1, matching method:

The so-called formula is to make some items of an analytical formula into the sum of one or more polynomial positive integer subsets by using the method of constant deformation. The method of solving mathematical problems with formulas is called matching method. Among them, the most commonly used is the full * mode. Matching method is an important method of constant deformation in mathematics, which is widely used in factorization, simplifying roots, solving equations, proving equality and inequality, finding extreme values of functions and analytical expressions.

2, factorization method:

Factorization is to change a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool, mathematical method plays an important role in solving problems such as algebra, geometry and trigonometric functions. There are many methods of factorization, except extracting common factors, formulas, grouping decomposition, cross multiplication and so on. What is introduced in middle school textbooks is the addition of decomposition and the root decomposition.

3. Alternative methods:

Method of substitution is a very important and widely used method to solve problems in mathematics. We usually call unknowns or variables variables. The so-called method of substitution is to replace a part of the original formula with new variables in a complicated mathematical formula, thus simplifying it and making the problem easy to solve.

4, discriminant method and Vieta theorem:

The discriminant △=b2-4ac of the root of the unary quadratic equation ax2+bx+c=0(a, B, ceR, a≠0) is not only used to judge the properties of the root, but also widely used in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even analytic geometry and trigonometric function operations as a problem-solving method.

Vieta's theorem not only knows one root of a quadratic equation, but also finds another root. Knowing the sum and product of two numbers, we can find the symmetric function of the root, calculate the sign of the root of quadratic equation, solve the symmetric equation and solve some problems about quadratic curve. , has a very wide range of applications.

5, undetermined coefficient method:

When solving mathematical problems, if we first judge that the obtained results have a certain form, which contains some undetermined coefficients, then list the equations about undetermined coefficients according to the conditions of the problem, and finally find out the values of these undetermined coefficients or find out some relationship between them, so as to solve mathematical problems, this problem-solving method is called undetermined coefficient method.

6. Construction method:?

When solving problems, we often use this method to construct auxiliary elements by analyzing conditions and conclusions, which can be a figure, an equation (group), an equation, a function, an equivalent proposition and so on. Build a bridge between conditions and conclusions, so that the problem can be solved. This mathematical method of solving problems is called construction method. Using construction method to solve problems can make algebra, trigonometry, geometry and other mathematical knowledge permeate each other, which is beneficial to solving problems.

7, reduce to absurdity:

Reduction to absurdity is an indirect proof method. First, a hypothesis contrary to the conclusion of the proposition is put forward, and then from this hypothesis, through correct reasoning, contradictions are led out, thus denying the opposite hypothesis and affirming the correctness of the original proposition. The reduction to absurdity can be divided into reduction to absurdity (with only one opposite conclusion) and exhaustive reduction to absurdity (with more than one opposite conclusion).

8, equal product (surface or body) method:

(three-dimensional) several. He Jinzhong's area (volume) formula and the property theorems related to area (volume) calculation derived from the area (volume) formula can be used not only to calculate the area (volume) but also to prove (calculate) geometric problems, sometimes with twice the result with half the effort. The method of proving or calculating geometric problems by using the area (volume) relationship is called equality (surface or volume)

9, geometric transformation method:

In the study of mathematical problems, the transformation method is often used to transform complex problems into simple problems and solve them. The so-called transformation is the mapping from any element of a set to the elements of the same set, and the transformation involved in middle school mathematics is mainly elementary transformation.

10, objective problem solving method:

Multiple-choice questions are a kind of questions that give conditions and conclusions and require correct answers according to certain relationships. The multiple-choice questions are cleverly conceived and flexible in form, which can comprehensively examine students' basic knowledge and skills, thus increasing the capacity and knowledge coverage of the test paper. Fill-in-the-blank question is one of the important questions in standardized examination. Like multiple-choice questions, it has clear phonetic objectives, wide knowledge coverage and accurate marking speed.

It is beneficial to students' analytical judgment and calculation ability, but the difference is that the fill-in-the-blank question does not give an answer. In order to prevent students from guessing answers, and to solve multiple-choice questions and fill-in-the-blank questions quickly and correctly, besides accurate calculation and strict reasoning, there are also methods and skills to solve multiple-choice questions and fill-in-the-blank questions.