Chapter 14 Chapter 14 Agreement, Problem Solving
"You are actually already reading advanced mathematics!" Huang Minglei exclaimed in surprise, looking at the book on Lin Yimu's desk.
Lin Yimu paused while flipping through the book, looked up at Huang Minglei who had not returned to his seat, and asked in confusion, "Any questions?"
Huang Minglei saw Lin Yimu's puzzled look, reached out and pointed at the advanced mathematics on his desk and said, "You are already studying advanced mathematics. Don't tell me you have already mastered all the knowledge in the textbook? It's only been less than a month since the start of school. You have only been enrolled for a short time, right?"
After hearing this, Lin Yi Mu suddenly understood what the other party was surprised about, so he said with a shy smile on his face: "You are right, but it's because my previous grades were too bad, and now I basically never put down my books, so I have the grades you see and hear now. But without the exam, I'm not sure if I can get good grades." As he said this, Lin Yi Mu also sighed.
"That's amazing, isn't it? You've only studied for a week, right? And now you've already seen advanced mathematics. Also, I heard your chemistry and physics teachers praising you. You are also very strong in these two subjects. I'm sure you will have no problem. I'll just wait for you to join the class after the monthly exam." Huang Minglei said with some admiration.
Lin Yimu looked at the book in his hand and checked the calculations on the draft paper, and said with a smile: "Thank you, please give me more guidance in the training class in the next month."
Huang Minglei saw how hard Lin Yimu was studying, and he couldn't help but feel admiration and unwillingness to admit defeat. He wanted to compare himself with Lin Yimu, so he said seriously, "Lin Yimu, how about we compete?"
Upon hearing this, Lin Yimu stopped his calculations and asked curiously, "What do you want to compare? How do you compare?"
Huang Minglei's eyes were full of excitement and a desire to challenge. He said, "Let's compete in the IMO competition. Whoever wins the gold medal will treat the other person to a meal, or agree to a reasonable request from the other person. How about that?"
After hearing this, Lin Yimu thought for a while and said, "Okay, but before that we have to join the national team. Also, the monthly exam will be in a few days, so don't let me suppress you." Lin Yimu stretched out his right hand and held Huang Minglei's right hand.
"Then I'll wait and see. I still hope that someone can surpass me. That means there are people who can improve and communicate with me, which is what I've always been looking forward to."
The two men loosened their hands, and their expressions showed appreciation for each other, a hint of confidence, and eagerness to try.
Lin Yimu didn't expect that he would meet several people with different personalities as soon as he arrived at the training class, and he also met friends with whom he could communicate, learn, and even encourage each other to make progress. This made Lin Yimu very excited, and even his mind became clearer because of the excitement.
When the bell for evening self-study rang, the math teacher of Grade 11 Class 1 walked into the classroom. He immediately saw Lin Yimu sitting in the back row concentrating on writing something, so he coughed slightly, walked up to the podium and said, "There's a new student in our training class today?"
As soon as the teacher finished speaking, several students in the class turned to look at Lin Yimu, and Lin Yimu also raised his head from the pile of books and looked at the podium, and found that the person who came in was Zhou Shaoyuan, the mathematics teacher of Class 1 and also the head teacher of the first grade.
Zhou Shaoyuan said with a smile on his face: "Student in the back row, don't sit in the back row, sit in the front rows, everyone should sit in the first three rows in the middle." As he said this, he pointed at Lin Yimu and the students in front of him.
Hearing this, Lin Yimu blushed a little as he packed his schoolbag, looked at the seats in the front rows, and quickly walked to the seat behind Huang Minglei and sat down.
After several people adjusted their seats, the math teacher began to talk about previous years' Olympiad questions with a serious look. After explaining several common Olympiad question types, Teacher Zhou saw that everyone was eager to try and understood, so he wrote a real question from last year's competition finals on the blackboard for everyone to solve.
Lin Yimu looked at the test question written by the teacher on the blackboard. It was a question about proving a function. The question was: Given the function f(x) = a \sin x - \cos 2x + a - \frac{3}{2}, where a \in \mathbb{R} and a \neq 0.
(1) If for any x \in \mathbb{R}, f(x) \leq 0, find the range of values of a.
(2) If a \geq 2, and there exists x \in \mathbb{R} such that f(x) \leq 0, find the range of values of a.
Lin Yimu frowned and looked at the question on the blackboard and pondered for a long time before he began to write down the verification and proof process on the draft paper.
The other dozen or so students in the class also started to concentrate on doing the questions, but as time passed, those who were originally eager to try now buried their heads and remained silent.
It was not until Lin Yimu figured out the entire verification process and looked around that he realized that except for Huang Minglei who was sitting in the row in front of him, everyone was still leaning over the table writing and drawing. It seemed that no one had figured it out yet.
Huang Minglei, who was sitting in front of him, seemed to have eyes on his back. He suddenly turned around and whispered, "Have you solved this problem? How do you feel?"
Lin Yimu also whispered: "I'm not as fast as you, but I've finished it. I feel it's okay and within my learning range. When did you finish it?" Lin Yimu was curious about Huang Minglei's speed in solving problems.
"Just a few minutes earlier than you."
As soon as Huang Minglei finished speaking, Teacher Zhou, who was sitting on the podium, coughed twice and said, "Students who have finished, please pay attention to classroom discipline and don't whisper to each other. Students who haven't finished, I'll give you another half an hour. I'll find students to solve this problem later."
After the teacher finished speaking, he glanced in the direction of Lin Yimu and Huang Minglei, obviously seeing their little movements.
