The second volume of the second day of junior high school summarizes the knowledge points of mathematics.
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 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.
The second volume of the second day of junior high school mathematics knowledge points
1. Definition of fraction: If A and B represent two algebraic expressions, and B contains letters, then this formula is called a fraction.
The meaningful condition of a fraction is that the denominator is not zero, the numerator of the fractional value is zero, and the denominator is not zero.
2. The basic nature of the fraction: the numerator of the fraction is multiplied by the denominator or divided by the algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.
3. General and approximate scores of scores: the key is to decompose the factors first.
4. Fractional operation:
Law of fractional multiplication: fractional multiplication, the product of molecules is the numerator of the product, and the product of denominator is the denominator.
Law of fractional division: a fraction is divided by a fraction, and the numerator and denominator of the divisor are in turn multiplied by the divisor.
Fractional multiplication: the numerator and denominator should be multiplied separately.
Addition and subtraction of fractions: addition and subtraction of fractions with the same denominator and addition and subtraction of molecules with the same denominator. Fractions with different denominators are added and subtracted, first divided by fractions with the same denominator, and then added and subtracted.
Mixed operation: The operation sequence is the same as before. It can be simplified by the operation speed.
5. The zeroth power of any number that is not equal to zero is equal to 1, that is; When n is a positive integer,
6. The operation property of positive integer exponential power can also be extended to integer exponential power (m, n is an integer).
(1) The power of the same base:;
(2) the power of power:
(3) the power of the product:
(4) Division of powers with the same cardinal number: (a ≠ 0);
(5) Power of quotient: (b≠0)
7. Fractional equation: an equation with a fraction and an unknown number in the denominator-fractional equation.
The process of solving the fractional equation is essentially to multiply both sides of the equation by an algebraic expression (the simplest common denominator) and transform the fractional equation into an integral equation.
When solving a fractional equation, when both sides of the equation are multiplied by the simplest common denominator, the simplest common denominator may be 0, which increases the root, so the fractional equation must be tested.
Steps to solve the fractional equation: (1) Simplify first and then simplify; (2) Multiplying both sides of the equation by the simplest common denominator, and transforming it into an integral equation;
(3) solving the integral equation; (4) Root inspection.
There are two conditions to add a root: one is that its value should make the simplest common denominator 0, and the other is that its value should be the root of the whole equation after removing the denominator.
Test method of fractional equation: bring the solution of the whole equation into the simplest common denominator. If the value of the simplest common denominator is not 0, the solution of the whole equation is the solution of the original fractional equation; Otherwise, this solution is not the solution of the original fractional equation.
What are the steps of applying the equation? (1) trial; (2) setting; (3) column; (4) solutions; (5) answer.
There are several types of application problems; What is the basic formula? There are basically four kinds:
(1) Travel problem: basic formula: distance = speed × time. Travel problems are divided into meeting problems and chasing problems.
(2) The number topic should master the representation of decimals in the number topic.
(3) The basic formula of engineering problems: workload = working time × working efficiency.
(4) Countercurrent problem: downstream = v still water +v water. V countercurrent =v still water -v water.
8. Scientific notation: The notation for expressing a number in one form (where n is an integer) is called scientific notation. When the absolute value of an n-bit integer is greater than 10, the exponent of 10 is
In scientific notation, when the absolute value is less than 1, the exponent of 10 is the number of zeros before the first non-zero number (including the zero before the decimal point).
Mathematics learning methods and skills
First, overcome psychological fatigue.
First, we should have a clear learning purpose. Learning is like pumping water from a river. The more power, the greater the water flow. Motivation comes from the purpose, and only by establishing the correct learning purpose can we have a strong learning motivation; Second, we should cultivate a strong interest in learning. The formation of interest is related to the excitement center of cerebral cortex, accompanied by pleasant, cheerful and positive emotional experience. Psychological fatigue is caused by the negative emotion of cerebral cortex resistance. Therefore, cultivating one's interest in learning is the key to overcome psychological fatigue. With interest, learning will have enthusiasm, consciousness and initiative, and psychology will be in a good competitive state; Third, we should pay attention to the diversification of learning. Book learning itself is boring and monotonous. If you study a course or a chapter repeatedly, it is easy to suppress the cerebral cortex, resulting in psychological saturation and boredom. Therefore, candidates may wish to review each course alternately.
Second, overcome the plateau phenomenon.
The plateau phenomenon in review refers to the phenomenon that when reviewing for a certain period, it often stagnates, not only making no progress, but also regressing. The platform period is not that there is no progress in learning, but that some progress and some retrogression are balanced with each other, which makes the review effect not fundamentally changed and makes people frustrated and disappointed. When candidates encounter plateau in the process of reviewing for the exam, don't be impatient or lose confidence, but find out the reasons for learning methods and enthusiasm. Adjust the review progress in time, make more efforts to use your brain scientifically and improve the review efficiency.
Third, pay attention to reviewing "mistakes"
If you are not good at coming out of mistakes in review, there will be more and more defects and loopholes. If left unchecked, the ant nest will eventually burst. During the preparation period, in order to reduce the error rate, in addition to timely revision and comprehensive and solid review, the key issue is to find out the reasons and constantly review the mistakes. That is, read the wrong questions regularly, recall the reasons for the mistakes, and sort out all kinds of wrong questions and reasons. For those problems that are repeatedly wrong, you can consider doing it again to avoid "future troubles." The reasons for the mistakes are: problems in conceptual understanding, problems caused by carelessness, and illusions caused by sloppy writing, so as to effectively avoid making similar mistakes in the exam.
Fourth, grasp the psychological characteristics and do a good job in reviewing before the exam.
Practice has proved that a person's temperament, personality, psychological stability and other factors will also affect the review before the exam. In the process of preparing for the exam, candidates should make an exam review plan according to their own psychological characteristics, adjust the review progress according to their own mentality, choose and use the review methods well, and make their exam review achieve the expected results.
1, textbooks can not be ignored.
For junior two students, they are all learning new lessons, and textbooks are important review materials that are easy to ignore. Usually, everyone takes notes in class at school, and basically doesn't read textbooks. Students are advised to read and understand the knowledge points repeatedly according to the textbook while reading notes, and to think, ponder and integrate exercises in after-school exercises to deepen their understanding of the knowledge points. We should also focus on memorizing the key contents and key examples in the textbook.
2. Wrong title
I believe that students with good study habits should have a wrong book, copy down the wrong questions in each exercise, homework and exam, make the answers clear, find out the reasons for the mistakes, find out the weak points in their knowledge and ability, and take them out and look at them often. When you encounter repeated mistakes, you should take the initiative to discuss with your classmates and ask the teacher to thoroughly understand the problem and avoid making similar mistakes again.
The second volume of the second day of junior high school summarizes the related articles of mathematical knowledge points;
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