1 definition of function, definition domain, range and expression of function, and image of function.

Linear function and proportional function, including their expressions, increase and decrease and images.

3 Look at equations, equations and inequalities from the perspective of functions

Chapter II Data Description

1 Understand several common statistical charts: bar chart, fan chart, line chart, composite bar chart and histogram, and understand the characteristics of various charts.

Bar chart features:

(1) can display the specific data of each group;

(2) Differences between data are relatively easy.

The characteristics of the fan chart:

(1) indicates the percentage of parts in the total with sector area;

(2) It is easy to display the size of each group of data relative to the total.

Characteristics of line chart;

It is easy to display the changing trend of data.

Features of histogram:

(1) can display the frequency distribution of each group;

(2) It is easy to show the difference of frequency between groups.

I will use various statistical charts to illustrate some practical problems.

Chapter III congruent triangles

1 the nature of congruent triangles:

Congruent triangles has equal sides and angles.

2 congruent triangles's judgment

HL Theorem of Side, Angle, Angle, Angle and Right Triangle

Properties of Trigonometric bisector

The distance from the point on the bisector of the angle to both sides of the angle is equal;

The points with equal distance to both sides of the angle are on the bisector of the angle.

Chapter IV Axisymmetry

1 axisymmetric graph and two graphs symmetric about a line

2 Axisymmetric property

The symmetry axis of an axisymmetric figure is the median vertical line of the line segment connected by any pair of corresponding points;

If two figures are symmetrical about a straight line, then the symmetry axis is the middle perpendicular of the line segment connected by any pair of corresponding points;

The distance between the point on the vertical line of the line segment and the two end points of the line segment is equal;

The points with the same distance from the two ends of the line segment are on the vertical line of this line segment.

3 Axis symmetry is expressed in coordinates.

The coordinates of the point (x, y) are (x, -y), (-x, y) and (-x, -y) respectively.

4 isosceles triangle

The two base angles of an isosceles triangle are equal; (equilateral and angular)

The bisector of the top angle, the median line of the bottom edge and the height line of the bottom edge of the isosceles triangle coincide; (three in one)

Two equal angles of a triangle have equal sides. (Equiangular and Equilateral)

The Properties and Judgments of Pentagonal Triangle

The three internal angles of an equilateral triangle are all equal, all equal to 60 degrees;

A triangle with three equal angles is an equilateral triangle;

An isosceles triangle with an angle of 60 degrees is an equilateral triangle;

Inference:

In a right triangle, if there is an acute angle of 30 degrees, then the right side it faces is equal to half of the hypotenuse.

In a triangle, the big angle is opposite to the big side, and the big side is opposite to the big angle.

Chapter V Algebraic Expressions

1 Algebraic Expression Definition, Similar Items and Their Combinations

Addition and subtraction of algebraic expressions

Multiplication of 3 algebraic expressions

Product of (1) same base powers:

(2) the power of power

(3) the efficacy of the product

(4) Multiplication of algebraic expressions

4 multiplication formula

(1) square difference formula

(2) Complete square formula

5 algebraic division

(1) Division of the same radix power

(2) Division of algebraic expressions

6 factorization

(1) factorization method

(2) Formula method

(3) Cross multiplication

Knowledge points in the second volume of the second day of junior high school

The first chapter scores

1 fraction and its basic properties

The numerator and denominator of a fraction are multiplied (or divided) by an algebraic expression that is not equal to zero at the same time, and the fraction is only the same.

Fractional operation of 2

Multiplication and division of (1) fraction

Law of multiplication: Fractions are multiplied by fractions, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product.

Law of division: divide a fraction by a fraction, exchange the numerator and denominator of the divisor and multiply it by the divisor.

(2) Addition and subtraction of fractions

Law of addition and subtraction: add and subtract with denominator fraction, and add and subtract molecules with denominator unchanged;

Fractions with different denominators are added and subtracted, first divided by fractions with the same denominator, and then added and subtracted.

Addition, subtraction, multiplication and division of exponential powers of three integers

4- Fractional Equation and Its Solution

Chapter II Inverse Proportional Function

Expressions, images and properties of 1 inverse proportional function

Image: hyperbola

Expression: y=k/x(k is not 0)

Nature: the increase and decrease of the two branches are the same;

2 the application of inverse proportional function in practical problems

Chapter III Pythagorean Theorem

Pythagorean Theorem of 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.

2 Pythagorean Theorem Inverse Theorem: If the sum of squares of two sides in a triangle is equal to the square of the third side, then the triangle is a right triangle.

The fourth chapter quadrilateral

1 parallelogram

Attribute: equilateral; Diagonally equal; Divide diagonally.

Judgment: two groups of quadrangles with equal opposite sides are parallelograms;

Two groups of quadrangles with equal diagonal are parallelograms;

Quadrilaterals whose diagonals bisect each other are parallelograms;

A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

Inference: The midline of a triangle is parallel to the third side and equal to half of the third side.

Special parallelogram: rectangle, diamond and square.

(1) rectangle

Properties: All four corners of a rectangle are right angles;

Diagonal lines of rectangles are equal;

A rectangle has all the characteristics of a parallelogram.

Judgment: a parallelogram with a right angle is a rectangle;

Parallelograms with equal diagonals are rectangles;

Inference: The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.

(2) Diamond shape

Property: all four sides of the diamond are equal;

Diagonal lines of the rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines;

A diamond has all the characteristics of a parallelogram.

Judgment: A set of parallelograms with equal adjacent sides is a diamond;

Parallelograms with diagonal lines perpendicular to each other are rhombic;

A quadrilateral with four equilateral sides is a diamond.

(3) Square: It is both a special rectangle and a special diamond, so it has all the properties of a rectangle and a diamond.

Trapezoid: right-angled trapezoid and isosceles trapezoid.

Isosceles trapezoid: two angles on the same bottom of isosceles trapezoid are equal;

The two diagonals of isosceles trapezoid are equal;

A trapezoid with two equal angles on the same base is an isosceles trapezoid.

Chapter V Data Analysis

Weighted mean, median, mode, range, variance