Mathematics is the foundation of the whole natural science and should be faced with a cautious and scientific attitude. Mathematics is characterized by extreme abstraction and conceptualization, which requires extremely high rational and logical thinking. Therefore, when I study mathematics, I should pay attention to concepts and study the connotation and extension of a certain mathematical concept in detail. However, after all, there must be a simple and effective solution to the exam, so I have to sacrifice a lot of time to do it and engage in sea tactics. But if you dare not choose, being trapped in the sea of questions will make people very tired. You must be able to get in, get out, get up and put it down. So my problem-solving principle is: to do a problem, you must know ten or dozens of problems. Because every math problem (mother problem) will cover several math problems (sub-problems). Do a motif, and every sub-topic is understood, so you don't have to do all the topics that belong to the motif, wasting limited precious time.
-Lv Zhipeng, the science champion of Heilongjiang Province
I have a trick to learn math, which may not be useful to everyone. I said it for reference only: you can learn math well by reciting examples. I don't like sea tactics. I like to find one or two typical "rote learning" from each question type. The first example may not be, but once or twice, after understanding it, when I see this type again, I will take the "example" and set it in it.
-Beijing liberal arts champion Duan Nan
I have my own way of learning mathematics. I always understand the connotation of various knowledge points in class, then deepen my understanding by doing some representative questions after class, and then read books to understand the basic knowledge points again. In mathematics learning, doing problems is not an end, but a means: doing problems is to achieve a deeper understanding. Don't do problems for the sake of doing them, but at the same time, do some representative exercises in moderation. Usually, after every exam, I always take a correcting book to copy down the wrong questions, correct them carefully, and indicate the methods used next to the key steps, then write comments after the wrong questions and summarize the reasons for the mistakes. Before every math exam, I always read this book carefully and remember why I made mistakes, so as to avoid making similar mistakes again.
—— Yan Haijin, the champion of liberal arts in Hubei Province
Wang Cong: I graduated from Shishi Middle School in Chengdu, Sichuan Province in 2004. The total score of college entrance examination is 602, and the score of mathematics (liberal arts) is 149.
Admission institution: university of international business and economics, majoring in international economy and trade.
Wang Cong: I really put a lot of effort into math. I don't like reading extracurricular books, but I like reading textbooks and reading them thoroughly, but I will use my own thinking to analyze problems and summarize methods. I think the following points are worth learning from-
First, don't be afraid to learn math. Many people lose interest at first, then lose confidence, and finally hate math, which leads to worse math. Actually, these links are related. As long as one aspect is improved, other aspects will also be improved. Of course, learning mathematics requires a certain talent, that's for sure, but getting a score of about 1 10 in the college entrance examination can be said to have nothing to do with talent. As long as you work hard, as long as you have a correct attitude and work hard, you will definitely have good results.
Second, there must be some exercise training, otherwise it is difficult to be sensitive to numbers. Mathematics is different from other subjects. If you don't practice at ordinary times, even if you understand the train of thought, you may not be able to calculate correctly, so you need to do a certain amount of questions to improve your proficiency, speed and accuracy. In addition, doing a certain amount of questions will make you more familiar with the test center and understand what the questioner wants to test you, which will help you solve the problem faster. For example, when I ask Tan about the center of symmetry, my first reaction is that the questioner will take points that are multiples of /2, because those points are symmetric centers, but they are meaningless and easy to be ignored. I will pay more attention to those points. For example, if you only do each question once, then you will spend a lot of time on each question, and you may not get it right. But if you do 3 ~ 5 questions of each type, you will know the direction, and then you will know which method to use when you encounter such questions.
Third, when learning each chapter, you must do the typical exercises of the corresponding chapter. Because it is easy to take the exam, and it can make you familiar with the test sites and "traps" of this chapter, such as the collection chapter. If there is a big exam, my first reaction is to take an empty exam, so I will be very careful.
Fourth, learn to sort out error-prone questions. The target of my speech does not include mathematical geniuses. We are not geniuses, so we can never forget our mistakes and never make them again. Therefore, you need a notebook to sort out the wrong questions and review them regularly, especially for senior three students, who will never forget what they have learned and make mistakes again and again as before. Therefore, a typo is inevitable.
Wang Yanmou, the expert head of the advisory group of famous teachers in the college entrance examination of Giant School and a famous math teacher in China.
