Rebirth of science and technology academic master

Because he had to participate in the provincial league, Qin Yuanqing's time suddenly became tight.

Just after taking the midterm exam, I immediately gathered with others, and then, led by the leader of the math group, took the bus to Rongcheng.

It takes 4 hours from Jinpu County to Rongcheng.

Qin Yuanqing directly took out the high school mathematics league test questions from previous years and continued to study them with great interest. Compared with the college entrance examination questions, the high school mathematics league test questions were more in-depth and broader, and even involved advanced mathematics.

Among the fifteen people who participated, the one with the best results won the first prize, but was not selected for the provincial team to participate in the National High School Mathematics League. This time, like Qin Yuanqing and others, he participated for the last time. Once he was unable to be selected for the provincial team, he would not be able to participate in the national competition, let alone be selected for the national team and compete internationally.

After a 4-hour long journey, the bus arrived at Rongcheng Experimental Middle School. This is the venue for this year’s provincial high school mathematics league. Participants from various cities and counties will compete here to win the first prize even if they fail to win the key points. The qualification for admission to the university can also be used as an extra point in the college entrance examination.

According to past practice, 40% of the contestants can win the second prize, 10% of the contestants can win the first prize, and not even 0.5% can enter the provincial team.

The leader of the mathematics group of Jinpu No. 1 Middle School gave everyone a few words and asked everyone to find the examination room, so as not to find the examination room during the exam tomorrow morning and be confused and confused.

And they will stay in a nearby hotel at night, a hotel without a star rating.

After viewing the examination room, Qin Yuanqing returned to the school gate. Others had not come back yet. It took about half an hour for everyone to arrive. Zhang Jiaji, the leader of the mathematics group, asked everyone to check their ID cards, signature pens, 2B pencils, rulers, triangles, etc. again. Compasses and admission tickets, after all, if the problem is discovered now, there is still time to remedy it. If it is discovered tomorrow, there will be no time to remedy it.

After checking into the hotel, two people sharing a room, Qin Yuanqing did not chat with another classmate, but studied the topic. His time was precious, and every minute and every second could not be lost.

Vaguely, Qin Yuanqing realized that many league questions seemed to be beyond the outline, but in fact they were not. They were just extended and made more difficult. As long as they continued to analyze deeply, they could still be solved.

Suddenly, Qin Yuanqing looked happy because he discovered that his attributes had changed:

Host: Qin Yuanqing

Age: 18 years old

IQ: 145

Emotional Quotient: 100

Subject:

Chinese: Level 4 (20/100000)

Mathematics: Level 5 (0/1000000)

English: Level 3 (100/10000)

Physics: Level 4 (20/100000)

Chemistry: Level 4 (20/100000)

Creature: Level 4 (20/100000)

Physical fitness: Level 1 (0/100)

He did not expect that his mathematical ability would reach level 5 at this time. Level 5 would not make much difference in his scores in the high school exam, but it would allow him to gain a lot of points in competitions such as the high school league. .

Sure enough, as his mathematics level reached level 5, Qin Yuanqing found that it became much easier for him to understand the questions of these mathematics leagues, as if he felt like he had opened up his meridians.

Qin Yuanqing took advantage of the fact that there was still some time in the evening and read through the questions one by one. It was not until 12 o'clock that Zhang Jiaji came to check the ward and reminded them that it was time to go to bed. Qin Yuanqing reluctantly put the book away and washed it. After taking a bath, I fell asleep.

After strict inspection procedures, except for the contestants' ID cards, admission tickets and basic examination tools, other mobile phones and all electronic devices are not allowed to be brought into the venue.

Qin Yuanqing came to his examination room and sat down in his own seat. The competition specifications were based on the college entrance examination, which was even more stringent than the college entrance examination, because there were only twenty candidates in one room, with four rows of desks and five rows in each row. The distance between each row is large to ensure that no one can see the people in front, back, left and right answering questions, and there are two invigilators in one room, constantly moving back and forth in the room.

Qin Yuanqing sat down and placed the signature pen, 2B pencil, ruler, compass, eraser, and triangle on the table. The admission ticket and ID card were placed in the upper right corner of the table, waiting to be opened and distributed.

After the announcement first sounded the examination room rules, examination time, and notes for candidates, the invigilator took out the test paper and indicated that the test paper had not been opened before. After verifying and signing it, the two students in the front row took out the test paper inside. Distribute the test papers and scratch paper one by one, and then remind everyone to fill in their names, ID cards, admission tickets and test paper codes first. Don't rush to answer the questions and wait until the announcement is broadcast before answering. Otherwise, it will be regarded as cheating.

After Qin Yuanqing filled in the name, admission ticket, ID card, school name, and test paper code on the test paper, he saw that there were still 10 minutes left before the exam, and he didn't remember to answer the questions. According to his own habits, he checked the test paper first and looked at the questions. I have a general understanding of the test question types and test points.

At 9 o'clock sharp, the exam started on time.

