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 number
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 expressions
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. Equality and inequality
Solutions of linear and quadratic equations with letter coefficients. 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. Function
Images and properties of y=|ax+b|, y=|ax2+bx+c| and y = ax2+bx+c.
The maximum value of a quadratic function in a given interval. Maximum value of simple fractional function, quadratic function with letter coefficient.
6. Logical reasoning problem
Pigeonhole principle (concept), divided into graphics to make drawers, congruent to make drawers, and dyed to make drawers.
Simple combination problem.
Logical reasoning problem, reduction to absurdity.
Simple extreme principle.
Simple enumeration method.
7. Geometry
Four propositions and their relations.
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.