Chapter 26 Actually, I am a master
This is the first time in Qiao Yu’s life that he has stood on the podium during class.
The perspectives are different, and the feelings are indeed different. It turns out that everything can be seen at a glance, and no small movements can be missed. It seems that many times he is still smart, always thinking that the teacher can't see some small movements below.
Actually, it’s just a matter of whether you want to care or not.
Especially these little ones... no, they are the brothers and sisters in high school. They don’t know how to hide their emotions at all. Whatever they are thinking in their hearts is written directly on their faces, and they look very easy to deal with...
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Then Qiao Yu glanced at Lan Jie, who was standing on the side of the podium.
Sure enough, the teacher is different. At least just looking at that emotionless face, one cannot explore his thoughts at this time.
After scanning around, he finally focused on the topic.
“Let’s take a look at this question first. Well, although it is a little simpler, it is a very typical functional equation analysis question. You should know at a glance that this question first requires considering the function at a specific point. value to solve the equation...
At the same time, you can also verify and eliminate multiple possibilities by constructing specific functions. With these two points of knowledge, I believe everyone already knows how to solve this problem. ”
"Ahem... Qiao Yu will explain your thinking directly." Lan Jie couldn't listen anymore and coughed twice beside him.
“Oh.”
Qiao Yu nodded and picked up the chalk resignedly: “The first step is to prove that f(x) is strictly monotonically increasing. Let’s start with the question. Starting with f(f(x))=f(x^2)+x, consider x on both sides Derivative. This can be assumed as f'(x) represents the derivative of f(x). Obviously when f′(x)=0, then 0=1, which is a contradiction. Therefore, f′(x)≠0... "
......
Five minutes later, Qiao Yu put down the chalk.
Next to him, Lan Jie sighed, as expected, he really couldn't help this kid.
Qiao Yu’s attention was focused on the new classmates in the audience. The situation seemed not to be good. It seemed that only five classmates were watching his problem-solving process thoughtfully, including those who followed him. He had dealt with Ma Yufei and Lu Jia.
The expressions of most people clearly did not look like they understood, especially many people who were secretly glancing at Lan Jie standing on the other side of the podium...
That pure and pure The innocent look doesn't seem to be fake.
Not only did they not understand, they didn’t even judge whether their explanation was correct or not!
Sure enough, Ma Yufei and Lu Jia were not alone in finding him. These guys seemed to have very low levels.
For a moment, Qiao Yu suddenly sympathized with Lan Jie.
It is indeed too difficult to expect these people to participate in competitions after training, and also expect them to win medals and help good people earn some bonuses.
This also made Qiao Yu immediately realize why Lan Jie was so kind to him.
A player like him who can participate in the competition without much training seems to be a scarce resource and a very sought-after one. Any school that has a choice will not send these high school students whose math skills are obviously not up to standard to participate in Olympiad training.
"Qiao Yu, you can go down first." Lan Jie nodded at Qiao Yu and then walked up to the podium.
When Qiao Yu stepped down from the podium and returned to his position with his back to the blackboard, Teacher Lan's voice also came.
“Student Qiao Yu’s problem-solving ideas are very clear, but he briefly mentions some key steps. You may not fully understand them yet. Let’s look at the second question analyzed by Qiao Yu. After considering the possibility through the construction method In the functional form of Use the method of contradiction To guide the analysis of the possibility of function differences, the step he omitted here is actually the monotonicity of the derivative derived from the first question. After supplementing, it is like this... In summary, answering this question requires the comprehensive use of differential calculus basics and function property analysis. And various mathematical tools such as construction method and proof by contradiction. Today I have prepared a thinking question for you... By the way, Qiao Yu, come with me to the office. ”
...
Qiao Yu was not given any time to stay in the classroom to discuss business with his classmates. After class, he took Qiao Yu back to his office.
However, Qiao Yu didn't feel too sorry. He had realized that helping these students explain the questions clearly was not an easy task.
For example, he just watched Lang Jie push through the conclusion of the last example question that was very obvious and could be thought of with a brain, and he vacated most of the blackboard. , was filled with supplements...
If it were him, after this class, just writing on the blackboard would be disabled, which made Qiao Yu deeply feel that the job of a teacher is indeed not easy.
"Come here, move a stool and sit next to me." As soon as he entered the door, Lan Jie waved directly to Qiao Yu.
Qiao Yu honestly brought a stool over and sat down.
Lanjie has already opened his notebook and opened the Overleaf interface.
“This is an online LaTeX editor. There is no Chinese version, but you should be able to use it depending on your English level. Let me introduce you to the main commands. The first is to create paragraphs...”
Lan Jie didn't talk nonsense. As soon as Qiao Yu sat next to him, he began to teach Qiao Yu how to use the LaTeX editor as promised on the phone yesterday.
The math teacher also witnessed Qiao Yu's talent again.
I didn’t see Qiao Yu taking any notes. He only needed to do all the operations once and he understood them clearly.
Commands, formula editing, various lists, commonly used macro package operations and debugging can all be restored perfectly.
At first, Lan Jie thought that Qiao Yu said he would do it, which was a bit reluctant, but when he asked Qiao Yu to get started, his skillful operation even made him wonder if this kid had been exposed to it before. I came here to tease him today.
Originally, Lan Jie planned to ask Qiao Yu to come to school again tomorrow. He would use the rest time to let this extremely talented student consolidate, but now it seems that there is no need.
"Okay, there are probably only so many things that need to be mastered. The definition of references is for writing papers, and you won't be able to use it for the time being. Go back and try to do a few questions using the test system on the official website of the Little Libaba Mathematics Competition. , and then upload the answer and you should be able to master it completely."
Seeing Qiao Yu finish the demonstration, Lan Jie said with infinite emotion.
After all, it took him at least a week to learn how to use this thing, and he was not as proficient as Qiao Yu now.
In the past, Lan Jie felt that the gap between himself and the top students from Huaqing and Yanbei was not that big. At most, it was just that he was a little unlucky. The tutors on the other side were very powerful and could provide more resources. . But now he has completely given up this idea.
The world is indeed very unfair. Many students seem to have excellent grades, but most of them have tried their best, and the best among them may just study casually. How can this be compared?
You must know that this guy skipped two days of classes two days ago and made money in an Internet cafe...
"It is indeed quite simple. If I had known it, I would have just found a tutorial yesterday and learned casually." Qiao Yu nodded and stated a fact.
Lan Jie glanced at the little guy wordlessly, and then warned: "By the way, you will start a round of mock exams next Monday. You, Class 13, don't have to make up classes on the weekend. You should prepare first. Except for mathematics, all the questions may be difficult.”
Qiao Yu glanced at Lan Jie and suddenly realized that this math teacher seemed to be very energetic and could arrange exams for the third grade of junior high school. It seemed that he was not as pitiful as he thought...
(End of Chapter)