Set is the basic knowledge of high school mathematics and one of the compulsory contents over the years. This paper mainly investigates the knowledge and understanding of the basic concepts of set, and investigates the application of set language and set thought as a tool. This section is mainly to help candidates deepen their understanding and application of set concept, set language and set thought by using set viewpoint.
Example: given the set A={(x, y)|x2+mx-y+2=0}, B={(x, y)|x-y+ 1=0, and 0≤x≤2}, if A∩B≦,
Knowledge Point 2: Determination of Sufficient and Necessary Conditions
Sufficient condition, necessary condition and necessary and sufficient condition are important mathematical concepts, which are mainly used to distinguish the relationship between condition P and conclusion Q of a proposition. This section mainly analyzes the meaning of necessary and sufficient conditions through different knowledge points, so that candidates can accurately judge the necessary and sufficient relationship between two given propositions.
Example: It is known that the quadratic equation with real coefficient x2+ax+b=0 of X has two real roots α and β. It is proved that | α | < 2 and | β|.
Knowledge 3: Solving problems with vector method
Plane vector is one of the contents added in the new textbook reform. In recent years, the national college entrance examination questions using new textbooks have gradually increased the examination of this part. The content of this section is mainly to help candidates use vector method to analyze and solve some related problems.
ExAMple: in the triangle ABC, A(5,-1), b (- 1, 7), c (1, 2), find the length of the median line am on the side of (1)BC; (2) The length of the cab bisector AD; (3) The value of cost ABC.
Knowledge point 4: Three "quadratic" and their relationship
The three "quadratic functions" of a quadratic function, a quadratic equation and a quadratic inequality are important contents of middle school mathematics, which are rich in connotation and closely related, and are also tools for learning many contents including quadratic curves. Nearly half of the college entrance examination questions are related to these three "secondary" questions. This section is mainly to help candidates understand the differences and connections, and master the ideas and methods of functions, equations and inequalities.
Example: It is known that for all real values of x, the value of quadratic function f(x)=x2-4ax+2a+ 12(a∈R) is nonnegative. Find the value range of the root of the equation about X =|a- 1|+2.
Knowledge point 5: Solving the resolution function
Solving the resolution function is one of the key contents of the college entrance examination, which needs attention. This section mainly helps candidates to master several methods of solving analytic functions, form their abilities, and cultivate their innovative ability and practical problem-solving ability on the basis of a deep understanding of the definition of functions.
Example: (1) Given f(2-cosx)=cos2x+cosx, find f(x- 1).
(2) It is known that the function f(x) satisfies f(logax)= (where a >；; 0, a≠ 1, x>0), find the expression of f(x).
(3) It is known that the quadratic function f(x)=ax2+bx+c satisfies | f (1) | = | f (-1) | = | f (0) | =1. What? The expression of f(x).