Top student: All my teachers are academic whizzes!

Chapter 8: The Monthly Exam Agreement

After math class, Han Chuan arrived at the door of the Grade 11 office.

The office door was ajar; he knocked and went inside.

"Teacher Cao."

Han Chuan walked to the desk and greeted them.

Cao Wen had left before him and had just returned to his office. He was currently organizing a lesson plan.

Upon hearing Han Chuan's voice, he then pointed to an empty chair on the table: "Sit down first."

Han Chuan sat down, subconsciously straightening his back.

This wasn't something done intentionally; it was a natural bodily reaction—the natural physical response of a high school student when facing a teacher.

Cao Wen didn't rush to speak. He picked up the enamel mug on the table, blew on the tea leaves floating on top, took a sip, and then turned his gaze back to Han Chuan.

Do you remember what score you got on the last monthly exam?

Han Chuan: "67 points."

He remembered that the number wasn't a memory from before his rebirth, but rather the math test paper from his last monthly exam, which was currently in his desk drawer.

The test paper was covered with red crosses, and some blank spaces still held equations that I had only half-finished writing during the last exam.

Some are simply blank, with only a "solution".

With a score of 150 on the test, he was far from even passing.

Cao Wen tapped his fingers lightly twice on the table, then asked, "So, you want to start learning from junior high math again, gradually building up your foundation?"

"Um."

Han Chuan nodded, his response concise but his tone certain.

Cao Wen didn't reply immediately. He turned around and fiddled with the computer for a few moments, the screen light reflecting off his glasses, making it unclear what he was doing.

After a while, he turned around and looked at Han Chuan.

"I just retrieved your middle school entrance exam scores from the computer. Your math score was 106, which isn't top-tier, but it's still acceptable."

He paused, as if considering his words, his tone carrying a hint of confusion and doubt.

"This shows that you have a foundation in mathematics; at least junior high school math shouldn't be a problem for you."

The middle school entrance exam math paper has a full score of 120 points. Scoring 106 means you're not top-tier, but your basic knowledge is definitely not a problem.

But the fact that this student was catching up on junior high school material puzzled and intrigued him.

Unless the other person cheated on the high school entrance exam.

But that's not quite right either. He had just checked Han Chuan's math grades in his first year of high school. Although they weren't excellent, they weren't bad either, much better than they were now.

The decline in grades follows the same curve as that of a normal underachieving student; it is a gradual decline.

This downward trajectory doesn't seem like something someone who cheated to get high scores on the high school entrance exam would exhibit.

Hearing this, Han Chuan paused for a moment, unsure how to respond.

After all, he couldn't very well say that this was something from his past life. Before his rebirth, he had delivered food for over a decade and worked like a beast of burden for over a decade, so he had long forgotten all that knowledge.

After thinking for a moment, he said, "Teacher Cao, I don't know either. I don't know when I started to fall behind. Maybe it was in the third year of junior high, or maybe it was in the first year of senior high."

"By the time I realized it, I found that I could no longer understand many things, including my high school textbooks, much of which I could no longer comprehend."

"So I can only start learning from junior high school."

Upon hearing this, Cao Wen looked at him with some surprise and asked with interest, "What have you relearned?"

Many students realize their shortcomings at some point in high school, but the vast majority choose to avoid or ignore them.

Very few students are able to start from scratch and rebuild their foundation bit by bit.

Moreover, for the vast majority of people, this resolve cannot be maintained for long.

Because rebuilding from scratch is easier said than done.

On the one hand, high school courses don't stop and wait for you. You have to keep up with the current pace while also having to relearn old knowledge from a few years ago. There isn't enough time, you can't keep up with the energy, and progress is slow. If you don't see obvious results in two or three days, most people will give up.

Very few people can actually stick to this.

But according to his observation, Han Chuan has persisted for almost ten days.

Han Chuan honestly replied, "A linear equation in two variables from the second semester of seventh grade."

Upon hearing this, Cao Wen's eyebrows twitched.

Han Chuan's score on the first-year middle school exam for a linear equation in two variables has dropped from 106 to this level, indicating that his current knowledge level may be worse than he anticipated.

But it also shows that this person was not trying to fool him.

After all, if Han Chuan just wanted to make a statement or establish a persona in front of him, he could have simply said that he had already studied up to the third year of junior high school, and it would have been difficult for him to verify it on the spot anyway.

