1, the idea of function and equation

Function thought is the abstraction, generalization and refinement of function content at a higher level, which plays an important role in the study of equations, inequalities, series, analytic geometry and so on.

Equation thought is the basic idea to solve all kinds of calculation problems and the basis of calculation ability. The thought of function and equation is considered as the focus of seven important ways of thinking.

2. The combination of numbers and shapes.

The objects of mathematical research are quantitative relations and spatial forms, that is, numbers and shapes.

In one-dimensional space, real numbers are in one-to-one correspondence with points on the number axis in two-dimensional space, and real numbers are in one-to-one correspondence with points on the coordinate plane. In the combination of form and form, multiple-choice questions and fill-in-the-blank questions pay attention to the transformation from number to form, consider the rigor of reasoning in solving problems, and highlight the transformation from form to number.

3. The concept of classification and integration

Classification is a basic logical method in natural science and even social science research.

From a specific point of view, choose the appropriate classification standard.

Division is only a means, and classification research is the purpose.

It is the essential attribute of the idea of classification and integration that there is division and combination, and division before combination.

4. Change and change of ideas

Turn complex problems into simple problems, difficult problems into easy problems, and unsolved problems into solved problems.

Flexible and diverse, there is no unified model, using dynamic thinking to find ways and means to help solve problems.

5, special and general ideas

Through the understanding and research of individual cases, we can form an understanding of things.

From shallow to deep, from phenomenon to essence, from part to whole, from practice to theory.

From special to general, and then from general to special.

6. Limited and infinite thoughts

Turning the study of infinity into the study of finiteness is the only way to solve the infinite problem.

The accumulated experience in solving infinite problems and transforming finite problems into infinite problems are the direction of solution.

7, the concept of possibility and inevitability

The two most basic characteristics of random phenomena are the randomness of results and the stability of frequency.

Find inevitability in the accident, and then use the law of inevitability to solve the accident.