# 2 # Introduction: The key to learning mathematics well is to summarize and classify it timely and properly. The following is an unorganized summary of mathematics knowledge points in the first volume of the eighth grade, hoping to help everyone. Chapter VI Knowledge Points

First, the function:

Generally speaking, there are two variables, X and Y, in a certain change process. If a value of X is given and a value of Y is determined accordingly, then we call Y a function of X, where X is the independent variable and Y is the dependent variable.

Second, the independent variable value range

The whole set of values of independent variables that make a function meaningful is called the range of independent variables. Generally speaking, we should consider algebraic expression (taking all real numbers), fraction (denominator is not 0), quadratic root (root is not negative) and practical significance.

Three representations of functions and their advantages and disadvantages

(1) relational expression (analysis) method

The functional relationship between two variables can sometimes be expressed by an equation containing these two variables and the symbols of digital operations. This representation is called relational (analytical) method.

(2) List method

A series of values of the independent variable x and the corresponding values of the function y are listed in a table to represent the functional relationship. This representation is called list method.

(3) Image method

The method of expressing functional relations with images is called image method.

Fourthly, the general steps of drawing its image by using functional relationship.

(1) List: List gives some corresponding values of independent variables and functions.

(2) Point tracking: Take each pair of corresponding values in the table as coordinates, and track the corresponding points on the coordinate plane.

(3) Connection: according to the order of independent variables from small to large, connect the tracked points with smooth curves.

Five, proportional function and linear function

The concepts of 1, proportional function and linear function

Generally speaking, if the relationship between two variables X and Y can be expressed in the form of (k, b is a constant, k0), then Y is a linear function of X (X is an independent variable and Y is a dependent variable).

In particular, when b=0 in a linear function (that is, k is a constant, k0), y is called a proportional function of x.

2. Images of linear functions: All images of linear functions are straight lines.

3. The main characteristics of images of linear function and proportional function: the image of linear function is a straight line passing through point (0, b); The image of the proportional function is a straight line passing through the origin (0,0).

Chapter VII Knowledge Points

1, binary linear equation

An integral equation with two unknowns whose terms are 1 is called a binary linear equation.

2, the solution of binary linear equation

A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation.

3. Binary linear equation

An equation group consisting of two linear equations with two unknowns is called a binary linear equation group.

4, the solution of binary linear equations

The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.

5, the solution of binary linear equations

(1) substitution (elimination) method (2) addition and subtraction (elimination)

Chapter VIII Knowledge Points

1. Describes the number of trends (average level) in the data set: average, mode and median.

2. Average

(2) Weighted average:

Step 3: Ways

The data with the highest frequency in a set of data is called the pattern of this set of data.

4. Median value

Generally, a group of data is arranged in order of size, and the data in the middle position (or the average of the two data in the middle) is called the median of this group of data.