First, the basic review stage-systematic arrangement, the first round of review to build a mathematical knowledge network, the so-called "knowledge article", in this stage, teachers will lead students to review the courses they have learned in Grade One and Grade Two, but this is not just a simple repetition of what they have learned before, but an important process of generating a new understanding of old knowledge from a higher angle, because in Grade One and Grade Two, teachers take knowledge as the main clue. In the first round of review, the teacher's main clue is the vertical and horizontal connection of knowledge. Take chapters as a unit, connect those fragmentary and scattered knowledge points in series, systematize and synthesize, and focus on the integration of various knowledge points. Usually review should pay attention to the concepts, theorems, formulas and so on in the textbook. At the same time, it pays more attention to the development and formation process of knowledge, the analytical thinking of examples and the process of solving problems. Review should be based on textbooks, lay a solid foundation, comprehensively sort out knowledge and methods, and pay attention to the reorganization and generalization of knowledge structure. It is necessary to systematically sort out the mathematics knowledge learned in senior high school, organically link the basic knowledge in the form of concise charts, and build a knowledge network so that students can have a comprehensive understanding and grasp of the whole senior high school mathematics system. In order to facilitate the storage, extraction and application of knowledge, it is also conducive to the cultivation and improvement of students' thinking quality, which is an important link in mathematics review. The first round focuses on reviewing the "three basics" (basic knowledge, basic skills and basic methods), with the goal of being comprehensive, solid, systematic and flexible. Students tend to ignore the mathematical thinking methods contained in reviewing important exercises in textbooks. For example, "What are the important thinking methods of analytic geometry" appeared in Shanghai college entrance examination. Jiangsu college entrance examination gave some questions, such as "finding the derivative of a function by definition". The exam instructions clearly point out that the proportion of easy, medium and difficult questions is controlled at about 3: 5: 2, that is, the middle and low-grade questions account for about 80% of the total score, which determines that the college entrance examination review must grasp the foundation and persevere. Only when the foundation is laid can we have a clear concept, be handy, do difficult problems and synthesize. The calculation is accurate. Therefore, in the review process, we should do the following: ① based on textbooks, quickly activate all the knowledge points we have learned. I suggest you read through the textbooks of Grade One and Grade Two in the summer vacation before Grade Three. (2) Pay attention to the changes in the coverage of the knowledge points used in the topic, and consciously think about and study the position and relationship of these knowledge points in the textbook. Note that the comprehensiveness of the teacher's topic selection is constantly strengthening. ③ Understand the knowledge structure of the textbook from front to back. Frame and network the whole knowledge system. Throughout the high school mathematics textbooks, it is composed of a continent, a peninsula and an archipelago. This continent is the shape and number of two-dimensional space, involving sets, mappings and functions, equations and inequalities, sequence and its limit, points and number pairs in rectangular coordinate system, curves and equations, intersections of curves, parametric equations and related parameters, their significance, derivatives and applications. This peninsula refers to solid geometry. Its system comes down in one continuous line with plane geometry, and both are classical axiomatic systems. Strict reasoning and argumentation are carried out, and solid geometry problems are generally reduced to plane geometry problems to solve. Of course, we should pay special attention to the function of vector as a tool and sum up the basic mode of solving solid geometry problems based on dosage. This archipelago refers to some pearls of discrete mathematics scattered in middle school textbooks. Such as permutation and combination, binomial theorem, probability statistics, mathematical induction, etc. The structure of middle school mathematics content can be regarded as a collection of numbers and points. The set of numbers forms four blocks: algebra, function, complex set, permutation and combination. The collection of points forms a graph, which is divided into three parts: plane graph (plane geometry), space graph (solid geometry) and coordinate plane graph (analytic geometry). This constitutes a network diagram of middle school mathematics knowledge, such as "function", which is a vertical and horizontal knowledge structure, which can extract the knowledge points used in solving problems and tell their sources. (4) often summarize the most used knowledge points, study the chapters where the key knowledge is located, and understand the position and role of each chapter in the textbook. The key points of each chapter are listed below for reference. 