In the afternoon, I hurried to the study room and started my daily life, burying my head at my desk to learn new knowledge. Considering that I will feel sleepy when reading words, I picked up the mathematics college entrance examination paper in recent years and planned to complete two difficult problems-conic curve and derivative. A total of * * * did four questions, even the analysis of * * * took nearly two hours, and finally got it. I think about it carefully, is this inefficient learning? No, I have to spend another half hour analyzing the routines of these questions.
I. Conic curve
16 and 17 are not difficult, but they have the same characteristics. Here we focus on the second question. After all, the first question is to send sub-questions. Consider whether the slope of a straight line exists. 17 examines the fixed-point problem, and 16 examines the value range.
On the fixed point problem. A problem I have seen before is to find a fixed point by using special circumstances and then verify whether the fixed point is positive or not. So I prefer this method to this problem, but the result is wrong, because I only got the abscissa in this process, so it is wrong to draw the conclusion that this point is on the axis. That is, in the wrong way. Then, I have to choose the conservative method, which is the omnipotent method. When I finished the trousers calculation, I found that carelessness held me back. As a result, it took me a long time to work out the result.
In the range of value. Because the conditions given in the question are clear, the chord length can be calculated step by step, but if the chord length of a circle is involved, the geometric method and Pythagorean theorem should be used as much as possible. I haven't seen other problems yet, and I am groping for them. ...
Second, derivative
These two problems, 16 and 17, both involve the zero point problem. The first question is still to discuss the parameters in different situations, and then find the monotonicity of the function or the range of parameters, which is a relatively simple question. Although every time I finish, I always doubt whether my answer is accurate. Pay attention to judge whether the equal sign is true.
Second, both of these questions involve skill. In contrast, the model in 17 is simpler, and the range of parameters is found according to the zero point. You can get the answer by elimination, but it needs further verification, which is a very troublesome thing, and the new value suddenly given in the answer is hidden by me at a glance. 16 is skillful, knowing zero and proving inequality. The trick is to transform the inequality into the inequality between function value domains and solve the maximum value in the monotonous interval. Of course, don't think it's over. Also, construct a new function, judge monotonicity, find extreme value, and complete.
There must be a reason why I can't get full marks in the exam because of such a tortuous second question. Not everyone can think of this step. Why do questioners make it difficult for candidates? Because my knowledge is not deep enough, I should do more such questions and find more feelings. Try to get 10 points.
02
In other words, my college entrance examination score 130 is the highest score in my high school career. Thank you for not being a very abnormal problem, for not hating math, and for still learning math.
I have been a professional for a long time, but I am not that professional. I only know that fur is not desirable, and in-depth research is the core. I hope I can go further and faster on the road of mathematics ... As the saying goes, if you can't learn from the dead, learn from the dead (what a perverted sentence! )。 Learning is the last word; Doing is truth.
Postscript: the size of half an hour, let's talk about it. Tomb-Sweeping Day has arrived. I wish you all a happy holiday. My holiday is dedicated to mathematics!
Would you like to take the college entrance examination again?