The solution to the final math problem in the college entrance examination 1. Function and equation thought
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 the functional relationship and using the image and nature of the function;
The idea of equation is to solve the problem by transforming the problem into an equation or inequality model with mathematical language from the quantitative relationship of the problem.
Students can use transformation ideas to transform functions and equations when solving problems.
Second, the combination of numbers and 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.
When solving math problems, students can draw as many pictures as possible to help them understand the meaning of the problems correctly and solve them quickly.
Third, the concept of special and general.
This kind of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it must also be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions.
Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.
Fourth, extreme thinking problem-solving steps
The general steps of extreme thinking to solve problems are:
1, try to conceive a variable related to the unknown quantity;
2. Confirm that the result of this variable through the infinite process is an unknown quantity;
3. Construct a function (sequence) and get the result with limit calculation rules or directly calculate the result with the limit position of the graph.
Five, classified discussion ideas
Students often encounter such a situation when solving problems. After solving a certain step, they can't continue with unified methods and formulas. 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. It is suggested that students should unify the standards when discussing and resolving different problems, and should not focus on or omit them.
The solution of NMET's last math problem is 1. To simplify a complex problem is to decompose a complex problem into a series of simple problems, divide a complex graph into several basic graphs, find similarities, find right angles, find special graphs and solve them slowly. NMET was taken down step by step. This way of thinking is particularly important. You can calculate first, prove first, and draw a conclusion by stepping on the main points.
2. The problem of motion is static. For dynamic graphics, first find the unchangeable line segments and angles, and whether there are always equal line segments, always congruent graphics and always similar graphics. All operations are based on them. After finding the relationship between the changing line segments, solve it slowly with algebra.
General problems are specialized, and some general conclusions cannot be solved. First look at special cases, such as the moving point problem, and see how it moves to the midpoint, how it moves to the vertical, and how it becomes an isosceles triangle. Find out the conclusion first, and then solve it slowly.