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, plane geometry

Basic requirements: master all the contents determined by the outline of junior high school mathematics competition.

Supplementary requirements: area and area method.

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

Several important extreme values: the point with the smallest sum of the distances to the three vertices of a triangle-fermat point. 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 center of gravity is the point in the triangle where the distance product of three sides is the largest.

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 and 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, finding n iterations, simple function equation.

N-element mean inequality, Cauchy inequality, rank inequality and their applications.

Exponential form of complex number, Euler formula, Dimov theorem, unit root, application of unit root.

Cyclic permutation, repeated permutation and combination, simple combinatorial identity.

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, 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

Kim's principle of tolerance.

Extreme principle.

Division of sets.

Cover.

References:

/f？ Kz= 1069838 19 Interviewee: l 1990060 1- Level 4 2008-5-7 22:55 Let me comment >> Related content? 6? 1 national high school mathematics league (just say which books are good) 1 2009-8-22? 6? 1 the examination range of Jiangsu senior high school mathematics league 1 2008-3-22? 6? 1 what is the scope of the high school mathematics league? 2005-9-24? 6? 1 I'm going to take part in the national senior high school math league. I hope someone will cheer me up. Thank you very much 2 20 10-9-4? 6? 1Do you have the answer to the question of the 2009 National Senior High School Mathematics League? I really need them, thank you! ! ! 20 10-8-3 1 more questions about the outline of senior high school mathematics league >> under the guidance of the policy of "improving on the basis of popularization", the national mathematics competition is in the ascendant, especially in recent years, Chinese athletes have made gratifying achievements in the international mathematics Olympics, which has inspired teachers, students and mathematicians in primary and secondary schools, and their enthusiasm has been rising constantly, and the mathematics competition has entered a new stage. In order to make the national mathematics competition sustainable, healthy and in-depth step by step, the outline of mathematics competition is formulated at the request of the teachers and students of middle schools and the coaches of mathematics Olympics at all levels to meet the needs of the current situation. This syllabus is based on the spirit and foundation of the "Full-time Middle School Mathematics Syllabus" formulated by the State Education Commission. "Syllabus" points out in the column of teaching day: "To realize the four modernizations, it is necessary to cultivate students' interest in mathematics and stimulate students to learn mathematics well". The concrete measures are: "For students who have spare capacity for study, they should fully develop their mathematical talents through extracurricular activities or offering elective courses"; "We should pay attention to the cultivation of their abilities, focusing on cultivating students' computing ability, logical thinking ability and spatial imagination ability, so that students can gradually learn important thinking methods such as analysis, synthesis, induction, deduction, generalization, abstraction and analogy. At the same time, we should pay attention to cultivating students' independent thinking and self-study ability. "The contents listed in the syllabus are the requirements of teaching and the minimum requirements of the competition. In the competition, there are higher requirements for the understanding and flexible application of the same knowledge content, especially the proficiency of methods and skills. And "classroom teaching is the main thing, supplemented by extracurricular activities" 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 can master them step by step and at different levels, implement the principle of "less but better", strengthen the foundation and constantly improve. Try the outline of the preliminary competition of the national senior high school mathematics league, which is completely in accordance with 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, and the method requirements are slightly improved, among which the probability and calculus preliminary tests are not taken. Test 1, basic requirements of plane geometry: master all the contents determined by the outline of junior high school mathematics competition. Supplementary requirements: area and area method. Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem. Several important extreme values: the point with the smallest sum of the distances to the three vertices of a triangle-fermat point. 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 center of gravity is the point in the triangle where the distance product of three sides is the largest. 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 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 and vector method. Planar convex set, convex hull and their applications. 2. Other contents required by algebra on the basis of the preliminary examination outline: periodic function and period, and 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, finding 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 permutation, repeated permutation and combination, simple combinatorial identity. 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, Fermat's last theorem, Euler function, Sun Tzu's theorem, lattice points and their properties. 3, solid geometry polyhedron angle, the nature of polyhedron 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. 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 axis of a circle. 5. Other archiving principles. The principle of gold tolerance. Extreme principle. Division of sets. involve