The league is divided into a test and an extra test (commonly known as the "second test"). The "preliminaries", "preliminaries" and "rematch" organized by provinces are not the official names and procedures of national leagues.
The initial test and additional test are conducted on the first Sunday in the middle of June 5438+ 10 every year.
Just try it.
The examination time is 8: 00-9: 20 am, and ***80 minutes. The test questions are divided into two parts: fill-in-the-blank questions and solution questions, with a full score of 120. Among them, there are 8 fill-in-the-blank questions, with 8 points for each question; Answer 3 questions, 16, 20, 20.
(The old rules in 2009 and the rules before 2008 are omitted. )
Additional test (second test)
The examination time is 9: 40- 12: 10, *** 150 minutes. The test questions are four solutions, with 40 points for the first two questions and 50 points for the last two questions, with a full score of 180. The test questions involve plane geometry, algebra, number theory, combinatorial mathematics and so on.
(The old rules in 2009 and the rules before 2008 are omitted. )
According to the test results, the provincial first, second and third prizes were selected. Among them, the provinces are responsible for judging the first prize, and then send the test paper of the first prize to the organizer (the organizer of the year), which will be re-evaluated by the organizer, and finally the competent unit (China Association for Science and Technology) will be responsible for the final evaluation and announcement. The second prize and the third prize are decided by the provinces.
Students who have won the first prize in various provinces, municipalities and autonomous regions can participate in the China Mathematical Olympics (CMO).
The latest news is that the examination rules of the 20 1 1 year math league are the same as those of the 201year. 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, try to expand the scope of knowledge and add the following knowledge points.
1. Plane geometry
Basic requirements: 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. The center of gravity is the point where the sum of squares of the distances to the three vertices of a triangle is the smallest. 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 the set of N-polygons with a certain circumference, the area of the regular N-polygon is the largest.
In a set of simple closed curves with a certain perimeter, the area of the 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. Algebra
Other requirements based on the first test outline:
Image of periodic function and periodic and absolute value function.
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, Euclid 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. Solid geometry
Polyhedral angle, properties of polyhedral angle. 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. Plane analytic geometry
Normal formula of 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 axis of a circle.
5. Others
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 Mathematical Olympics. The general 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 available 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 it may be tested in the winter camp of chinese mathematical society Popularization Committee.
(August 2006)
general rule
Since 198 1 the National Senior High School Mathematics League was held by the chinese mathematical society Popularization Committee, under the guidance of the principle of "continuous improvement on the basis of popularization", the national mathematics competition is in the ascendant, attracting millions of students to participate in it every year. From 65438 to 0985, China stepped into the International Mathematical Olympiad, which strengthened the international exchange of extracurricular mathematics education. In the past 20 years, China has become one of the powerful countries of the International Maritime Organization. Mathematics competition plays a positive role in developing students' intelligence, broadening their horizons, promoting teaching reform, improving teaching level and discovering and cultivating mathematics talents. This activity has also stimulated teenagers' interest in learning mathematics, attracted them to actively explore, and constantly cultivated and improved their creative thinking ability. The educational function of mathematics competition shows that this activity has become an important part of middle school mathematics education.
In order to make the national mathematics competition sustainable, healthy and in-depth, chinese mathematical society Popularization Committee has formulated 1994 "Outline of High School Mathematics Competition", which has played a good guiding role in the development of high school mathematics competition, and the activities of high school mathematics competition in China are becoming more and more standardized and regular.
In recent years, the implementation of the new syllabus has changed the system, content and requirements of middle school mathematics curriculum in China to some extent. At the same time, with the development of mathematics competitions at home and abroad, there are some new requirements for the knowledge, ideas and methods involved in the competition, and the original high school mathematics competition outline can no longer meet the development and requirements of the new situation. After extensive consultation and many discussions, the outline of senior high school mathematics competition was revised.
This syllabus is based on the spirit and foundation of Mathematics Syllabus for Full-time Senior Middle Schools. "Mathematics Teaching Syllabus for Full-time Senior High Schools" points out: "In order to promote the development of every student, we should not only lay a solid foundation for all students, but also pay attention to the development of students' personalities and specialties ... In class and extracurricular teaching, we should proceed from the reality of students, give consideration to students with learning difficulties and spare capacity, meet their learning needs through various ways and methods, and develop their mathematics talents."
Students' mathematics learning activities should be a lively and personalized process, which should not be limited to acceptance, memorization, imitation and practice, but also advocate reading self-study, independent exploration, hands-on practice and cooperative communication, all of which are helpful to give full play to students' initiative in learning. Teachers should give specific guidance according to students' different foundations, levels, interests and development directions. Teachers should guide students to actively engage in mathematics activities, so that students can form their own understanding of mathematics knowledge and effective learning strategies. Teachers should stimulate students' enthusiasm for learning, provide them with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. For students who have spare time to study and have a strong interest in mathematics, teachers should set up some elective contents for them, provide them with enough materials to guide them to read and develop their mathematical talents.
The contents listed in "Mathematics Teaching Syllabus of Full-time Ordinary Senior Middle Schools" in 2000 by the Ministry of Education are the requirements of teaching and the minimum requirements of competition. In the competition, for the same knowledge content, there are higher requirements in understanding, flexible application ability and proficiency in methods and skills. "Classroom teaching is the main thing, and extracurricular activities are the auxiliary thing" is the principle that must be followed. Therefore, the extracurricular teaching contents listed in this syllabus must fully consider the actual situation of students, so that students of different degrees can develop correspondingly in mathematics and implement the principle of "less but better".
Just try it.
The scope of knowledge involved in "National Senior High School Mathematics League (Trial)" does not exceed the full-time senior high school mathematics syllabus published by the Ministry of Education in 2000.
Second division
The National Senior High School Mathematics League (plus test) has expanded its knowledge and appropriately added some contents beyond the outline. Add the following:
The second test range: plane geometry
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.
The scope of the second test: 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 *.
The scope of the second test: 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 *.
The scope of the second test: the 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 outline was discussed and adopted at the14th Law Popularization Conference in 2006.