Lin Yimu and Huang Minglei quickly stopped talking and started reading the book on the table. The other students who were originally concentrating on checking their calculations, upon hearing this, knew that someone had already done it, and their hands began to write even faster, but no one was distracted and looked around.
There were only a dozen or so people in the training class. Since the seniors in their third year of high school had to prepare for the college entrance examination, they basically would not attend, so the class was populated by students in their first and second years of high school. They were all good math students recommended by teachers from various classes, but some of them were at a loss when faced with the questions on the blackboard.
It was not until half an hour later that Teacher Zhou knocked on the blackboard and everyone stopped writing. They lowered their heads in shame and did not dare to look at the podium.
Teacher Zhou looked at the students who didn't dare to look up at the podium, and said with some regret: "Look at you, you were so eager to try just now, and now I've written you a question that changes form but doesn't change spirit, and you can't do it? Are there any students who want to come up and solve this problem?"
No student dared to say a word below the podium, and each of them wished that the teacher could not see them at this moment.
Teacher Zhou, who hadn't seen any students raise their hands for a long time, slowly turned his eyes to Lin Yimu and Huang Minglei who had just spoken, and directly called on them: "Lin Yimu, Huang Minglei, you two come up and solve this problem using your own ideas."
As soon as Teacher Zhou finished speaking, the class, which had been relatively quiet, suddenly became buzzing with discussion.
"Teacher Zhou actually asked Lin Yimu to come up and do the exercises! Do you think his math is really as good as the teacher said?"
"If he wasn't good, the teacher wouldn't have let him go up to do the questions!"
"Is there going to be another great player coming to our training class? It's bad enough that I was beaten by Huang Minglei, but now there's another person coming to beat me."
"Let's see how he solves the problem first. The teacher uses this to criticize me every day. I'm almost depressed."
On the podium, Lin Yimu and Huang Minglei stood on each side and began to write down the problem-solving process and ideas.
(1) If for any x \in \mathbb{R}, f(x) \leq 0, find the range of values of a.
First, we analyze the function f(x) = a \sin x - \cos 2x + a - \frac{3}{2}.
We know that... So a \leq \frac{1}{4} contradicts a \geq 2, so there is no a that satisfies the conditions.
Lin Yimu proudly wrote down his solution and answer on the blackboard, put down the chalk and walked down from the podium.
Huang Minglei finished solving the problem almost at the same time as him, and the two of them walked down the podium one after the other.
The students in the audience were already confused by the problem-solving process written by the two people.
What on earth is this written about?
What on earth did we see?
They could understand the problem-solving process at the beginning, but they were completely confused in the middle and couldn't understand what the two people were writing at all.
Some high school sophomores who had learned functions could barely follow the train of thought and picked up their pens to check the calculations together, but those freshmen who had just entered the first year of high school could only stare at the blackboard numbly with confusion in their heads.
Until the last two people finished writing down the steps to solve the problem, except for some students who had been exposed to the Olympiad since childhood, everyone else had stopped checking the calculations with their pens and could only look forward to the teacher's explanation.
At the same time, everyone became curious about Lin Yimu.
They have been in this training class with Huang Minglei for almost a month and have fully understood his academic genius attributes and are no longer surprised by it, but what about this new student? His mathematical ability is comparable to Huang Minglei. He doesn't look like a poor student at all. He is simply another academic genius.
While everyone was muttering to themselves, they did not forget the calculations they were doing. Although they already understood the solution and the formulas used, they were still a little overwhelmed.
Teacher Zhou stood by and watched the two people solving the problem from beginning to end, and couldn't help but nod repeatedly.
After the two returned to their seats, he nodded with satisfaction and said, "Not bad, not bad. Both students' ideas for solving the problem are very clear. Although the processes are different, they are both correct. Especially Lin Yimu's solution process, which is simpler and easier to understand."
"Everyone, come to the blackboard! It's okay if you can't solve the problem, but you have to understand the idea of solving the problem. Now I will explain the problem to you!"
Teacher Zhou looked at the students who had not finished the questions and looked listless. After comforting them, he began to talk about their problem-solving ideas and the formulas they used, but he sighed helplessly in his heart.
In fact, many high schools in Yancheng City have interest classes, such as Japanese, Russian, French, and Spanish. Everyone can sign up according to their interests, and they will get corresponding extra points in the college entrance examination. Competition training classes are actually a kind of interest class, but many people do not know how to enter the competition.
The competition training classes include not only Olympiad training classes, but also physics and chemistry competition training classes, all of which are located on this floor of the teaching building. Students who want to sign up must not only be top-notch in the corresponding subjects, but also have spare time to learn. In addition to participating in the competition training, they must also be able to cope with the school's various monthly exams and midterm and final exams. If they fail in any of these two items, they will be advised to return to the class. Many parents do not understand the so-called competition. They just want their children to study hard, get into a good university and find a good job after graduation. So even though there are more than a dozen students in the training classes now, there still has to be a round of elimination to determine the final participants in the competition.
After all, if you can't even solve the high school competition questions, you may not even be able to pass the qualifying round. In that case, it would be better to shift your focus away from the competition as soon as possible, study hard in school to lay a solid foundation, and pass the college entrance examination to get into a good university in the future.
However, there was something that made him happy tonight, and that was Lin Yimu and Huang Minglei. Their mathematical talents gave Zhou Shaoyuan a glimmer of hope. Perhaps Yancheng No. 1 High School could make it to the finals this year, or even the national competition.
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