘诀!每一个秘诀的准确率都在 95%以上，甚至是 100% 吴军英语高分密码,真正做到了立竿见影！甚至是一剑封喉！马上用吴军英语高分密码对照历年所有的高考真题进行逐一的验证吧! 遇到吴军老师，您太幸运了！超级雷人的技巧 顶极给力的规律2012 高考英语阅读矩阵法则（教案）什么是矩阵法则？在复杂的阅读问题中，往往存在许多成对的质量因素将这些成对因素找出来，分别排列成行和列，其交点就是其相互关联的程度，在此基础上再找出
15、存在的问题及问题的形态，从而找到解决问题的思路。2012 高考英语如何才能 “马”上成功？ 努力+骑上一匹好马！你和马赛跑，谁跑的快？当然是马！尤其是一匹可以成为冠军的快马！即使你没成为冠军，但因骑在“马”上，从而也非常接近成功了！众所周知，姚明因 NBA 火箭队这匹快马而星光璀璨！您的孩子就如同刚刚加入 NBA 小牛队的易建联！矩阵法则将使您的孩子 快速提分 易如反掌！学习信心 建入佳境！金榜题名 浮想联翩！还记得吗？吴军老师在 2011年高考英语阅读中帮您解决了下列问题 ：高考英语如何才能瞬间大幅度提分？模棱两可处和看不懂，该怎么办？2012 年将为您解密高考阅读标准答案设置规律: 矩阵法
16、则比如我给你三个矩阵法则序列，来选择下列无法定位的 2007 辽宁卷 58 题：出题大概是按照顺序出的；选项中被动结构的容易是答案；找不到或找不全关键字无法确定出题点时,可按出题顺序,大致找到未出题的段落,然后看段首尾有没有段落中心句,没有就看该段反复出现了哪个名词 ,含有它或与其意思倾向就是答案了.What will people die of 100 years from now? If you think that is a simple question, you have not been paying attention to the revolution that is taki
17、ng place in bio-technology(生物技术). With the help of new medicine, the human body will last a very long time. Death will come mainly from accidents, murder and war. Todays leading killers, such as heart diseases, cancer, and aging itself, will become distant memory.In discussion of technological chang
18、es, the Internet gets most of the attention these days. But the change in medicine can be the real technological event of our times. How long can humans live? Human brains were known to decide the final death. Cells(细胞) are the basic units of all living things, and until recently, scientists were su
19、re that the life of cells could not go much beyond 120 years because the basic materials of cells, such as those of brain cells, would not last forever. But the upper limits will be broken by new medicine. Sometime between 2050 and 2100, medicine will have advanced to the point at which every 10 yea
20、rs or so, people will be able to take medicine to repair their organs(器官). The medicine, made up of the basic building materials of life, will build new brain cells, heart cells, and so on-in much the same way our bodies make new skin cells to take the place of old ones.It is exciting to imagine tha
21、t the advance in technology may be changing the most basic conditional human existence, but many technical problems still must be cleared up on the way to this wonderful future.56According to the passage, human death IS now mainly caused by_.Adiseases and aging Baccidents and warCaccidents and aging
22、 Dheart disease and war57In the author s opinion, todays most important advance in technology lies in_. 细节题可根据提干关键字到原文中定位！Amedicine B. the Internet Cbrain cells D. human organ58Humans may live longer in the future because_.Aheart disease will be far away from usBhuman brains can decide the final dea