Do the questions you know quickly.
1. Regardless of the size of the problem, first grasp the problem that can be done, then grasp the problem with a door, then spell the difficult problem, and finally pick the problem that can't be done. This can ensure that you can get more points in a limited time.
2. hurry up. Don't dwell on trifles. The average number of multiple-choice questions is controlled within one and a half minutes.
3. Adhere to the "5, 2, 2 principles". Keep your eyes on the first five multiple-choice questions, the first two to three fill-in-the-blank questions and the first two answers. These questions are all graded and won't be difficult. 4. Set aside inspection time. Give up the questions that you really can't do, and ensure that the previous questions get points. For example, the last two answers are usually high-level questions, and the ability is not hard enough. It's better to leave time for those definite questions.
5. The combination of mental arithmetic and mental arithmetic. Mental arithmetic is easy to make mistakes under special circumstances, so we must combine mental arithmetic with written arithmetic.
133, Mathematics 129, English 146, Literature and Literature 244.
Admission: Peking University Law Department thoroughly understands the textbook method.
Many students think that the topics in math textbooks are very simple, and they are all said by the teacher in class. After class, they often put their textbooks aside and do other exercises that they think are more difficult. That's what I did at first. But when it comes to exams, difficult questions are often asked, but simple questions are easy to lose points-especially some small questions such as multiple-choice questions and fill-in-the-blank questions. Therefore, we should pay special attention to learning textbooks and do every question well in textbooks, which is also the first point I want to say. The second point is the basic concepts and ideas in textbooks. Textbooks are not only important for exercises, but also for basic concepts and ideas. There are many big concepts in bold in math textbooks, which we usually pay attention to, but in some small words, there are often some very subtle concepts and principles that are easy to be ignored, and when we take the exam, we often take out those problems that we ignore. And once the exam is over, everyone will "pour a big chunk." Therefore, when reading textbooks, we must see every word, sentence and even tiny truth clearly. There are many important conclusions in the exercises of trigonometric function, solid geometry and analytic geometry, which should be remembered. Understand the textbook thoroughly, and we can't emphasize its importance too much.
2. Jiangxi science champion: Li Chao's total score in the college entrance examination: 690 points (including 10 plus points)
Single subject scores: Chinese 13 1, Mathematics 142, English 133, Science 274.
Admission: Tsinghua University Department of Materials Science and Engineering, HowNet Law.
There are many knowledge points in mathematics, so it is not easy to master them in an orderly way. It is necessary to string these scattered knowledge points together with a line. Knowledge network method can be summarized as the following two modes. First, formula derivation. Summarize the formulas that must be mastered, and know why, and deduce them by using the correlation between formulas. The knowledge points of the college entrance examination come from textbooks. By adapting the examples in the textbook, you can get a college entrance examination question. If you synthesize some basic questions or knowledge points, it can become a difficult problem. We can break through all the difficulties according to the daily knowledge points. The second method, composition memorization, is to mark the relationship, applicable conditions and characteristics between knowledge points by drawing charts. From chapter to chapter in the book, subdivide layer by layer, summarize the knowledge points, and finally recall that there is no connection between books. This method sounds boring and complicated, and it can be combined with specific exercises in actual operation (preferably not difficult but comprehensive). The composition memorization method pays attention to the foundation and improves the ability.
Champion Li Chao said:
These methods may still not meet everyone's learning requirements, but the key is to suit themselves, plus persistence and confidence. Hard work and skilled work will surely succeed!
3. Hubei science champion: Zhu Shida's total score of college entrance examination: 70 1 admitted to Peking University Yuanpei experimental class.
Single subject scores: Chinese 129, Mathematics 150, English 14 1, Science 28 1.
Construction method of mathematical knowledge network
In the process of solving problems, many students often can't write because they can't find ideas. There are only two kinds of math problems: solving problems and proving problems. Solving a problem allows you to seek a result, and proving a problem allows you to prove a conclusion. Personally, I prefer this method: list the known conditions and see what conclusions can be drawn. These conclusions are also conditions, and then see what new conclusions can be drawn from these new conditions, layer by layer, just like branches of the trunk, more and more. Since it can be deduced forward, it can also be deduced backward. Starting from the results you require or the problems you need to prove, you can see what conditions you need for the desired results and what conditions you need to get these conditions, step by step and think backwards. When the branches stretch out more and more, eventually two will be intertwined, and the problem will be solved. When you start using this method, it is really time-consuming, but it is still quite effective. After you are more proficient, you can often see the key to the problem at a glance and find a breakthrough quickly.
