The ninth grade mathematics knowledge points summarize the unary linear inequality and unary linear inequality group.
1. Generally, the formula connected by the symbol ""(or "≥") is called inequality.
The value of the unknown quantity that can make the inequality hold is called the solution of the inequality. The solution of inequality is not unique. All that satisfy the inequality are liberated together to form the solution set of the inequality. The process of finding the solution set of inequality is called solving inequality.
An inequality group consisting of several linear inequality groups is called a linear inequality group.
Solution set of inequality group: the common part of each inequality solution set in linear inequality group.
The basic property of equation 1: Add (or subtract) the same number or algebraic expression on both sides of the equation, and the result is still an equation. Basic property 2: the result of multiplying or dividing the same number on both sides of an equation (the divisor is not 0) is still an equation.
Second, the basic properties of inequality 1: the same algebraic expression is added (or subtracted) on both sides of the inequality, and the direction of the inequality sign remains unchanged. (Note: The shift term should be changed, but the equal sign remains unchanged. ) property 2: both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality remains unchanged. Property 3: When both sides of the inequality are multiplied by (or divided by) the same negative number, the direction of the inequality changes. Basic properties of inequality
Other properties of inequality: reflectivity: if a >；; B, then bb, b>c, then a>c.
Third, the steps of solving inequality: 1, denominator; 2. Remove the brackets; 3. Transfer projects and merge similar projects; 4. The coefficient is 1.
Fourth, the steps to solve the inequality group: 1, the solution set of inequality 2, indicating the solution set of inequality on the same axis.
5. Enumerate the general steps of solving practical problems with linear inequality of one variable: (1) examining questions; (2) Set an unknown number and find an (unequal) relationship; (3) setting independent variables, setting inequalities (groups) (according to inequalities) (4) solving inequality groups; Test and answer.
6. Frequently asked questions: 1, find the nonnegative solution of 4x-6 7x- 12. 2. It is known that the solution of 3(x-a)=x-a+ 1r is suitable for 2(x-5) 8a, and the range of a. 3 is found. When taking the value of m, 3x.
Decomposition factor
1. formula: 1, ma+mb+mc=m(a+b+c)2, a2-b2=(a+b)(a-b)3, A2+2ab+B2 = (a+b) 2. Convert a polynomial into the product of several algebraic expressions. 1. Turning the product of several algebraic expressions into a polynomial is a multiplication operation. 2. Turning a polynomial into the product of several algebraic expressions is factorization. 3.ma+mb+mc m(a+b+c)4。 Factorization and algebraic expression multiplication are opposite deformations.
3. Let all terms of a polynomial contain the same factor, which is called the common factor of each term of this polynomial. To decompose a factor by the common factor method is to convert a polynomial into a monomial and then multiply it with this polynomial. The general steps to find the common factor are: (1) If each coefficient is an integer coefficient, take the greatest common factor of the coefficient; (2) Taking the same letter, the index of the letter is lower; (3) Take the same polynomial with lower exponent. (4) The product of all these factors is the common factor.
4. The general steps of factorization are as follows: (1) If there is a "-",first extract the "-",if the polynomial has a common factor, then extract the common factor. (2) If the polynomial has no common factor, choose the square difference formula or the complete square formula according to the characteristics of the polynomial. (3) Every polynomial must be decomposed until it can no longer be decomposed.
5. A formula in the form of A2+2ab+b2 or a2-2ab+b2 is called a completely flat mode. Method of factorization: 1, method of extracting common factor. 2. Use the formula method.
Methods to improve math scores. The test questions are precise, not quantitative.
The improvement of mathematical ability is inseparable from doing problems. Everyone knows the simple truth that "practice makes perfect". But the problem is not to engage in sea tactics, but to think of many problems through one problem.
You should focus on the thinking process of solving problems, find out the significance and role of basic mathematical knowledge and basic mathematical ideas in solving problems, and study various ways to solve the same mathematical problem with different thinking methods. In the process of analyzing and solving problems, you should not only establish the horizontal connection of knowledge, but also develop the habit of thinking from multiple angles.
Instead of rushing in a class and sweating twenty or thirty repetitive questions, it is better to master a typical problem thoroughly.
For example, deeply understand the various connotations of a concept and try to deal with a typical problem in many ways from many ideas, that is, multiple solutions to one problem.
We should try to use * * * to explore the law of problems, that is, to solve more problems. Constantly change the conditions of the topic and test your knowledge from all aspects, that is, a topic is changeable.
The value of a question lies not in doing it right or doing it right, but in knowing what the question wants to test you.
Understanding the problem from this angle can not only quickly find a breakthrough in solving the problem, but also not easily enter the trap set by the teacher.
Analyze test papers and sum up experience.
There are some mistakes in every exam, which is not terrible. It is important to avoid similar mistakes in future exams. Everyone's first monthly exam is basically over. You can analyze yourself with the help of the first monthly exam paper:
Usually pay attention to write down the wrong questions. The wrong notes include three aspects:
(1) Write down what the error is, preferably in red.
(2) What is the cause of the error? Analyze from four aspects: examining questions, classifying, copying knowledge and finding answers.
(3) Error correction methods and precautions. According to the analysis of the cause of the error, put forward the correction method to remind yourself what to pay attention to next time you encounter similar situations.
If you can record and analyze the mistakes in each exam or exercise, and try your best to ensure that the same mistakes will not occur in the next exam, the probability of making mistakes in the senior high school entrance examination will be greatly reduced.
Turn good practices into habits.
Good habits will benefit for life, bad habits will regret for life and suffer for life. For example, does "mistakes in examining questions" lie in being eager for success?
The tactics of "one slow and one quick" can be adopted, that is, the examination of questions should be slow and clear, the steps should be in place, the action should be fast, the work should be gradual, the stability should be fast, and the success should be based on one time. Don't get into the bad habit of being afraid of not finishing, rushing to do things and hoping to be checked.
In addition, the general examination is regarded as an important way to accumulate examination experience, and the general examination is regarded as the senior high school entrance examination, which is constantly debugged and gradually adapted from all aspects. Pay attention to the writing standard, you can't lose important steps, and losing steps means losing points.
According to the characteristics of graded answers, we might as well make a psychological transposition. According to their own actual situation, from the requirement of "correctly completing all homework" to the requirement of "based on completing some topics or some topics". Don't spend too much time on a problem, sometimes giving up may be the best choice.
The mid-term exam is coming. If you want to improve your math scores, you have to change it now. Although the mid-term exam is only a means to test the knowledge of this semester, whether you do well in the exam has a great influence on your child's future study.
Students who study hard at ordinary times are full of confidence at this time; Students who don't study well at ordinary times are afraid.