First of all, pay attention to the teacher's introduction. Many people think this is useless, because many teachers basically pass by, and some even don't introduce it at all, saying that we are learning a new chapter today. If this happens, then I suggest you study the textbook itself carefully after class. Because this part of the content often appears in the form of material analysis from the examination level; Most importantly, what does this part actually tell us about the purpose of this knowledge point? Don't many people know the use of this knowledge? Do some people think they are useless, so they don't want to learn? Then this is the answer. And there are often some interesting things. When you calm down and analyze them carefully, you will have a deeper understanding of the concepts to be learned next. Of course, if the teacher talks, you can listen carefully in class and you will get what I just said!
Secondly, we should pay attention to what the concept itself is, understand it word by word, and think from the perspective of Chinese. Don't change from understanding to rote learning at the early stage of learning new concepts.
For example, an ellipse is defined as the trajectory of a moving point P. The sum of the distances between the moving point P and the fixed points F 1 and F2 in a plane is equal to a constant (greater than F 1F2), and F 1 and F2 are called the two focuses of the ellipse. So how do you listen?
These two points are fixed points. Is the fixed point arbitrary? Are there any other requirements? If you think about this question for the first time, you won't ask why the focus of the ellipse we learned is on the coordinate axis and must be symmetrical about the origin. In fact, the ellipse itself does not have this requirement, because there is no such requirement in the definition, but for the convenience of research and examination, we have added a special condition to the ellipse studied in senior high school, that is, the focus is on the coordinate axis and is symmetrical about the origin. If this is not the case, then the so-called long axis, short axis and standard equation are not what we have learned.
This is the sum of the distances from one point to two fixed points. It must be greater than the distance between two fixed points. Why? Teachers usually draw an ellipse by themselves or demonstrate it with multimedia. If equals, you can't draw an ellipse. Such a moving point can only be on the line segment formed by two fixed points. If you notice such an error-prone point when you first study, you won't make mistakes in the future. After all, preconceived ideas are still very important.
Can all the moving points that meet this standard be calculated according to the standard equation of ellipse? Of course, aren't most of the first trajectory questions of the conic section in the college entrance examination the definition of ellipse? Aren't they all used directly like this? But isn't this kind of problem still popular every year? The fundamental reason is that I didn't learn the concept for the first time.
Finally, listen to the teacher talk about the error-prone points of this concept and its application; Of course, listening carefully can be used in after-class exercises and exams. More importantly, the error-prone points of a knowledge point determine a student's mastery and score of this concept, because multiple-choice questions basically focus on the error-prone points of knowledge points. At the same time, the special values that we substitute first when we adopt the exclusion method are often error-prone. Even the traps set by multiple-choice questions are basically error-prone. This is also the place where the gap has widened the most. The teacher summed it up for you, saving you a lot of time!