Factorization method
Factorization is to transform a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry and trigonometry problems. There are many methods of factorization, such as extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce the use of decomposition and addition, root decomposition, exchange elements, undetermined coefficients and so on.
Concepts of functions and equations
The idea of function and equation is the most basic idea in middle school mathematics. The idea of function is to analyze and study the quantitative relationship in mathematics from the point of view of movement change, establish the functional relationship or construct the function, and then analyze and solve the related problems by using the image and nature of the function. The idea of equation is to analyze the equivalence relation in mathematics, construct an equation or an equation, and analyze and solve problems by solving or using the properties of the equation.
Basic solution of fill-in-the-blank problem
1. direct method: according to the conditions given by the stem, the correct answer can be directly obtained through calculation, reasoning or proof.
2. Illustration: Provide information according to the stem of the question, draw a graph and get the correct answer.
Although the fill-in-the-blank questions are mostly low-graded, many candidates often make mistakes in answering questions, which should attract our attention.
Discrimination and Vieta Theorem
The root discrimination of unary quadratic equation ax2+bx+c=0(a, B, C belongs to R, a≠0) and△ = B2-4ac is not only used to judge the properties of roots, but also widely used in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even geometric and trigonometric 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.
The above is a collection of common problem-solving methods in junior high school mathematics that I compiled for you.