A Letter
Shen Qi not only memorized the key points, but also repeatedly recited the name of his Military Theory lecturer— Wei Junqiang.
Shen Qi completed the Military Theory exam with equal ease.
There will be a week of rest afterward. A week later, the mathematics students will take an exam on a fundamental mathematics course: Analytic Geometry.
Of the three essential introductory materials for the Mathematics Department, analytic geometry is relatively the Analytic Geometry.
Mathematics is worth 15 credits and is taught from Mathematics I to Mathematics III, over three semesters.
The course in Advanced Algebra is worth 10 credits and consists of two semesters: Advanced Algebra and Second Academic Algebra.
Analytic Geometry 5 credits, has only one textbook, and is studied for one semester. First-year students in the Big Mathematics Department at Yenching University use the Analytic Geometry textbook produced by Yenching University itself.
Shen Qi considered it and decided that he would complete 10 credits of Advanced Algebra ahead of schedule. As for Mathematical Analysis, he would see if he could apply for early exams this semester, and the procedure would be similar to that for the 36th question in Advanced Algebra.
There's no need to take Analytic Geometry in advance. Just follow the group and take the Analytic Geometry final exam as usual.
Being able to take the final exams normally is too easy, let's do it that way.
Within a week, the scores for College English and Military Theory were released one after another.
Shen Qi checked, and it was 100!
Another 100!
Both College English and Military Theory were 100.
Zhou Yu'an checked, and it was 100!
82!
Zhou Yu'an scored a perfect 100 in English and 82 in Military Theory.
My roommates Luo Ji and Cai Qing both scored only in the 80s in English, but both scored above 90 in Military Theory.
"I feel like dying. My Military Theory is the worst in the whole dorm again." Zhou Yu'an was depressed. He couldn't compare with Shen Qi in math major courses, and he couldn't even pass general courses like Marxist Philosophy and Military Theory as well as Shen Qi. He was even worse than his two other roommates.
"But Zhou Yu'an, your English is amazing, a perfect score!" Cai Qing said enviously. "My English is terrible. High schools in our small town focus on Science and Engineering, and students there generally don't do well in English."
Zhou Yu'an, having participated in the IMO in the UK before, spoke in good English: "Cai Qing, your English is poor, but you still got over 80 points, didn't you? Don't be too modest. Excessive modesty is just showing off. Don't be like that person."
Someone was flipping through a book on Professional English for Mathematics when he said, "I never try to show off."
Then Zhou Yu'an, Cai Qing, and Luo Ji went to bed, not wanting to talk to Shen Qi.
Mid-December.
First-year students in the School of Mathematical Sciences are facing their final exams in Analytic Geometry; students from all five departments are required to take this course.
Shen Qi glanced at the test paper; it contained three problem-solving questions. The first question was worth 30 points, the second was also worth 30 points, and the third was worth 40 points.
There were no multiple-choice or fill-in-the-blank questions.
You can pass if you answer any two of the three questions correctly.
This kind of exam, similar to a math competition, evoked fond memories for Shen Qi.
The first question was quite challenging. There was a diagram with a complex shape drawn in a coordinate system. At first glance, it looked like a spaceship, but upon closer inspection, it was an abstract version of a spaceship from Star Trek.
Question: What is the radius r of circle G?
In other words, what is the radius of the exhaust vent of the abstract spaceship?
"Interesting, quite interesting."
Shen Qi fell into deep thought.
Curve equations are a must-know topic in Analytic Geometry, but unexpectedly, Professor Qu, the approachable and easy-going Analytic Geometry teacher, can be surprisingly ruthless when it comes to setting questions.
After thinking for three minutes, Shen Qi picked up his pen and wrote his answer.
The first thing to do is to set the equation of an Algebraic Curves as f(x, y)=0, which is a very basic operation.
Mathematics Department students can always find a translation to eliminate the constant term of polynomial f.
