1, familiar with. First of all, we should be familiar with the basic knowledge of this chapter and this section. The degree of familiarity is not to recite formulas and do exercises after class, but to understand how those theories and summaries come from, to deduce its ideas step by step according to calculus in textbooks, and to draw the final results from which angle and with what special ideas and methods. This is only on the basis of thinking, but we must understand it and never take it for granted and be ambiguous. You have to ask yourself repeatedly why you want to do this, and you must get the result through positive calculation. At this time, you can calculate the problem on the basis of your own ideas, see where the problem starts and push it step by step. After this step, your basic knowledge is deeply absorbed, and at the same time, after your own thinking, you won't forget it as easily as memorizing formulas and don't know how to use it. Some people listen carefully in class. Although there is not much time after class, the exam is also to solve problems. At the same time, the exercises after the textbook are the exercises of your current basic knowledge, through which you can deepen your impression. Although these problems are only basic, there are many proofs and inferences. These problems should be sorted out by our own ideas, which is the expansion of basic knowledge. If necessary, you need to write down some conclusions from the exercise in your notes. Some multiple-choice questions and fill-in-the-blank questions can directly apply those conclusions.
2. Practice these questions. The exercises after the textbook are to consolidate the basic knowledge. Other exercises (not very profound, moderately difficult, slightly higher than the exercises) are usually some exercise books and bought counseling materials. These exercises are to expand the strain. In these questions, many knowledge points will be mixed together, and you only need to analyze them step by step. Note: You don't just start with the first question. You have to figure out in your mind from which angle, what is the first step and what is the second step. You can get twice the result with half the effort if you have real ideas. The purpose of practicing doing exercises is not to solve problems, but to train your thinking and develop adaptability, that is, to see a certain condition and what conclusion you can think of. Train slowly in this step and don't be lazy, which will become the key point for you to solve problems later. Every condition reflects a message, and there must be a related conclusion between the two conditions, and this conclusion may be the key to your problem solving, so you need a solid foundation here to see the corresponding conclusion immediately. At this point, you begin to gradually improve the speed of solving problems, but you can't relax. This is just the beginning, but it is also very important: a journey of a thousand miles begins with a single step.
3. Think more. In the process of solving a problem, don't let it go when you work out the answer. The ideas formed for the first time in the early days are often complicated, not the quickest and most convenient, so you should think from many aspects to solve more problems for one problem. When you feel that there is no better way, ask your classmates and teachers, see their opinions, and absorb more ideas that can solve problems efficiently.
4. Chart. In the process of solving problems, charts are very important. Sometimes you just need to draw a picture to know the answer, so you must draw more pictures in the process of solving problems, which will save you a lot of time in calculating problems.
5. Remember the question. Some issues are obviously representative. Seeing them will make you feel that your mind has been opened. As long as you think the problem-solving ideas or special algorithms are useful to you, write them down in a notebook and practice them often. At that time, as long as a certain condition of that type of problem appears, your mind will immediately reflect the conclusion.
6. expand. In fact, this can be done with energy, provided that the previous foundation is well practiced. Through the above training, your problem-solving speed will be obviously improved. But there will always be some questions or conditions that you haven't seen before, and it may waste a lot of time to solve problems with your previous knowledge, so look at the conclusions of some reference books, look at their problem-solving ideas, and see what simple and quick methods are available.
7. speed up. Why speed up? In fact, it should be evil, that is, the way you can solve this problem at once. This is to accumulate problem-solving skills in the process of practicing doing problems. Is it possible to reflect some conclusions by seeing some conditions of the problem? Or can you apply the proof conclusion you encounter when solving problems? Is it a novel and quick way of thinking when doing problems? Or do you draw pictures to solve problems according to known conditions? Is it expressed through negative conditions? Or bring in questions according to the answers given to see if the conditions are met? Wait, as for these, you should accumulate them slowly in the process of solving problems.
8. solve the problem. The problem solving here is not as simple as the above exercises, which is equivalent to the problems you find difficult in the exam, especially some big problems that solve problems. To achieve this step, we must work hard to move forward. The answer in the exam looks terrible, but in fact, many chapters and knowledge points are combined, just like the' vacuum cleaner' composed of five cars in Transformers. As long as you are familiar with the knowledge points of each chapter and see the corresponding conditions, you can know some conclusions, and often these conclusions will be linked by another condition, step by step, interlocking. Of course, many people don't know how to start when they see so much when solving problems. First of all, they have no idea to solve the problem. Second, a certain condition does not remind him of relevant knowledge points, and they don't know how to quote the calculated conclusions, which often leads to disjointed problem solving. When solving a problem, don't look at the whole, so you will have no clue, and you will find the problem difficult and even less confident. Mosquitoes don't attack the lion as a whole, but only attack its weaknesses. This involves the perspective of solving the problem. You can see what conclusions can be drawn from the conditions of the question first. It's usually a big problem. It is suggested that all conditions should be listed on the draft paper first and marked with numbers. This will also prevent missing conditions when solving problems, and see which conditions can lead to what conclusions and which conclusions can lead to what results. Sometimes, you can get the answer. But usually according to this line, you will get some conclusions, depending on whether your conclusions are profound enough. If you go deep enough, you will get closer to the truth, but it will not appear as the answer to the question. A long time ago, there was an article about Zhan Tianyou building a railway. A tunnel needs to be dug on the way to build the railway. If it is dug from one end, it will be postponed. Zhan Tianyou adopted the method of digging at both ends and cutting in the middle, which greatly shortened the construction period. This passage came to me when I was solving a big problem in high school, and it also became my perspective. Some conclusions can be drawn through conditions or multiple conditions, and some results may be drawn between conclusions and conditions or conclusions. If you don't have a clue at this time, you can start from the back of the question and see what the question asks and what information you can usually get. How can the conclusion be just related to this information, which constitutes the whole problem-solving idea: look at the problem and ask the question.
I hope it works for you!