pjbooks Chapter 9: A First Test
Chapter 9: A First Test
After the bell rang for evening self-study, the classroom of Class 09 in the second year of high school did not empty out as quickly as usual.
The reason is simple—Li Hao is standing by the podium, holding a CD carefully wrapped in a plastic sleeve, and shouting loudly.
"Brothers, come on over, don't go! Today I'm going to show you a historic moment!"
As he spoke, he waved the CD in his hand, its plastic sleeve gleaming under the fluorescent light.
The dozen or so students who hadn't left the classroom all turned their attention to this.
The girls sitting in the front row frowned and turned their heads away, but they didn't leave. They just lowered their heads and pretended to be doing their homework, occasionally stealing glances out of curiosity.
"Li Hao, what's gotten into you again?"
Zhou Yu, sitting in the third row, leaned out halfway, looking on with an expression of watching the excitement.
"I'm not going crazy, I'm just fulfilling my bet!"
Li Hao slammed the CD on the podium, his voice rising even louder: "Ten days ago, I made a bet with Han Chuan—if he could stick to studying diligently for ten days, this treasured item would be his!"
"Ten days have passed! Today is the day to check the results!"
His words immediately made the classroom lively.
The students gradually gathered around, forming a small circle. Some leaned over the desks, while others simply straddled the desks next to them.
High school life is boring for most students, but if there is anything funny, it can attract a crowd of onlookers.
Li Hao's shouting quickly attracted the interest of many people, and everyone started discussing it.
"A bet? What bet!"
"Li Hao, what are you betting on?"
"A treasured possession? Holy crap, whose is this?!"
"What kind of bet did you make?"
In the back row of the classroom, Han Chuan looked up at Li Hao with a bewildered expression.
"What the hell? Is this what they're betting on?"
Li Hao looked over and said with a grin, "Of course, I definitely won't let you suffer a loss!"
"I've been thinking about it these past few days, and a week's worth of breakfasts is way better than three days without my phone, so I'm going to hold onto this disc!"
Han Chuan's lips twitched, a mixture of amusement and exasperation on his face.
"No, what would I need your disc for!"
Li Hao patted him on the shoulder and grinned slyly, "I get it! I get it all too well!"
After saying that, he turned to the other classmates who had gathered around him and said loudly, "Fellow villagers!"
"Ten days ago, I made a bet with Han Chuan—if he could stick to studying hard for ten days, I would forbid him from using his phone for three days and he could have this collector's edition of the latest Yoshizawa Akiho anime!"
"If he fails to do that, he'll ask Ang Lee to bring me ten days' worth of deluxe breakfasts!"
"Now it's time for you upright officials to make your judgment!"
"Has Han Chuan actually studied diligently these past ten days?!"
Upon hearing this, the students watching nearby immediately became excited.
"Holy crap? Akiho Yoshizawa's latest anime?"
"I'm voting for Brother Chuan! We absolutely have to get our hands on this and take a good look at it!"
Li Hao, with his sharp ears, immediately caught the remark and pointed at his nose, shouting, "Wait, buddy, what's going on? Are you a referee or a cheerleader? What's your stance?"
"I call this being fair and objective."
The boy who spoke retorted with a grin, then said righteously, "Besides, Han Chuan has indeed been reading for the past ten days, it's not like I didn't see it."
"Go away, go away, stop causing trouble!"
Li Hao waved his hand and looked at the other classmates: "How about we cast a vote?"
Upon hearing this, the surrounding students started discussing it animatedly.
"I'm voting for Trump. He does seem to have been studying seriously lately."
"Indeed, putting everything else aside, Han Chuan really comes to morning self-study now, and he sits down and reads as soon as he arrives."
"Every night after the lights are out, he would turn on a flashlight and snuggle under the covers to read, but I don't know if he was reading novels or actually reading books."
As soon as he said that, the surrounding classmates burst into laughter.
At this moment, Jiang Wei, the top student sitting in the front row, looked over with interest and said, "Your bet is a bit unclear."
Upon hearing this, Li Hao looked over and asked blankly, "Why isn't it clear?"
Jiang Wei pushed up his glasses and continued, "It seems there's no standard for judging this bet. Studying diligently for ten days is a difficult and ambiguous thing to assess."
"If Han Chuan says he studied diligently for ten days, and you say he didn't, then an argument will break out, and neither of you can convince the other."
