In my opinion, high school mathematics contains many contents and plates, which intersect with each other and form a huge knowledge structure system. First of all, we must master some basic formulas and individual knowledge points, and remember clearly some difficult and error-prone points and the applicable scope of some formulas, so as to draw inferences from one case to another. Some basic methods: (1) such as the application of mean inequality (2) such as the application of coordinate system, (3) the analysis method is to gradually deduce the conditions that can make it hold according to the verified results until the facts are known; Analysis is the direct proof of "causal". (4) Based on the proved conclusions and formulas, the comprehensive method gradually deduces the required conclusions. Synthesis method is a direct proof method of "leading from cause to effect" and smooth narration. (3) Analysis and synthesis are two basic methods to prove mathematical problems. The "causal analysis" method is clear in thinking and easy to find a solution to the problem, but it is difficult to describe clearly because of the high requirements on writing format, so the analysis method and the synthesis method are often used alternately. Analysis and synthesis are widely used, and almost all problems can be solved by these two methods. (5) Reduction to absurdity is an important method of mathematical proof, because proposition P is contrary to its negation, so to prove a proposition is true, it is only necessary to prove its negation is false. This method of first proving the contradictory proposition (that is, the negation of the proposition) to be false and then proving the proposition to be true is called reduction to absurdity. The general steps of proof by reduction to absurdity are: counter-hypothesis: the conclusion of the hypothesis proposition is not established, that is, the opposite of the hypothesis conclusion is established; Reduction to absurdity: 10 the method of solving senior high school math problems according to the instructions. Method 1: "tight inside and loose outside", concentrate and eliminate anxiety and stage fright. Concentration is the guarantee of success in the exam. A certain degree of tension and nervousness can accelerate nerve contact and be conducive to positive thinking. It is called inner tension, and the thinking is extremely positive, but if you are too nervous, you will go to the opposite side, forming stage fright and anxiety. Method 2: Adjust the brain's thinking, eliminate distracting thoughts and distracting thoughts before entering the mathematical situation in advance, so that the brain is in a "blank" state, create the mathematical situation, then brew mathematical thinking, enter the "role" in advance, and comfort yourself by counting utensils, prompting important knowledge and methods, and reminding you of common misunderstandings and your own mistakes in solving problems, so as to relieve stress, go into battle lightly, stabilize emotions, enhance confidence and make thinking active. Method 3: Accept the challenge calmly and make sure that the flag is won, so as to cheer up the spirit. A good beginning is half the battle. From the psychological point of view of examination, this is indeed very reasonable. After you get the test questions, don't rush for success, and start solving the problems immediately. Instead, we should browse through the whole set of questions, get a thorough understanding of the situation, and then firmly grasp one or two easy questions, so as to have a good feeling of "winning the flag" method four, "six before six after", because people have to read through the whole volume, successfully complete simple questions, their emotions tend to be stable, their situations tend to be single, their brains tend to be excited, and their thinking tends to be positive, and then it is the golden season to give full play to their ability to solve problems on the spot. At this point, candidates can choose to implement the tactical principle of "six before six after" according to their own problem-solving habits and basic skills, combined with the structure of the whole set of questions. 1. Easy first, then difficult. Is to do simple questions first, and then do comprehensive questions, should be based on their own reality, decisively skip the topics that can't be chewed, from easy to difficult, but also pay attention to take every question seriously, strive for practical results, and can't just skim through it and retreat when it's difficult, which hurts the mood of solving problems. 2. Mature first and then grow. Looking at the whole volume, we can get many favorable positive factors and some unfavorable factors. For the latter, there is no need to panic. We should think that the test questions are difficult for all candidates. Through this hint, you can ensure emotional stability. After grasping the whole volume as a whole, you can practice the method of pre-cooking, that is, you can do those questions with familiar content, familiar question structure and clear thinking of solving problems. In this way, while winning familiar questions, you can make your thinking fluent and extraordinary, and achieve the goal of winning advanced questions. 3. Similarity before difference. Doing the same topic in the same subject first, thinking more deeply, exchanging knowledge and methods easier, is conducive to improving the efficiency of unit time. Generally, college entrance examination questions require the "focus of excitement" to be transferred quickly. "Same before different" can avoid the "focus of excitement" jumping too fast and too frequently, thus reducing the burden on the brain and maintaining effective energy. 4. Small problems are generally less informative and easy to master, so don't let them go easily. We should try to solve major problems as soon as possible before they appear, so as to gain time for solving major problems and create a relaxed psychological foundation. In recent years, most of the math problems in the college entrance examination are presented as "gradient problems", which need not be examined in one go, but should be solved step by step, and the solution of the previous problems has prepared the thinking foundation and problem-solving conditions for the later problems, so it is necessary to proceed step by step, from point to surface. 