1. Functions and Inequalities (Topic). Algebra focuses on functions. The combination of inequality and function is a "hot spot". The properties of (1) function, such as monotonicity, parity, periodicity (usually based on trigonometric function), symmetry, inverse function, etc., can be tested everywhere. Specific functions are often combined with geometric intuition of images, and sometimes they are properly abstracted. This kind of problem is difficult, and finding common functions that meet the conditions is a good way to solve this kind of problem. It is the most important, and the training of its nature and application should be in-depth and extensive. The research focus on the function value domain (maximum) is the quadratic function or the value domain transformed into quadratic function, and the quadratic function value domain with parameter variables should be the focus. Methods The formula method, substitution method and basic inequality method were mainly introduced. The distribution and discussion of the roots of the unary quadratic equation, the discussion of the solution of the unary quadratic inequality and the intersection of the quadratic curve are closely related to the unary quadratic function, which should occupy a large proportion in training. Strengthen the review of "three types". (3) Proof of inequality. The proof of function-related inequality, the combination of mathematical induction and sequence is the key point. Methods The comparative method and the formula method using basic inequalities were emphasized. Although scaling method is not the focus of college entrance examination, it is necessary to master several simple scaling skills because scaling method will be used more or less in exam questions over the years. To prove inequalities, we should be good at analyzing the substructure characteristics of formulas and looking for the differences between known proofs. Find the connection with related theorems as a breakthrough to solve the problem. (4) In solving inequalities, flexible transformation and classified discussion are emphasized with the goal of mastering the unary quadratic inequality and the comprehensive title that can be transformed into unary quadratic inequality. Solving inequalities often has letters, which need to be discussed. It is also necessary to master the method of transformation, the combination of numbers and shapes, the idea of functions and equations, and the general solutions of eight common inequalities. 2. Series (main body). The general term, sum and limit of sequence are investigated by arithmetic sum ratio. As for the abstract sequence (given by recursive relation), it is not limited to "inductive proof", but also needs to strengthen several methods of sequence summation, such as union and division. Common methods such as split term and dislocation subtraction must be mastered (pay attention to the discussion of Q). 3. Triangle (non-subject). Adjustment opinions. "sum difference, product difference eight formulas, no need to remember." The difficulty of the examination questions is not diminished. In training, we should master the clever use of basic formulas and emphasize the use of positive, negative and variable. There are two main forms of triangle problem: one is to find more complex triangles. Second, about the angle in the triangle. Any problem of trigonometric formula transformation can be solved by analyzing the differences in angle, function type and formula substructure characteristics. 4. Plural numbers (non-subjects, liberal arts are not tested) have shown a cooling trend in recent years. The training questions, methods and difficulty can reach the textbook level. 5. Solid geometry (subject) highlights "space" and "solid" pyramids, focusing on one side edge or the side perpendicular to the bottom, and the combination of prisms and pyramids should also be paid attention to. The positional relationship focuses on judging or proving verticality, highlighting the flexible application of the three vertical theorems and inverse theorems. The spatial angle focuses on dihedral angle, which strengthens the angle determination method of the three vertical theorems. Spatial distance focuses on the distance between points and faces and the distance between lines and faces. The combination of the two is particularly important. Equal product transformation and equidistant transformation are the most commonly used methods. The calculation of angle and distance is finally converted into a triangle. The calculation of area and volume is mostly related to pyramids (especially triangular pyramids), because the solution of triangular pyramid volume is flexible and has a wide range of ideas. 6. Analytic geometry (discipline). The equations of straight lines and conic curves, their related properties and mutual positional relationship are important contents. The objective problem is only a superficial phenomenon. The position relationship between straight line and conic curve is the main problem in college entrance examination. It is a common problem to highlight the intersection, midpoint, chord length and trajectory of a straight line and a quadratic curve, but the range with parameters is a difficult one. Highlight the connection between function and vector. Second, the comprehensive review stage-comprehensive deepening, mastering mathematical ideas and methods, usually called "method articles." It starts from the second semester and ends in mid-April. At this stage, this paper mainly studies mathematical thinking methods. In the review, we should focus on improving our mathematical ability, and improve our logical thinking ability, calculation ability, spatial imagination ability, problem analysis and solving ability, mathematical inquiry and innovation ability. We should broaden our horizons, improve the knowledge structure required by the college entrance examination, optimize the quality of thinking, and fundamentally improve mathematics literacy. These are the directions and goals that we must focus on in math review. Learning mathematics requires solving problems. But solving problems is not the whole of mathematics, and mathematical thinking method is the soul of mathematics. It is foolhardy to solve problems without mastering mathematical thinking methods, and it is "going to Baoshan empty-handed" to learn mathematics without solving problems, and it is impossible to grasp the true meaning of mathematics. Teachers no longer pay attention to the order of knowledge structure, but aim at improving students' ability to solve, analyze and solve problems, and adopt "matching method, undetermined coefficient method, substitution method, etc." Solve a class of problems and a series of problems by combining numbers and shapes and discussing them in categories. The second round of review is generally a special intensive training, with the goal of improving students' ability to answer questions in the college entrance examination. At this stage, students should not indulge in the rehearsal of test papers, but should, under the guidance of teachers, focus on problem-solving strategies, take typical examples as carriers, take the flexible use of mathematical thinking methods as clues, and