Hearing this, Li Hao asked blankly, "That seems to be true. So what do you suggest we do?"
Jiang Wei: "Simply put, learning is one thing, but how much knowledge you actually acquire is the key! Doing a few problems will tell you whether you've been studying seriously."
After a pause, he continued, "To be fair, the scope of the questions will be based on what Han Chuan has been reading these past few days, but the questions will be set by Li Hao, so there won't be any problems."
"how?"
The suggestion immediately sparked a discussion among the students nearby.
"This is good!"
"Indeed, if I were just reading and spacing out, I could do it for ten days straight!"
"That's bullshit. You'll fall asleep after watching it for ten minutes straight, even if you watch it for ten days straight."
Although it was a discussion, everyone's attention was focused on Li Hao and Han Chuan, since they were the two who made the bet.
Han Chuan smiled and nodded, saying, "That's fine too."
If the test covers all the knowledge points from the entire high school curriculum, he'd be a little worried. But if it only tests the knowledge points he's studied during this period, he's guaranteed to win!
Beside him, Li Hao looked at Han Chuan, crossed his arms, and said with absolute certainty, "This is much harder than studying diligently for ten days. Are you sure?"
Han Chuan smiled and said, "I'll make you admit defeat."
"Okay, okay!"
Li Hao shoved a pen into Han Chuan's hand, a confident smile on his face: "Come on! Let's pick ten questions. I'll allow you to get three wrong, buddy! No problem, right?"
Han Chuan: "Okay."
......
Although Li Hao was also a poor student and couldn't even set questions.
However, with the help of other enthusiastic classmates, it was still possible to find ten questions from extracurricular tutoring books.
Looking at the title written on the blank draft paper, Han Chuan unfolded it and spread it out on his desk.
Multiple choice question 1: Given sets A = {x | x² < 4} and B = {x | x > 0}, then A ∩ B equals ( ).
A.{x|0 His gaze lingered on the question for two seconds. Then I picked up a pen and drew a checkmark under option B. "Wait a moment!" Seeing that Han Chuan answered the first question correctly so quickly, Li Hao immediately stopped him, saying, "You can't just choose the answer; you have to explain why. If you answer incorrectly, it's considered a guess!" "Indeed, you can guess the right answer on multiple-choice questions." Several classmates nearby nodded in agreement. This request was reasonable—it was a multiple-choice question; guessing correctly was always an option. Don't you see how, during exams, they write down A, B, C, and D on a piece of paper, crumple it up, throw in the dice, and if they're lucky, they can guess several questions correctly? Han Chuan glanced at him, smiled, and said, "Alright, then I'll make you admit defeat wholeheartedly!" He paused for a moment, looked at the question on the paper, and then said, "This question is very simple. You can see at a glance that A is an open interval from -2 to 2, and B is from 0 to positive infinity." "Then the intersection of A and B is the open interval between 0 and 2." As he spoke, he pointed to option B: "This is it." Upon hearing this, Li Hao paused for a moment and looked at Han Chuan with suspicion. Is this person progressing that fast? Han Chuan scored 67 points in the last monthly exam, while he scored 69 points, placing them at the same level. However, he himself couldn't solve this problem. He gritted his teeth and continued, "One question is nothing, there are still nine!" Upon hearing this, Han Chuan glanced at him, smiled, and quickly wrote down the answer to the second question. Given sets A = {x | x² - 3x + 2 = 0, x ∈ R} and B = {x | 0 < x < 5, x ∈ N}, the number of sets C that satisfy the condition A ⊆ C ⊆ B is _____. A: 1, B: 2, C: 3, D: 4. Correct answer: D. After writing down the answer, Han Chuan looked up at Li Hao and said with a smile, "This question is also very simple; it's just solving a quadratic equation." "We need to find {x|x²-3x+2=0, x∈R}={1,2}, and B={x|0＜x＜5, x∈N} can be seen at a glance as {1,2,3,4}. Since A⊆C⊆B, according to the definition of a subset, set C must contain elements 1 and 2, and may contain elements 3 and 4." "According to the problem, we need to find a subset of the set {3, 4}, which means 2² equals 4, or four subsets." At this point, Han Chuan paused, looked at Li Hao, and smiled, "Any more questions?" The classroom was quiet. The boys who had been making a ruckus just moments before exchanged glances, unsure of what to say. At this moment, many people stared at Han Chuan with a strange look in their eyes. The first question wasn't difficult; most of them could answer it. But the second question was more challenging, and even if they could solve it, it would take some time. But Han Chuan, who only scored 67 points in the last monthly exam, solved the problem almost without thinking and was able to explain his solution to them so clearly and methodically. The smile on