Eight-grade mathematics knowledge points
Collection, collation and description of data
I. Knowledge framework
Two. The concept of knowledge
1. Comprehensive survey: The survey method for all the subjects is called comprehensive survey.
2. Sampling survey: The survey method of investigating some data and estimating the whole according to some data is called sampling survey.
3. Population: All the investigated objects are called population.
4. Individuals: Each survey object that constitutes the population is called an individual.
5. Sample: All the extracted individuals constitute a sample.
6. Sample size: The number of individuals in a sample is called sample size.
7. Frequency: Generally speaking, the number of times the data falls into different groups is called the frequency of that group.
8. Frequency: The ratio of frequency to total data is frequency.
9. Number of groups and distance between groups: When counting data, the data is divided into several groups according to a certain range, and the number of groups is called the number of groups, and the difference between the two ends of each group is called the distance between groups.
The second volume of the second day of junior high school summarizes the knowledge points of mathematics.
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 the 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.
Math learning skills in grade two of junior high school
The cultivation of self-study ability is the only way to deepen learning.
When learning new concepts and operations, teachers always make a natural transition from existing knowledge to new knowledge, which is the so-called "reviewing the past and learning the new". Therefore, mathematics is a subject that can be taught by itself, and the most typical example of self-study is mathematician Hua.
We listen to the teacher's explanation in class, not only to learn new knowledge, but more importantly, to subtly influence the teacher's mathematical thinking habits and gradually cultivate our own understanding of mathematics.
The stronger the self-study ability, the higher the understanding. With the growth of age, students' dependence will be weakened, while their self-learning ability will be enhanced. So we should form the habit of previewing.
Therefore, solid mathematics learning in the past laid the foundation for future progress, and it is not difficult to learn new lessons by yourself. At the same time, when preparing a new lesson, it goes without saying that it is great to listen to the teacher explain the new lesson with questions when you encounter any problems that you can't solve.
Learn to learn, knowledge is still someone else's. The test of whether you can learn math well is whether you can solve problems. Understanding the definitions, rules, formulas and theorems related to memory is only a necessary condition for learning mathematics well, and being able to solve problems independently and correctly is the symbol of learning mathematics well.
Confidence can make you stronger.
In the exam, I always see that some students have a lot of blanks in their papers, but they haven't done a few questions at all. Of course, as the saying goes, art is bold, art is not timid. However, it is one thing to fail, and it is another thing to fail. The solution and result of a slightly more difficult math problem are not obvious at a glance. It is necessary to analyze, explore, draw, write and calculate. After tortuous reasoning or calculation, some connection between conditions and conclusions will be revealed and the whole idea will be clear.
When solving a specific problem, we must carefully examine the problem, firmly grasp all the conditions of the problem, and don't ignore any one. There is a certain relationship between a problem and a class of problems. We can think about the general idea and general solution of this kind of problem, but it is more important to grasp the particularity of this problem and the difference between this problem and this kind of problem. There are almost no identical problems in mathematics, and there are always one or several different conditions, so the process of thinking and solving problems is not the same. Some students and teachers can do the questions they have talked about, while others can't. They just talk about the matter and stare at some small changes in the problem, and they can't start.
The topics of mathematics are infinite, but the ideas and methods of mathematics are limited. As long as we learn the basic knowledge well and master the necessary mathematical ideas and methods, we can successfully deal with endless problems. The topic is not to do more, the better. The ocean of topics is endless, and you will never finish reading it. The key is whether you have cultivated good mathematical thinking habits and mastered the correct mathematical problem-solving methods.
Solving problems requires rich knowledge and more confidence. Without self-confidence, you will be afraid of difficulties and give up; With self-confidence, we can forge ahead, not give up easily, study harder, and hope to overcome difficulties and usher in our own spring.
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