Top scholar Zhu Shida's speech:
Details determine success or failure! I think this is a portrayal of my review process.
Don't always compare your grades with others, don't let others control your standards, and compare with yourself every time. If the goal is 650 points, you will succeed if you reach it, even if others are taller than you.
How high can a person climb without seeking his will with both hands; How far can a person go? Don't ask about your feet, ask about your beliefs.
With all the students who have passed the college entrance examination and are heading for it.
4. Chen Bo, the top liberal arts scholar in Hunan Province, scored 682 points in the college entrance examination.
Single subject scores: Chinese 1 18, Mathematics 146, English 136, Literature Synthesis 282.
Admission: Guanghua School of Management, Peking University, with multiple-choice method to remove options.
There are many ways to solve multiple-choice questions. In the face of simple multiple-choice questions, some simple skills are also needed, and students need to explore slowly in their studies. But I think the best way to solve multiple-choice questions is to get rid of the option method. Cultivate your ability to solve problems, that is, cultivate your ability not to be disturbed by wrong options. Especially in the face of some difficult and complicated multiple-choice questions, we can remove these options and fill in the blanks. After writing the answer, we can look for it from the options. If we can't find them, it means you must be mistaken. This can avoid many problems-for example, some students are easy to misread the topic. When he does the purpose of the problem, he often does it according to some data he misreads, just because there is such an answer in the option. In this case, he will choose the wrong answer; Furthermore, some topics are theoretical multiple-choice questions, and perhaps their choices are misleading. If you remove the options, you won't be misled by them.
Testimony of top scholar Chen Bo:
In the whole examination process, we should maintain a mentality of "attaching importance to the process and ignoring the results" and be firm and have no desire.
It takes sweat to get good grades in the college entrance examination, but it is more important to master the correct learning methods. Too many diligent students stumble in the college entrance examination, and I think it is often counterproductive to increase the study intensity blindly.
Of course, there will be many difficulties in the study of senior three. Everyone should have a healthy attitude to face these challenges, and the eagle that has experienced the storm can fly to a broader blue sky. Facing the upcoming senior three life with full self-confidence, there is no unattainable ideal. I wish you all a dream come true in next year's college entrance examination and become the first.
Chen Min, the top science scholar, scored 689.
Single subject scores: Chinese 124, Mathematics 135, English 144, Science 286.
Admission: Peking University Yuanpei experimental class actively seeks solutions to problems.
In the process of studying, I had such an experience. Sometimes I can't find the idea when I see the topic, so I can't wait to see the answer. When I read the answer, I often feel that every step of the answer is logical, and it is very simple to use any theorem and method, so I think I have understood the topic thoroughly. Do this problem again in a few days, and there is still no way to start. I think this situation is mainly because my acceptance of this issue is a passive process. In this process, I only saw the specific problem-solving process mechanically, but I didn't really understand the problem-solving idea.
Actively seeking ways to solve problems is just the opposite of this passive learning method. This method emphasizes starting with simple exercises, because simple exercises will be easier to do, and then go from shallow to deep after finishing. When you encounter a difficult problem in practice, consciously force yourself not to look at the answer, the formula or ask others for help (these are passive methods), but to calm down, actively mobilize your brain knowledge base and actively seek ideas to solve the problem. In this way, you can train yourself from the shallow to the deep, plus the classification analysis of common problems. When you see the math and physics exercises, you will reflect the knowledge points and ways of thinking examined in this question at the first time, and you will feel handy.
Xie Ni, the top liberal arts scholar in Shaanxi, scored 686 points in the college entrance examination.
Single subject scores: Chinese 136, Mathematics 149, English 132, Comprehensive Literature 269.
Admission: the wrong problem set method of Guanghua School of Management, Peking University.
Besides typical examples, we also need to pay attention to our own mistakes. The wrong problem set is necessary for many students with good grades, and I am no exception. What I emphasize here is how to make full use of my wrong problem set.
