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. For example, in the second half of 20 13, 1 multiple choice questions, the parity of the function is investigated.

2. Derived creatures

For this knowledge point, the application of derivative generally requires derivative function, judging the monotonicity of the function in a certain interval according to the sign of the derivative function, and then finding the extreme value and the maximum value. For example, in the second half of 20 13, we took the multiple-choice question of 1 to judge whether a point is an extreme point according to the image of the derivative function; In the second half of 20 14 1 the content of the multiple-choice question is to judge monotonicity according to the sign of the 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. For example, the second half of 20 13 investigates 1 solution to investigate the probability that two independent events are evenly distributed in the interval; In the second half of 20 14, the solution of 1 was investigated, and in the case of putting it back, the probabilities of the same color and different color of the ball touched twice were obtained respectively. In the second half of 20 15, 1 multiple choice questions and 1 analytic questions were investigated, and the influence of sample size on the average and the probability of finding simple random events were 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 second half of 20 13, the solution of 1 was tested, which is to find the linear equation according to the oblique point in the plane rectangular coordinate system; In the second half of 20 14, 1 multiple-choice questions and 1 analytical questions were investigated, and the curve equations were obtained according to the parameter equations in the spatial rectangular coordinate system and the sine value of the included angle between the straight line and the plane respectively.

5. Vector

In the second half of 20 14, the 1 multiple choice question was tested, and the necessary and sufficient conditions for the modulus length of the sum of two vectors to be less than that of the difference of vectors were investigated. In the second half of 20 15, we also took the 1 multiple choice question to investigate the operational nature of vectors.

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 that the majority of exams will learn analogy and master its standard equation, eccentricity, directrix and other concepts. 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. For example, in the second half of 20 14 and 20 15, the solution of 1 was tested in order to find the surface equation under certain conditions. The majority of candidates should 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. For example, the 1 multiple choice question in the second half of 20 13 is pure calculation. To take the test, we should master several common methods of 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. For example, a multiple-choice question in the second half of 20 15 examines the inequality-preserving nature 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 the second half of 20 14, the 1 multiple choice question was tested to investigate the necessary and sufficient conditions for the function sequence to converge to the function; In the second half of 20 15, a multiple-choice question examines 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. For example, in the second half of 20 14, we are required to estimate the approximate value of e by Taylor formula; In the second half of 20 15, Lagrange's mean value theorem was proved, and the relationship with middle school mathematics content was briefly described.

13. Integral (finding integral, application of integral)

Including the calculation of integral and the related application of integral. First of all, the majority of candidates should master two integral calculation methods, namely, element exchange method and integration by parts, and then do more exercises. In the second half of 20 13, 1 multiple choice questions were investigated. Let's 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 the majority of candidates are required to find the inverse matrix by elementary transformation according to the nature of determinant.

15. Linear transformation

Candidates are required to master the definition and matrix representation of linear transformation. In the second half of 20 13, 1 multiple choice questions and 1 analytical questions were investigated, and the differences between linear change and rotational change and the curve equation obtained by finding the curve corresponding matrix under linear change were investigated respectively.

16. Separability theory

The written test of teacher qualification certificate is no longer a simple division of numbers, but a polynomial division. It is suggested that the majority of candidates master the method. For example, 20 15, 1 multiple choice questions about the quotient and remainder of the division of two polynomials.

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. The second half of 20 13 survey 1 multiple choice question asked me to find out the feature vector to which the feature root belongs.

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. In the second half of 20 13, 1 solutions were investigated. Let's briefly describe the teaching characteristics of "integration and practice". 1 multiple choice questions were investigated in the second half of 20 14, and 1 analytical questions were given in the second half of 20 15, and the basis for determining the content of mathematics courses was investigated.

With regard to the course objectives, in the second half of 20 13, we investigated the solution of 1 and the meaning of "four basics" in mathematics. The basic concept of the course focuses on teaching activities and learning evaluation. In the second half of 20 13, we investigated the solution of 1. Let's explain what the guiding role of teachers is in teaching activities.

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. For example, in the second half of 20 13, we visited 1 multiple choice questions to find out who are the four mathematicians Zu Chongzhi, Qin, Sun Simiao and Yang Hui? In the second half of 20 14, 1 multiple choice questions were also investigated. Let's choose the mathematician who founded analytic geometry.

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.