Chabashira Sae's tone held not a trace of warmth:
"Where do you think this is, some ordinary public university?"
"This is an elite school established by the Sakura Nation. Trash and defective products that cannot create value for society have no right to remain on this campus."
"Rules are rules."
"If you can't meet the school's requirements, pack up and leave. There is no room for negotiation."
The Class 1-D students, who had just been excitedly discussing points, now felt as though they were walking on thin ice.
"Alright, now for today's main event."
Chabashira Sae gave them no time at all to catch their breath or process what they had heard.
She pulled out the mock exam papers she had prepared beforehand from beneath the podium.
"Begin the mock exam immediately."
Chabashira Sae divided the papers into several stacks and handed them to the students in the front row.
"Pass them back."
"You have forty-five minutes. The full score is one hundred."
"Fortunately, this exam has nothing to do with expulsion, but I advise you to give it everything you've got."
"Because this mock exam concerns the upcoming midterms."
The papers quickly made their way around the classroom.
To the Class 1-D students, the rustling of papers was no different from a death knell.
Sudo Ken took the paper with trembling hands. The instant he saw the densely packed mathematical formulas, beads of sweat the size of soybeans appeared on his forehead.
"W-What are these things?"
"How could anyone possibly understand questions like this?"
Ike Kanji let out a despairing groan.
The entire classroom descended into chaos as panic spread wildly.
Tatsuya Sakuya accepted the paper passed from the row ahead and casually laid it flat on his desk.
He gave the questions a rough scan.
The questions on the first page were extremely easy, almost all basic problems that anyone who had studied even a little could score on.
Question One:
Question Two:
The first two were practically free points. As long as he followed the standard steps and avoided calculation errors, they were guaranteed scores.
His gaze continued downward to the advanced calculus section.
Then Tatsuya Sakuya spotted a rather interesting question.
Bonus Question: [Let f(x) be differentiable on the interval (a,b). Prove:
A necessary and sufficient condition for the derivative of f(x) to be strictly increasing on (a,b) is:
For any x1 ＜ x2 ＜ x3 in (a,b),
(x3 - x2) * (f(x2) - f(x1)) ＜ (x2 - x1) * (f(x3) - f(x2)) always holds.
Tatsuya Sakuya fell into thought, inwardly grumbling:
It was only the first month of school. The advanced mathematics curriculum had not even reached the Mean Value Theorem yet.
Besides, this problem was far from simple. It could even be called quite difficult.
To prove necessity, one only had to apply Lagrange's Mean Value Theorem twice, once on [x1, x2] and once on [x2, x3].
But proving sufficiency was difficult, so much so that there was no obvious place to start.
After thinking deeply for a while—
I see.
It was hard to tackle it head-on, so why not try proof by contradiction?
He could prove sufficiency through contradiction using the definition of the derivative and limits.
Tatsuya Sakuya felt secretly pleased, though he had no other intention behind it.
It was simply the thrill of suddenly finding inspiration and solving a difficult problem after racking his brains over it.
This mock paper had been designed quite interestingly.
The easy free-point questions at the beginning were meant to test the students' minimum level of intelligence.
The final bonus question, meanwhile, was both a trap and a touchstone placed there by the school.
On one hand, it was meant to determine whether the class hid any genuine academic prodigies.
On the other, it used such an extreme gap in difficulty to crush the students' wishful thinking.
From the corner of his eye, Tatsuya Sakuya glanced at Horikita Suzune beside him.
Her pen had clearly stalled over the latter half of the paper, and her breathing had grown somewhat hurried.
Evidently, those out-of-syllabus questions had caused her no small amount of trouble as well.
So, what score should I get?
It was only a mock exam anyway. The score itself did not matter.
Tatsuya Sakuya pondered for a moment.
His pen moved smoothly across the paper.
He quickly filled in the earlier basic questions selectively.
Then he carefully wrote out the bonus question in full, without missing a single word.
He precisely controlled his score within a range that was excellent, but by no means shocking.
Around seventy points.
That was enough to keep him at a decent level in Class 1-D, at least without ending up at the bottom.
Only the soft scratch of pens against paper remained in the classroom, along with the occasional sound of swallowing and sighing.
Forty-five minutes was neither particularly long nor particularly short.
For Tatsuya Sakuya, forty-five minutes was enough to finish every question.
But for people like Sudo and Ike, it felt as though every second lasted an age.
Ding-dong, ding-dong.
The bell rang right on time.
"Time's up. Everyone, raise your right hand immediately and stop writing."
Chabashira Sae rose to her feet, both hands pressed against the podium, her gaze icy.
"Stand up. Collect the papers from back to front."
"Any violation will be scored as a zero."
Wails of anguish erupted through the classroom once more.
Sudo Ken let go of his pen, his face ashen.
"I... couldn't do any of it."
Ike and Yamauchi were even worse off, slumped in their seats like soulless puppets.
The papers were swiftly collected and handed to Chabashira Sae.
Chabashira Sae organized and counted the papers on the podium.
She coldly swept her eyes over the heavily shaken students below.
"The results will be out tomorrow."
"One more thing."
Holding the papers, Chabashira Sae paused before leaving the classroom and delivered one final, heart-piercing remark.
"Enjoy your last moments of peace at this school."
The entire Class 1-D classroom sank completely into unprecedented gloom and despair.
"If the midterms are this difficult, I don't even dare imagine it."
"I couldn't understand the questions at all. There was even a bonus question."
Some students had even begun saying goodbye to their classmates beside them.
"Brother, let's have a proper farewell. At least I'll be able to say I once attended this class."
It was easy to imagine just how difficult the mock exam had been.
"If we just let everyone complain, then this mock exam will have been meaningless."
Hirata Yousuke stepped forward to encourage everyone. He did not want the class atmosphere to worsen.
"Everyone, this was only a mock exam, not the real thing."
"We still have time. Everyone, hurry and identify what you're lacking, then study hard."
"After all, every one of us genuinely earned admission to this elite school. As long as we put our hearts into it, we can make up for the lessons we've neglected."
"Just like you, Hirata. Everything you say always puts people at ease."
"If I were a girl, I'd already be in love with you."
Hirata Yousuke's words encouraged some of the dispirited students.
Tatsuya Sakuya watched all of this while thinking about tomorrow's points.
Then a voice suddenly interrupted him.
"Shiba, could you teach me how to solve this problem?"
Before you continue