What knowledge points are taught in junior high school mathematics in the United States?
Let's talk about methods first, review in spring, and the basic knowledge will always be our attention. First, systematize the basic knowledge. When we see a question, we need to know what it is testing, and we need to know clearly which part of knowledge each knowledge point comes from. Keeping in mind the key points, difficulties and error-prone points of each part of knowledge can greatly reduce our error rate. Just like when you see a fractional equation, you will definitely think of checking the root, when you see a quadratic equation, you will definitely think of calculating delta, and when you see an isosceles triangle, you will definitely pay attention to classification and discussion, and you will definitely think of the integration of three lines. All the knowledge learned in junior high school has its most basic part and difficult part, which corresponds to the three different requirements of ABC in our senior high school entrance examination requirements. We should know every part of knowledge, especially geometric models, such as single tangent, double tangent and triple tangent between circles and tangents, and non-vertical similarity, double vertical similarity and triple vertical similarity models in similarity, so that we can get the idea of doing the problem faster and more clearly. Furthermore, for constructing isosceles triangles and right-angled triangles, it is often necessary to discuss who is the waist, who is the bottom, which is the right-angled side and which is the hypotenuse, so the systematic method here becomes particularly important. In order to ensure that the discussion is not lost, it must be divided according to certain principles, otherwise it may be lost and repeated. Therefore, we must learn to summarize the basic questions and basic knowledge points, so as to ensure smooth and rigorous problem solving. Second, the basic knowledge is comprehensive. Why this is important, because comprehensive knowledge can provide us with new ideas and a broader space to solve problems. For example, many students will say that the bisector, median line and height are important segments in the triangle, so there is actually a very important segment-the median line. Although this line segment is not discussed with the first three, it is often used in solving triangle problems, so if you don't realize the problem of triangle center line when solving problems, you may not be able to make auxiliary lines. Therefore, it is very beneficial for us to associate and apply knowledge points as a whole. For another example, what method can be used to solve the length of a line segment? Most students can name many kinds, such as Pythagorean Theorem, similar triangles, congruent triangles, trigonometric functions, and the properties of special triangles. However, methods such as area method and constructing parallelogram are often forgotten. This is the incompleteness of induction, which is often a possible method to solve comprehensive problems, so it is very important to summarize thoroughly. For another example, in addition to the three-line octagon that everyone has always been sensitive to, after we have learned similarity and congruence, we are often used to solving the relationship between angles with these methods. In fact, there are two very important methods that are most easily overlooked. One is "the sum of the internal angles of a triangle = 180", and the other is "one external angle of a triangle is equal to the sum of two non-adjacent internal angles". A blank stare means that many students can't see that this is an outer corner. Therefore, after the knowledge we have learned is gradually enriched, we should be good at sorting out, string together every knowledge point we have learned and hang it in a series of circles, so that we can know how many theorems there are in a * * * and how many kinds of reminding common problems there are; When giving a string of right angles, we should think about where we can see right angles and what are the properties and functions of right triangles. Therefore, we should comprehensively summarize the knowledge involved in each part of the test center and the problem-solving methods involved in each kind of knowledge. Only in this way can we ensure that our thinking is broad and our methods are flexible, so that we won't say that we can't think of a way to look at a problem and we can't think of the way to use it. Third, deepen the basic knowledge. This part is related to the comprehensive problem behind us. Depth is the application and migration of basic knowledge. There is no problem in the senior high school entrance examination. The problem we are talking about is just to organically combine many simple knowledge points, or slightly deform them or hide them. Then this part needs everyone to use our basic knowledge flexibly and skillfully to answer. The premise of flexible application is a deep understanding of knowledge points. For example, the sum of two sides is greater than the third side, and the difference between the two sides is less than the third side. Many students can only think of using it to solve the range problem, but in fact, in the comprehensive problem, this part of knowledge is used to solve the line segment relationship and the maximum problem. If we can have this understanding, we can naturally think of translating line segments to construct