Jiangxi teacher recruitment (national compilation) examination junior high school mathematics professional examination content includes high school and university content, professional examination content can refer to the examination outline for review ~

The following is the outline of the recruitment examination for some primary and secondary school teachers in Jiangxi Province.

Outline of junior high school mathematics examination

The first part of the discipline professional foundation

First, mathematical analysis.

(a) real number sets and functions

1. Real number: the concept, properties, absolute value and inequality of real number.

2. Number set and supremum principle: interval and neighborhood, bounded set and unbounded set, supremum and supremum, supremum principle.

3. The concept of function: the definition of function, the expression of function (analytical method, list method, mirror method), piecewise function.

4. Functions with certain characteristics: bounded function, monotone function, even-odd function and periodic function.

Requirements: understand the concept of real numbers, understand the properties of absolute inequalities, and solve absolute inequalities; Master the concepts of interval and neighborhood, and understand the concept and principle of supremum; Master the definition and representation of function and understand the operation of function; Understand some special types of functions.

(2) Limit of sequence

1. Limit concept.

2. The properties of convergent sequence: uniqueness, boundedness, sign-preserving, inequality-preserving and forced convergence.

3. Conditions for the existence of sequence limit: monotone bounded theorem, Cauchy convergence criterion.

Requirements: Understand and master the concept of sequence limit; Understand the basic properties of convergent sequence and the existence conditions of sequence limit (monotone bounded function and forced convergence theorem), and can use the properties of convergent sequence to find the limit; Cauchy convergence criterion for understanding the limit of sequence.

(3) Function limitation

The concept of 1. function limit.

2. The properties of function limit: uniqueness, local boundedness, local sign-preserving, inequality-preserving and forced convergence.

3. Conditions for the existence of function limit: resolution principle (Heine theorem) and Cauchy criterion.

4. Two important limitations.

Requirements: Understand the concept of function limit; Understanding Cauchy criterion of function limit: mastering the nature and solving principle of function limit; Two important limits can be used to deal with limit problems.

Functional continuity

The concept of 1. function continuity: definition of single point continuity, definition of interval continuity, and discontinuous point.

2. Properties of continuous functions: local properties (local boundedness, local sign preservation) and four operations; The properties of continuous function on closed interval (maximum theorem, intermediate theorem, uniform continuity theorem), the continuity of composite function, and the continuity of inverse function.

3. Continuity of elementary functions.

Requirements: Understand the concept of continuity of univariate function; Understand the concept of function discontinuity; Understand the local properties of continuous functions; Can correctly describe and simply apply the properties of continuous functions on closed intervals; Understand the continuity of inverse function, composite function and elementary function.

(5) Derivative and differential

1. The concept of derivative: the definition of derivative, derivative function and geometric meaning of derivative.

2. Derivation rule: derivation formula, derivation operation (four operations), derivation rule (inverse function derivation rule, compound function derivation rule).

3. Differential: the definition, algorithm and application of differential.

4. Higher derivative and higher differential.

Requirements: understand the concepts of derivative and differential, and understand their geometric significance; Can skillfully use the operational properties of derivatives and the derivative rule to find the derivative of functions; Understand the relationship between derivability and continuity; Master the solution of higher derivative; Understand the geometric application of derivative and the application of differential in approximate calculation.

(VI) Basic theorem of differential calculus

1. Mean value theorem: Rolle mean value theorem, Lagrange mean value theorem, Cauchy mean value theorem.

2. Several special types of infinitive limits and Robida's law.

3. Taylor formula.

Requirements: Understand the content and application of the mean value theorem; Knowing Taylor formula and its application in approximate calculation, we can expand some functions according to Taylor formula; You can use Robida's law to find the limit of infinitive.

..... There are too many outlines, and the full version can be viewed in Gong Yi Education/Online.

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