23、thCthe basic materials of cells will last foreverDhuman organs can be repaired by new medicine59We can learn from the passage that _. 推论在尾段，找不到就向中心靠拢，或找 but 句。Ahuman life will not last more than 120 years in the futureBhumans have to take medicine to build new skin cells nowCmuch needs to be done be
24、fore humans can have a longer lifeDwe have already solved the technical problems in building new cells发现此细节题通过关键字无法定位，但 57 和 59 题都解决了，发现第二大段没出题或只出了一个题，按出题顺序，本问题 58 题应该定位在第二段。通过选项中被动结构的容易是答案原则，可定位 58 题 D 选项容易是答案！然后划 D 项中的名词 medicine 和 organs，到第二大段中去找。发现 medicine 在第二大段中反复出现，即为中心词。当然就可以确定 D 是答案了！我们刚刚出炉
25、的 2012 高考英语阅读矩阵法则，因商业秘密而只能点到为止，欢迎懂英语的父母或其亲属认真考核，从速折扣预定！吴军英语高分密码真的有这么神奇吗？是！一点儿没错！效果是绝对的真实！作为一种标准化考试，选择题本身是有很多缺陷的,这些缺陷就是暗示点，就是解题的突破口!吴军英语高分密码通过对历年真题的长时间的研究，对这些暗示点进行了全面、深入、细致的挖掘和整理,将其转化为超级解题秘诀!每一个秘诀的准确率都在 95%以上，甚至是 100% 吴军英语高分密码,真正做到了立竿见影！甚至是一剑封喉！马上用吴军英语高分密码对照历年所有的高考真题进行逐一的验证吧! 遇到吴军老师，您太幸运了！请上 或上百度, 输
26、入“沈阳高分英语家教吴军“查询!现在预定吴军 2012 高考英语高分秘诀系统教案巨划算！2012 高考英语阅读 矩阵法则 教案 原价 3200 元 现 5 折 1600 元2012 高考英语 完形圣经 秘诀教案 原价 3200 元 现 5 折 1600 元2012 高考英语 3 天提分秘诀教案 原价 6000 元 现 6 折 3600 元2012 高考英语高频答案词汇教案 原价 5000 元 现 5 折 2500 元2012 年 4 月初恢复原价！唤起迅捷激情 震撼学子心灵2012 高考英语完形圣经秘诀教案透 过已知信息 推断未知信息不易策略，扫描选项，在万变中找到不变的规律！ 简易策略，瞻前
27、顾后，化繁为简，化难为易！变易策略，左顾右盼，以变制变，熟能生巧！首尾段首尾句,边做边看选项中与中心同现词或复现词!扫描选项 同义词 / 同类词排除高频答案词相反项有解同现思路 瞻前顾后 复现 逻辑结构左顾右盼 P 原则关联结构技巧归纳: 感情色彩 时态暗示法 动词综合法(主语/宾语是人是物 ? 及不及物?过程还是结果?), (略) 共 20 多项法则,交叉都指向同一个答案才最准确!满分策略: 五四运动法 串线交叉法 主线贯穿法, (略) 节选教案试看!瞻前顾后 同现 复现 逻辑结构同现中心同现是指段落的首段的中心词或段落中反复出现的名词或名词词组,在被选空格内的句子中也重复出现或与其意思倾斜
28、向;词汇同现是指属于同一词汇搭配范畴或者某一领域的词汇在文章中共同出现，达到语义衔接的目的。一般来说，上下文中词汇的范畴越小，上下文的衔接关系越紧密。首段首句一般都是中心句,名词是核对重点!Then , mountain - climbing began to grow popular as a sport. To some people, there is something greatly _28_ about getting to the _29_ of a high mountain: a struggle against nature is finer than a battle _
29、30_other human begins. And then , when you are at the mountain top after a long and difficult _31_, what a _32_ reward ( 奖品 ) it is to be able to look _33_ on everything within _34_! At such time , you feel happier and prouder than you can ever feel down _35_. 与首尾句名词 动词 形容词 副词倾向!28.A.excited B. inte
30、rested C.dangerous D.terrible 32.A.surprising B.excited C.disappointing D.astonishing Dorothy Brown was very happy as she sat in the theatre listening to the music. Today her little daughter Lauren was giving her _1_ concert. She had been waiting for this _2_ for years and years. “Now it is here at
31、last,” she thought. “How beautiful her _3_ is.”The song made her _4_ to the days when she was Laurens _5_. As a young _6_, Dorothy wanted to be a concert singer. She studied _7_ in France, Italy and in the United States. “You can become a fine _8_ in the future,” her teachers told her. “But you must
