I really just want to be a scholar

Chapter 273 Qin Kezhi Ning Qingyun's New High School Olympic Mathematical Thinking Theory System
The brown-haired invigilator looked at the time. It had been 4 hours since the exam started, and there were less than 55 minutes left. It would be good to finish one question in such a short time.

At this time, another candidate held up a sign asking for help, and the brown-haired invigilator was not interested in seeing Qin Ke's situation anymore, so he walked away quickly.

Liang Shaoping saw Qin Ke start to answer the questions from a distance, he was relieved immediately, and inexplicably motivated to do the questions.

Hold on, hold on!

Teacher Qin doesn't hand in the paper, and I will never hand in the paper either!

Qin Ke didn't pay any attention to the movement of the outside world, he didn't even pay attention to whether other people handed in the paper.

His pen tip scratched the numbers and mathematical symbols one by one on the paper at a rhythmic and uniform speed, and the lines of correct handwriting were extended to form a complete problem-solving step.

If the brown-haired invigilator is still there, he will be surprised to find that Qin Ke used a total of five methods for the first question, and none of the solutions exceeds ten lines!
This question stumped most of the candidates. In the eyes of Qin Ke, who created his own Olympiad theory at this time, it was like dough that could be kneaded at will, or like a peeled banana. There was no secret at all. , You can eat whatever you want. (Originally I wanted to use the common "what" without wearing "what", but after thinking about it, it is too easy to be 404. Dear readers, please replace this metaphor in your heart)

However, in about 8 minutes, Qin Ke completed the five solutions to the first question, each of which is a completely different way of solving the problem. Among them, there are not only the thinking that applies the Lagrange median value theorem, but also Leib's solution. The connotation of Nietzs formula is all the way of thinking in college mathematics, but all the knowledge points of high school mathematics are used.

He is like a superb chef, using the simplest ingredients to cook the most delicious and gorgeous top-level meals.

After finishing the first big question, Qin Ke went on to the second, third, fourth, and fifth questions without stopping...

The following questions were both difficult and easy, but Qin Ke took the "master key" in his hand and played them into 10 shapes with ease. In less than [-] minutes, Qin Ke had finished writing the answer sheet and put it down. Pen.

Uh... I'm a little embarrassed, although five solutions are used for each question, but because the steps do not exceed ten lines, one answer sheet is all written.

The teacher asked for two extra answer sheets in vain.

Qin Ke checked it again, and there was nothing wrong with it. Looking at the time, it was almost time to hand in the papers, so he simply didn't raise a sign to trouble the invigilator to collect the papers in advance.

As he ate the biscuit, he pondered a very important question.

——What is the name of my own original Olympiad theory system?
……

In the end, when the bell rang at the end of the exam, Qin Ke thought of the most satisfying name.

He decided to refer to Beethoven's approach and named his theory "Zhi Ning Qingyun". Of course, the official name is "Qin Kezhi Ning Qingyun's new high school Olympic mathematical thinking theory system".

This set of theories is scientific, concise, and easy to understand. It is better and more advanced than what he taught to the Olympiad training team before. It can improve high school students' interest in learning Olympiad and problem-solving skills to a considerable extent. To grasp its essence, one must at least have a talent in science of Ning Qingyun's level.

"It seems necessary to have another crash course tonight." Qin Ke was thinking, when the paper-collecting teacher came, Qin Ke picked up his stationery and ID, and let the paper-collecting teacher put away the rest of the test papers and answer sheets seal.

Sometimes fate is a very strange thing, and the person who came to collect Qin Ke's papers happened to be the brown-haired invigilator.

The first thing he saw were Qin Ke's two unwritten blank answer sheets, and he said "ah" in his heart, but the blank answer sheets had to be taken away as well. It was Qin Ke's first answer sheet.

It is densely packed with answers.

After a rough look, all five questions were answered, but I didn't know whether it was correct or not.

Um? proof one? proof two...proof five?What the hell is this?Five different methods of proof?

real or fake?But each method of proof is too short, right?There are no more than ten lines!
The brown-haired invigilator looked at the calm Qin Ke in surprise and doubt, and couldn't help but glance at the name column on the answer sheet, where it was written in Chinese and English: "Qin Ke Qin Ke".

He silently memorized the name, and then sealed Qin Ke's paper.

……

"Teacher Qin!" Liang Shaoping chased after Qin Ke, and asked curiously, "Why did you answer the questions in the last hour? Have you finished all the work?"

"It's done." Qin Ke didn't brag about his five methods, he said with a smile: "Four hours before the exam, I just had an inspiration and came up with a new method system for solving problems. I called everyone at night, and I shared it with you." a bit."

Liang Shaoping was startled, and then gave a thumbs up in amazement: "Teacher Qin is a bull, and he finished five difficult problems in one hour! And he is still thinking about new ways to solve the problems! Today's problems are better than the selection papers we usually do. It's still difficult, I only made two and a half questions! Looking forward to Teacher Qin's sharing tonight!"

"Don't worry, you might be able to solve three or even four questions tomorrow. Let's go." Qin Ke smiled, and met Deng Hongguo, Ning Qingyun and three other team members at the exit of the examination room, and returned to the hotel together.

The DAY1 exam ended here. Deng Hongguo didn't feel comfortable asking everyone how they did in the exam. He just encouraged everyone to persevere. There will be DAY2 exam tomorrow.

As the captain, Qin Ke had a good relationship with the team members, so naturally he didn't have so many worries, so he asked everyone about their answers in private.

