The Reincarnated Science Whiz

Chapter 12: National Competition

As the captain of the provincial team, Qin Yuanqing delivered another pep talk to encourage everyone. Many people are turned off by “inspirational fluff.” But at critical moments, such motivational speeches can often make a huge difference. “Friends, Shancheng University is now home to the nation’s top math students. The stage is set—are you ready?” Qin Yuanqing scanned the crowd. “We’re ready!” the crowd roared in unison. Sometimes, a long speech actually doesn’t do much good. As representatives of the provincial team, they were all the finest mathematical prodigies in Fujian Province this year; they carried a natural sense of pride within them. Once that pride was ignited, they would charge forward more fiercely than anyone else. Seeing this, the vice president couldn’t help but feel a sense of satisfaction. On November 15, a solemn atmosphere hung over the entire Mountain City University. Contestants, holding their ID cards and admission tickets, filed through one by one and, led by volunteers, made their way to the exam hall. No one was allowed to bring cell phones or any other electronic devices. Qin Yuanqing entered his exam room, found his seat, and sat down. He closed his eyes briefly to rest; with half an hour left before the exam, he couldn’t afford to waste that time—it was the perfect opportunity to get himself in the right frame of mind. At 8:58, the public address system announced the exam room rules and instructions for candidates. At the same time, the proctors distributed the exam papers. At exactly 9:00, the announcement declared the exam officially open. Qin Yuanqing began by filling in his name, admission ticket number, and ID number. He didn’t rush to answer the questions but instead quickly skimmed through the exam. After that, Qin Yuanqing began answering the questions. The multiple-choice questions were clearly a notch more difficult than those in the provincial competition; for each one, he had to lay out his steps as if it were an open-ended problem in order to arrive at the correct answer. Although each question covered material taught in high school, they could not be solved without applying deeper analysis and extension. After finishing the multiple-choice questions, Qin Yuanqing didn’t rush to the fill-in-the-blank section. Instead, he first transferred his answers to the answer sheet, checked them to ensure they were correct, and only then moved on to the fill-in-the-blank section. The fill-in-the-blank questions were actually considerably more difficult than the multiple-choice ones. After all, with multiple-choice questions, the four options are listed right there; if the answer you arrive at isn’t among them, you know it’s wrong, and you can check your steps to find the mistake. But with fill-in-the-blank questions, there’s no way to check your work. You simply write down whatever answer you come up with, with no way of knowing whether it’s right or wrong until the test is graded and the answers are released. If the test maker sets a trap, many students will fall into it and be unable to escape. This kind of situation is actually quite common; every year there’s at least one question designed to trick students, and students often fail to notice and end up with the wrong answer. After Qin Yuanqing filled in all the answers, he began working on the problem-solving questions. There were only three problem-solving questions, each worth 20 points. The first question was, as always, a function problem—though this one combined functions with geometry, requiring a graph and analysis to prove the solution. This was the easiest of all the open-ended questions; if a student couldn’t solve this one, there was no point in even thinking about the second or third questions. After finishing the first problem, Qin Yuanqing moved on to the second, which involved solving an inequality that combined logarithmic operations and powers. Qin Yuanqing found it interesting because it had two possible solutions, both of which drew on high school-level concepts. Sure enough, the High School Math League places the greatest emphasis on mathematical thinking! That said, it’s true that math relies on talent; those with exceptional talent, as long as their logical reasoning is sound, are unlikely to make mistakes in their solutions. A large number of college students have studied calculus, algebra, and other subjects in college, yet their proficiency still falls short of that of some high school math whizzes. After finishing the second problem, Qin Yuanqing moved on to the third, which combined functions and geometry to find the minimum area of an intersection. For problems like this, you have to draw a graph to visualize the functions; otherwise, relying solely on imagination makes it easy to make mistakes. Once Qin Yuanqing finished his graph, he worked through the problem step by step. If this had been half a month ago, he wouldn’t have been able to solve it, but now, while it was still challenging for him, the difficulty was manageable. When Qin Yuanqing finished the last question, there were still ten minutes left. Seeing that only one-third of the test-takers remained in the classroom, he was speechless. Could it be that students from other provinces were this skilled? However, he remembered that Yang Xin, a member of the Fujian Province team, was also in the same exam room—so why wasn’t he there anymore? However, Qin Yuanqing didn’t hand in his exam yet. Instead, he reviewed his answers, thought for a moment, and wrote an alternative solution for the first problem—one that utilized college-level knowledge and reduced the number of steps by a third. Just as Qin Yuanqing finished writing this solution, the bell signaling the end of the exam rang. The proctors had already instructed the test-takers to stop writing and began collecting the answer sheets. Qin Yuanqing left the exam room and went to the assembly area at the school gate, where he saw that the entire team from Fujian Province had gathered. Curious, he asked, “Yang Xin, why did you turn in your paper so early? I looked up for a moment and you were gone!” “Waaah~~” Yang Xin threw her arms around a girl standing next to her, Chen Xue, and burst into tears—she was so heartbroken. Qin Yuanqing was puzzled. What was going on? Was the exam that easy, and was Yang Xin just too excited and happy? But it couldn’t be that bad. “Captain, do you think everyone’s as crazy as you?” Chen Xue said irritably. “Yang Xin and I left after only half an hour. Who could possibly solve such difficult problems?” “Exactly. The questions were so hard this time. For the problem-solving section, I didn’t even finish any of the questions except for the first one.” “For the problem-solving section, I just wrote ‘solution.’ ” The others chimed in one after another, sounding dejected. Qin Yuanqing scratched his head in confusion. It couldn’t be that bad—the exam was challenging, but not that difficult. “Don’t be discouraged, everyone. This year’s league exam was significantly harder than in previous years. I spoke with the heads of other provinces, and we all agree this is the most difficult exam we’ve seen in recent years,” the vice president hurried to reassure them, then turned to Qin Yuanqing and asked, “Qin Yuanqing, how did you do on the exam?” “Not bad. I finished all the questions. For the first and second essay questions, I wrote out two different solution methods. I figure I should have no problem scoring around 140 points,” Qin Yuanqing replied honestly. “That’s insane!” “That’s way too harsh!” “It’s just not fair!” Hearing this, the other boys let out a chorus of sighs. They hadn’t been able to answer any of the questions, but Qin Yuanqing had not only solved them all but also provided two different methods for each—it was enough to drive anyone crazy. “140 points shouldn’t be a problem? Is that even human? They weren’t even sure they’d make the 90-point passing mark, yet Qin Yuanqing just casually said 140 points should be no problem. The girls, meanwhile, were crying even harder—they’d worked so hard, drowning in a sea of problems day after day, and now… The vice president was flustered, trying to comfort the students while feeling overjoyed inside—with such high scores, a first prize was a sure thing. After all, last year in Fujian Province, not a single student won a first prize in the National Math Competition. As for making it onto the National Team, not a single student did. As the vice president in charge of the competition, he had almost lost face among his peers. Unlike in previous years, there were some reforms to the competition this year: the National High School Math Competition finals would award up to twenty First Prizes—representing 1 percent of participants. There would be one hundred Second Prizes, with a 5 percent probability, and three hundred Third Prizes, with a 15 percent probability. Only winners of First, Second, or Third Prize are eligible to participate in the China Mathematical Olympiad (CMO). Winning a prize essentially guarantees a student a spot in college through their high school’s recommendation program; first-prize winners might even receive invitations from top “Double First-Class” universities such as Shuimu University, Yan Da University, and Fudan University. Furthermore, participants receive at least a 10-point bonus on their college entrance exam scores, and in some provinces, the bonus can be as high as 20 points. The vice president had no reason to doubt Qin Yuanqing’s words, as after spending half a month with him, he had come to know Qin Yuanqing well—he was the real deal! Moreover, Qin Yuanqing was indeed the strongest competitor on the Fujian Province team. If Qin Yuanqing really scored 140 points this time, he might even have a shot at making the National Team! However, the vice president didn’t ask any further questions. He took everyone out for a meal, then told them to get a good night’s rest—the supplementary exam in the afternoon was just as important. Qin Yuanqing didn’t study either; instead, he listened to some music to relax, and by 1:30 p. m. , he lay down to sleep. At exactly 3:00 p. m. , the supplementary exam began on time. Qin Yuanqing saw that the exam paper contained only three questions, but the answer sheet spanned six pages—an average of two pages per question. If he ran out of space, he could even ask the proctor for additional pages. At a glance, Qin Yuanqing saw that the difficulty of the first question was comparable to the second problem from that morning’s exam; clearly, this supplementary exam was even more challenging than the morning session. Qin Yuanqing completed the first and second questions smoothly, but he furrowed his brow at the third. It consisted of three sub-questions, each drawing on high school-level knowledge, yet requiring integration with calculus, algebra, and linear algebra. For example, the first sub-question involved Gauss’s Theorem; without a deep understanding of it, one could barely write down a solution and would be at a loss as to how to proceed. The second sub-question was closely related to the first and dealt with calculus. While calculus is taught in high school, its application there is very superficial; attempting to solve this problem with only high school-level math knowledge was simply a pipe dream. After finishing the second sub-question, Qin Yuanqing paused at the third sub-question, which was worth a full 30 points—more than the first and second sub-questions combined. After a brief moment of thought, Qin Yuanqing began his answer. For this single sub-question alone, he filled four pages—even more densely written than the previous ones—and managed to fit the answer into the very last line; otherwise, he would have had to add another page. At that moment, there was only one minute left until the end of the exam. He glanced around and realized he was the only one left in the entire classroom. Qin Yuanqing quickly checked his name, admission ticket, and ID card—everything was correct—and just then, the bell rang. “Way to go, kid!” The proctor collected Qin Yuanqing’s exam paper and gave him a thumbs-up. After everyone else had left the classroom, they had been standing behind Qin Yuanqing, watching him write down one formula after another. To them, it was like reading a foreign language—they couldn’t make heads or tails of it, and some of the mathematical symbols were completely unfamiliar to them. They didn’t know if Qin Yuanqing’s answers were correct, but they couldn’t help but feel a sense of awe.