triangles or parallelograms in comprehensive problems. For another example, an image of a quadratic function intersects with any straight line, which not only shows that the two images intersect, but also shows that the binary linear equation they form has real roots. For right triangle, it is not only the object we solve, but also we should realize that it is a very good tool for angle transformation. When a special angle appears, we should be able to think of constructing a right triangle and transforming the conditions. These are all ways to deepen the understanding of basic knowledge after doing a certain amount of questions. To sum up, why do we always emphasize our basic knowledge? Because in the whole junior high school mathematics, there will be no problems outside the syllabus or problems that have never been studied at all, certainly not. They are all based on our basic knowledge individually or in groups, so if we master the basic knowledge, we will certainly be able to do the easy problems well, solve the difficult problems well, make a mountain out of a molehill, and slowly and steadily tackle the big problems. In addition to paying attention to basic knowledge, we should also pay attention to strengthening the cultivation of our own mathematical sensitivity in the review process. This includes observation and induction. Two triangles form a butterfly diagram, two line segments form a right angle, and three perpendicular lines appear in a square. Many ideas come from our careful observation when doing a good job. This ability is highlighted in the last question in the blank and the 22nd question in the answer. To put it bluntly, these questions are testing everyone's observation ability, discovery ability, induction ability and application ability. In the case that the basic knowledge has been reviewed almost, we should have a pair of keen eyes and a good inductive mind for these problems. The outstanding point of these two problems is change. We should be good at finding the unchangeable things in the process of change, whether it is graphic change, condition change or digital change, there are always unchangeable things among them. Either the thinking of solving the problem remains unchanged, or the auxiliary line drawing method remains unchanged, or the relationship between the two quantities remains unchanged, or the conclusion remains unchanged. We observe the figures, observe the conditions, and observe the conclusion drawn from the previous question. There will always be a line to string them together, which provides a good idea for us to do the next question. Therefore, in this review stage in spring, training your observation ability and induction ability will help you find a way of thinking faster and more accurately. Next, let's talk briefly about mentality. No matter whether your grades are good or bad now, our spring review is to improve your grades and ensure that your grades are as stable as possible. In addition to studying at home on weekdays, relax and talk to your parents about things other than study, and combine work and rest. But be careful not to be disturbed by other trifles. In grade three, we are experiencing the process of mental maturity. At this time, everyone has their own ideas about many things, so there will be frictions, emotions and all kinds of emotions in life, no matter which one, don't let those affect your concentration when reviewing. Because everything can be solved in the future, except for the senior high school entrance examination. At this time, I will begin to learn to be responsible for myself. We should always be able to distinguish our priorities and adjust our mood. We must try to solve this problem. In the third year, the whole class saw that the new paper was done like a tiger pouncing on food, because everyone wanted to prove that they were strong and enjoy the envy and admiration of others, so there was nothing wrong with our greed in the third year. At home, I thought, if I "secretly" use more effort, maybe I can surpass one or two classmates, and maybe I can be farther away from the expected school. So it's best to have such fighting spirit. To sum up, the spring review lasted until the first model exam. The most important thing for students is to master the basic knowledge in a down-to-earth manner, implement every knowledge point in the textbook, do more questions and summarize more, especially the first touch and mid-term exam questions over the years. Follow the teacher at school, communicate with classmates at ordinary times, and summarize at home. What needs to be emphasized is that at this stage, when we do the questions, we should not rush into it. We must consolidate them as much as possible under the premise of ensuring the correct rate, especially for the weak links, which need us to continuously strengthen. Therefore, for this part, first of all, we can't give up on ourselves, because it is relatively easy for the weak links to be upgraded to the upper-middle level, so don't sell yourself short and give up, and certainly don't set too high a goal of quick success and instant benefit. In short, the review task in spring is still arduous, but the effect is often obvious. A model exam is basically the vane of the senior high school entrance examination, so we should seize these two months, implement the foundation, exercise our ability, adjust our mood and mentality, and work hard for the ultimate goal of junior high school!