1.Interpretation and Analysis of the Revision of Mathematics Examination Outline in 2005
(1) Based on the different requirements of engineering and economic management disciplines for graduate students' mathematical knowledge and ability, the unified mathematics test paper is still divided into Mathematics I, Mathematics II, Mathematics III and Mathematics IV.
(2) In the advanced mathematics section of Mathematics Volume I and Volume II, the requirement of "understanding the concept of elementary function" was added in Article 4 of the examination requirements of "function, limit and continuity".
It was changed from "mastering the nature and graphics of basic elementary functions" to "mastering the nature and graphics of basic elementary functions and understanding the concept of elementary functions".
Comments: Further emphasize the basic knowledge points.
(3)
In the advanced mathematics part of the first part of mathematics, the sixth requirement of the examination of differential calculus of multivariate functions and the third requirement of the examination of calculus of multivariate functions, the original "knowing the rules of how to use implicit functions" is changed to "knowing the existence theorem of implicit functions will find the partial derivatives of multivariate implicit functions".
Comments: Further emphasize the importance of basic knowledge points and concept understanding.
(4) The examination of "Function, Limit, Continuity" in the third and fourth mathematics papers requires that the third item be changed from "Understanding the concepts of inverse function and implicit function" to "Understanding the concepts of inverse function and implicit function".
Understand the concepts of compound function, inverse function, implicit function and piecewise function.
Comments: Further emphasize the basic knowledge points.
Article 1 of the one-dimensional differential examination requirements adds the requirement of finding the tangent equation and normal equation of the plane curve.
Understand the concept of derivative and the relationship between derivability and continuity, and understand the geometric and economic significance of derivative (including the concepts of margin and elasticity).
Understand the concept of derivative and the relationship between derivability and continuity, understand the geometric and economic significance of derivative (including the concepts of allowance and elasticity), and find the tangent equation and normal equation of plane curve.
Comments: further emphasize the basic knowledge points and further enhance the requirements for candidates' ability.
(5)
In the linear algebra part of mathematics test papers 3 and 4, the fourth requirement of "linear equations" is changed to "4". Understand the structure of solutions of nonhomogeneous linear equations and the concept of general solutions. 5. Master the method of solving linear equations with elementary line transformation ".
The original text is "4. Master the solution of the basic solution system of nonhomogeneous linear equations, and express the general solution of nonhomogeneous linear equations with its special solution and the basic solution system of the corresponding derivative group. "
Comments: further enhance the requirements for candidates' ability.
(6) Some concepts, test contents and test requirements of the probability theory and mathematical statistics in the first and third papers of mathematics and the probability theory in the fourth paper of mathematics were revised in words to make them more standardized and unified.
(7) Revise the sample papers of Mathematics I and II.
(8)
The expression of examination contents and requirements in mathematics test paper 1, 2, 3 and 4 is further clear, standardized and unified. The content part of the exam only lists the content range, while the requirement part lists the required level of relevant content and the problems that can be solved by applying these contents.
2.2005 Graduate Mathematics Characteristics
In 2005, the examination paper of the joint entrance examination will further strengthen the accuracy and comprehensiveness of the examinee's mastery of basic mathematics knowledge, and at the same time strengthen the basic ability of comprehensive cross-application of different knowledge points. In terms of difficulty, it will maintain the level of 2004.
Math test questions in 2004 are the simplest and most basic set of test questions in recent five years.
The outline of 2005 is basically the same as that of 2004, but it further strengthens the emphasis on basic knowledge points and standardization requirements. For example, the concept of "accurately connecting with the concept of elementary function" has been added in univariate differential calculus, and "the tangent equation and normal equation of plane curve can be solved", while multivariate differential calculus emphasizes that "understanding the existence theorem of implicit function can solve the partial derivative of multivariate implicit function". Linear algebra emphasizes "understanding the structure of solutions of nonhomogeneous equations and the concept of general solutions", "mastering the method of solving linear equations by elementary line transformation" and so on. Accurate and comprehensive concept understanding and excellent basic computing ability will be the key for candidates to win in 2005. It is our suggestion to strengthen the basic, systematic, comprehensive and cross-cutting training of knowledge, and strive to improve the insight of knowledge, so as to constantly change and eliminate misleading.
