The wall clock in Class XII Science 1 ticked with a rhythmic, clinical precision, marking 10:15 AM. Outside, the Sukabumi sun had begun its ascent, baking the tiled roofs of the school complex until the air shimmered with heat.
However, inside the air-conditioned sanctuary of the classroom, the atmosphere was frozen. It was a sterile, pressurized silence—the kind of cold that didn't just bite the skin but settled deep into the marrow of one's bones.
Second Period: Advanced Mathematics with Mr. Arman.
Mr. Arman was no ordinary educator. Within the hallowed, expensive halls of Rajawali High, he was a living legend. Rumor had it that he was once a distinguished visiting professor at a top-tier international university before deciding to "descend from the mountain" to teach high schoolers for reasons known to no one.
His teaching style was as eccentric as it was brutal; he loathed students who merely memorized formulas. He hunted for those who could think. And today, Mr. Arman was in the mood for a hunt.
On the expansive white board that spanned the front of the room, Mr. Arman had just finished scrawling a word problem. It was a challenge involving Related Rates intertwined with three-dimensional geometry. On the surface, it looked deceptively simple—a classic cone-shaped water tank problem. But the variables provided were sparse, almost as if he had deliberately stripped away half the vital information.
THE PROBLEM:
"An inverted conical container has a base radius of 4 cm and a height of 12 cm. If water is poured into the container at a rate of 2 cubic cm per second, how fast is the water level rising when the depth of the water is exactly 6 cm?"
Mr. Arman capped his marker with a sharp click and turned to face the thirty elite students. His steady, baritone voice was calm, yet it carried an intimidating weight.
"This is a standard national entrance exam problem. In fact, it might be considered too elementary for an Olympiad level," he said, his eyes scanning the room like a radar. "However, I want you to solve it without using partial derivatives or rote-memorized shortcuts. I want pure geometric logic combined with foundational calculus. Who dares to step up?"
Total silence.
Nadia, seated in the front row, gnawed on the end of her expensive gel pen. Her brow was furrowed in a deep, agonizing line of concentration. She knew the "shortcut" formulas taught at her high-end cram schools—tricks designed to bypass the 'why' and jump straight to the 'how.'
But Mr. Arman had forbidden the "back alleys." He demanded a "highway" constructed from the ground up, built on first principles.
While the rest of the class struggled until their mental gears practically smoked, Salim Nur Hidayah was occupied in a world of his own at the back of the room.
His math notebook was open, but there wasn't a single number on the page. On the very back leaf, Salim was meticulously sketching a crude but detailed masterpiece: a piece of Bakwan—a deep-fried corn fritter—wearing a tattered superhero cape and a mask, locked in mortal combat against a monstrous, oozing 'Tahu Gejrot' creature. He had dubbed the character "Captain Corn: The Oily Avenger."
"Pst," Dani hissed beside him, leaning over. "What the hell are you doing, Lim? You're drawing fried snacks while Arman is in 'Beast Mode'?"
"I'm still hungry, Dan. The canteen ran out of Bakwan during the first break. I only managed to snag a piece of Tempe Mendoan that was so undercooked the flour felt like wet clay," Salim replied without looking up. He was currently adding cross-hatch shading to the individual corn kernels on the hero's chest. "Besides, the problem is boring. It's a classic. The answer is bound to be an ugly fraction."
"Shut it! Don't be cocky. Look at Nadia—she's literally sweating," Dani whispered, glancing toward the front.
Sure enough, Nadia's ambition eventually outweighed her hesitation. She raised her hand, her movements stiff. "I'll try, Sir."
Mr. Arman gave a curt nod. "Proceed, Nadia."
Nadia marched to the front. The black marker in her hand danced across the white surface with mechanical precision. She began by drawing a perfectly scaled diagram of the cone, followed by the ratios of similar triangles to establish the relationship between the radius (r) and the height (h) of the water.
Next, she laid out the volume of a cone:
V = (1/3) * π * r² * h
Substituting the radius in terms of height (r = h / 3):
V = (1/3) * π * (h / 3)² * h = (π / 27) * h³
Nadia's steps were systematic, neat, and strictly procedural. She proceeded to differentiate with respect to time (t):
dV/dt = (π / 27) * 3 * h² * (dh/dt)
2 = (π / 9) * (6)² * (dh/dt)
She continued writing until the board was almost entirely consumed by symbols and calculations. A bead of cold sweat rolled down her temple. She was terrifyingly meticulous, double-checking every decimal and power. After nearly seven minutes of grueling mental labor, she finally arrived at the conclusion.
dh/dt = 1 / (2π) cm/sec
Nadia stepped back, exhaling a breath she hadn't realized she was holding. She looked at Mr. Arman with a flicker of pride. "Finished, Sir. The answer is 1 over 2π."
Mr. Arman studied the board without expression. He didn't offer immediate praise. Instead, his eyes traced the path of her logic, lingering on every line.
"A solid process, Nadia. Organized. Very... procedural," he commented. There was a subtle hint of disappointment in the word 'procedural.' "The answer is correct. But you spent seven minutes and half my marker's ink on something that could have been resolved in three lines."
Nadia's face burned a sudden, violent crimson. She had done everything perfectly, yet she still felt inadequate in his eyes.
"Does anyone have another way? A more... elegant approach?" Mr. Arman asked, his gaze sweeping the room again.
His eyes came to a dead stop in the back corner, near the window. There, Salim was struggling to suppress a chuckle at his silly drawing of Captain Corn.
"Salim," Mr. Arman called out. It wasn't loud, but it was enough to make the entire class swivel their heads.
Salim jerked upright, his heart hammering against his ribs. He slammed his notebook shut with a loud thwack. "Uh, yes, Sir? What is it? Is the Tahu Gejrot attacking?"
