It can be seen from the content distribution of examination papers over the years that all the contents mentioned in the examination syllabus may be tested, and even some unimportant contents may appear in the big questions of a certain year. For example, in Mathematics No.1 Middle School in 1998, not only the third question was pure analytic geometry, but also two questions were combined with linear algebra to test the content of analytic geometry. It can be seen that the review method of guessing questions is not reliable, but we should refer to the examination outline and review it comprehensively without leaving any omissions.
Comprehensive review is not about memorizing all the knowledge. On the contrary, it is about grasping the essence and content of the problem and the essential connection of various methods, and minimizing the things to be memorized (try to make yourself understand what you have learned, grasp the connection of the problem more, and memorize less knowledge). Moreover, if you don't remember, you will, and if you remember, you will be reliable. Facts have proved that some memories will never be forgotten, while others can be obtained by using the relationship between them on the basis of remembering the basic knowledge. This is the significance of comprehensive review.
Second, focus on key points and strive for perfection.
In the requirements of the examination syllabus, there are three levels of requirements for the content: understanding, understanding and knowing; There are two levels of requirements for mastering methods, knowing (or knowing). Generally speaking, the content to be understood and the methods to be mastered are the focus of examination. In previous years' exams, the probability of this aspect is relatively high; The same test paper, the test questions in this area also occupy more scores. People who "guess the questions" often have to work hard in this respect. Generally speaking, you can really guess a few points. But when it comes to comprehensive questions, these questions contain secondary content in the main content. At this time, "guessing questions" will not work.
When we talk about highlighting the key points, we should not only work hard on the main content and methods, but more importantly, we should find the connection between the key content and the secondary content, so that the main content is the secondary content and the key content covers all the content. The main content is thoroughly understood, and other contents and methods will be readily solved. We should grasp the main content, don't give up the secondary content and isolate the main content, but naturally highlight the main content by analyzing the relationship between the contents and comparing them. Such as differential mean value theorem, Rolle theorem, Lagrange theorem, Cauchy theorem, Taylor formula and so on. Because Rolle theorem is a special case of Lagrange theorem, Cauchy theorem and Taylor formula are the generalization of Lagrange theorem. By comparing these relations, we naturally come to the conclusion that Lagrange's theorem is the core, and we can thoroughly understand this theorem and grasp several other theorems from the connection. In the examination syllabus, Rolle's theorem and Lagrange's theorem are both required to be understood and are the focus of the examination. We highlight Lagrange's theorem more, which can be described as Excellence.
Third, the basic training is repeated.
To learn mathematics, we should do a certain number of problems and thoroughly practice the basic skills, but we do not advocate the tactics of "problems" and advocate refinement, that is, we should repeatedly do some typical problems, solve many problems for one problem and change one problem. Training the ability of abstract thinking, proving some basic theorems, deducing basic formulas and doing some basic exercises don't require writing, just like a chess player's "blind chess", you only need to meditate with your brain to get the exact answer. This is what we mentioned in the preface, 20 minutes to complete 10 objective questions. Some questions can be answered at a glance without writing. This is called well-trained, "practice makes perfect" people with solid basic skills have many ways to solve problems and are not easily stumped. On the contrary, when doing problems, I always find difficult problems, and as a result, I will encounter similar problems I have done before when I go to the examination room. Many candidates misjudge the questions they can do, which is classified as carelessness. It is true that people are careless, but people with solid basic skills will find out immediately when they make mistakes, and rarely make "careless" mistakes.
Remember, be firm. Facts have proved that some memories will never be forgotten, while others can be obtained by using the relationship between them on the basis of remembering the basic knowledge. This is the significance of comprehensive review.
People will find out immediately when they make mistakes, and rarely make mistakes "carelessly".