After thinking about it, Cao Wen decided to test it out. He took out a blank sheet of paper from his desk drawer, wrote a math problem on it, and pushed it over.

"Take a look at this question."

After saying that, he handed over the pen he was holding.

Han Chuan took the pen and looked down at it.

This is a fill-in-the-blank question: [The interval representation of the set A{X²<4} is ().]

His gaze fell on the question, and the answer (−2, 2) immediately came to mind.

This question tests basic set operations, which is not difficult for him at present.

Just as he was about to write down the answer, he thought for a moment and then wrote down the solution process in a blank space next to him.

The inequality x²<4 can be transformed into |x|<2, and solving it yields -2

Therefore, the set can be represented by the open interval (−2, 2).

Cao Wen glanced at his solution and answer for a second, then wrote down another question: "How about this one?"

This question tests the domain of a function. It was a fill-in-the-blank question from the last monthly exam. He seemed to remember that Han Chuan had left it blank.

Han Chuan looked down at the question.

Find the domain of f(x) = √(x+1)/(x-2).

His mind started working—the denominator cannot be zero, so x-2≠0, that is, x≠2.

The expression under the square root must be greater than or equal to zero, so x+1≥0, that is, x≥-1. Taking the intersection of the two conditions, the result is [-1, 2)∪(2, +∞).

This is the most common and ordinary problem-solving approach.

After finishing writing, Han Chuan subconsciously thought for a moment whether there were other ways to solve the problem.

Thinking about it, he picked up his pen again.

函数定义域需同时满足：{x+1≥0；x-2≠0，解得x≥-1，且x≠2。

The intersection is represented by an interval: [−1, +∞)∩(−∞, 2)∩(2, +∞)=[−1, 2)∪(2, +∞), therefore, the domain is [-1, 2)∪(2, +∞).

Han Chuan casually wrote down the solution and answer in the blank space and pushed the paper back.

After glancing at the answer, Cao Wen looked at the two different problem-solving approaches with some surprise.

There are two solutions. The first is the standard intersection operation, which starts from the given conditions, solves the inequalities separately, and then takes the intersection.

This is a method he taught in class, and any student who listened attentively should be able to write it down.

But the second one is different.

In the second solution, Han Chuan reversed the entire thought process.

He first wrote down the numerical range corresponding to each constraint, and then used the intervals to find the intersection, turning the problem into a jigsaw puzzle.

But he never taught this method in class.

It's not because it's difficult, but because most students, when learning about the domain of a function, are still struggling with inequalities and never think of using an "interval perspective" to reverse-engineer the problem.

This requires students to have a holistic understanding of the relationships between sets, inequalities, and number lines in order to naturally realize this.

But Han Chuan wrote it down.

After glancing at the second solution, Cao Wen put the manuscript back on the table and lightly tapped the last line of the second solution with his finger.

"How did you come up with this solution?"

Han Chuan was stunned for a moment.

When he wrote the second solution, he wasn't actually thinking too much about it.

I just thought, "It seems like this is a valid way to calculate it," and wrote it down on a whim.

It's like walking down one road for too long and suddenly discovering a side road. Without thinking too much, your feet will automatically turn to that side.

"It's about breaking down the conditions, treating them like number lines, and then piecing them together."

After a slight pause, Han Chuan added, "I feel... this is more intuitive."

Cao Wen didn't speak immediately. He looked at Han Chuan with a deep scrutiny in his eyes, as if confirming something.

After a while, he finally spoke and asked, "Did you come up with this yourself?"

Han Chuan hesitated for a moment.

This habit actually came from Ge Jun, who guided him.

From the moment the book spirit was accidentally summoned, Ge Jun instructed him to learn the "Three-in-One Thinking Method".

The so-called "three-in-one thinking method" refers to three concepts: multiple solutions to one problem, multiple problems to one solution, and multiple problems to one problem.

Ge Jun has never advocated the "sea of ​​questions" approach; he prefers a better learning method that involves thoroughly understanding and solving a single problem.

Over time, this habit has formed a subconscious prototype in his mind.

But this doesn't mean that this problem-solving method was the learning approach that Ge Jun taught him.

I guess so.

Han Chuan gave a vague reply, saying that there wasn't much of a problem with saying it that way.

After all, although Ge Jun taught him the "three-in-one thinking method", the specific problem-solving approach was something he came up with himself.

