From child prodigy to chief scientist

This problem involves finding the maximum area of ​​a triangle within an ellipse.

Actually, Xu Xiao wasn't without a solution to this problem.

The conventional solution involves first establishing a system of equations for the straight line, then using Vieta's formulas to express the area, and finally taking the derivative.

This method is a bit cumbersome, especially for fill-in-the-blank questions, where there's absolutely no need for such a complicated approach.

"Using the idea of ​​affine transformation, first treat the ellipse as a circle, find the case where the area is maximized, and then transform it back."

This method is much faster than the conventional method, and Xu Xiao got the result in just a few minutes.

Xu Xiao finished answering all eight fill-in-the-blank questions in less than twenty minutes.

At this point, many students in the exam room had only completed four or five fill-in-the-blank questions, and even He Muzhou was still stuck on the calculations for the eighth question.

With one hour left to work on the last three problem-solving questions, there is plenty of time.

The first problem-solving question tests the combination of functions and derivatives.

These kinds of questions often seem very tricky, even more difficult than the final question in the college entrance examination.

However, for Xu Xiao now, these are all relatively standard question types.

"This is the Peano remainder form of the Taylor expansion; just apply the Lagrange mean value theorem."

In fact, Xu Xiao had already thought of two different proof methods, but there was no need to show off during the exam; getting the points steadily was the most important thing.

The subsequent problems involving solid geometry and sequence inequalities did not pose too much of a problem for Xu Xiao.

After answering all the questions on the test paper, Xu Xiao saw that there was still a lot of time left, so she started to check her answers from the beginning.

"The solution process for the problem should be correct, and the calculations have all been verified."

After carefully checking everything, there were still 20 minutes left before the end of the first test.

However, Xu Xiao did not choose to hand in the paper early. Instead, she continued to use the remaining time to redo the questions on the test paper using other methods on the draft paper.

This is not only to further verify whether my answer is correct, but also to maintain my learning status and include the learning time in the statistics of the vocabulary task.

According to Xu Xiao's experience, even if he didn't put in too much effort, as long as his study session wasn't interrupted, his study time could still be fully recorded.

When the exam bell rang, Xu Xiao handed in her paper, went to the restroom, and then took a walk in the corridor to relax her mind and body.

There was a 20-minute break between the first and second rounds of testing. However, after the first round ended, a few students packed up their things and left the examination room.

Some of them had no intention of participating in the second test, while others failed the first test and their Dao hearts shattered on the spot, leaving them with no courage to face the second test.

After all, the second round is much more difficult than the first round. If you can't answer many questions in the first round, it will be very difficult to get many points in the second round.

As the second round of auditions approached, Xu Xiao returned to her seat and quietly activated the vocabulary list.

The next test will be the real showdown.

At 9:40, the second test began on time.

As expected, the four questions in the second round were geometry, algebra, number theory, and combinatorics.

Each of these questions has relatively few conditions in the question stem; some are only one or two lines long, while others are only a few lines long.

If someone is not familiar with the math competition, they might think that the second round is not that difficult, perhaps only slightly more difficult than the first round.

But only students who actually participate in the training know that sometimes the problems that seem very simple are the most difficult to solve.

Xu Xiao quickly focused his mind, and his brain began to work at full speed.

Xu Xiao's intense focus made her lose track of time, her mind completely absorbed in solving the problem.

Xu Xiao didn't know how much time had passed, but she finally finished the first three questions.

Except for the first one, all three questions are definitely not easy.

Even though Xu Xiao had given it his all, he still had to try several different approaches before he was able to solve the problem.

Just as Xu Xiao was about to continue his assault on the last question, he suddenly felt a change in his state of mind.

"Oh no... I can't maintain my focus anymore."

Continuous high-intensity mental work takes a severe toll on Xu Xiao's brain.

With his still-developing brain, he had indeed reached his limit to withstand such immense strain.

At this moment, Xu Xiao clearly felt that he was finding it difficult to concentrate.

Even the sounds of other students writing, flipping through test papers, and the proctor walking around the classroom were distracting him.

In this state, it was definitely impossible to solve the questions at the second-round level, so Xu Xiao had no choice but to stop temporarily and relieve the fatigue in his brain.

I glanced at the time; there were still more than thirty minutes left until the end of the exam.

"Let's try again. Regardless of whether we can make it or not, we definitely can't give up easily."

After a short two-minute break, Xu Xiao continued to attempt the last question.

However, due to excessive mental exertion, Xu Xiao was unable to find any complete ideas.

Left with no other choice, Xu Xiao had to write down everything she could think of, hoping to get as many points as possible.

The bell rang, signaling the end of the second round of testing. Everyone stopped answering their questions and handed in their papers.

"Sigh... I'm still lacking something. It seems there's still a lot I need to improve."

Xu Xiao still felt some regret about her performance in the second round of auditions.

Perhaps if he had a little more time, or if his focus had lasted a little longer, he might have been able to solve the last problem as well.

However, since the exam is over, there's no point in making these assumptions anymore. What's more important is to learn from the experience and continue to improve yourself in the future.

"If I can answer the first three questions in the second round correctly, I should still have a chance to make it into the provincial team."

Xu Xiao had previously learned about the provincial team cutoff scores from previous years. The highest scores were around 210 or 220, while the lowest were even less than 200.

Even if you don't get points on one of the big questions in the second round, as long as you don't lose too many points on the other questions, you still have a chance to make it into the provincial team.

Apart from Xu Xiao, the other students in the classroom also looked exhausted.

That morning, their brains had been working continuously for more than four hours, and most of the problems they faced were far more difficult than those in the college entrance examination mathematics.