6. that is, the second half of the exam, we should pay attention to time efficiency. If it is estimated that you can do both questions, then do the high score questions first. It is not easy to estimate the two questions. First, the high-scoring questions should be graded by sections, and the score should be increased on the premise of insufficient time. Method 5: "Slow" and "Fast" complement each other. Some candidates only know that the examination room should be fast, and as a result, the meaning of the question is unclear and the conditions are incomplete, so they are eager to answer. Do you know that haste makes waste? As a result, their thinking is blocked or they come to a dead end, leading to failure. It should be said that the questions should be slow and the answers should be quick. Examination of questions is the "basic project" in the whole process of solving problems, and the questions themselves are the information sources of "how to solve problems". We must fully understand the meaning of the question, synthesize all the conditions, extract all the clues, form an overall understanding, and provide a comprehensive and reliable basis for the formation of problem-solving ideas. Once an idea is formed, it can be completed as quickly as possible. Method 6. Another feature of emphasizing standardized writing and striving for both correct and complete examinations is that examination papers are the only basis. This requires not only conformity, but also correctness, correctness, completeness, completeness and standardization. Unfortunately, it will be wrong; Yes, but incomplete, the score is not high; Non-standard expression and scrawled handwriting are another major aspect that causes non-intellectual factors to lose points in the college entrance examination mathematics paper. Because the handwriting is scrawled, it will make the marking teacher have a bad first impression, and then make the marking teacher think that the candidates are not serious, the basic skills are not too hard, and the "emotional score" is correspondingly low. This is the so-called psychological "halo effect". It is this truth that "the handwriting should be neat and the papers can be scored". Method 7: Make sure the calculation is accurate. With the capacity of a successful math college entrance examination, 120 minutes can complete 26 questions. Time is tight, and it is not allowed to do many detailed post-solution tests. Therefore, the calculation should be as accurate as possible (key steps, strive for accuracy, rather slow than fast), based on one success. The speed of solving problems is based on the accuracy of solving problems, not to mention the intermediate data of mathematical problems often affect the answers of subsequent steps not only in quantity, but also in quality. Therefore, under the premise of taking speed as the first priority, we should be steady and steady, well-founded at all levels and accurate step by step. We should not lose accuracy or even important scoring steps in pursuit of speed. If speed and accuracy cannot be achieved at the same time, we have to be quick and accurate, because the answer is wrong, and it is meaningless to be quick. Method eight. Facing difficult problems, pay attention to methods. Of course, the topics that can be scored must strive to be right, complete and get full marks. More questions are how to grade the questions that cannot be completely completed. There are two common methods. 1. Missing step solution. When a problem is really difficult to solve, a wise solution is to divide it into a sub-problem or a series of steps. First, solve part of the problem, that is, to what extent it can be solved. After calculating several steps, write several steps, and each step will get a score. For example, from the beginning, translating written language into symbolic language, translating conditions and goals into mathematical expressions, setting the unknowns of application problems, setting the coordinates of moving points of trajectory problems, and drawing figures correctly according to the meaning of problems can all be scored. There are also simple situations such as completing the first step of mathematical induction, classified discussion, and reduction to absurdity, all of which can be scored. Moreover, it is expected that in the above treatment, from perceptual to rational, from special to general, from local to whole, we will have an epiphany, form ideas and successfully solve problems. Step by step. When the problem-solving process is stuck in an intermediate link, you can admit the intermediate conclusion and push it down to see if you can get the correct conclusion. If you can't get it, it means that this method is wrong and you can't get the correct conclusion immediately. If you can't get it, you can immediately change your direction and find another way. If we can get the expected conclusion, we will go back and concentrate on overcoming this transitional link. If the intermediate conclusion is too late to be confirmed due to time constraints, we have to skip this step and write the subsequent steps to the end; In addition, if there are two problems in the topic, the first problem can't be solved, the first problem can be called "known" and the second problem can be completed. This is called skipping problem solving. Maybe later, due to the positive transfer of solving problems, I remembered the intermediate steps, or if time permits, I tried to catch the intermediate difficulties and could make up for them at the end of the corresponding questions. Method 9: Take retreat as progress, based on special divergence. Generally speaking, for a relatively general problem, if you can't get a general idea at the moment, you can take the general as special (for example, solving multiple-choice questions in a special way), abstract as concrete, whole as part, parameters as constant, weak conditions as strong conditions, and so on. In short, retreat to the extent that you can solve it, and solve the "special" by thinking and inspiring thinking, so as to achieve the purpose of solving the "general". Method 10. Grasp the reason, think backwards, and if it is difficult, think positively about a problem. When thinking is blocked, using the method of reverse thinking to explore new ways to solve problems can often make breakthrough progress. If you have difficulty in pushing forward, you can push back, which directly proves that you have difficulty and can disprove it. If you use analysis, you can start with a positive conclusion or intermediate steps to find sufficient conditions. By reducing to absurdity, we can find the necessary conditions from negative conclusions. I hope I can help you and wish you progress in your study.