There are probably two kinds of wrong questions: one is that you can't do it at all because it's too difficult and there is no idea; The other is that you can do it yourself and make mistakes because of carelessness. In my opinion, the most valuable wrong question is the second category. Because there are many kinds of carelessness, we should also analyze it. First, read the wrong topic. Is it a wrong number or a wrong meaning? Why did you read the wrong question? How did you misunderstand the meaning of the question? Will you make the same mistake in the future? Second, the starting point and thinking are wrong, and such a thinking solution is not suitable for this kind of topic at all. Third, the calculation is wrong. Why is it wrong? Is there any way to stop it? How can we be really careful? In fact, how many questions are there in the college entrance examination that you won't do? The final contest is still about how much you can do right. If you can put an end to your careless mistakes, you will certainly get very good grades in the college entrance examination.
Graduated from Zhang zhen Middle School, the top science scholar in Shandong Province: The total score of the college entrance examination in Zaozhuang No.8 Middle School in Shandong Province is 7 17 (including 20 points plus points).
Single subject scores: Chinese 125, Mathematics 133, English 146, Science 293.
Admission: Tsinghua University mathematical basic science professional knowledge points network summary method.
The first way for me to learn mathematics is the network summary of knowledge points. When doing math problems at ordinary times, some problems often make us feel at a loss. At this time, if we can connect the knowledge points investigated in this question, we can use this as a clue to prescribe the right medicine and find a breakthrough to solve the problem. The so-called network summary method of knowledge points means that if you encounter a difficult topic in solving problems, you will list the problem-solving methods and knowledge points related to this topic next to the topic, and then summarize them in your notebook. In this way, after a period of training, you can see the topic in the exam and associate it with the relevant knowledge points, and quickly find the corresponding solution. On the one hand, this method can improve the speed of solving problems and save a lot of time for candidates, on the other hand, the correct rate of doing problems is high and the hit rate of solving problems is improved.
Yang Nannan, the champion of Henan liberal arts, scored 662 points in the college entrance examination.
Single subject scores: Chinese 127, Mathematics 138, English 143, Comprehensive Literature 254.
Admission: Peking University Yuanpei experimental class abandoned reading properly.
"Give up, give up, give up what you have" is a common saying. For the subject of mathematics, I think we should accurately position ourselves according to our own strength, ensure that all the basic questions are answered correctly, and give up the high questions that we can't do, so as to achieve the optimal allocation of intellectual resources and achieve better results.
Everyone has their own advantages and disadvantages, which should be an effective test method. As the saying goes, "Bears eat sweet potatoes with their big mouths, and sparrows peck sesame seeds with their small mouths." I am a "sparrow" with a small mouth, and I don't have much advantage in math study. In the usual exam, the last question of mathematics is quite difficult for me. I often just do the first question, and the second question is basically helpless and often defeated. When I was in the college entrance examination, I saw that the second question of the last question was quite difficult, so I quickly decided to give up this difficult "sweet potato" and go back to check the questions I had done before. Fortunately, I found a wrong five-point multiple choice question. Perhaps, it is precisely because of this strategy of doing what one can, that I kept the sesame seeds, the basic questions, and only dropped 12 points on the more difficult questions, and all the other questions were done correctly, which made the math exam super-level.
Class notes are very important when learning mathematics, so how to take class notes?
First, remember the outline.
Most teachers have an outline when giving lectures, and they will write the outline of preparing lessons on the blackboard when giving lectures. These outlines reflect the key points and difficulties of the lecture, and they are organized, so they are more important and should be recorded in the notebook.
Second, remember the problem.
Write down the questions you don't understand in class in time, so that you can ask your classmates or teachers after class and make the questions clear.
Third, remember the doubts.
If you have any questions about what the teacher said in class, you should write them down in time. This doubt may be your own misunderstanding or the teacher's negligence. After writing them down, it is convenient to discuss with the teacher after class.
Fourth, remember the method.
Remembering the problem-solving skills, ideas and methods taught by teachers is helpful to inspire thinking, broaden horizons, develop intelligence, cultivate ability and improve the level of problem solving.
Fifth, remember to summarize.
Pay attention to remember the teacher's after-class summary, which is very useful for concentrating the content of a class, finding out the relationship between key points and parts, mastering basic concepts, formulas and theorems, discovering existing problems, discovering laws and integrating classroom content.