Learn to use the idea of combining numbers and shapes
The idea of combining numbers with shapes refers to a mathematical idea that studies the relationship between numbers by using the properties of geometric figures to seek the solution of algebraic problems, or studies the properties of geometric figures by using the relationship between numbers to solve geometric problems.
Throughout the country in recent years, most of the final exam questions are related to the plane rectangular coordinate system, which is characterized by establishing the corresponding relationship between points and numbers, that is, coordinates. On the one hand, we can study the properties of geometric figures by algebraic methods, on the other hand, we can get the answers to some algebraic problems through geometric intuition.
Learn to use functions and equations.
Starting with the analysis of the quantitative relationship of the problem, the unknown number is set appropriately, and the quantitative relationship between the known quantity and the unknown quantity in the studied mathematical problem is transformed into a mathematical model of equations or equations, so as to solve the problem. This is the thinking method of the equation. The key to solving problems with equation thinking is to construct equations (groups) by using known conditions or conclusions in formulas and theorems. This idea is widely used in algebra, geometry and real life.
Straight line and parabola are two important functions in junior middle school mathematics, that is, linear function and quadratic function. Therefore, no matter how to find its analytical formula and study its properties, it is inseparable from the idea of functions and equations. For example, to determine the resolution function, it is often necessary to establish equations or equations and solve them according to known conditions.
Learn to check
Check to be focused, check a person's concentration, and have the patience to review the questions that have been done.
Of course, it is also necessary to check whether the objective questions on the answer sheet are wrong and whether the format conforms to the regulations (fractional equation test, unit, solution and proof, classified discussion, etc. ).
Finally, check the calculation, and pay attention to the correct attitude when checking.
Trilateral relation theorem and inference of triangle
(1) Trilateral Relation Theorem: The sum of two sides of a triangle is greater than the third side.
Inference: The difference between two sides of a triangle is smaller than the third side.
(2) Trilateral relation theorem of triangle and its inference function;
(1) Judge whether three known line segments can form a triangle;
② When two sides are known, the range of the third side can be determined;
③ Prove the inequality of line segments.
The above is the final problem of junior high school math problems that I summarized for you, and the skills to easily break through the problems are for reference only, hoping to help you.