Summary of eighth grade mathematics knowledge points
Function and its related concepts
1, variables and constants
In a certain change process, the quantity that can take different values is called a variable, and the quantity whose value remains unchanged is called a constant.
Generally speaking, there are two variables, X and Y, in a certain change process. If for each value of X, Y has a definite value corresponding to it, then X is an independent variable and Y is a function of X. ..
2. Resolution function
The mathematical formula used to express functional relationship is called resolution function or functional relationship.
The whole set of values of independent variables that make a function meaningful is called the range of independent variables.
3. Three representations of functions and their advantages and disadvantages.
(1) 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 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.
4. General steps of drawing images with resolution function.
(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.
Summary of Mathematics Knowledge Points in Book 2 of Grade 2
Solve a linear equation with one variable
1. Equation and Equivalence: An equation connected by "=" is called an equation. Note: "Equivalent value can be substituted"!
2. The nature of the equation:
Properties of equation 1: Add (or subtract) the same number or the same algebraic expression on both sides of the equation, and the result is still an equation;
Property 2 of the equation: both sides of the equation are multiplied (or divided) by the same non-zero number, and the result is still an equation.
3. Equation: An equation with an unknown number is called an equation.
4. Solution of the equation: the value of the unknown quantity that makes the left and right sides of the equation equal is called the solution of the equation; Note: "The solution of the equation can be substituted"!
5. Moving term: after changing the sign, moving the term of the equation from one side to the other is called moving term. The shift term is based on the equality attribute 1.
6. One-dimensional linear equation: An integral equation with only one unknown number, degree 1 and non-zero coefficient is a one-dimensional linear equation.
7. The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
8. The simplest form of linear equation with one variable: ax=b(x is unknown, a and b are known numbers, a≠0).
9. General steps for solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terms ... merging similar terms ... and converting the coefficient into 1 ... (testing the solution of the equation).
10. Solving application problems by listing linear equations of one variable;
(1) reading analysis method: reading analysis method
Read the stem carefully, find out the key words that express the equal relationship, such as "big, small, many, few, yes, * * *, combination, right, completion, increase, decrease, match-",list the literal equations with these key words, and set the unknown number according to the meaning of the question. Finally, using the relationship between quantity and quantity in the question, fill in the algebraic expression and get the equations.
(2) Drawing analysis method
Analyzing mathematical problems with graphics is the embodiment of the combination of numbers and shapes in mathematics. Read the question carefully, and draw the relevant figures according to the meaning of the question, so that each part of the figure has a specific meaning. Finding the equation relationship through graph is the key to solve the problem, so as to obtain the basis of concise equation. Finally, using the relationship between quantity and quantity (unknown quantity can be regarded as known quantity), filling in the relevant algebraic expression is the basis of getting the equation.
Experience of Mathematics Learning in Junior Two.
Pre-math preparation for junior and middle schools.
If junior high school students want to learn math well, they should use the time before class to preview what the teacher will say in class. Pre-class preparation of junior high school mathematics is to understand what the teacher said in class, which is beneficial to junior high school students to organize their own knowledge structure and convenient.
Junior high school students can also learn what they don't understand by previewing mathematics before class, so that they will concentrate on listening in class and won't slip away and be distracted. At the same time, preview before class can also form a system of knowledge points, which can help junior high school students establish a complete knowledge structure.
Mathematics in junior and middle schools is the key.
Junior high school students want to learn students well, and class is a word: follow. Keep up with the teacher in junior high school math class. The teacher must keep up with where he talks, look at the teacher's blackboard carefully, and always know where the teacher talks and what the knowledge points are. Some junior high school students like to take notes, so I want to remind you not to take notes in junior high school math class.
Your main purpose is to follow the teacher, not just take notes. Even if there is something you can't do, you should write it down quickly and concisely, and you can improve it after class. It is most important to keep up with the teacher's thinking, which means that you understand the teacher's analysis and problem-solving process.
You can do some basic math problems in junior high school after class.
After each class, junior high school students can do some basic problems of junior high school mathematics after class. When doing this kind of problem, I suggest that you don't make mistakes, and learn to think and organize after you finish the problem. When there is no problem with your basic math problems in junior high school, you can do some difficult upgrading problems. If you can't do it, you can look at it according to the analysis.
But remember never to do this kind of problem in large quantities. It is helpful for junior high school students to do difficult problems occasionally, but it is not good to concentrate. At the same time, we should learn to sort out and summarize our mistakes.
Mathematics is developed from simple things step by step, so as long as people who study mathematics understand it honestly and step by step, and remember its main points for later use, they will certainly understand all its contents. In other words, if they understand the first step, they will certainly understand the second step, the first step and the second step, and they will certainly understand the third step. It's like a ladder class. As long as his legs are long enough to cross the first step, he will certainly be able to climb from the first step to the second step, and from the second step to the third and fourth steps ... At this time, he just does the same thing over and over again, so anyone should be able to do it.
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