Qin Yuanqing started to do the questions. The first big question was the same as the college entrance examination questions. They were multiple-choice questions. Qin Yuanqing couldn't calculate it mentally. He kept calculating on the draft paper and then filled in the answers. After answering all the multiple-choice questions, Qin Yuanqing wrote the answers. Use a 2B pencil to scribble on the answer sheet. After checking that everything is correct, start the second big question. The second big question is a fill-in-the-blank question. This kind of question seems simple, but it is actually much more difficult than multiple-choice questions. Sometimes Not one answer, but two answers. If you write one less answer, half the score will be deducted.

And no one knows whether the answer they filled in is correct or incorrect. In this case, there is no time to do it a second time.

In terms of type, there are 6 multiple-choice questions, each worth 6 points, totaling 36 points. There are 6 fill-in-the-blank questions, each worth 6 points, totaling 36 points. The third largest type is the solution to proof questions, with a total of 4 questions, each question is worth 20 points, totaling 80 points, with a full score of 152 points.

Answer question No. 1, which is also question 13, is to test the knowledge related to the intersection of parabola and straight line. The question is: Given parabola C: y=ax2 (a\u003e0), straight line y=a+2 intersects the parabola at points A and B. , M is the midpoint of line segment AB, and the perpendicular to the x-axis passing through M intersects parabola C at point N. (1) Prove: The tangent line of parabola C at point N is parallel to AB. (2) Whether there is a real number a such that if it exists, find the value of a; if it does not exist, please explain the reason.

Qin Yuanqing listed the parabola and the straight line as a system of equations on the test paper. Since they are intersection points, it means that y is equal, and we get ax2-x-2=0. Then we set A (x1, y1), B (x2, y2), and use this to find value, convert it into a new equation, and use the slope k of the tangent line of parabola C at point N to prove the parallel conclusion.

The second point (2) is that for problems like this, we first assume that there is a real number a to make the equation true, and then use the known conditions to deduce the value of a. If the value of a can be calculated, it exists, and if there is no solution, it does not exist.

Hey, this test paper isn't difficult, is it? After Qin Yuanqing finished answering question 14, he couldn't help but murmured in his heart: Did I make a fake paper?

Although I was puzzled, it seemed that this test paper was not too difficult. It was much simpler than the questions in the National High School Mathematics League. Although there was a lot of calculations, it did not appear to be a sky-high difficulty.

Question 15 is to find the smallest positive real number k such that the inequality ab+bc+ca+k(1/a+1/b+1/c)≥9 is true for all positive real numbers a, b, c.

Qin Yuanqing suddenly thought of 1. When a=b=c=1, k≥2. Then k=2 is brought into the original equation to form a new equation, thereby proving that the inequality is true.

Qin Yuanqing continued with the 16th question, which was the last question. This was a proof question that combined necessary and sufficient conditions and inequalities, and was the most difficult.

Qin Yuanqing frowned slightly and broke it down step by step. He wrote a lot of the entire proof steps. As soon as he wrote down the conclusion of the proof, the bell rang. The invigilator announced the end of the exam, and every candidate stood up, and then the invigilator collected the papers one by one.

As soon as the exam was over and they just walked out of the exam room, some students were complaining, why is it so difficult? It’s hard to live.

Qin Yuanqing breathed a sigh of relief. He found that the provincial league was not as difficult as he imagined, and it was only slightly more difficult than the college entrance examination mathematics test.

So Qin Yuanqing seemed very relaxed, eating and drinking when he should, but was laughed at and scolded by the head of the mathematics group for being big-hearted and heartless.

. . . . . .

As soon as the provincial competition ended in the morning, the judges from the Provincial Mathematical Society began to review the test papers in the afternoon. A total of more than 1,200 high school students across the province have signed up to participate this time. They need to correct test papers and tally scores as soon as possible. Although the multiple-choice questions are graded through a computer program, the workload is also very heavy.

In addition, two graduate students are responsible for statistics and inputting data into excel to facilitate final statistics and ranking.

Lin Feng, Ludao Shuangshi Middle School, 110 points.

Zhou Hu, Shuitou scored 89 points.

Wang Lin, Provincial Experimental Middle School, 118 points.

Li Peirong, Narcissus scored 105 points

Tang Liang, Jianyang No. 1 Middle School, 8 points... Wow, only 8 points. You can score more than 8 points with your eyes closed.

Look, there is another one here who got 4 points. Each question gets 1 point for writing a solution.

The two graduate students are both from the Department of Mathematics. They had countless joys participating in this statistics. Sometimes their stomachs hurt from laughing. Some of them counted 1 point, but it was not the lowest. The lowest was 0 points. And there are quite a few with 0 points.

The two of them were also speechless, so lazy that they didn't even bother to write an explanation. Or the writing is so sloppy that deciphering it is like drawing a ghost charm.

Wow, this person is so awesome. Ludao Shuangshi Middle School scored 140 points, the highest score so far!

No, look, this one is amazing, Qin Yuanqing, Jinpu No. 1 Middle School, 152 points! The first full-scoring test paper is actually from Jinpu County No. 1 Middle School in Shuixian City!

Both of them looked surprised.

Jinpu No. 1 Middle School is the best school in Jinpu County and a key high school in Narcissus City. But in the whole province, it seems a bit insignificant and has no reputation at all. After all, it is not a provincial key middle school at all. Everyone only knows those provincial key middle schools. Who knows about a middle school in an ordinary county.