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.
2. Learn to use the combination of numbers and shapes.
The idea of combining numbers with shapes refers to a mathematical idea of using the properties of geometric figures to study the quantitative relationship to seek the solution of algebraic problems (using shapes to help numbers) or using the properties of geometric figures to solve geometric problems (using numbers to help shapes). The idea of combining numbers and shapes skillfully combines quantitative relations with geometric figures to solve 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.
3. learn to score points.
The failure to solve a math finale problem in the senior high school entrance examination does not mean "I don't know anything, I don't know anything". We should turn the whole problem-solving idea into a scoring point. For example, there are generally two or three small questions under the big question of the final exam. The difficulty level is 1. Small questions are relatively easy, and most students can get points. The second problem is moderate and plays a connecting role; The third question is more difficult, but it is often based on two small questions: 1 and 2. Therefore, when we answer the questions, we must get the score of item 1, the score of item 2 and the score of item 3, which greatly improves the possibility of getting high marks in mathematics in the senior high school entrance examination.
The scoring standard of the senior high school entrance examination is to score according to the knowledge points examined in the topic. If you understand the knowledge points and grasp the scoring points, you will get points. Therefore, for the final math exam, we should try to answer "close" scores, give full play to our own level, and turn the final math exam into a stepping stone to high scores.
4. Learn to use the idea of equivalent transformation.
Transforming thinking is a basic mathematical thought to solve mathematical problems. When learning mathematical problems, we usually turn unknown problems into known problems, complex problems into simple problems, abstract problems into concrete problems and practical problems into mathematical problems. The connotation of transformation is very rich. Known and unknown, quantity and graph, graph and graph can all be transformed to solve problems.
Any mathematical problem can't be solved without returning to thought. The transformation in junior middle school mathematics generally includes the transformation from known to unknown and from complex to simple. As the final question of the senior high school entrance examination, we should pay more attention to the connection and transformation between different knowledge. A final test of senior high school entrance examination is generally a comprehensive test of algebra, geometry and trigonometry, so we should make full use of transformation ideas.
The final exam questions are not isolated knowledge points, nor are they personal ways of thinking. It is a comprehensive investigation of candidates' comprehensive ability, involving a wide range of knowledge and using comprehensive mathematical thinking methods. Therefore, some candidates are afraid of the finale, thinking that their level is average, they can't do it, and they give up without even looking at it. Of course, they don't get the points they deserve. In order to improve the scoring rate of the final question, it is necessary to have a scoring strategy of sub-topic and sub-paragraph.
5. Learn to use the idea of classified discussion.
The idea of classified discussion can be used to test the accuracy and rigor of students' thinking, often through the variability of conditions or the uncertainty of conclusions. If we do not pay attention to the classified discussion of various situations, some problems may have wrong solutions or missing solutions. Throughout recent years, it has become a new hot spot to solve the final exam questions by classified discussion.
When solving some mathematical problems, sometimes there will be many situations, which need to be classified and solved one by one, and then integrated solutions. This is the classified discussion method. Classified discussion is a logical method, an important mathematical thought and an important problem-solving strategy, which embodies the idea of breaking the whole into parts and the method of sorting out.
Classification principle: (1) Each part of classification is independent of each other; (2) Classification according to standards; (3) Classification discussion should be gradual. The correct classification must be comprehensive, without repetition or omission.