There is never a shortcut to learning. Every subject has its own learning method, but it is always inseparable. Mathematics, like Chinese and English, needs memorization, recitation and practice. The following are some eighth-grade math knowledge points I have compiled for you, hoping to help you.

Summary of mathematical knowledge points in the second volume of the second day of junior high school Beijing Normal University Edition

The first chapter scores

1, the numerator and denominator of the fraction and its basic properties are multiplied (or divided) by an algebraic expression that is not equal to zero at the same time, and the fraction is only constant.

2. Fraction operation

(1) The law of multiplication, division and multiplication of fractions: Fractions are multiplied by fractions, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product. Law of division: a fraction is divided by a fraction, and the numerator and denominator of division are multiplied by the divisor in turn.

(2) Law of fractional addition and subtraction: fractional addition and subtraction with the same denominator, and numerator addition and subtraction 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.

3. Addition, subtraction, multiplication and division of exponential powers of integers

4. Fractional equation and its solution

Chapter II Inverse Proportional Function

Expressions, images and properties of 1. inverse proportional function

Image: hyperbola

Expression: y=k/x(k is not 0)

Nature: the increase and decrease of the two branches are the same;

2. The application of inverse proportional function in practical problems.

Chapter III Pythagorean Theorem

1, Pythagorean theorem: the sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.

2. Inverse theorem of Pythagorean theorem: If the sum of squares of two sides in a triangle is equal to the square of the third side, then this triangle is a right triangle.

Knowledge point induction in the second volume of mathematics in the second day of junior high school

right triangle

◆ Prepare for Sun Tzu's Art of War

1. Correctly distinguish Pythagorean theorem and its inverse theorem, and master the commonly used Pythagorean number.

2. When solving problems related to right triangle, we should pay attention to the Pythagorean theorem as a bridge, establish equations (groups) to solve problems, and realize algebra of geometric problems.

3. When solving the related problems of right triangle, we should pay attention to whether the problems include special angles (30, 45, 60). If so, we should use some related special properties to solve the problem.

4. When solving many calculation and proof problems of non-right triangle, it is often solved by transforming the height into right triangle.

5. Folding is one of the hot topics in the new senior high school entrance examination. When dealing with the folding problem, we should do it by hand, observe it carefully, give full play to our spatial imagination, pay attention to the changes of line segments and angles during the folding process, and find ways to solve the problem.

center of gravity of triangle shape

It is known that in △ABC, D is the midpoint of BC, E is the midpoint of AC, AD and BE intersect at O, and the extension line of CO intersects with AB at F. It is proved that F is the midpoint of AB.

Prove: According to the dovetail theorem, S(△AOB)=S(△AOC), S(△AOB)=S(△BOC), ∴S(△AOC)=S(△BOC), and then apply the dovetail theorem to get AF=BF, and the proposition is proved.

Several properties of the center of gravity:

1. The areas of the three triangles formed by the center of gravity and the three vertices of the triangle are equal.

2. The sum of squares of the distances from the center of gravity to the three vertices of the triangle is the smallest.

3. In the plane rectangular coordinate system, the coordinate of the center of gravity is the arithmetic average of the vertex coordinates, that is, its coordinate is ((X 1+X2+X3)/3, (y1+y2+y3)/3); Spatial rectangular coordinate system-abscissa: (X 1+X2+X3)/3 ordinate: (Y 1+Y2+Y3)/3 ordinate: (Z 1+Z2+Z3)/3.

4 The ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint of the opposite side is 2: 1.

5. The center of gravity is the point of the distance product of a triangle to three sides.

If it is proved by Seva theorem, it is easy to prove that three midlines intersect at one point.

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, reminding everyone 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.

Articles related to important knowledge points of eighth grade mathematics;

★ Sort out and summarize the knowledge points of eighth grade mathematics.

★ Arrangement of Mathematics Knowledge Points in Grade Eight

★ Summary of knowledge points in the first volume of Mathematics in the second day of junior high school

★ Summarize the knowledge points of eighth grade mathematics.

★ Summarize the knowledge points of eighth grade mathematics.

★ Summary of Mathematics Knowledge Points in Senior Two.

★ Summary of eighth grade mathematics knowledge points

★ Summarize the knowledge points of eighth grade mathematics.

★ Review and arrangement of mathematics knowledge points in Grade Two.