(1) transformation and regression: this idea will be used in almost all mathematical problems, specifically, transforming the unknown into

As we all know, such a step-by-step transformation can turn a complex problem into several simple small problems.

Then solve the problem.

(2) the relationship between function, equation and inequality:

This idea is generally ignored. In fact, both equation problems and inequality problems can be transformed into functions.

Problem, the root of the equation and the interval endpoint of the inequality solution set are both zero points of the function. Sometimes I study or solve equations with inequalities.

Type problem can be transformed into function problem, which can be solved by function image.

(3) Combination of numbers and shapes:

The idea of combining numbers and shapes is often applied to functions, derivatives and analytic geometry. These topics

They all construct the function first (some questions directly give the function expression), and then according to the analytical properties of the function (monotonicity, parity)

And periodic symmetry) to solve the problem. Most people will think of using this idea, but it is difficult to use it well. Here it is.

Need to do exercises to train.

(4) Zoom:

Scaling is the abbreviation of enlargement and reduction, which is often used in inequality problems (mean value theorem

Inequalities in optional parts and inequalities in derivative parts are often used). This kind of thinking is the most difficult mathematical thinking.

It's hard to use when you don't know, and sometimes even if you know the idea of scaling, you won't zoom in or

Shrinking, zooming in or zooming out may not be appropriate. It is futile to enlarge too much or reduce too little. ordinary

To master this mathematical idea well requires not only a lot of practice, but also inspiration (that is, luck), but

Fortunately, the college entrance examination does not focus on this part, and sometimes it does not test related topics at all.

(5) Others: There are many other mathematical ideas, but what I said above can be used in high school. ...