consolidate, improve, synthesize and improve themselves on the basis of the first round of review. To strengthen the cultivation of thinking quality and comprehensive ability, we should mainly focus on knowledge reorganization and establish a complete structure of knowledge ability, including method ability, thinking ability and expression ability of the subject, but this must be based on knowledge memorization ability, understand the source of knowledge and its mathematical thinking method, grasp the vertical and horizontal relationship of knowledge, and cultivate the ability to explore and study problems. Learn to connect theory with the situations and problems of materials, and find the combination point with the main knowledge according to the materials given in the topic. Learn to form systems and methods, that is, problem-solving ideas, including the extraction of effective information, the methods and skills needed to solve problems, the analysis and judgment of factual materials, the evaluation and reflection of conclusions, etc. If you don't pay attention to the "hard work" of the method, you should do the problem on the basis of clarifying the basic concepts and basic knowledge structure. Sometimes you can deepen your understanding of basic knowledge in doing problems. It is inefficient and sometimes even meaningless not to pay attention to summing up the law of solving problems and mathematical thinking methods. Students should do the following: ① Take the initiative to split and reorganize related knowledge. Find out that a certain knowledge point will appear in a series of problems, and a certain method can solve a class of problems. ② When analyzing problems, focus on knowledge points from the original text. Gradually transform into exploring ideas and methods to solve problems. From now on, solving problems must be very standardized. As the saying goes, "If you are not afraid of scoring difficult problems, you are afraid of deducting points for each problem", so everyone must write the problem-solving process clearly and rigorously. ④ Select appropriate simulated test papers and previous college entrance examination questions, and gradually clarify the scope and focus of the college entrance examination. Thirdly, strengthen the review stage-strengthen training and improve actual combat ability. About a month's time, also called "strategy paper", the teacher mainly talks about "solutions to multiple-choice questions, fill-in-the-blank questions, application questions, inquiry questions, comprehensive questions and innovative questions", teaching students some special methods and skills to improve the speed of solving problems and test-taking strategies. The third round is generally simulated reinforcement, with the purpose of regulating students' intelligence and emotions. Make students gradually familiar with the requirements of mathematics college entrance examination for students. At this stage, students should strengthen their reflection after solving problems, and are willing to spend some time to study the exam outline, exam instructions, previous college entrance examination questions and simulation questions all over the country again, master the college entrance examination information and proposition dynamics, improve the accuracy and practice speed, and sublimate to perfection in practice. In practice, we should pay attention to the following points: solve problems in a standardized way. As the saying goes, "Difficult problems are not afraid of scoring, but they are afraid of deducting points for each question." Therefore, it is necessary to write the problem-solving process in a clear hierarchy and complete structure. What matters is the quality of solving problems rather than the quantity, and we should refine our own problems selectively. We are not satisfied with what we can do, but emphasize the reflection after solving problems and experience the essence of problem-solving strategies and thinking methods, especially some college entrance examination questions, new questions and slightly difficult questions. This kind of reflection is more important, so we should think more and understand the essence. Students should do: I will choose the most time-saving and trouble-saving method from various methods, try to think from multiple angles and angles, and gradually adapt to the requirements of the college entrance examination for "simple thinking". Pay attention to my problem-solving speed, slow examination, comprehensive thinking, accurate writing and quick answer. Sometimes it's just a symbol error, which will make you feel the taste of "missing a mile, missing a thousand miles". If you regret it for life at a critical moment, the return of the space shuttle Columbia to the ground will be ruined because of the failure of a heat insulation tile. These learning qualities will benefit you for life in your future work. ③ Develop the habit of analyzing the proposer's intention in the process of solving problems, and think about how the proposer organically combines the knowledge points examined, what thinking methods are compounded in it, what the proposer wants to test me and what I should do. Be aware that. The fourth stage of preparing for the exam-psychological adjustment and adapting to the college entrance examination-is the sprint stage, also called "preparing for the exam". At this stage, the teacher will give you the initiative to review. In the past, the key points, difficulties, methods and ideas were all based on the teacher's will, but now you should study the exam notes directly and actively, learn the college entrance examination questions in recent years and master the college entrance examination. Lock in the most important things and master the most important knowledge to the point of perfection. ② Grasp the error-prone points in thinking and pay attention to typical questions. Browse the exercises and papers you have done before, recall the course of learning relevant knowledge, and do a good job of "correcting again". (4) extensive reading, extensive learning, rote memorization, make yourself well informed, pay attention to the new background, new methods, representative knowledge. ⑤ Don't do difficult problems and digressions. Common problem-solving methods; Test problem-solving skills; Psychological guidance for exams.