Representation, divisibility and judgment of integer and carry system

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.

Concept and representation of rational number, closure of irrational number, real number, rational number and real number.

2. Algebraic expressions

Comprehensive division and remainder theorem.

Factorization.

Disassembly, addition, formula and undetermined coefficient method.

Symmetry and rotational symmetry.

Identities of algebraic expressions, fractions and roots.

Identification.

3. Equality and inequality

The solution of linear equation and quadratic equation with letter coefficient, the distribution of roots of quadratic equation.

Solutions of linear equations with absolute values and quadratic equations with absolute values.

The solution of one-dimensional linear inequality with letter coefficient, the solution of one-dimensional quadratic inequality.

One-dimensional linear inequality with absolute value.

Simple multivariate equation.

Simple indefinite equation (group).

4. Function

Images and properties of y = | ax+b |, y = | ax2+bx+c | and y = ax2+b | x |+c.

The maximum value of quadratic function in a given interval, the maximum value of simple fractional function.

Quadratic function with letter coefficient.

5. Geometry

The unequal relationship between the angles in a triangle.

Area and equal product transformation.

The heart of a triangle (inner heart, outer heart, hanging heart, center of gravity) and its properties.

Concepts and properties of similar shapes.

Circle, four-point * * * circle, circle power theorem.

Four propositions and their relations.

6. Logical reasoning problem

Pigeon hole principle and its simple application.

Simple combination problem.

Simple logical reasoning problem, reduction to absurdity.

Simple application of extreme value principle.

Enumeration and its simple application.