The first part is the characteristics of the 2022 math test proposition. In 2022, the full mark of the mathematics test paper of the college entrance examination is still 150, and the examination time is still 120 minutes. In terms of test paper content, calculus has been reduced by one chapter and linear algebra has been added. The question structure still follows the examination form after 20 19. Details are as follows:
First, the content and structure of the test paper: Calculus accounts for about 80%, and linear algebra accounts for about 20% (30 points). The details are as follows:
As shown in the above table, the chapter "Vector Algebra and Spatial Analytic Geometry" has been deleted from the new syllabus. Although this chapter is the geometric basis of multivariate function calculus, it has little influence on the study of the following chapters. Moreover, in the postgraduate entrance examination, there is no such chapter in Math II and Math III, so it is easy to understand to delete this chapter. Added linear algebra. Although there are two chapters in the new syllabus, in college textbooks, it is actually four chapters: determinant, matrix, vector and linear equations, covering a large area.
Ⅱ. After slightly changing the examination questions of 2019, the examination questions have not changed, and the corresponding scores have not changed after continuing to use the new syllabus:
Judging from the test questions, the new syllabus has not changed, reducing the burden of preparing for the test, and the regular test questions can still be prepared according to the previous ones.
Three. Distribution of examination contents According to the characteristics of examination questions in 2023 and previous years, combined with the new syllabus, we can simply predict the distribution of examination contents in 2022:
As can be seen from the above table, around 2023, differential, integral and multivariate function calculus account for 70%, and the rest are roughly evenly distributed in the other four chapters. In this way, we can roughly predict the distribution of examination content in 2022. According to the new syllabus, calculus accounts for 80%, so calculus and multivariate function calculus should account for at least 60%, or even more. Linear algebra accounts for 20%, and the chapter of vector and linear equations is easier to examine big questions, so it is predicted that its proportion will be slightly larger.
Four. Discipline characteristics For calculus, the focus is on the knowledge of the first three chapters, especially the differential calculus of unary function and the integral calculus of unary function. This is not only the key chapter of the exam, but also the basis of learning multivariate function calculus. In independent chapters, ordinary differential equations mainly use these two parts of knowledge. So if you want to learn calculus well, you must learn the first three chapters well, among which the core is the calculation of limit, derivative and indefinite product.
For linear algebra, many schools have not offered this course before (it may be added later), and many students are not familiar with it. It is a mathematics subject completely independent of calculus. Even without the foundation of calculus, there is no problem in learning this part. Similarly, no matter how good the foundation of calculus is, it is not very helpful to this part of learning, and it still needs to be studied step by step. The characteristic of linear algebra is "trivial and messy". Trivial is reflected in the fact that there are many things to remember in this part, and messy is reflected in the close relationship between several knowledge blocks. It can be said that "you have me and I have you", which is particularly confusing and increases the difficulty of learning this part. The core of linear algebra can be considered as matrix, especially the elementary transformation of matrix.
As mentioned earlier, the second part of the change of 202 1 examination syllabus, as the first year of reform, has great guiding significance for preparing for the exam, but we can't ignore the previous things, especially the examination questions of the past few years, which have obvious regularity. Let's talk about the changes in the new syllabus in combination with previous years' exam questions.
ⅰ. The chapter of calculus function, limit and continuity remains basically unchanged. According to the experience of previous exams, the function section will not be given a separate question, and the distribution of questions basically revolves around the concept of function limit, two important limits, the comparison of infinitesimal, the concept of function continuity and discontinuity.
In addition to some common test sites (such as the concept of derivative, the calculation of derivative differential, the limit of L'H?pital's law, the description of function graph, the proof of inequality, etc. ), there are two places to pay attention to. The first is to "understand and apply Rolle's theorem and Lagrange's mean value theorem", although it was also in the previous syllabus.
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