32、 be _9_ to study hard and work for many years. 3. A. voice B. face C. dress D. life7. A. French B. music C. piano D. dance8. A. actress B. student C. singer D. dancerK抓住中心意思-围绕什么话题 (在文章中出现频率最多的词 )Every Thursday afternoon, my art history class meets not in our usual lecture hall ( 演讲厅 ) but in our un
33、iversity Art Museum. We spend our one-hour class discussing two or there of the _1_, many of which are by artists that we have already studied in class. The professor begins by selecting one _2_ of art. After giving us a quick background on the artist , he will open up for class _3_. 1. A. subjects
34、B. paintings C. speeches D. lectures仅有技巧和词汇是不够的,高频答案词及短语,是突破的关键!但相当多的具体情况和难以处理的选项,做起来还是有些吃力,怎么办?吴军老师刚刚出炉的 2012 高考英语完形暗示点全归纳将使您傲视群雄!宾语从句是特殊疑问句 WH-或 whether/if 时,要选下列动词:ask, doubt, wonder, want to know, know, guess答题选动词:2011全国新课标卷The professor 37 the lecture hall, placed upon his desk a large jar fill
35、ed with dried beans(豆 ), and invited the students to 38 how many beans the jar contained. After 39 shouts of wildly wrong guesses the professor smiled a thin, dry smile, announced the 40 answer, and went on saying, “You have just 41 an important lesson about science.38. Acount B. guess C. report D.
36、watch考察动词，或根据后文 wildly wrong guesses 的提示，考虑复现选 B。反过来选 WH-或 whether/if:2011安徽卷One afternoon. I walked into a building to ask 41 there were any job opportunities(机会 )，The people there advised me not to continue my job search in that 42 .41. A. why B. wherever C. whether D. whenever一天，作者走进一座大楼去问“是否”(wh
37、ether) 有自己能做的工作。选 C。A 项为“为什么”；B 项为“ 无论在那”；D 项为“无论何时”怎么样?这样做题快吗?为了让您更加深信不疑,我们再免费发布一个法则,你可以马上用下列真题或你学校的模拟练习题来验证一下,好使,就要赶紧预定呦!每省仅限定 10 套,额满即!止正面的,积极的,肯定的, 还是负面的,消极的,否定的?“Im sorry, but we have enough 27 for the newspaper already. Come back next year and well talk then.” Jenna smiled 28 and left. “Why is
38、 high school so 29 ?” she sighed.叹气 sighed 说明是勉强的,选消极的 weakly28. A. widely B. weakly C. excitedly D. brightlyTired and sad,she told her story 38 ,not to anyone in particular.38.A.tearfully B.seriously C.carefully D.calmlyIt seems funny that we are _40_ for things, with which we are unfamiliar or abo
39、ut which we are _41_, but we all, my friends as well as I, consider this one of lifes _42_ .41. A. uncertain B. unhappy C. not pleased D. careful 2011四川卷I truly feel that my mother led me here, to Morzaine, and to my future as a happy wife and businesswoman. When Mum 21 in October 2007, I was a cook