Of course, the premise of coming up with this idea is that I saw the detailed mathematical structure through the cheat code, and then derived it based on that.

Cao Wen looked at him for a few seconds and didn't ask the question again.

Teaching mathematics is one thing, understanding it is another. In the same classroom with the same teacher, some people study for three years and only learn to copy the formulas, while others can grasp it in just one month. The difference lies not in who works harder, but in who "uses their brain to think."

Han Chuan's behavior just now clearly falls into the latter category.

He smiled, then refrained from posing any more questions. Instead, he asked, "If you're catching up on middle school material now, will you be able to keep up with the pace in class?"

Han Chuan shook his head and said, "I can't keep up with many things. For example, in solid geometry today, I could only think of translating auxiliary lines. I haven't caught up on the cosine theorem and the relationship between sides and angles from the junior high school textbook."

Cao Wen: "So you're thinking of first reviewing all the junior high school material, then going back to the first year of high school and catching up on each topic one by one?"

Han Chuan nodded and said, "Mm."

"So how much time do you spend studying junior high school math every day?"

After thinking for a moment, Han Chuan replied, "I'll study the junior high school textbooks during morning and evening self-study sessions, then do practice problems, and then study some more after returning to the dormitory."

"What time do you see?" Cao Wen seemed to notice something and immediately followed up with a question.

"Sometimes it's past midnight, sometimes it's one or two in the morning," Han Chuan replied honestly.

What should I do if I fall asleep in class the next day?

"It's okay for now, I guess I've gotten used to it."

It's not a habit, it's excitement.

Every time he finally understands a concept he couldn't grasp before, he feels a sense of clarity, as if the whole world has been illuminated.

After listening, Cao Wen neither praised him nor criticized him for not taking breaks. He simply continued, "All about math?"

"Um."

"So you're not going to care about your other subjects?"

"Currently, I'm mainly focusing on improving my math skills."

Han Chuan frankly stated, "Mathematics is the foundation of all science subjects. I plan to solidify my mathematical foundation first, and then allocate time to physics and chemistry."

Cao Wen smiled and looked at Han Chuan, asking, "Do you want to catch up?"

"certainly!"

"That's fine then."

Cao Wen nodded and continued, "From now on, you can come here to find me during evening self-study sessions every Monday, Wednesday, and Friday. I can explain to you the connection between what you are learning now and our current courses."

"You don't need to follow the class schedule; just follow your own pace in learning junior high math. If you don't understand anything, just ask."

Han Chuan raised his head and looked at Teacher Cao Wen.

Cao Wen held his enamel mug, his expression calm, as if what he had just said was just a trivial matter.

"It's not just for you."

Perhaps feeling a little embarrassed by Han Chuan's gaze, Cao Wen took a sip of tea and added casually.

"Your learning situation is also a kind of observation sample for me. If possible, I'll see if I can replicate your learning methods and progress on other students who are struggling to keep up."

He paused for a moment, then continued, "Also, this isn't free."

"There are still ten days until the next monthly exam. I don't expect you to get a high score, but you can't afford to lose points on the material I'm tutoring you on. Can you do that?"

"Thank you, Teacher Cao."

Han Chuan bowed deeply to express his gratitude.

He knew very well that if Cao Wen was only observing samples, there was absolutely no need to tutor him during evening self-study sessions every Monday, Wednesday, and Friday.

"Alright."

Cao Wen waved his hand: "Go back to class first. If you want to come find me during evening self-study on Mondays, Wednesdays, and Fridays, I'll usually be here."

"good!"

Han Chuan nodded: "I will try my best to keep up with the progress, Teacher Cao."

"Um."

As he reached the door, he heard Cao Wen say something behind him.

"Han Chuan".

He turned around.

Cao Wen didn't look at him, but was flipping through the lesson plan in his hand, speaking casually as if it were just a casual remark.

"You just said in class, 'I can't do it right now, but I can explain my thought process.' In my almost ten years of teaching, you are the second student to say that to me on your own initiative."

Han Chuan stood frozen at the doorway.

"And the first one?" he asked, almost as if possessed.

Cao Wen looked up at him and said, "The first one got into Peking University and is now pursuing his doctorate."

Upon hearing this, Han Chuan opened his mouth as if to say something, but nothing came out.

Peking University's first-year student?

Will he be able to pass the exam?

......