Chapter 5 Leisure during exams

"Okay, classmates, please bring your schoolbags and books. We will hand out the papers soon."

In the first examination room, the invigilator greeted the thirty students present.

At a glance, you can see that this is like being in Science Class 1, because most of the students in this examination room are students in Science Class 1, that is, students in Rocket Class.

The examination rooms of Jincheng Middle School are sorted according to the ranking of the last examination. There are thirty people in one examination room, so the top thirty in the last examination can sit in the first examination room. It is also jokingly called the battlefield of academic masters by the students of the school. , people from other examination rooms want to come in, but people here don’t want to go out.

Lin Xiao sat in the fifth and second seat of the last row, which meant that he was ranked 26th in the last exam.

Behind him is Chen Ang, who ranked 27th in the last test.

After putting their schoolbags on the podium, they chatted for a while before the teacher handed out papers.

Chen Ang pointed to the first column and asked: "Old Lin, are you going to rush into the sequence of gods this time?"

The first column in the examination room is what they call the God Sequence, that is, the top six in the grade are regarded as the Gods of Study. Of course, at the end of each exam, the top six will change, and the competition is still relatively fierce, that is, One or two of the few can stay at the top.

Lin Xiao rolled his eyes: "Ah, yes, yes, how do you know."

Chen Ang: "Look at your state for more than half a month, even Jiang Jie can't imitate you."

"You're in your senior year of high school. If you don't work hard, will you work on a construction site in the future?"

"You are quite aware."

"No more, the exam is coming soon." Lin Xiao waved his hand, too lazy to say more to him.

Chen Ang prayed: "Don't try "Pipa Xing" when writing ancient poems silently."

The mock exam is naturally simulated in the form of the college entrance examination. The first Chinese test lasts two and a half hours.

Lin Xiao had no way to deal with this. The linguistic system didn't recognize it.

So he could only write honestly based on what he had learned before.

However, when I was writing ancient poems silently, I accidentally came across a line from "Pipa Xing": "The silver bottle is broken, the water slurries burst out, and the cavalry stands out with swords and guns." Lin Xiao can even hear Chen Ang's voice from behind. C language.

There's nothing much to say about Chinese, just use it normally for Lin Xiao.

Soon it was time for mathematics in the afternoon, which was the main meal for Lin Xiao.

After getting the test paper, he briefly browsed through all the questions. In the past half month, he had basically learned all the knowledge points of high school mathematics by heart, and quickly came to a conclusion.

150 points, stable.

He couldn't find any question that made him lose his way.

Whether it's the big questions at the end, or the next few difficult questions where you choose to fill in the blanks.

Then, he began to write.

As he wrote, he even found that he had not entered that immersive state.

This is probably because his brain is too lazy to concentrate on thinking about this kind of problem.

Because whether he has entered the immersive state or not, the speed of solving this problem is the same, just like playing Minesweeper with a GTX1080TI, the fan does not even turn.

So just like that, he almost finished all the questions by blocking functions and geometry.

After finishing writing, he looked at the clock hanging in the classroom. Good guy, it was only an hour later, which meant that he finished the paper an hour early.

In the past, he definitely couldn't do this.

This made him feel a kind of blissful helplessness, because the examination room only allowed submission of papers half an hour in advance. If he finished writing an hour in advance, he would have to wait for half an hour.

I turned around and looked at the people around me. Well, they were all still working hard.

He shook his head, simply picked up the scratch paper, wrote down the Taylor mean theorem that he had just learned some time ago, and began to try to deduce the proof method of this theorem.

Taylor's mean value theorem is one of the basic theorems in differential calculus and plays an important role in the mean value theorem of differential calculus.

The best way to understand a theorem is to learn how to prove it.

Therefore, Lin Xiao is now trying to prove it using every method he can think of.

As for what method to use?

He fell into thinking. His knowledge reserve was limited to high school and junior high school, and he didn't have many proof tools at his disposal. And he didn't want to use the methods he knew before to prove, such as using Cauchy's mean value theorem or L'Hôpital's rule, etc. .

After all, this is like a free time challenge for him, and he has to make his own way.

It's probably like walking on the sidewalk, looking at the bricks below, and challenging yourself not to step on the white bricks.

Not for anything else, just to feel happy.

Ever since, writing the test paper did not put him into an immersive state, but now he fell into it because of thinking about this problem.

Not long after, his eyes suddenly lit up and he found an idea.

That is to use mathematical induction, which is also one of several proof methods he mastered in high school.

Once you have an idea, start writing.

He quickly turned over the draft paper, and this side was blank.

In fact, after finishing the paper, he didn't use much of the first side of the scratch paper because he solved the answers directly on the answer sheet. Some questions relied on mental arithmetic. If there were too many calculations, he would use the scratch paper. .

Without saying much, he started writing from the top.

[Taylor's mean value theorem: If the function f(x) has a derivative up to order (n+1) in an open interval (a, b) containing x, then when x is in (a, b), f(x) It can be expressed as the sum of an n-degree polynomial of (x -x) and a remainder R(x): f (x)= f(x0)+ f′(x0)(x-x0)+……]

[Lemma 1: f(x) is differentiable on [a, b], and f ′(x)≥0, then f(x)≥f(a), x∈[a, b].

Proof: Since f′(x)≥0, so...

Let g(x)……

Construct function h(x)……

Prove n using mathematical induction:

If n=0, it is obviously true;

...]

Proving such a problem for the first time is also a challenge for Lin Xiao, but this cannot stop him from thinking quickly enough.

In this way, he kept writing, recalling in his mind the advanced mathematics knowledge he had recently learned, as well as the knowledge that could be used in high school mathematics.

In addition to increasing his learning efficiency, the system also improved his memory. Although he could not forget everything he had ever seen, he would not forget the knowledge he had learned so easily.

Those mathematical knowledge are like abstract concepts. You don't need to remember the detailed text, you only need to remember what it says in general, and then, when you use it, you can directly associate it with the relevant knowledge.

Time passed slowly, and from the outside, Lin Xiao looked like other students, immersed in math papers.

An invigilator suddenly came down from the podium and began to inspect.

The invigilator's name is Ding Ping, a mathematics teacher. He is also the teacher who trains Jiang Jie's students who participated in the mathematics league.

As a national special teacher, his attainments in mathematics are quite high. At least for high school mathematics, he is basically completely knowledgeable.