Li Hao's face had vanished, replaced by a complex emotion in his eyes—the expression of someone who, after two years of being classmates, suddenly doesn't recognize the person next to them. "Go on to the third question. You've probably already seen the first two. I don't believe you can understand all the concepts in ten days!" After a moment of silence, Li Hao spoke stubbornly, his lips pressed into a thin line. At this point, it's no longer a matter of betting. Instead, he didn't believe it. He didn't believe that his former deskmate, who was also a poor student, could surpass him by far after studying diligently for ten days! This is impossible! Han Chuan smiled, drew a horizontal line under option C for the third question, and continued his explanation. "The answer to this question is C. The even roots of negative numbers are undefined in the real number domain, so the converse of option C is not true." "The answer to question 4 is A. It tests the inclusion relationship of sets. The empty set is a subset of any set." "The answer to question 5 is D. It tests the properties of inequalities; when both sides are multiplied by a negative number, the inequality sign changes direction." "Question 6..." Han Chuan continued working through the exercises one after another, his pen lightly gliding across the options on the workbook, each stroke clean and crisp. Without hesitation, without corrections, and without even making a draft, they directly circled or wrote down the answers. Then came a clean, concise, and to-the-point explanation. The students around him had fallen silent. Li Hao stood next to Han Chuan, looking down at the questions in his training book, his lips pressed into a thin line. His facial expression changed slowly, first with confusion, then disbelief, and finally something indescribable. "Han Chuan, could you explain question seven to me again?" In the quiet classroom, Jiang Wei, sitting in the front row, suddenly spoke up and asked, "I don't quite understand this question. Why is the answer B?" Upon hearing the question, the other students gathered nearby looked at Jiang Wei with some surprise, and at Han Chuan with some confusion and astonishment. Although Class 09 is an ordinary class and most of the students have average grades, it doesn't mean there aren't any students with good grades. Jiang Wei is one of the few students who gets good grades; he scored 127 in math on the last monthly exam. Although this score wouldn't be considered anything special in the top class, it would place him in the top five in Class 09, an ordinary class. Even he couldn't figure it out, but Han Chuan, this poor student, solved it effortlessly? "The seventh question?" At the desk, Han Chuan glanced at Jiang Wei, then looked down at the training book, and then explained. This question tests the monotonicity of functions. The question provides the graph of a quadratic function and asks you to determine its monotonicity on a certain interval. This kind of problem was like a foreign language to him ten days ago, but after ten days of relentless intensive training from Ge Jun, he was able to solve quadratic functions. Pointing the pen tip in his right hand to the function graph in the question, he explained, "The key to this question is the direction of the opening." "Note this: if the opening is upward, the left side of the axis of symmetry is monotonically decreasing, and the right side is monotonically increasing." As he spoke, Han Chuan casually drew an auxiliary line on the paper and continued: "The interval given in the question stem is to the right of the axis of symmetry, which is x=2. That is, the interval starts from 2 and goes to the right." "So to the right of the axis of symmetry, the parabola keeps going upwards. It reaches its minimum value at x=2, and then increases all the way up to x=4." "Therefore, the function is monotonically increasing over the entire interval [2, 4]." Therefore, it is monotonically increasing, so the answer is B. Standing to the side, Jiang Wei pushed up her glasses, frowned and pondered for a while, then pointed to the vertex of the auxiliary line that Han Chuan had drawn on the manuscript paper. "What if the interval is [0, 4]?" "That means reducing first and then increasing." Han Chuan continued almost without pausing: "It decreases from 0 to 2 and increases from 2 to 4. The monotonicity of a quadratic function is opposite on both sides of the axis of symmetry, which is determined by the derivative—by its increasing and decreasing pattern." Upon hearing this, Jiang Wei's eyes lit up, as if she had finally understood, and she spoke with a tone of realization. "I see! No wonder I never understood it." As soon as he finished speaking, the students around him finally came to their senses and started making a fuss. "Holy crap, Han Chuan, when did you become so amazing? You were able to explain a problem that even Jiang Shen couldn't figure out." "Yeah, didn't you say before that you were reviewing middle school math to improve your basics?" "Clap! Clap!" .....