40、 In December that year. while I was working for a wedding, a pearl necklace Mum had left me 22 . I was distraught（忧心如焚的） .Some days later, I was 23 that a guy who was working with us that day. “could probably have made a fortune 24 he necklace he found.” 25 , he returned it. 22.A. burned B. disappea
41、red C . broke D. dropped 22 空就近 distraught（忧心如焚的）是负的,只有 disappear 是负的；burn 燃烧；break打破；drop 降低，落下。有后文的我感到 “忧心如焚”及“ 归还”（return）可知此处是指项链丢失了。B2011安徽卷Nearly ten minutes later, he 45, He asked me about my plans and encouraged me to stay 46 . Then he offered to take me to Royal Oak to 47 a job. 积极的!I was a
42、 little surprised. but had a 48 feeling about him. Along the way ,I realized that I had 49 resumes(简历). Seeing this, the man 50 at his business partners office to make me fifteen 51 copies. He also gave me some 52 on dressing and speaking. I handed out my resumes and went home feeling very 53 . The
43、following day, I received a 54 from a store in Royal Oak offering me a job.46. A. silent B. busy C. positive D. comfortable他问了问我的打算，鼓励我要振作起来，不要灰心。选 C。A 项为“沉默不语的”；B项为“忙绿的”；C 项为“积极乐观的，有信心的”；D 项为 “舒适的，舒服的”。48. A. dull B. good C. guilty D. general作者对他的主动帮助感到有点惊奇，但是对他充满了“好感” (good feeling)。选 B。A项为“阴暗的，无趣
44、的” ；C 项为“内疚的”；D 项为“一般的，普通的”。53. A. lonely B. funny C. disappointed D. satisfied我分发完简历回到家感到非常“满意”(satisfied) 。选 D。A 项为“寂寞的，孤独的” ；B项为“滑稽的，可笑的” ；C 项为“失望的，沮丧的”。2011四川卷Some days later, I was 23 that a guy who was working with us that day. “could probably have made a fortune 24 the necklace he found.” 25
45、, he returned it. Hearing how Id 26 Mum for six months before her death, he said, “Christmas is going to be 27 why not go out to the Alps for a couple of weeks?27.A.long B. hard C. merry D. freedeath.在 27 空附近是负的,B 项对应。在万家团圆的圣诞节，母亲刚去世，对我来说一定很难熬。B吴军英语高分密码真的有这么神奇吗？是！一点儿没错！效果是绝对的真实！作为一种标准化考试，选择题本身是有很多缺陷
46、的,这些缺陷就是暗示点，就是解题的突破口!吴军英语高分密码通过对历年真题的长时间的研究，对这些暗示点进行了全面、深入、细致的挖掘和整理,将其转化为超级解题秘诀!每一个秘诀的准确率都在 95%以上，甚至是 100% 吴军英语高分密码,真正做到了立竿见影！甚至是一剑封喉！马上用吴军英语高分密码对照历年所有的高考真题进行逐一的验证吧! 遇到吴军老师，您太幸运了！请上 或上百度, 输入“沈阳高分英语家教吴军“查询!号外！想揭秘高考出题者的答案最爱吗？想毫无顾忌地秒杀正确答案吗？梦想今天就可以成真！联想记忆法,词根记忆法,记忆树学词汇和右脑记忆法是挺好的,但就是学起来太累!而且还与答题语境和正确选项无
47、关！好不容易记住了,考试却选错了! 付出了 100%却得不到 5%的回报! 另外，有些知名的英语考试专家，虽然发现了很多规律，但相当部分都是太复杂，好比又多学了一科哲学课程。那么，有没有既简单又易理解,还能在考试中立竿见影的学习秘诀呢？继沈阳吴军老师 2011-2012 年推出的高分密码后，2012 年他又创意出高考英语高频答案词一本通教案。这套系统教案在发布高频答案词的同时，又大量加入了 11 年来高考真题和模拟题做为考例并做出详尽的辨析和解析，另外还设计了过关试题并配备了答案。可以说，它是目前最简单,最迅捷的正确答案确认方式! 学习不到考纲 1/6 词汇（还没有中考的词汇多），就使 60-
48、110 分的同学和艺考生再也不会有“ 背得慢 ”、“背了老忘”和“老背不完”等老难题。不读文章直接做题，准确率 80%以上；只读一遍，准确率达到 95%！再配合语境答题技巧，准确率达到 100%也不再是梦！解决了同学们“做题慢、浪费时间 ”和“准确率低”等困难。2011 年末吴军高分英语巨献，2012 高考提分最快、最 in2012高考英语高频答案词 高频考点 必考点高频答案词一本通目录：一、单选、完形高频答案词二、高频句型核心词三、高频核心短语（以介词和副词为中心）四、语法考点高频答案词五、阅读词汇题及完形熟词僻义高频考点六、吴军 2012 高考英语必考点解密七、阅读高频答案词及其核心特征完形高频答案词 可快速向标准答案靠拢!解决“发挥不稳定”及“看不懂短文或看懂了还错”的两大难题。知道了第一类高频答案词就可以马上秒杀答案
