2. Mathematics (2) exam, high number part 18 questions, including 6 multiple-choice questions, 5 fill-in-the-blank questions and 7 answer questions. Because the examination scope of Mathematics (2) is much smaller than that of Mathematics (1), the examination content is more concentrated. From the analysis of the examination rules in recent 15 years, the main test sites are: limit, derivative and differential, application of derivative, application of definite integral and definite integral, differential equation, differential and extreme value of multivariate function and double integral. These test sites are basically compulsory every year, and some have more than one question. Candidates should focus on reviewing.
3. In recent 15 years, the contents and problems are as follows:
1) function part includes: four properties of function (bounded/monotone/parity/period), asymptote, discontinuity, zero theorem and mean value theorem; 2) Limits include: function limit, sequence limit and infinitesimal; 3) Derivative and differential include: definition of derivative, implicit function and derivative, higher derivative, piecewise function and inverse function of function expressed by parametric equation; 4) Mean value theorem: Proved by mean value theorem; 5) The applications of derivatives include monotonicity, concavity and convexity, extremum and curvature; 5) definite integral includes: definite integral calculation, definite integral size comparison, variable limit integral, improper integral and definite integral inequality proof; 6) The applications of definite integral include: geometric applications (area, volume, lateral area, arc length) and physical applications (motion, work, gravity, pressure, center of mass, center of mass, etc. ); 7) Differential equations: first-order, second-order, third-order, homogeneous, separable and reducible differential equations; 8) The differentiation of multivariate functions includes: first-order and second-order partial derivatives, total differentiation, partial derivatives of composite functions and implicit functions; 9) Extreme values of multivariate functions include: extreme values of binary functions, conditional extreme values of multivariate functions, maximum/minimum values and their applications; 10) Multiple integrals include: double integrals.
Summary of the main points and rules of linear algebra examination
Math (2) exam, there are 5 questions in linear algebra, including 2 multiple-choice questions, 2 1 fill-in-the-blank questions and 2 solutions, accounting for 34 points. Compared with advanced mathematics, the examination proportion of linear algebra is lower and the score is smaller, but the review of linear algebra can not be ignored. From the analysis of examination questions in recent 15 years, the main test sites are linear equations, eigenvalues and eigenvectors. These test sites are basically available every year, and often appear in the form of big questions (solutions), so candidates should focus on reviewing.
The content and types of questions frequently tested in recent 15 years are as follows: 1) Determinant part: Determinants are rarely tested separately, and are usually combined with matrices, linear equations or eigenvalues. There are usually only two common determinant questions: one is to calculate the ordinary determinant with no more than 4 orders, and the other is to calculate the special determinant with n orders; 2) Matrix part: the basic operation and properties of matrix, and the rank of adjoint matrix and matrix are high frequency test sites; 3) linear equations: the structure of the solution of the equations, the solution and the judgment of whether there is a solution are constant measuring points; 4) vectors: linear correlation and irrelevance and linear representation of vector groups, and the rank of vector groups is constant measuring points; 5) Eigenvalues and eigenvectors: calculation of eigenvalues and eigenvectors, similarity and diagonalization of matrices; 6) Quadratic type: Quadratic type was rarely tested six years ago, but it has been tested every year in recent six years, and the form is often combined with eigenvalue and eigenvector.