No Pressure at All, and I Even Feel Like Crying a Little
There wasn't much time to ask questions, because the college entrance exam was still in progress.
After finishing the Chinese exam in the morning, Shen Qi went straight home with his parents. After a short rest, he had another exam in the afternoon. He also had two more exams tomorrow.
Shen Qi didn't know where his classmates were taking the college entrance exam, or which middle school and classroom they were in.
Shen Qi hopes that Chen Xiaoting and Gu Xiaodan can achieve their desired scores. He will not contact them or anyone else in the next two days. His phone is switched off and will remain switched off for two consecutive days.
It can be said that Shen Qi put in all his efforts to prepare for the college entrance examination, for no other reason than to work hard to achieve miracles. Who asked me to have a strange word in my name?
The second subject of the college entrance examination began at 3 p. m.
Compared to Chinese, the second subject of the college entrance examination was no challenge for Shen Qi.
The second exam was in mathematics.
Math questions are not as complicated as language arts questions; there are only three types: multiple choice, fill-in-the-blank, and short answer.
The maximum score for Chinese, Mathematics, and English is 150, while the maximum score for the Science Comprehensive /humanities subjects is 300. Shen Qi's province uses this model for the college entrance examination.
Sets, arithmetic sequences, three-view diagrams of Solid Geometry, Flowchart, Induction Formula, Trigonometric Function graph transformations... These 12 multiple-choice questions were child's play for Shen Qi; he solved one question in an average of 20 seconds.
After all, it's the college entrance examination; we must be cautious and careful.
Normally, Shen Qi could solve a problem in 10 seconds.
It took Shen Qi a little over four minutes to finish all the multiple-choice questions.
Fill-in-the-blank questions were equally easy to answer.
Operations on Plane Vectors, applications of Linear Programming, properties of hyperbolas, volumes of geometric solids... none of them could escape the fate of being destroyed.
Shen Qi completed four fill-in-the-blank questions in 3 minutes and did some simple calculations on the scratch paper.
Within 8 minutes, Shen Qi finished the multiple-choice and fill-in-the-blank questions.
The highlight of the college entrance examination mathematics paper is, of course, the short answer questions.
Short answer questions are generally divided into calculation questions and proof questions.
Whether it's a calculation problem or a proof problem, they're all free points for Shen Qi.
Short answer question 1:
"Given the functions f(x) = -x^2 + ax + 4 and g(x) = |x + 1| + |x - 1|."
"(1) When a=1, find the solution set of the inequality f(x)≥g(x);"
"(2) If the solution set of f(x)≥g(x) includes [-1,1], find the range of values for a."
This question is worth 12 points.
"These are such easy questions, they're practically free points with absolutely no skill required."
Shen Qi didn't even have a chance to draft the solution; he solved it directly on the exam paper.
Very quickly, he found the solution set of f(x) ≥ g(x) as follows:
{x|-1≤x≤-1+√[17]/2}
(√[] represents the radical sign, for example, √[17] means there is a 17 below the radical sign, the same below)
The first question was solved just like that; it wasn't even as sophisticated as a fill-in-the-blank question, at least the last fill-in-the-blank question was harder.
The second question is another easy point.
Shen Qi quickly determined that the range of values for a is [-1, 1].
You tell me, weren't the two parts of the first short answer question a free 12 points?
The knowledge points used are nothing more than dividing intervals and taking absolute values, solving inequalities separately, taking the union of the intervals as the solution set of the original inequalities, and so on—the most basic high school mathematics knowledge.
The following short-answer questions cover topics such as finding the expected value of a normal distribution, the positional relationship between a straight line and a conic section, and parametric equations...
Giving away points, giving away more points.
More than 20 minutes passed, and Shen Qi completed the questions that scored 136 points.
Shen Qi didn't use any advanced knowledge, yet he swept through the exam like he was bullying an elementary school student, demonstrating just how simple this college entrance exam math paper was.
"Damn, anyone could score over 140 on this, right?" Shen Qi was speechless. If math is this easy, is it even math anymore?
After all the exams, the CMO and IMO exams are still the most exciting; that battlefield is the real battlefield for men.
"The most boring subject in the college entrance examination is mathematics."
Shen Qi was extremely disappointed, deeply saddened, and almost lost his last bit of passion.
But there was no way around it; this was the college entrance exam, and Shen Qi had to continue being bored and finish the math exam.
The final, most challenging question was a function problem, worth 14 points.
Generally speaking, the last question on the math exam papers in each province across the country is the most difficult.
"Please, don't disappoint me any further. The entire math exam was so weak. Even if I got a perfect score, what difference would I make from the other test takers?"
"At least the final essay in Chinese class has some semblance of its final quality, but you, math, my main talent, please don't let me down, let me down, and let me down again." Shen Qi began to carefully examine the question, the final function problem.
The last question's wording is:
Given the function f(x) = 1/√[1+x] + 1/√[1+a] + √[ax/ax+8], x∈(0,+∞).
As the trial progressed, Shen Qi felt utterly disheartened. He was doomed; he was hopelessly unlucky.
Just by looking at this question, you can tell it's not a good one.
He's such a weakling.
It was so simple that Shen Qi wanted to cry.
The first question asks for the monotonic intervals of f(x) when a = 8.
"As expected..." Shen Qi felt a chill.
How interesting! How hilarious! The simplest college entrance exam math paper in history is fresh off the press!
Everyone can get a perfect score! Don't miss out!
Heartbroken and utterly disappointed, Shen Qi solved the first part of the final math problem:
When a=8, f(x)=(1+√[x]/√[1+x])+1/3
We obtain: f'(x) = 1 - √[x] / 2√[x(1+x)]
Therefore, when x∈(0,1], f'(x)≥0;
When x∈[1,+∞), f'(x)≤0
Therefore, f(x) is monotonically increasing in (0,1] and monotonically decreasing in [1,+∞).
This question tests very basic knowledge points, namely the properties and applications of functions, and the solution and application of inequalities.
"I want to cry, I really want to cry." Shen Qi looked distressed. All those practice problems from the "53" series were for nothing, all those math books I wrote were for nothing, it was all fake, all fake.
If you were doing this kind of easy question, wouldn't you cry?
You might not cry, and you might even feel a little like laughing.
But the IMO champion almost burst into tears, but fortunately Shen Qi held back thanks to his strong willpower.
This college entrance exam math paper was disheartening for Shen Qi. The first part of the final question was worth only 6 points. Not to mention me, even Chen Xiaoting could have easily solved it. Chen Xiaoting might even have gotten a perfect score.
"Hehehe..." Shen Qi laughed inexplicably, his laughter tinged with bitterness.
The proctor was startled. Oh no, one of them has gone crazy during the exam; he clearly exhibits neurotic traits.
Such incidents are commonplace in the college entrance examination halls.
Wait a minute, the candidate with exam number 1010XXXX, whose name is Shen Qi, looks somewhat familiar. Could he be that Olympic Math champion?
Are Olympic Math champion all driven crazy by exams?
This math exam is way too difficult!
The proctor continued to monitor Shen Qi's movements.
"Hoo..." Shen Qi took a deep breath, needing to calm himself down.
Fortunately, the second question in the final challenge brought Shen Qi a little bit of joy.
The second question asks: For any positive number a, prove that 1 < f(x) < 2.
I don't know which professor set the second question, but the method... is somewhat similar to that of math competitions.
Shen Qi rallied his spirits and, full of energy, moved on to the second question, which was also the last question on the college entrance examination math paper...