Factorization and grouping decomposition

Simplification of quadratic root, application of formula, rationalization of denominator, simplest quadratic root

Fraction operation A mixed operation of fractions with different denominators (general division, symbol, operation order)

The application of Vieta's theorem, the root formula of quadratic equation in one variable and the cross multiplication.

Fractional equation is solved by denominator method, and fractional equation is solved by substitution method (root test)

Inequality solution inequality system

Determine the properties of the proportional function (the relationship between the positive and negative of k and the image) and the analytical formula.

The nature of linear function (the relationship between the positive and negative of k and b and the image), the determination of analytical formula, the intersection with x and y axes, the intersection of two straight lines,

Area problem

Basic properties of quadratic function (opening direction, symmetry axis, vertex coordinates, maximum value) and determination of analytical formula (three forms)

The relationship between the positive and negative of A, B and C and the image, the distance formula between two intersections of parabola and X axis, the number of intersections of parabola and X axis, the image characteristics of y=ax2 y=ax2+c y=ax2+bx, and the sign judgment of a+b+c, a-b+c, 2a+b, 2a-b, and vieta theorem.

Two forms of inverse proportional function definition y=kx-1, area invariance and central symmetry.

The application of function solves the problem according to the function image, and calculates the maximum (minimum) value according to the function relationship of the problem.

Statistical model, median, average and its variation law, variance formula, variation law of variance, standard deviation, frequency and frequency properties.

Probability tree diagram, list method to find probability, calculation method to find probability

geometry

The nature of triangle is special triangle (isosceles triangle, right triangle)

Congruent triangles's Judgment and Nature

Similar triangles often uses "corners" to remember the basic types of similarity (such as the types of items in the scale) and judge similarity, but don't ignore "corners"

Quadrilateral parallelogram, rectangle, diamond, square (key) property, isosceles trapezoid property, auxiliary line method of trapezoid

Formula of polygon inner angle sum and calculation of the number of sides of regular polygon by using outer angle sum

Solve the definitions of sine, cosine, tangent and cotangent of right triangle, trigonometric function value of special angle, etc.

Important theorems of circle: vertical diameter theorem, equivalence theorem inference, determination of circumferential angle.