The best answer was of course Ning Qingyun, a Chinese cabbage from his family, who solved all five questions, followed by Wang Changai who solved four questions, Sun Bingfei and Wei Yuyuan who solved three questions each, and Liang Shaoping who solved two questions. Half of the questions, but Sun Bingfei and Liang Shaoping did not do the threshold questions, and they will actually be deducted 7 points.

After the evening, Qin Ke called several team members to his room. Deng Hongguo came to listen curiously when he heard that Qin Ke had a new method of doing the questions.

Qin Kezao asked the hotel for a small whiteboard and an erasable writing pen, then looked around the anxious and expectant eyes of everyone, smiled and said: "I only summarized this theoretical method system in the afternoon, and there are probably some differences. If it is too perfect, it will take a long time to really master it, but it doesn’t matter, I have basically figured out the direction of the IMO topic and the idea of ​​​​the topic today. I use my new theory and method system for IMO , give you a special training."

Speaking of this, Qin Ke looked at Xiaobaicai in his family, and said with a smile: "This set of theories is called 'Zhi Ning Qingyun', and the full name is 'Qin Ke Zhi Ning Qingyun's new high school Olympic mathematical thinking theory system', ha, Don't laugh."

Originally, everyone could hold back, but they all laughed after hearing what he said: "Mr. Qin, can you stop giving us dog food, it's too sweet for us!"

Ning Qingjun's face was blushing, and she couldn't help giving him a blank look: "Why do you involve me?"

"Because this is based on the Olympiad skills I have taught you for more than half a year." Qin Ke patted the whiteboard with a smile: "Okay, from now to ten o'clock in the evening, three hours, you guys Whether you can do three or more questions tomorrow depends on how much you can absorb tonight!"

……

The DAY2 exam came as scheduled, but because there was no opening ceremony, the time was advanced to 9:00, and the end time was also advanced to 14:00 accordingly.

It is still the original examination room, with the same biscuits, chocolates and small bottles of mineral water.

Liang Shaoping walked into the examination room excitedly, and Qin Ke next to him patted him on the shoulder: "Shaoping, don't get too excited, keep calm, so that you can calm your mind."

"I'm sorry, Teacher Qin." Liang Shaoping said embarrassedly: "I thought about your theory of 'Zhi Ning Qingyun' all night last night, and I almost didn't fall asleep. If I could hear this one day earlier, I could do it yesterday It's the first threshold question."

"And today, don't worry, you should do better than most people in the exam today."

"Mmm! Thank you, Teacher Qin!" Liang Shaoping returned to his seat with a lot of energy.

As soon as Qin Ke sat down, Hill from the US team came over and said in English, "QIN, what happened to you yesterday? You handed in a blank paper?" His voice was filled with suppressed anger.

Qin Ke said with a smile: "No, I'm done, but I didn't hand in the paper in advance."

Hill's anger disappeared immediately, and he took a deep look at Qin Ke: "In this IMO, only you and Yevgeny from Xiongguo can be called my strong rivals. I am impressed." After saying that, he turned and returned to his seat.

"Want to impress? Yes, I will satisfy your wish." Qin Ke smiled lightly, imitating Hill's way of turning his pen, huh?It's a bit difficult, this kid's pen-twisting level is so high, how many years has he practiced?

The melodious bell rang again, and the test papers were distributed to the candidates in advance.

Qin Ke scanned the next question.

The first threshold question is the big geometry question:

"1. In the acute triangle ABC, AB is greater than AC, let ⊙O be its circumscribed circle, H be its orthocentre, F be the vertical foot raised from vertex A, M be the midpoint of side BC, Q be A point on ⊙O makes ∠HQA=90 degrees, and K is a point on ⊙O such that ∠HKQ=90 degrees. The known points A, B, C, K, and Q are different from each other, and they are arranged in this order ⊙O. Prove: the circumcircle of triangle KQH is tangent to the circumcircle of triangle FKM."

Indeed, the difficulty is not small. As expected of DAY2, the simplest question is equivalent to yesterday's first threshold question, and today's threshold question is even more difficult.

It just happened to be used to continue to improve my "Zhi Ning Qingyun" Olympiad theory system!

As soon as Qin Kelue thought about it, he used his new theoretical system to see the intention of the questioner. He only needed to make a few auxiliary lines to transform the problem into proving that the four points of E, K, D, and H are coaxial, and that Q, M , H three points collinear, and HA · FH = HD · HG.

It took Qin Ke about 10 minutes to complete five proof methods, and the steps of each proof method did not exceed ten lines.

Now holding the theoretical system of the New Austrian Math, he is like killing a chicken with a sledgehammer, relaxed and happy.

The only one of the next four big questions was relatively difficult, and it only took Qin Ke about 15 minutes to complete the five solutions.

In less than an hour, Qin Ke finished the entire paper.

He checked it, and when there was no problem, he held up the "HELP" sign, ready to hand in the paper and leave.

It was the brown-haired teacher who came to collect the papers. He ran here from a distance on purpose. Another invigilator who was about to pass gave him a strange look, but the brown-haired teacher ignored him and hurried to Qin Ke's side.

　Thanks to "Brother Ziming" for the reward!

　　Thank you for your monthly tickets and recommended tickets!Double the monthly ticket today, continue to ask for the monthly ticket!
　　In the afternoon, we will start adding rewards and monthly tickets!

　　The balance of rewards that have not been added yet: 18967 starting coins / 10000 starting coins

　　Current unrenewed monthly pass balance: 495/300

　　At present, the balance of recommendation tickets that have not been added: 1700/5000

　　There is currently no change in book recommendation promotion balance: 5 time / 5 times

　　A total of 3 chapters are owed.In the afternoon, I will make up a large 4K chapter to cover two chapters!There are more nights!

　　
　
(End of this chapter)