It is not difficult to investigate this knowledge point, but function is the basic knowledge of mathematics, so candidates are advised to lay a good foundation. We will mainly study the parity of functions.

2. Derived creatures

For this knowledge point, the application of derivative generally needs to find the derivative function, judge the monotonicity of the function in a certain interval according to the sign of the derivative function, and then find the extreme value and comparison value. According to the image of derivative function, it is judged whether a point is an extreme point or monotonicity according to the sign of derivative function.

3. Probability and statistics

The survey is about high school knowledge. The topic is less difficult, but the frequency of investigation is very high. Investigate the probability that two independent events are evenly distributed in the interval; In the case of putting it back, the probabilities of the same color and different colors of the ball touched twice are obtained respectively; The influence of sample size on the average discovery rate and discovery probability of simple random events was investigated respectively.

4. The positional relationship between straight line and plane

In this knowledge point, candidates not only need to master the positional relationship between linear equations and graphs on the plane, but also need to master various positional relationships in space. In the plane rectangular coordinate system and the space rectangular coordinate system, the curve equation and the sine value of the included angle between the straight line and the plane are obtained according to the parameter equation.

5. Vector

The necessary and sufficient conditions for the modulus length of the sum of two vectors to be less than the modulus length of the difference between vectors are studied. The operational properties of vectors are studied.

6. Series

There are many tests for special series, such as finding the general formula of series that meets certain conditions and finding the sum of the first n terms. We should master appropriate methods, such as dislocation subtraction and crack cancellation.

7. Conic curve

Conic curves include ellipses, hyperbolas and parabolas. I hope I can learn analogy and master its standard equation, eccentricity and directrix. When solving problems in this test, the amount of calculation is often relatively large, which requires simultaneous equations and Vieta theorem to calculate.

8. Surface equation

This knowledge point is still difficult for most candidates, because we are used to understanding lines and faces in a plane. This knowledge point is to expand the two-dimensional plane into the three-dimensional space and find the equation of the surface in the space. Under certain conditions, find the surface equation. It is necessary to master the basic methods of solving surface equations, such as substitution method and parameter method.

9. Seek the limit

For the limit, it is usually a trial calculation, and it is necessary to master several commonly used methods for finding the limit, such as definition, general division, method of substitution, equivalent infinitesimal method of substitution and so on.

10. Sequence limit

The knowledge points commonly tested include the nature of the limit of sequence and the four operations of the limit. Boundedness, sign-preserving, inequality-preserving, squeezing criterion and monotone boundedness of sequences are common properties. This paper discusses the inequality-preserving properties of the limit of sequence.

1 1. Function limit and function continuity (uniform continuity)

Common knowledge points are the convergence of series and the uniform convergence of function sequence. In this paper, we study the necessary and sufficient conditions for the sequence of functions to converge to the function, that is, the convergence interval of power series. For the convergence of positive series, the methods to be mastered are ratio discrimination, root discrimination, integral discrimination and Rabe discrimination.

12. Differential mean value theorem and its application (Taylor formula and Lagrange mean value theorem)

It usually appears in the form of solving problems, and the application of Taylor formula and Lagrange mean value theorem is frequently investigated. Estimate the approximate value of e by Taylor formula; It is to describe and prove Lagrange's mean value theorem and briefly describe the connection with middle school mathematics content.

13. Integral (finding integral, application of integral)

Including the calculation of integral and the related application of integral. First, master two methods of integral calculation, replacing integral method and integration by parts, and then do more exercises. Find the value of definite integral. Secondly, to grasp the geometric meaning of definite integral in application, we can find the area according to definite integral and the volume through double integral.

14. Determinant and inverse matrix

It is not difficult to investigate this knowledge point, so it is required to find the inverse matrix by elementary transformation according to the nature of determinant.

15. linear transformation wechat NTCECN

Candidates are required to master the definition and matrix representation of linear transformation. The difference between linear change and rotation change is discussed, and the curve equation obtained by finding the curve corresponding to the matrix under linear change is also discussed.

16. Separability theory

The written test of teacher qualification certificate is no longer a simple division of numbers, but a polynomial division. Candidates are advised to master the method.

17. Eigenvalues and eigenvectors

Candidates are required to understand that the eigenvalues and eigenvectors of the matrix can be obtained by solving the general solutions of polynomial equations and homogeneous linear equations. 2

18. Mathematics curriculum standards

The content, objectives and basic concepts of the course are tested more frequently.

The course content includes four aspects: number and algebra, graph and geometry, probability and statistics, synthesis and practice, which need to be memorized by everyone. This knowledge point basically appears in the form of solving problems every year, so it is very important.

History of mathematics.

In the history of mathematics, mathematicians are often tested. Candidates are required to memorize, and in the process of reading, pay attention to which mathematicians have made contributions. 、

20. Teaching design

Instructional design usually doesn't let us write lesson plans directly. The knowledge points we investigated include teaching objectives, teaching difficulties, teaching fragment evaluation, teaching process, mathematical thinking methods and so on.