Therefore, if you want to learn high school mathematics well, you have to start on the basis of memory, and the basic knowledge is solid, and the thinking of solving problems will naturally be clearer. Today, the math teacher of Chengdu Famous Teacher Education Super High School sorted out and summarized the common problem-solving ideas of high school mathematics for everyone. Students should understand and absorb well, master the relationship between mathematical knowledge, and sort out their own problem-solving ideas, which will become a magic weapon to win the exam.
Solve the absolute value problem
It mainly includes simplification, evaluation, equations, inequalities, functions and other issues. The basic idea is to turn a problem with absolute value into a problem without absolute value. The specific transformation method is as follows:
① Classification discussion method: according to the positive, zero and negative scores of numbers or formulas in absolute value symbols, the absolute value is removed.
② Zero-point subsection discussion method: it is suitable for the case that a letter has multiple absolute values.
③ Two-sided flat method: it is suitable for equations or inequalities with non-negative edges.
④ Geometrical meaning method: It is suitable for cases with obvious geometrical meaning. factoring
It is an important skill to choose the method according to the number of terms and follow the general steps. The general steps of factorization are:
Extract common factor
Select formula → cross multiplication → grouping decomposition method → item splitting and item addition method.
Method of completing a square
Using the complete square formula to change a formula or part into a complete square is the matching method, which is an important method and skill in mathematics. The main basis of the matching method is:
Alternative method
Method of substitution is used to solve some complicated special equations. The general steps for method of substitution to solve equations are: setting elements → exchanging elements → solving elements → simplifying elements.
The undetermined coefficient method is a method to find the object under the condition of knowing the shape of the object. It is suitable for solving some important problems, such as coordinates, resolution function and curve equation. The steps to solve the problem are: setting, arranging, solving and writing.
Skills of using complex algebraic equality conditions: the left side is zero and the right side is deformed.
Factorization type: (-) (-) = 0. Both cases are OR type.
Match to square type: (-) 2+(-) 2 = 0. Two cases were combined type.
The two greatest problem-solving ideas in mathematics (1) are to find the equations or equations of numerical letters.
The idea of evaluation domain is the inequality or inequality group of letters in evaluation domain. The basic idea of simplifying quadratic roots is to turn √m into a completely flat way.