After eliminating the constant term, it is easy to obtain the equation of the tangent line to the curve at the origin, where the origin is not a point of reference.
If the curve has no first-order terms, then there are several different cases.
If the origin is a doubly key point, then the equation of the nylon curve must be calculated.
Shen Qi derived the equation of the nylon curve and obtained y^2 - x^2 = 0 from the quadratic term.
However, reaching this point in solving the problem only meant avoiding the trap set by Professor Qu; it did not mean truly escaping danger.
Shen Qi would certainly consider another scenario: when the two tangents are imaginary, the coordinates of the conjugate point satisfy the equation of the curve, but this point is separated from the rest of the curve.
Whether it's Clay, Guadeloupe, or Maclaurin, they have all directly or indirectly demonstrated the inflection point issue.
The real genius was Newton; algebra was merely a tool for him, and Newton's true passion lay in geometry.
Shen Qi used Newton's fluxion number method, thus ignoring imaginary branches.
Ultimately, Shen Qi calculated that the radius r of circle G is 2/3 or -6/5.
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6/5 should be discarded, so the answer is 2/3.
"These 5 credits in Analytic Geometry are hard-earned."
Shen Qi spent half an hour on the first question, and the exam time was 90 minutes.
The Mathematics Department can be considered the core of the entire School of the Mathematics Department students have the strongest overall academic strength.
However, even for the Mathematics Department students, including IMO gold medalists like Zhou Yu'an, this Analytic Geometry exam was not easy.
Shen Qi also had a tough time. He spent 80 minutes completing all three questions, and 10 minutes checking, making it exactly 90 minutes.
After the exam, Mathematics Department students complained, "You can't judge a book by its cover! Who would have thought that the gentle and refined Professor Qu was actually this kind of person!"
"Professor Qu, who hides a dagger in a smile!"
"Fat Old Sun, Skinny Old Lu, and Professor Qu is a smiling tiger!"
"Advanced Algebra is difficult, mathematical analysis is tedious, Analytic Geometry is a bomb!"
"I'm done, I'm done. I can only solve one problem on this Analytic Geometry exam."
"Whoever says Analytic Geometry is easy, I'll argue with them!"
Seeing that the situation was not good, Shen Qi quickly convened a meeting with all the students in the Mathematics Department: "Everyone, tell me, what's going on?"
"What's there to say? You failed!"
"Let's rebuild it!"
"Go ahead and cry!"
Shen Qi asked Ou Ye, "What about you? Did you hang up too?"
Ou Ye shook her head. "It won't hang."
"She said she can't fail," Shen Qi told the other classmates.
Other students. "She's different from us."
Shen Qi asked his three roommates, "What about you guys?"
Zhou Yu'an looked worried. "I can only get around 90 points. I missed answering one of the three parts of the last question."
Luo Ji: "I scored around 80 points; I didn't answer two questions."
Cai Qing: "I had no problem with the last question, but I wasn't too confident about the first one. I'd either get 70 points or a perfect score."
Shen Qi added, "I think there shouldn't be any problems with my three questions. My answers are 2/3, 1..."
Zhou Yu'an clutched his head. "It's ruined, it's ruined! I got 90 points!"
Luo Ji covered his face. "Oh no, oh no, I only got 80 points!"
Cai Qing was overjoyed. "My answers to three questions are exactly the same as Shen Qi's, so I might get a perfect score! If I don't lose points for the steps."
Shen Qi glanced at Ou Ye.
Ou Ye said, "My answer is the same as yours."
Shen Qi addressed the class, saying, "Class, look, almost everyone scored above 80 points, so stop blaming Professor Qu and look for problems within yourselves."
The students went crazy. "So showing off is contagious! Shen Qi, you four in your dorm, you're all showing off as a group! And you, Ou Ye!"
Zhou Yu'an shrugged and said, "This is what you call showing off? A true King of Show Offs never does it intentionally. Wait, where's the King of Show Offs? Where did Shen Qi go?"