You must learn all the contents of the textbook for senior one and senior two, and the content of mathematical induction for senior three. In addition, you should read at least one Olympic Games book (just click on the gold medal) and give you an exam outline. The knowledge involved in the National Senior High School Mathematics League (try) does not exceed the teaching requirements and contents stipulated in the "Full-time Senior High School Mathematics Syllabus" promulgated by the Ministry of Education in 2000, but the requirements for methods have been improved. The national senior high school mathematics league entrance examination (re-examination) is in line with the international mathematics Olympics, expanding the knowledge; Appropriately add some contents outside the outline, and the added contents are: 1. Several important theorems of plane geometry: Menelaus Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem. Several Special Points in Triangle: Imitation Center, fermat point and Euler Line. 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. Algebraic 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. The second mathematical induction. Mean inequality, Cauchy inequality, rank inequality, Chebyshev inequality, univariate convex function. 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 virtual root pairing theorem of polynomials with real coefficients. Function iteration, simple function equation * 3. Elementary number theory congruence, Euclid division, Pei tree theorem, complete residue class, quadratic residue, 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. The combination questions are arranged circularly, the arrangement and combination of repeated elements are combined, and the combination identities are combined. Combinatorial counting, combinatorial geometry. Dove cage principle Exclusion principle. Extreme principle. Graph theory problems. Division of sets. Cover. Planar convex set, convex hull and their applications. Note: Contents marked with * will not be tested in additional tests, but may be tested in winter camps.