The idea of (1) function is to abstract, generalize and refine the content of the function at a higher level, which plays an important role in the study of equations, inequalities, series, analytic geometry and so on.

(2) Equation idea is the basic idea to solve all kinds of calculation problems and the foundation of calculation ability.

The college entrance examination regards the thought of function and equation as seven important ways of thinking.

Second, the combination of numbers and shapes:

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

(2) In one-dimensional space, real numbers correspond to points on the number axis one by one.

In two-dimensional space, real number pairs establish a one-to-one correspondence with points on the coordinate plane.

In the combination of number and shape, multiple-choice questions and fill-in-the-blank questions pay attention to the transformation from number to shape, and consider the rigor of reasoning in solving problems, highlighting the transformation from shape to number.

Third: the idea of classification and integration.

(1) classification is a basic logical method in natural science and even social science research.

(2) Select the appropriate classification standard from the specific situation.

(3) Classification is only a means, and classification research is the purpose.

(4) It is the essential attribute of the idea of classified integration to divide and combine, and then divide and combine.

(5) The research on the classification and integration of mathematical problems of letter parameters pays attention to the rigor and thoroughness of students' thinking.

Fourth: transform ideas.

(1) Divide complex problems into simple ones, difficult ones into easy ones and unsolved ones into solved ones.

(2) Flexibility and diversity, there is no unified model, and dynamic thinking is used to find ways and methods to help solve problems.

(3) The college entrance examination pays attention to the commonly used transformation methods: general and special transformation, complex and simple transformation, structural transformation, and equivalent transformation of propositions.

Fifth: Special and General Thinking

(1) form an understanding of things through the understanding and research of individual cases.

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

(3) From special to general, and then from general to special.

(4) Construct special functions and special sequences, find special points, establish special positions, and use special values and special equations.

(5) Taking the new content as the material, highlighting the special and general ideas will become the direction of proposition reform.

Sixth: finite and infinite thoughts;

(1) It is the only way to solve infinite problems by transforming the study of infinity into the study of finiteness.

(2) The accumulated experience in solving infinite problems and transforming finite problems into infinite problems are the direction to solve.

(3) In solid geometry, the surface area and volume of a sphere are solved by division. In fact, it is a typical application of finite and infinite mathematical thought, which divides the sphere into finite times and then sums it up to find the limit.

(4) With the curriculum reform in senior high school, the investigation of new content will be deepened, and the investigation of limited and unlimited will be strengthened.

Seventh: the thought of possibility and inevitability;

Two basic characteristics of (1) random phenomenon, one is the randomness of results, and the other is the stability of frequency.

(2) Find the inevitability in the accident, and then solve the accident with the law of inevitability.

(3) The probability of equal possibility events, the probability of one occurrence in mutually exclusive events, the probability of simultaneous occurrence of mutually independent events, independent repeated trials, the distribution list of random events, and mathematical expectations are the key points of examination.