[Reprint] college entrance exam mathematics II: of transformation and conversion black Saburo _ righteousness _ Sina Blog

Original address: college entrance exam mathematics II: of transformation and transformation author: Li Guangxue teachers according to many students and parents of the suggestions and requests, at the same time in order to realize the grade three students provides guidelines for blog useful study guide, publication of this blog from today will be the college entrance examination of mathematical thinking and the college entrance examination topics PETS article, look forward to everyone's support. Shanghai City seven Po middle school Li Guangxue of return and transformation of thought in solving in the of application a, and knowledge integration 1. solution mathematics problem Shi, often encounters some problem directly solution more difficulties, through observation, and analysis, and analogy, and Lenovo, thinking process, select using appropriate of mathematics method for transform, will original problem transformation for a new problem (relative,, on themselves more familiar of problem), through new problem of solution, reached solution original problem of purpose, this a thinking we called "of return and transformation of thinking". 2. contact the essence of transformation and transformation is revealed to achieve transformation. Except in very simple math problems, each mathematical problem solutions are achieved through into known issues. In this sense, settlement is a process of transformation from unknown to known mathematical problems. Of transformation and transformation of ideas is fundamental to solve mathematical problems, and problem solving process is actually a step by step conversion process. Mathematical transformation of abound, such as the transformation of unknown into the known and transformation of complex problems into simple questions, and new knowledge to the transformation of the old knowledge, conversion between the proposition, and transformation of space to the transformation of a plane, to the transformation of low-dimensional high dimensional, $ plural to a conversion, high order to low conversion, beyond the transformation to algebra, functions and equations of transformation, is the embodiment of the transformation thought. 3. transformation of equivalent transformation and transformation of non-equivalence. Before and after the conversion is necessary and sufficient conditions for the equivalence, equivalence transformation as possible; in the case of a last resort, not equivalent transformation, should additional restrictions, to maintain the equivalence, concluded or to be the necessary validation. 4. transformation and conversion should follow the basic principles: (1) become familiar with the principles of: convert a strange question to become familiar with the problems in order to facilitate the knowledge, experience, and that we make use of familiar problems to solve. (2) simple principle: the complex problem of transformation to a simple question, through the simple solution of the problem, achieve the purpose of solving complex problems, or get some inspiration and basis of solving problems. (3) the principle of harmony: conditions or conclusions of transformation, making it more in line with the harmony of form and internal representation of the number, or transformation of proposition, its deduction to use a certain method or methods to meet law of people's thinking. (4) principles of Visual: compares the abstract into intuitive problem to solve the problem. (5) are difficult to reverse the principle: when the front when discussing the difficulty of the problem, consider the problem of negative, sought from back to the problem of searching, solution to the problem. II, and examples analysis cases 1. a factory 2001 production profit monthly increased, and monthly increased of profit same, but due to manufacturer is transformation construction, Yuan month inputs funds construction exactly and January Chief of profit equal, as inputs funds of monthly increased, and monthly increased inputs of percentage same, to December inputs construction funds and exactly and December of production profit same, asked annual total profit m and annual total inputs n of size relationship is ( ) A.m>N B.m<N C.m=N d. cannot determines [Analysis] monthly of profit group will conditions Xia, this road often does not pass, then if can change main Yuan, transfer variable Yuan in problem in the of status, on can makes problem solved. Beside, if $ x to deal with, both breeding and error-prone and principal components transformation, the problem becomes a inequality on p, realizing the problem to the low-dimensional transformation from high-dimensional, easy ways of solving problems. c summary of refined 1. skills, basic skills, a solid grasp of the basics and the basic approach is the basis for conversion; rich association and shrewd observation, comparison, analogy is the transformation of the subtle bridge training their own sense of conscious transformation and conversion needs with theorem, equations and principles have a deep understanding of nature and the summary of the typical problems and extraction, proactive contact consciously, to discover the essence of things. "Seizing the base, conversion" is the golden key to learn Mathematics. 2. for the implementation of effective return, you can either change the condition, you can also change the conclusion, we can transform internal structure of the problem, but also to transform problems of external form, either from an algebraic point of view to understand the issues, is available from the geometric angles to tackle the problem. please continues to reading: Shanghai City seven Po Middle School Li Guangxue provides high three: mathematics review must note of several key problem regression textbooks again Shang stepped college entrance examination mathematics: exam in the last of 15 minutes is important college entrance examination mathematics high min key: should ensure Foundation min does not loss teacher guide: college entrance examination examination skills college entrance examination mathematics: breakthrough capacity type small questions results again Shang stepped seven Po Middle School Li Guangxue college entrance examination mathematics common trap large search seven Po Middle School Li Guangxue college entrance examination mathematics high min key: should ensure Foundation min does not loss teacher guide: college entrance examination examination skills college entrance examination solving specially enrollment: overall thinking Tongji students: taught mathematics learning success a enrollment college entrance examination mathematics solving entrance: intuition thinking method learning mathematics of key links: how listening to good mathematics class college entrance examination review common of clinic programme let Arts student fell in love with mathematics college entrance examination mathematics review Mo go "a mere formality" master examination technical improve results college entrance examination mathematics knowledge shorthand mnemonics mathematics learning into���ؾ�:���ij־á�������ǿ�߱���ѧ���ѧ����:�߿���ѧ��������200ƪ���ѧ�߿���ѧ����:�𱩲���ͻ��30��!������Ķ�:�Ϻ����߱���ѧ���ѧ�ṩ �¸���:��ѧ��ϰ����ע��ļ����ؼ�����ع�α�����̨���׸��¸���:��ѧ�ܸ�ϰ�����߿���ѧ˼�뷽��֮һ:�����뷽�̵�˼��wbr>�߿���ѧ˼�뷽��֮��:������ת���߿���ѧ˼�뷽��֮��:���������߿���ѧ˼�뷽��֮��:���ν���߿���ѧ˼�뷽��֮��:����˼ά�߿���ѧ˼�뷽��֮��:���⻯˼��wbr>�߿���ѧ��ϰ�����ע������wbr>�����ѧ��ϰЧ�����Ҫ;��:�����˼�߿���ѧ����:ת��˼��Ľ�������߿���ѧ֪ʶ�ټǿھ�!-- ���Ľ��� -->