Regarding the characteristics and structure of the 2005 entrance examination questions, there are the following points:
(1) Test Paper Scoring Problem
Since 2003, the score of the mathematics test paper in the examination center of the Ministry of Education has been set at 150, which shows that the state attaches great importance to the mathematics quality and ability of talents. However, the topic capacity of the mathematics test paper has not increased, but the assignment of each topic has increased, such as multiple-choice questions and fill-in-the-blank questions (a total of 13 small questions) from 3 to 4. Every time there is one more candidate, there will be one more point in math efforts.
(2) the structure of the test paper
In 2005, the math test paper 1, 2, 3 and 4 had the same structure, all of which were 23 questions, of which about 40% were multiple-choice questions and fill-in-the-blank questions (56 points in total), and the rest were analytical questions.
Test paper 1: Calculus is about 60%, algebra is about 20%, and probability statistics is about 20%;
Test paper 2: Calculus is about 80% (multiple calculus is needed until double integral),
Algebra is about 20% (until eigenvalue and eigenvector are needed);
Test paper 3: Calculus is about 50% (excluding curve and surface integral, triple integral and field theory).
Algebra is about 25% (until quadratic form is required, the same as test paper 1), and probability statistics is about 25%;
Test paper 4: Calculus is about 50% (excluding curve and surface integral, triple integral and field theory).
Algebra is about 25% (until eigenvalue and eigenvector are needed), and probability theory is about 25% (excluding statistics);
(3) The basic situation of marking in 2004
According to a preliminary estimate, the average score in Beijing is around 70, and the topics of calculus, linear algebra and probability statistics are relatively basic, with the minimum shift limit above 90. Among them, the answer sheet of probability statistics is the best, and the scores of calculus and linear algebra are higher than in previous years.
(4) General information of candidates
The general situation is that the teaching level of undergraduate mathematics and English in China is far from the actual requirements of the national postgraduate entrance examination. The reason for this situation does not lie in the candidates themselves.
Facing the postgraduate entrance examination, the characteristic of mathematics examination is to comprehensively examine the accuracy of students' understanding of basic knowledge points. Our suggestions are: to strengthen the accuracy, comprehensiveness, completeness and systematization of the understanding of basic knowledge points, and to enhance the cross-comprehensive application ability of basic knowledge points. In order to ensure this teaching effect, the math tutorial class of the basic class of Tsinghua Postgraduate Entrance Examination should generally be kept at 120- 160 hours, which is the only guarantee.
3. About the accuracy, completeness and systematicness of understanding basic knowledge points.
To understand the basic knowledge points, we must first be accurate. Without accuracy, nothing can be said. Only accuracy can be more comprehensive. Accurate and inaccurate understanding of basic knowledge points, or inaccurate, will greatly affect the examination results. However, the problems of accuracy and comprehensiveness are the shortcomings of most candidates, and they need to make up lessons seriously.
Generally, the topic of complete foundation accounts for more than 60 points (full mark 150), and foundation also occupies an important part in the comprehensive topic. The so-called basic knowledge includes the elementary properties of elementary functions, the limit mode defined by constructing derivatives and its deformation, the propositional form of limit existence and propositional attributes (sufficient? Is it necessary? Is it still necessary? ), limit operation rules, concepts and properties of inverse function and implicit function, concepts of solutions of linear differential equations, formulas of solutions of first-order linear differential equations, structures of solutions of homogeneous and nonhomogeneous linear differential equations, concepts of elementary transformation and rank of matrices, linear correlation and irrelevance of vector groups, relationship between rank of vector groups and structure of solutions of linear equations, relationship between elementary transformation of matrices and solutions of nonhomogeneous linear equations, probabilistic event operation, Five basic formulas of classical probability, distribution rate, distribution density, the properties of distribution function and their relationships, the definition and basic operation formula of numerical characteristics, simple random samples and their numerical characteristics, etc.
Errors in basic knowledge often lead to errors in the entry point of comprehensive questions, which eventually leads to overall errors. At the same time, we should also pay attention to the background of basic concepts and the relationship between various knowledge points, and don't give more difficult questions. Summarize and analyze the methods and skills involved in the basic topics, and strive to draw inferences from others, so that when encountering individual problems, you can easily find the breakthrough point and ideas.
Reference: Liu, the responsible professor of the Department of Mathematics and Physics in Tsinghua University, teaches in the postgraduate remedial class in Tsinghua University.