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. At present, China's middle school students' mathematics competition is becoming more and more standardized. In order to make the national mathematics competition develop healthily and continuously, at the request of the teachers and students of middle schools and the coaches of mathematics Olympics at all levels, and to meet the needs of the current situation, the Outline of Junior Middle School Mathematics Competition (Revised Draft) is formulated. This syllabus is based on the spirit of "Nine-year compulsory education junior high school mathematics syllabus" formulated by the State Education Commission. The syllabus points out in the column of teaching purpose: "To realize the four modernizations, we must cultivate students' interest in mathematics and stimulate them 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 … ",and pay attention to 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 competition. In addition to the contents listed in the syllabus, this syllabus also adds the following contents. The content of these extracurricular lectures must fully consider the actual situation of students, so that students can master them step by step in stages and at different levels, implement the principle of "less but better", and handle the relationship between popularization and improvement, thus strengthening the foundation and constantly improving. 1, real decimal integer and its representation. Divisibility, the judgment of being divisible by 2, 3, 4, 5, 8, 9, 1 1. Prime numbers and composite numbers, greatest common divisor and least common multiple. Parity number, parity analysis Division with remainder and classification with remainder. Complete square number. Representation of factorization, calculation of divisor. Representation of rational number, closure of four operations of rational number. 2. Algebraic comprehensive division and remainder theorem. Disassembly, addition, formula and undetermined coefficient method. Partial score. Symmetry and rotational symmetry. 3, identity and identity deformation identity, identity deformation. Identities of algebraic expressions, fractions and roots. Identification. 4, equations and inequalities, the solution of the letter coefficient of one-dimensional linear and quadratic equations. Distribution of roots of quadratic equation with one variable. Solutions of linear and quadratic equations with absolute values. Solution of one-dimensional linear inequality with letter coefficient, solution of one-dimensional linear inequality. One-dimensional linear inequality with absolute value. Simple linear indefinite equation. Solving application problems with column equations (groups). 5. Images and properties of functions y=|ax+b|, y=|ax2+bx+c| and Y = AX2+BX+C. Maximum value of quadratic function in a given interval. Maximum value of simple fractional function, quadratic function with letter coefficient. 6. Reasoning pigeonhole principle (concept) logically, making drawers by figures, drawers by congruence categories and drawers by dyeing. Simple combination problem. Logical reasoning problem, reduction to absurdity. Simple extreme principle. Simple enumeration method. 7. Four propositions of geometry and their relationships. Unequal relation of triangle. Unequal relations between angles in the same triangle and between angles in different triangles. Area and equal product transformation. The heart of a triangle (inner heart, outer heart, hanging heart, center of gravity) and its properties.