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Review outline of junior high school mathematics knowledge points
Summary of junior high school mathematics knowledge points
The induction of mathematics knowledge points in the third grade of People's Education Press
Summarize and sort out the knowledge points of junior high school mathematics
Induction and arrangement of junior high school mathematics knowledge points
Basic knowledge of mathematics in grade three
First, the related concepts of circle
1, the definition of a circle
In each plane, the line segment OA rotates around its fixed end point O, the figure formed by the rotation of the other end point A is called a circle, the fixed end point O is called a center, and the line segment OA is called a radius.
2. The relationship between a straight line and a circle.
1. When there is only one * * * between the straight line and the circle, click to call it straight and cut the circle line.
2. The circle connected by triangle is called the outer center of the three-center angle.
3. The chord tangent angle is equal to the central angle of the clamping arc.
4. The circle tangent to the internal shape of the triangle is called the center of the three-center angle.
5. The semi-straight line perpendicular to the diameter must be the tangent of the circle.
6. A straight line that passes through a point outside half the diameter and ends vertically at that point is a tangent to a circle.
7. The semi-straight line perpendicular to the diameter is the tangent of the circle.
8. The tangent of the circle is perpendicular to the radius of the point.
3, the geometric representation of the circle
The circle centered on point O is marked as "⊙O" and pronounced as "circle O"
Second, the vertical diameter theorem and its inference
Vertical diameter theorem: the diameter perpendicular to the chord bisects the chord and bisects the arc opposite to the chord.
Inference 1: (1) bisects the diameter (not the diameter) of the chord perpendicular to the chord and bisects the two arcs opposite to the chord.
(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.
(3) The diameter of the arc bisecting the chord bisects the chord vertically and bisects another arc opposite the chord.
Inference 2: The arcs sandwiched by two parallel chords of a circle are equal.
The vertical diameter theorem and its inference can be summarized as follows:
Over the center of the circle
Perpendicular to the chord
The diameter bisects the chord to know two and push three.
The best arc to bisect the chord.
A lower arc that is split in two by a chord.
Three, chord, arc and other definitions related to the circle
1, string
A line segment connecting any two points on a circle is called a chord. (AB in the figure)
2. Diameter
The chord passing through the center of the circle is called the diameter. (such as the upcoming CD)
The diameter is equal to twice the radius.
3, semicircle
The two endpoints of a circle with any diameter are divided into two arcs, and each arc is called a semicircle.
4, arc, arc, arc.
The part between any two points on a circle is called an arc.
The arc is represented by the symbol "⌒", and the arc with A and B as endpoints is marked as "",which is pronounced as "arc AB" or "arc AB".
An arc larger than a semicircle is called an optimal arc (usually represented by three letters); An arc smaller than a semicircle is called a bad arc (usually represented by two letters).
Tips for learning junior high school mathematics well
(1) interest
It is said that interest is the best teacher, and the most important thing is to be interested in mathematics. If you are tired, you can't keep it.
(2), understanding ability
Mathematics is a science, and understanding ability is very important. Without understanding ability, your math and even all science studies will be very difficult. However, the cultivation of understanding ability is very difficult. You must try to understand some philosophical theories and relatively abstract mathematical models that are difficult for you. The simplest training is also very difficult, so for a moderately difficult question, it is necessary to see that the auxiliary line can reflect its practice within 1 minute. Secondly, we should not only understand what the teacher said, but also try to figure out the specific mental process when the teacher did the problem. This is the basic ability of many people to learn mathematics well.
(3) diligence
I met many students who worked hard but still couldn't learn science well. The dumb thing about the math exam is that it is easy to pass as long as you study hard according to the teacher's requirements, but it is far from enough to get 145 by the teacher's practice. Even poor students still have simple and easy learning methods. Only by mastering the correct methods can we gain something through diligence.
How to improve junior high school math scores
1.
Xi: Before class, browse the unit content that the teacher will teach, and pay attention to what you don't understand.
2. Listen carefully:
(1) There are many new definitions of terms or new ideas at the beginning of the new curriculum. The teacher's explanation must be clearer than the students' own reading. Be sure to listen attentively, don't be smart and make mistakes.
If the teacher says what you didn't understand in the preview, you should pay special attention.
Some students think that the teacher's explanation is simple, and then they are distracted to do other things, but they miss the most wonderful and important words, which may be the key to getting the wrong answer in the future exam.
(2) While listening to the lecture, recite the key points. Definitions, theorems, formulas and other key points should be memorized in class so that teachers can understand the essence of teachers when giving examples.
After returning home, it only takes a short time to review the lessons learned today. Get twice the result with half the effort. Unfortunately, most students enjoy the teacher's performance as easily as watching a movie in class, and they don't remember anything after class. It's a pity to waste a class in vain.
homework
：
(1) finishing points
In the evening of math class, we should sort out the contents taught that day, and memorize definitions, theorems and formulas. Some students think that mathematics focuses on reasoning and does not need to recite anything. This concept is incorrect. Generally speaking, the so-called immortal rote learning refers to the immortal rote learning method, but the basic definitions, theorems and formulas are our tools to solve problems. If we don't remember these things, we can't use them flexibly when solving problems, just as a doctor can't save people in the first place if he doesn't memorize all medical knowledge and medication knowledge. Many students didn't do well in math test, that is, they didn't understand the definition clearly and didn't recite some important theorems and formulas completely.
(2) Proper exercise
After you finish the key points, you should practice properly. In class, do the examples explained by the teacher first, then do the textbook exercises, spare no effort, and then do the reference books or supplementary questions issued by the teacher. If you can't solve it for a while, you can skip it first to avoid wasting time, and then challenge it in your spare time. If you still can't solve it, discuss it with your classmates or teachers.
(3) When practicing, you must do calculus by yourself. Many students often can't go on when they solve problems in the middle of the exam. The reason is that he watches while doing exercises, and many key steps are ignored.
test
：
(1) Before the exam, it is necessary to sort out the key points within the scope of the exam, and pay attention to the important questions specially prompted by the teacher.
(2) When taking an exam, you must do the right questions. Students who often make calculation mistakes should try to slow down the calculation speed, carefully move items and add, subtract, multiply and divide, and use less "mental arithmetic".
(3) During the exam, our purpose is to get high marks, not to do academic research. So if you encounter a difficult topic, skip it first, and then use the rest of the time to challenge the problem, so as to fully show your strength and achieve the most perfect performance.
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