Chapter 31 The Story of the Competition and the College Entrance Exam
Chapter 31 The Story of Competition and College Entrance Examination (I have something to do tonight, so I’ll send it in advance)
"This question is really not easy."
After getting the test paper, Xu Chuan stared at the first geometry question for five minutes before sighing.
A plane geometry question almost applies all five axioms and five postulates of Euclidean geometry. It can be said that the geometric characteristics of flat space are fully utilized.
The most critical thing is that this question almost blocks the geometry knowledge learned in most college mathematics. It is difficult to apply the new geometry theory of Prince Gauss or the absolute geometry and non-Euclidean geometry of the great god Borgio to this question.
superior.
The professor who asked this question definitely has a high level of achievement in geometry.
There are only a handful of domestic mathematicians who have achieved high achievements in geometry. Xu Chuan thought about it and found that the most famous among them are Mr. Qiu and Mr. Chen.
But the probability of these two big guys coming up with the question is almost zero.
Although Qiu Lao has high attainments in geometry and is still in China, his geometric achievements are mainly in differential geometry, and his attainments in plane geometry are not considered top-notch.
Moreover, this boss is older, so he may not remember the geometry knowledge clearly in high school and college.
As for Mr. Chen, he passed away ten years ago, so it is even more impossible for him to come up with the question.
As a result, all CMO candidates in 2014 were wiped out, and not one of the more than 400 people got a perfect score.
Especially since this year's questions have all been read by Mr. Zhang, even if they are slightly less difficult than Geometry, they won't be much different.
Later, the Mathematical Society did not let this big boss take action, for fear of damaging the confidence of the reference students.
However, there is no easy question in the second half of the national final.
There are no multiple-choice questions or fill-in-the-blank questions in the National Number Competition. They can't do it even if they want to throw dice or guess the answers with paper balls.
In the process of solving the problem, almost all twenty-six letters were used, and characters like A and A were also used to represent auxiliary lines, which shows how difficult this problem is.
For the 21-point question, among hundreds of candidates across the country, only a handful of students got 7 points for the first question, while the other students all turned in blanks.
What didn't happen yesterday happened today.
At most, write a ‘solution’.
Of course, it can only give you an answer, and you still need to write the derivation and proof process yourself.
A geometry problem has stumped hundreds of students, and the smarter ones have already bypassed it and solved the next problem.
At the same time, this big boss also screened other test questions, resulting in this year's CMO results being miserable, with scores above 100 points being less than one slap in the face.
These students, who were in high spirits in the first half of yesterday and felt that CMO this year was not that difficult, were immediately confused today.
Students who have participated in these three CMOs tremble when they hear the name of this big man.
This was the longest time he had spent on a question since he participated in the math competition, taking more than half an hour.
These three auxiliary lines are quite secretive, and one of them is sandwiched between the two circles. It is quite difficult to find this auxiliary line.
Later, he participated in the CMO questions in 2015 and 2016, and the results of these two times were equally dismal.
After solving the first question, Xu Chuan breathed a sigh of relief and looked up at the alarm clock on the blackboard of the podium, which read nine thirty-five.
Although Xu Chuan is not sure whether this geometry question was created by Academician Zhang Weiping, the teacher who asked this question is definitely at the same level as him.
"Crouching Tiger, Hidden Dragon, this year's CMO, the question maker actually has such a super boss involved."
After carefully checking it twice to confirm that there was no problem, he handed in the paper in advance and left the examination room.
Certification completed!
"Miscellaneous" is just one word, so what's the big deal?
Full marks? In the hands of this boss, that's unthinkable.
The students in a row were either looking up at the sky or looking down at the ground.
In 2016, it was the same 21-point question, but there was no perfect score.
In 2015, he assassinated all the candidates that year with a single three-dimensional geometry.
The geometric figures of this question were too complex, and he was too lazy to copy them onto scratch paper.
That is to go back to basics and use a protractor to measure directly, but it is only useful for plane geometry.
The rest is a blank.
Thinking about it, Xu Chuan turned his head and looked at the classroom.
With a sigh, Xu Chuan picked up the protractor and drew on the geometric diagram. After confirming that the angle he guessed was correct, he began to draw auxiliary lines on the test questions.
However, after three attacks, his reputation in the math industry was as good as that of Ge Junge, the boss who specializes in dealing with college entrance examination candidates.
This method can solve more than 90% of geometry problems.
In fact, in geometry problems, there is a fairly simple method to determine the desired numerical value and angle.
This is probably 'Is it okay if I have sex?'
If he had come up with the question, he would indeed be able to do this.
Up to this point, the story of this big man has not stopped yet.
This big shot just happened to serve as a director of the 10th Council of the Mathematical Society last year.
After the auxiliary lines were drawn, the rest of the proof was just ordinary for Xu Chuan. Although the proof process was more complicated, after climbing Mount Everest, do you still worry about not being able to climb Mount Tai?
Solution: According to Pascal's theorem, the three points P, Q and R are collinear, because ∠DTF=AC+DF/2=AB+DF/2=
Therefore, if QK is extended and handed over to BC, SK/KT = BN/NC
In the same way, we can know that △CQN∽△APC, and CN=QN·AB/PB, so we know that BN/NC=
Rotate △ABP around point A to △ACL
It can be proved that the angle of ∠KIP is thirty-five.
This geometry question extremely tests students' derivation and graphic observation abilities. It requires at least three auxiliary lines to accurately derive the required angle.
It is worthy of being asked by a figure as famous as the mathematician Ge Jun. Even if he did it so hard, it is probably even harder for other students.
This big boss won the honor of being an academician of the Academy of Sciences in 2008, and is now in his prime. In addition, he is a close disciple of Mr. Chen. It is logical that he will continue on the mathematical path of geometry. It can be said that he has made great achievements in plane geometry.
His attainments are quite high.
The CMO's test teachers are basically selected from the directors of the Mathematics Society. In 2014, this year, this big boss personally compiled two geometry questions and entered them into the 2014 National Mathematics Competition Finals.
It took Xu Chuan an hour and a half to complete three major questions in an orderly manner.
This move completely stimulated the other students in the same examination room. Some gritted their teeth, some bowed their heads in silence, and some cruelly followed suit and left early.
However, this reminded Xu Chuan of another person in the country, Academician Zhang, Mr. Chen’s close disciple ‘Zhang Weiping’.
The black pen in his hand continued to list rows of calculations on the answer sheet, almost filling the entire A4-sized answer sheet, and the geometry question was finally answered.
This also caused the admission score of this year's training team to drop from the average of more than 85 points in previous years to 65 points, which directly reduced the admission score by nearly 20 points.
In fact, Xu Chuan's guess was indeed correct. The two geometry questions in this year's IMO, yesterday's and today's, were written by Academician Zhang Weiping.
After all, with such a difficult question, it’s normal to hand in a blank paper at the same time, right?
Anyway, I’m not the only one with a blank roll.
I want monthly votes, recommendation votes, follow-up reading, and the new Eight-Tails. I want everything.
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