The National Senior High School Mathematics League (plus test) has expanded its knowledge and appropriately added some contents beyond the outline. Add the following:

1. Plane geometry

Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem;

Imitation center, fermat point and Euler line of triangle;

Geometric inequality;

Geometric extremum problem;

Transformation in geometry: symmetry, translation and rotation;

Power and root axis of a circle:

Area method, complex number method, vector method, analytic geometry method.

2. Algebra

Periodic function, a function with absolute value;

Trigonometric formula, trigonometric identity, trigonometric equation, trigonometric inequality, inverse trigonometric function;

Recursion, recursive sequences and their properties, general formulas of first-order and second-order linear recursive sequences with constant coefficients;

Second mathematical induction;

Mean inequality, Cauchy inequality, rank inequality, Chebyshev inequality, one-dimensional convex function and their applications;

Complex number and its exponential form, triangular form, Euler formula, Dimov theorem, unit root;

Polynomial division theorem, factorization theorem, polynomial equality, rational root of integer coefficient polynomial *, polynomial interpolation formula *;

The number of roots of polynomials of degree n, the relationship between roots and coefficients, and the pairing theorem of imaginary roots of polynomials with real coefficients;

Function iteration, find n iterations *, simple function equation *.

3. Elementary number theory

Congruence, Euclid division, Peishu theorem, complete residue system, indefinite equations and equations, Gaussian function [x], Fermat's last theorem, lattice point and its properties, infinite descent method *, euler theorem *, Sun Tzu's theorem *.

4. Combination problem

Cyclic permutation, permutation and combination of repeated elements, combinatorial identity;

Combinatorial counting, combinatorial geometry;

Pigeon cage principle;

Exclusion principle;

Extreme principle;

Graph theory problems;

Division of sets;

Coverage;

Planar convex set, convex hull and their applications.

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

Note: The above contents are extracted from the Outline of Senior High School Mathematics Competition (Revised Discussion Draft), which was formulated by the chinese mathematical society Promotion Committee and discussed and passed at the14th promotion meeting in August 2006.