plum

Students, entering senior three means the coming of the college entrance examination. In order to realize the beautiful ideal of entering a higher school, the learning quality of Grade One is the key, so we should not only have confidence and perseverance, but also have scientific and effective learning methods, like leverage, get twice the result with half the effort.

First, make good use of textbooks. Some students said, "What's so good about textbooks? Isn't it just a few definitions, theorems and formulas? " I don't know, just a few definitions, theorems and formulas, but with their profound and rigorous ideological connotation, they have built a building of mathematics. For those who find it difficult to learn mathematics, a common problem is the lack of thorough and comprehensive understanding and mastery of mathematics. Therefore, a comprehensive and profound understanding and mastery of definitions, theorems and formulas is an important task for reviewing and improving grades. To make good use of teaching materials, we should focus on the following aspects.

1. Re-recognize mathematical concepts, deeply understand their connotation and extension, and distinguish easily confused concepts. For example, taking the concept of "angle" as an example, there are many kinds of "angles" in textbooks, such as the oblique angle of a straight line, the angle formed by two lines of different planes, the angle formed by a straight line and a plane, the principal value of a complex radiation angle, the included angle, and the chamfer. Has its own definition.

2. Deepen the understanding and mastery of theorems and formulas step by step, and pay attention to the applicable conditions and scope of each theorem and formula. If the mean inequality is used to find the maximum value, three conditions must be met, all of which are indispensable. Some students make mistakes, either because they are not familiar with the structure of mean inequality or because they ignore the conditions that should be met. For another example, Dimov's theorem is aimed at the triangular form of complex numbers, such as the sum of the first n terms in a series and the sum of the infinite series s (s).

3. Master the ideas and methods embodied in typical propositions. For example, the proof method of equality provides a general method to find the sum of coefficients of binomial expansion or polynomial expansion.

If (1-2x) = a+a x+ a x +…+ a x, then ① a+a+a+…+a =; ②| A |+| A |+| A |+| A |+| A | =。 For example, the sum of the coefficients of all terms in the expansion (x+ 1) (x+ 1) ... (x+ 1) is

Therefore, correct thinking, careful reading, comprehensive mastery, combined with other materials and exercises, deepen the understanding of basic knowledge, thus laying a solid foundation for improving problem-solving ability.

Second, have a good class. The main position of students' learning is the classroom, and the learning quality of the classroom is the key link that affects their academic performance.

1. There will be classes. Some students will say, "Who can't attend class yet?" Actually, it's not. Being able to attend classes means being active in thinking. What should I do if the teacher asks questions and thinks before the teacher? Think about all possible ways and methods to solve this problem, and then compare it with what the teacher said. Maybe some ideas are not feasible, maybe the teacher's method is better, maybe your method is concise and wonderful. Don't wait for the teacher to tell you bit by bit, just because you understand, you think you have learned. Actually, you have to wonder. No wonder many students said that they made a mistake when the teacher told them, because they didn't really think about it.

2. take notes. What the teacher says in class contains important concepts, conventional ideas and methods of various problems, error-prone problems, and some applicable laws and skills, so it is necessary to take notes in class.

3. Review in time. According to the law of memory, review should be timely, once a day and once a week, and each summary is better.

3. Do more exercise. Learning mathematics is inseparable from doing problems, especially in senior three. It is impossible to learn mathematics well without doing a certain amount of exercises, but we should pay attention to the following problems:

1. The difficulty is appropriate. Now there are many review materials and topics, and the review should follow the teacher's requirements. Don't blindly do difficult and comprehensive questions. Setting the goal too high will not only consume a lot of time, but also reduce self-confidence. It is also easy to ignore some seemingly simple basic questions and details, and lose points in the exam, causing irreparable losses. Therefore,

2. The topic is the essence. It is good to practice more when possible, but this is the essence. First, the topic should be combined with the requirements of the exam instructions and the direction of the college entrance examination questions in recent years, with the focus on "three basics" and "universality and generality". Secondly, it is very important to think and summarize when doing the problem. Every time you do a problem, you should recall your own solution ideas and see if you can solve one more problem. Optimize the process of solving problems. Third, we should be willing to spend time on key issues and do more problems. Fourth, in the review process, we should constantly do some application problems to improve our reading comprehension and practical problem-solving ability, which is also one of the directions of college entrance examination reform.

