High school entrance examination mathematics | Comprehensive questions of the finale questions are always difficult to break through, and there are many difficulties in solving problems. The method is the key
Many contents in the high school entrance examination mathematics study are based on the foundation, so many students think that the amount of learning is very large when studying, and training for each type of question takes a long time. Even so, there are certain difficulties in the basic content. If you think about breaking through your own thinking and make a difference in the finale, it will be even more difficult.
During the recent special explanation of the preparation topic of the junior high school entrance examination, many students felt that it was difficult to find a breakthrough in the final questions and comprehensive questions. The application of methods and the combination of knowledge points have also become a major difficulty. So how can we achieve a breakthrough in thinking during the preparation stage, and for different final questions, the formation process of their problem-solving ideas is more clear. In addition to having a comprehensive understanding of various types of questions and clarifying their test points and methods, we must also have a proficient mastery of the problem-solving methods and techniques. Teacher Tang hopes to help everyone make breakthroughs in thinking based on the two important methods used in the recent video explanation.
It is easy to apply methods to solve similar problems during the learning process of junior high school mathematics, which invisibly creates obstacles to the breakthrough in problem-solving thinking and the early application of this method is relatively smooth. In the middle and later, it will be found that in the process of solving problems, when the method cannot be applied, the itinerary will be more difficult to solve the problem-solving ideas according to the actual situation. This is also what we call the bottleneck period in learning. If we can break through this thinking barrier and improve the methods and skills of solving problems, then the ability of mathematical thinking will also be improved.
Today, Teacher Tang focused on the two methods, namely, the ideological methods of , combining numbers and shapes with and the ideological methods of classification discussion.
First of all, the combination of numbers and shapes is an important method in our comprehensive solution to the comprehensive problem type. The so-called combination of numbers and shapes and algebra and geometry can be used in a comprehensive way. When encountering geometric problems, the problem can be solved by algebraic methods, and when encountering algebraic problems, the geometric methods can be used to solve them. These important contents have laid a certain foundation for the use of the combination of numbers and shapes. It is clear the scope of its investigation and reminder how to use the combination of numbers and shapes in the future. This is what everyone will make a key breakthrough in the next order.
In recent years, many of the final questions of the junior high school entrance examination will appear related to plane rectangular coordinate system . Its characteristic is that everyone needs to use algebraic methods to explore the properties of geometric figures, or use the properties of geometric figures to study. The quantitative relationships in the question seek to use algebra to solve problems. Moreover, some more complex problems in algebra can be quickly solved through the intuitive expression of geometric figures.
And among the geometric problems, the representative triangle function problems are relatively common. We can use algebraic methods and set unknown numbers to establish the relationship between the sides and corners of the triangle. List the corresponding equations to get the length of the last edge. Therefore, the use of the combination of numbers and shapes can allow everyone to have a full understanding of the diversity of mathematical thinking, and in the process of thinking expansion, they will make more attempts and explorations, thereby promoting the improvement of mathematical thinking.
Secondly, learn the ideas and methods of classification discussion.
Classification Discussion Thoughts can quickly judge the accuracy and rigor of students' thinking about the learning content during learning. The questions are usually drawn through some hidden conditions and uncertainty in the conditions and the conclusions. Many times, if the conditions are not classified and discussed, it may lead to misunderstandings or missed solutions. Moreover, if there is no classification discussion in the big questions, and the flexible application of classification discussion in the final questions in recent years has also become the focus of the investigation.
For example, the very classic isosceles triangle problem. When an isosceles triangle appears in the question, we must carefully read the information in the question to see if we can determine the sides and angles of the unity triangle. For the case where equality satisfies isosceles triangles, different sides and angles meet equal base angles or equal waists are divided into three categories for discussion. For the case of finding parameters in the question, different parameter values can be obtained after classification discussion and calculation results, and finally the synthesis is carried out.
Analysis of the situation where classified discussions are needed is also the most difficult part for students. When will the classification discussions be conducted? How to conduct classified discussions? Then everyone only needs to follow the following classification principles.
Each part of the first category is independent of each other.
Second, the classification is carried out according to one standard, and if necessary, the classification is carried out again.
Third, classification discussion should be carried out step by step, and the correct classification must be a situation where it is not repeated or omitted.
The idea of classification discussion does not only appear in a question type. Different classification situations have their own specific methods according to different standards, so pay attention to summary among different question types. Teacher Tang will also share with you more question types and problem-solving ideas that need to be discussed.
at the end. Although there are many basic questions in junior high school mathematics, if you want to break through your mathematical thinking and gradually improve your mathematical learning ability and problem-solving ability, then the ideological method that combines the ideological method of classification discussion with the number and shape is a very important breakthrough. It appears frequently in the final questions of the junior high school entrance examination and is also particularly important for the subsequent mathematical learning. What do you think?
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