Learn to use the idea of combining numbers with 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.
The first skill to solve the final problem of junior high school mathematics is to use the idea of function and equation. Based on the knowledge of straight line or parabola, the analytical expression of equation or system of equations is obtained, and its properties are studied.
The second is to use the idea of classified discussion. Investigate and explore the variability of conditions or conclusions of problems. The third is to use the idea of transformational mathematics. From known to unknown, from complex to simple. The last question of the senior high school entrance examination is a comprehensive investigation of the comprehensive ability of candidates, which involves a wide range of knowledge and uses comprehensive mathematical thinking methods. Therefore, the final problem can be divided into relatively independent, single chunks of knowledge or methods to think and explore.
The difficulty of the mathematical finale is agreed in the senior high school entrance examination over the years, and the finale is generally composed of three small questions. (1) questions are easy to use, and the scoring rate is above 0.8; Question (2) is slightly more difficult and generally belongs to the conventional question type, with a scoring rate of 0.6-0.7. Question (3) is difficult and requires high ability, but the scoring rate is mostly between 0.3 and 0.4. In the past ten years, the scoring rate of the final item is below 0.3, which only happens occasionally, but once it happens, it will attract the attention of all parties. Controlling the difficulty of the finale has become the knowledge of each proposition group. "Low starting point, slow slope and slightly warped tail" has become a major feature of Shanghai mathematics test paper design. In the past, most of the finale questions of Shanghai papers were impartial, and the scoring rate was stable between 0.5 and 0.6, that is, the average score of candidates was 7 and 8. This shows that the finale is not terrible.
The above are the skills I have compiled for you to solve the final problem of junior high school mathematics. I hope I can help you. Please continue to pay attention to this site for more information about the senior high school entrance examination!