3. pay attention to correcting mistakes. Some students only pay attention to the quantity of problem solving, ignoring the quality, which shows that they don't ask right or wrong after doing the problem, especially the teacher turns a blind eye to the reviewed content. How can this progress? If you make a mistake, you should not only correct it, but also write it down and analyze the reasons and enlightenment of the mistake, especially the test paper. Only by constantly correcting your mistakes can you make progress.

4. Pay attention to the summary. It includes not only the summary of problems, methods and rules, but also some basic problems. For example, there is an equation in solid geometry: the angle formed by AC and plane is that the projection AB of AC and AB in AC plane forms an angle, let ∠BAC=, and prove: cos cos =cos. This equation brings convenience to the calculation of a problem in solid geometry.

If you are familiar with the parity, monotonicity, extreme value and image of the function f(x)=x+, you can easily find the maximum value of some analytical formulas.

Do a good job in reviewing each stage. After entering the third year of high school, I basically began to review. You should obey the teacher's plan and arrangement and accomplish the tasks in each stage in a down-to-earth manner. Generally divided into four stages.

1. The first stage is systematic review. Time is about nine months. The focus is on comprehensive review, focusing on the foundation, that is, chapter by chapter, with the "three basics" as the core, systematically and comprehensively sorting out every knowledge point, mastering generality and methods skillfully, and paying attention to the formation of knowledge system.

"Three basics" refers to the basic knowledge, skills and methods of mathematics. Mastering the "three basics" requires a process, which can only be achieved through proper training. Therefore, it is necessary to develop good study habits, treat each exercise as an opportunity to consolidate learning, associate the related knowledge points involved in such problems and general methods to solve problems as soon as you see them, and gradually master the "three basics".

If you encounter the problem of finding dihedral angle, you will immediately think of its basic methods: first, use the area projection formula cos α =; The second is to find the plane angle. There are three methods to find the plane angle: ① definition method; (2) Three vertical theorems or theorems; ③ Make the vertical plane of the edge. The most important thing is the three perpendicular theorem, and the most important thing is the vertical line of the plane. Only in this way can we grasp the problem as a whole, cut in quickly and solve it smoothly.

Pay attention to the formation of knowledge system. Reviewing the "three basics" is not a simple repetition. It is important to deepen our understanding and discover the essential connection of mathematical knowledge, so as to classify, sort out and synthesize, and gradually form an organized, orderly and networked organism, truly from coarse to fine.

Pay attention to the improvement of mathematical ability. Through a lot of problem-solving exercises, I can improve my computing ability, logical thinking ability, spatial imagination ability, and my ability to analyze and solve problems by using what I have learned.

Pay attention to the application of thinking methods. The famous mathematician Paulia pointed out: "The perfect way of thinking is like the North Star, and many people find the right path through it." This shows how important it is to master the thinking method. For example, some complex algebraic problems can be solved easily and quickly if numbers and shapes are combined.

2. The second stage is focused on review. It takes about a month and a half. The key point is to improve the "three natures", that is, the comprehensiveness, application and innovation of knowledge and ability. This is the reform direction of examination questions since 1999. After the first stage of review, students have a certain grasp of the "three basics", and then the teacher will organize some special topics for students, including:

Functions, equations, inequalities and other knowledge-related topics; Special topics on functions and sequences; Function images and curves of equations.

Special topics of thinking methods, such as: thinking methods of functions and equations; The thinking method of combining numbers and shapes; The idea of classified discussion; Thinking method of movement and transformation; Transformation and transformation thinking methods, etc.

Apply special topics, further strengthen all kinds of exercises, improve reading comprehension and establish mathematical models.

Special topics on innovative thinking. Strengthen thinking training, carry out creative thinking on the basis of "commonness and commonness", and reflect more, less or no rush to calculate.

Students work harder and seize the opportunity. Doing well at this stage will greatly improve your knowledge and ability!

3. The third stage is comprehensive practice. It takes about a month. The key point is to improve the level of examination. Through the repeated practice of comprehensive examination papers, we should strengthen the training in answering strategies and time allocation, especially in reading questions with one feeling, one cut and one success.

4. The fourth stage is the heat preservation and free review stage. Keep a good mental state and calm mind, firmly believe in your own strength, and meet the college entrance examination with confidence.

In short, students should strengthen their confidence, do it seriously according to the teacher's requirements and their own situation, adopt scientific learning methods and persevere, and will certainly achieve excellent results.