Function thought refers to analyzing and studying the quantitative relationship in mathematics from the viewpoint of movement change, and analyzing, transforming and solving problems by establishing functional relationship (or constructing function) and using the image and nature of function; The idea of equation is to transform the problem into an equation (equation group) or an inequality model (equation, inequality, etc.) to solve the problem. ) By using mathematical language. Using the idea of transformation, we can also transform functions and equations.
The second thought of solving problems in college entrance examination mathematics: the idea of combining numbers with shapes
The object of middle school mathematics research can be divided into two parts, one is number, the other is shape, but there is a connection between number and shape, which is called combination of number and shape or combination of shape and number. It is not only a "magic weapon" to find the breakthrough point of solving problems, but also a "good prescription" to optimize the way of solving problems. So when we solve math problems, we should draw pictures as much as possible to help us understand the meaning of the problems correctly and solve them quickly.
Special thinking and general thinking: the third thinking of solving problems in mathematics in college entrance examination
This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. According to this, we can directly determine the correct choice in multiple-choice questions. Not only that, it is also wonderful to explore the problem-solving strategies of subjective questions with this way of thinking.
The fourth thought of solving problems in college entrance examination mathematics: the steps of solving problems with extreme thoughts
The general steps of solving problems with extreme thinking are as follows: (1) Try to conceive a variable related to an unknown quantity; (2) Confirm that the result of the infinite process of this variable is an unknown quantity; (3) Construct a function (sequence) and use the limit calculation rule to get the result or use the limit position of the graph to directly calculate the result.
The fifth idea of solving problems in college entrance examination mathematics: classified discussion
It is often encountered that after solving a certain step, it can no longer be carried out in a unified way and formula. This is because the research object contains a variety of situations, which requires classifying all situations, solving them one by one, and then summarizing them to get a solution. This is a confidential discussion. There are many reasons for the discussion of classification, and there are many situations in the mathematical concept itself, such as the limitations of mathematical operation rules, some theorems and formulas, and the uncertainty and change of graphic position. When discussing and solving problems by classification, we should unify the standards, and we should not focus on them or leave them out.