In the final sprint stage of the college entrance examination, the teacher will tell students some exam taking skills in the exam. Almost every math teacher will say to the students, "the last big math problem, if you give up, you'd better not waste time and give up! I sorted out why the last math problem in the college entrance examination can't be done and what's the significance. Welcome to use it for reference.
Why can't you do the last math question in the college entrance examination
The final question has only one function, which is to distinguish good, medium and poor students. In the final question, the really difficult part is only 4-5 points. The so-called finale problem is different from the difficult problem of Mathematical Olympiad. It is more comprehensive than skill. It is a combination of a series of basic knowledge and basic graphics, and then combined with basic mathematical methods and ideas to become a comprehensive problem. The reason why many students make mistakes is not that they can't find ideas. Many of them appear in basic operations, or the basic concepts and graphics are not clear, resulting in the loss of points.
First, let's talk about the structure of the final question. The questions of the mid-term examination and simulated examination in recent years are generally composed of three small questions, which are generally divided into two categories: parallel type and progressive type.
The so-called "parallel" is that each question is independent of each other, and the calculation error of a minor question will not affect another sub topic. The conditions in general questions can be invoked, while each of the questions can only be invoked in the sub title, but it is independent and not absolute, because many ways of thinking can be extended, especially those from special to general structure.
The so-called progressive type means that the results of the previous question can be used as the conditions of the latter question, and can also be regarded as a hint from the propositioner to the examinee. For the questions with this structure, we should not only pay attention to the relevance, but also pay attention to the calculation of data. We must verify it repeatedly to avoid affecting the following conclusions.
Netizen 2:
The question type of the final axis question is generally based on the basic graphics, such as special quadrilateral, triangle, circle and some similar basic graphics. Therefore, special quadrilateral, triangle, circle and similarity are the focus of the proposition, and then often combined with graphic motion, that is, the hot spot in recent years - dynamic geometry; Dynamic geometry includes: jog, linear motion and shape motion. Among them, jogging is the most important and common way of investigation. Almost all districts and counties have such problems in the simulation volume, and it is often accompanied by classification discussion and the mathematical idea of functional equation. For this type of question, it is necessary to examine the meaning of the question, clarify the scope of the point movement, whether it is on the edge (line segment), on the ray or on the straight line, excluding the end point, whether the figure always exists or has changed after the movement, Candidates need to draw and study carefully. If the spare map is not enough, they even have to add it by themselves.
Secondly, linear motion can basically be transformed into point motion. Finally, shape movement, that is, graphic movement, includes three basic movements: translation, rotation and folding, as well as the movement of points. The essence of the three basic movements is the congruence of the figures before and after the movement, plus some of the characteristics of various movements. For example, in the case of translation, the connecting lines of each corresponding point are equal and parallel, in the case of rotation, the included angle of the corresponding edge is equal to the rotation angle, in the case of folding, the connecting lines of the corresponding points are vertically and evenly divided by the axis of symmetry.
Netizen 3:
As for the solution method of the final problem, the specific problems still need to be analyzed in detail. We can't talk about them one by one. Generally speaking, the ideas are as follows:
1. Simplification of complex problems is to decompose a complex problem into a series of simple problems, divide the complex graphics into several basic graphics, find similarities, find right angles, find special graphics, and solve them slowly. The middle school entrance examination scores step by step. This way of thinking is particularly important. If you can calculate first and prove first, you can score when you step on the key points. Even if you can't draw a conclusion, there are still many points to get in the middle.
2. The problem of motion is static. For dynamic graphics, first find the constant line segments and constant angles, whether there are always equal line segments, always congruent graphics and always similar graphics. All operations are based on them. When finding the relationship between changing line segments, use the generation to solve it slowly.
3. General problems are specialized. Some general conclusions cannot find a general solution. First look at special situations, such as the moving point problem, to see how to move to the midpoint, how to move to the vertical, and what will happen if it becomes an isosceles triangle. First find out the conclusion, and then solve it slowly.
