There are 25 questions in this part, and the examination time is 45 minutes. The examination paper contains five parts: arithmetic, algebra, geometry, unary calculus and linear algebra, each accounting for 20%, all of which are multiple-choice questions.

Third, the scope of the proposition

The propositional scope of the basic mathematical ability test mainly includes the basic knowledge of arithmetic, algebra, geometry, unary calculus and linear algebra and its application in daily life, scientific research and practical engineering. Candidates are required to have a profound and rational understanding of the listed mathematical knowledge; Systematically grasp the internal relationship between mathematical knowledge; Solve related problems by giving examples, explaining, analyzing and inferring; Use relevant knowledge and logical reasoning methods to analyze and solve complex or comprehensive problems.

1. Knowledge requirements for basic mathematics ability test

The knowledge involved in the basic ability test of mathematics is: arithmetic, algebra, geometry, unary calculus and linear algebra.

(1) arithmetic

The concept and properties of numbers, four operations and applications.

(2) Algebra

Transformation and calculation of algebraic equality and inequality. Including real numbers and complex numbers; Multiplier and prescription; Algebraic expressions and factorization; The solution of the equation; Inequality; Mathematical induction, sequence; Binomial theorem, permutation, combination and probability, etc.

(3) Geometry

Calculation and application of angles, perimeters and areas of plane geometric figures such as triangles, quadrilaterals, circles and polygons; Calculation and application of surface area and volume of various standard three-dimensional figures such as cuboid, cube and cylinder; Trigonometry; And knowledge of analytic geometry.

(4) Unary calculus

① Function and its graphics: set, mapping, function and function application.

② Limit and continuity: the limit of sequence, the limit of function, the algorithm of limit, two criteria for the existence of limit and two important limits, continuous function, infinitesimal and infinity.

(3) Derivative and differential: the concept of derivative, derivative rule and basic derivative formula, higher derivative and differential.

④ Application of differential mean value theorem and derivative: application of mean value theorem and derivative.

⑤ Integral: the concepts of indefinite integral and definite integral, Newton-Leibniz formula, the calculation of indefinite integral and definite integral, and the geometric application of definite integral.

(5) Linear Algebra

① Determinant: the concept and properties of determinant, the line-by-line expansion theorem of determinant, and the calculation of determinant.

② Matrix: the concept of matrix, the operation of matrix, the inverse matrix of matrix and the elementary transformation of matrix.

③ Vector: N-dimensional vector, the linear correlation of vector group has nothing to do with linearity, and the rank of vector group is the rank of matrix.

④ Linear equations: Cramer's rule of linear equations, discrimination rule of solutions of linear equations, solutions of homogeneous and heterogeneous linear equations.

⑤ eigenvalue problem: the concepts of eigenvalue and eigenvector, the calculation of similarity matrix, the conditions and methods of transforming eigenvalue and eigenvector into diagonal matrix.

2. Ability requirements for basic mathematics ability test

(1) Logical reasoning ability

Observe, compare, analyze, synthesize, abstract and summarize mathematical problems; Inference can be made by deduction, induction and analogy.

(2) Mathematical operation ability

According to the concept, formula, principle and law of mathematics, the correct operation and deformation of numbers, formulas and equations are carried out; Through the analysis of the known conditions, a reasonable and simple operation mode is sought and designed.

(3) Spatial imagination

Draw correct figures according to the conditions of mathematical problems, and imagine intuitive images according to the figures; Graphics can be decomposed, combined and deformed.

(4) Comprehensive thinking ability

Understand and analyze problems expressed in mathematical language; Comprehensive application of mathematical knowledge and thinking methods to solve the problems raised.

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