-Try it.

The outline of the preliminary test competition of the national senior high school mathematics league matches the teaching requirements and contents stipulated in the full-time middle school mathematics syllabus, that is, the knowledge scope and methods stipulated in the college entrance examination are slightly improved, and the preliminary test of probability and calculus is not taken.

Second division

1. basic requirements of plane geometry: master all the contents determined by the junior high school competition outline. Supplementary requirements: area and area method. Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem. Several important extreme values: fermat point, the point with the smallest sum of the distances to the three vertices of a triangle. Square of the distance to the three vertices and the minimum point-center of gravity of a triangle. The point in a triangle with the largest product of the distances from three sides-the center of gravity. Geometric inequality. Simple isoperimetric problem. Understand the following theorem: In a group of N-polygons with a certain perimeter, the area of a regular N-polygon is the largest. In a set of simple closed curves of a cylinder with a certain circumference, the area of a circle is the largest. In a group of N-sided polygons with a certain area, the perimeter of the regular N-sided polygon is the smallest. In a set of simple closed curves with a certain area, the circumference of a circle is the smallest. Motion in geometry: reflection, translation and rotation. Complex number method, vector method. Planar convex set, convex hull and their applications.

2. What does algebra require on the basis of the preliminary outline: periodic functions and periodic images with absolute values of functions. Triple angle formula, some simple identities of triangle, triangle inequality. The second mathematical induction. Recursion, first and second order recursion, characteristic equation method. Function iteration, find n iterations *, simple function equation *. N-element mean inequality, Cauchy inequality, rank inequality and their applications. Exponential form of complex number, Euler formula, Demefer theorem, unit root, application of unit root. Cyclic arrangement, repeated arrangement, combination. Simple combinatorial identities. The number of roots of an unary n-degree equation (polynomial), the relationship between roots and coefficients, and the pairing theorem of imaginary roots of real coefficient equations. Simple elementary number theory problems should include infinite descent method, congruence, Euclidean division, nonnegative minimum complete residue class, Gaussian function [x], Fermat's last theorem, Euler function *, Sun Tzu's theorem *, lattice points and their properties.

3. The polyhedral angle of solid geometry and its properties. Basic properties of trihedral angle and straight trihedral angle. Regular polyhedron, euler theorem. Proof method of volume. Sections, sections, and surface flat patterns will be made.

4. Normal formula of plane analytic geometric straight line, polar coordinate equation of straight line, straight line bundle and its application. The region represented by binary linear inequality. The area formula of triangle. Tangents and normals of conic curves. Power and root cause axis.

5. Dove cage principle. Exclusion principle. Extreme principle. Division of sets. Cover. Note: The basic principle of the second test proposition of the national senior high school mathematics league is to be close to the international mathematics Olympics. The overall spirit is slightly higher than the requirements of the high school mathematics syllabus, and the knowledge is slightly expanded, and some contents that are not in the classroom are appropriately added as extracurricular activities or teaching contents of the Olympic school.

Teachers and coaches are required to master the contents listed above step by step, and carry out appropriate teaching according to the specific conditions of students.

The content marked with * will not be tested in the second test for the time being, but may be tested in the winter camp.