In addition, there are some details to pay attention to. The triangular ratio should be good at using. As long as there are right angles, it can be used. From the perspective of simplified operation, the triangular ratio is better than the proportional formula and better than the Pythagorean theorem. The proposition of the middle school entrance examination will not set too many calculation obstacles. If you encounter complicated and difficult operation, you should turn back in time to avoid cutting corners.
Netizen 4:
First, there are many knowledge points to be investigated in a subject, especially in the subject of function. The combination of number and shape not only investigates the calculation of algebra, but also often combines with graphics. When investigating geometric knowledge points, it is necessary to organically combine and apply many knowledge points when solving the problem, and it is necessary to have a complete knowledge system and good methods.
Second, the investigation of a topic has a deep investigation of knowledge points. For example, the final axis of mathematics will investigate a variety of mathematical thinking and methods, equation thinking, classified discussion thinking, overall thinking, replacement thinking, hypothetical thinking, etc. these ideas and methods are the key to solving the final axis. Without good thinking and methods, it is difficult to break through the final axis.
So, how to test the final axis of a function and how to solve it? The final question, ideas and methods are the key. Many students can't do it, just because they can't find a breakthrough. If a breakthrough is found, the rest is conventional operation and reasoning.
Netizen 5:
First of all, you must know what is the final axis problem. If you just understand the problem as the final axis problem, it will be too one-sided. For example, even if the Mathematical Olympiad in many primary schools is done for college students, there are not many that can really be done.
In fact, whether in the college entrance examination or in the middle school entrance examination, many students are like you, and their knowledge extension ability is not strong. Of course, this is also related to the process of the teacher's own explanation. Many teachers focus on the conclusion rather than the process, so that the students know that the conclusion can only solve the problem with the conclusion, while the final question is the overturning application of the source of the principle. If you can't understand this sentence, it proves that the source of a lot of your knowledge is not clear enough, For example, when you study series in high school, many students are the most ordinary students. They can only use the general formula of equal difference and equal ratio to solve problems. If the problem is changed slightly, most of them will be confused, let alone the evolution on this basis.
Netizen 6:
The existential problem is also the final question. How to solve it? Generally, the hypothesis method is used to assume existence. First, analyze and answer according to the existing situation. If the correct result can be obtained or the conditions corresponding to the topic symbol can be obtained, it will exist. If the conclusion contrary to the known topic is obtained, it will not exist. This play needs to be understood and mastered.
In junior high school, we mostly use geometric problems to solve the function problems in the rectangular coordinate system. We should solve them from the graphics as much as possible. For example, to solve the coordinates of points, we can make a vertical line to the coordinate axis, convert it into the length of the line segment, and then solve it in combination with the basic methods of finding the line segment: pythagorean theorem, similarity and trigonometric function, so as to avoid using the distance formula between two points to set up equations as much as possible.
What's the point
The mathematics content within the scope of the college entrance examination is actually the basis of the competition, and the content of the competition is also the extension and promotion of the content of the college entrance examination, especially the first try. Therefore, competition is helpful for the final question.
Another evidence is that the test questions that are particularly difficult in many years are often issued by teachers with competition background. For example, Ge Jun, known as the emperor of mathematics, engaged in competition training in his early years. His topic is considered to be from a strategically advantageous position. In fact, his own statement: my topic is only a little flexible to investigate the mathematical thought, which is probably the level of the first try of the mathematical competition, that is, the difficulty of the introduction of the competition party.
In fact, the final questions have been diluted in the past two years. The final questions in many provinces are not difficult, but just medium and upper difficulty. In many cases, it is also a trend that can not be ignored that the difficulty of the final questions is equally divided - the college entrance examination no longer makes the final questions particularly difficult, but disperses the difficulty into several previous questions to achieve a balance. The result is that the overall difficulty of the test paper increases and the difficulty of the final questions decreases.