A ripple of suppressed laughter went through the room. Rinto, the wealthy student sitting across the aisle, snorted with derision. "Useless peasant. Still trying to be a village clown in an elite class."
Mr. Arman didn't laugh. He stared at Salim with a piercing intensity. "It seems you have something far more fascinating than Calculus on your desk. Come forward. Solve this problem using a method different from Nadia's. If you fail, you will leave my classroom and stand at the flagpole until the final bell rings."
Dani looked at Salim with a ghostly pale face. "You're dead, Lim. The sun is at its peak out there."
Salim let out a long, weary sigh. His expression shifted from startled to his usual 'default mode'—one of profound laziness. He stood up, his sneakers squeaking softly on the polished ceramic floor as he walked toward the front.
He stopped before the board, standing right next to Nadia's cramped, dense calculations. He glanced at the problem for a brief second, then turned to Mr. Arman.
"Sir, can I borrow the red marker? To spice things up? I'm bored of the black ink—it reminds me too much of the future of my wallet," Salim remarked flatly.
Mr. Arman tossed the red marker. Salim caught it mid-air with one hand without even looking.
Salim didn't erase Nadia's work. Instead, he drew a small, simple horizontal line next to her cone diagram.
"Nadia focused too much on the volume formula," Salim murmured, his voice carrying clearly in the silent room. "But the rate of height change is actually just a matter of the water's surface area at that specific instant."
Salim began to write in red ink:
Line 1: Surface Area (A) calculation
A = π * r²
(At h = 6, r = 6/3 = 2)
A = π * (2)² = 4π
Line 2: Relationship between Flow Rate (Q) and Velocity (v)
Q = A * v
2 = (4π) * v
Line 3: Final result
v = 2 / (4π) = 1 / (2π)
Done.
Total time taken: 15 seconds.
Salim capped the marker. "That's it, Sir."
The silence that followed was different this time. Before, it was the silence of calculation; now, it was the silence of pure, unadulterated shock. Nadia stared at the three lines of red ink, her mouth slightly agape. The long, winding path she had trekked with such difficulty had been bypassed entirely by Salim's simple logic.
"Wait," Rinto interrupted, unable to accept what he was seeing. "Where did that formula come from? Flow = Area x Velocity? That's a physics formula for fluid dynamics in a cylindrical pipe! This is a cone, Salim! The surface area is constantly changing with the height. You can't use a static formula!"
Nadia nodded in agreement, her eyes flashing. "Exactly, Sir. It's just a lucky coincidence. Conceptually, it's wrong because he's treating the cross-sectional area as a constant."
Salim turned, looking at Rinto and Nadia with a look of profound boredom. His "Cold Mode" had activated.
"You guys are overcomplicating things," Salim said. "I didn't treat the area as a constant. I calculated the area at that exact second. At the second where h = 6, the cross-section is 4π."
He tapped the diagram. "Imagine the water entering as an infinitely thin disc being placed on top of that 4π surface. The thickness of that disc is the rise in height. So, you just divide the incoming volume by the surface area at that moment. It's the core principle of integration, Nadia. Integrals are just a stack of thin discs."
Salim pointed at the board with the tip of the marker. "Mathematics isn't about memorizing which path to take. It's about knowing your destination and finding the shortest route so you don't get tired. I'm hungry, and I need to conserve my energy."
Mr. Arman smiled. It was a wide, genuine grin—a sight as rare as a solar eclipse.
"Infinitesimal logic," Mr. Arman whispered. "You are using Leibniz's fundamental concept. Viewing change as a series of instantaneous, thin slices. Rinto, Nadia, what Salim did is entirely valid. It is the very heart of differential calculus. He dissected the phenomenon of the 'moment' rather than the phenomenon of the 'whole'."
Mr. Arman patted Salim on the shoulder. "Sit down, Salim. And... as for that Bakwan drawing of yours? Add some chili sauce to it. It'll taste better."
The classroom erupted in laughter, the tension finally breaking. Salim walked back to his seat with a vacant expression, as if he had just finished taking out the trash rather than solving a complex problem in front of a killer teacher.
As he sat down, Dani shook his head in disbelief. "You're a freak, man. Seriously, what's in your brain? Fiber optic cables?"
"Electricity bills and a plan to buy a data package, Dan," Salim replied, reopening his sketchbook.
Across the room, Maya turned around. She gave Salim a sweet, lingering smile—an look of admiration she couldn't quite hide. Salim, noticing the gaze, gave a stiff, awkward nod and immediately pretended to be busy looking for an eraser.
However, not everyone was impressed.
In the middle row, Rinto's knuckles turned white as he clenched his fists. He hated Salim. He hated how this scholarship kid—with his beat-up bike, his worn-out shoes, and his faded uniform—could shine so brightly in front of everyone. Especially in front of Maya.
"Just luck," Rinto hissed to his seatmate. "Let's see him during the actual exams. He's just a fluke."
Meanwhile, Salim had returned to his drawing. He was adding more detail to the Tahu Gejrot monster. This time, he gave the monster a face that looked suspiciously like a pouting Nadia.
"Lim," Rizki whispered from the seat in front, turning slightly.
"Yeah, Ki?"
"Do you even realize?" Rizki asked softly, his eyes narrow and analytical. "The way you thought just now... that's not how a high schooler thinks. You bypassed the logic. You eliminated the time variable. It was... efficient. Dangerously efficient."
"I told you, Ki. Lazy people always find the fastest way to get work done," Salim replied airily.
"Or maybe you're just a natural strategist," Rizki countered. "It's a shame you only use that talent to calculate the discount on fried snacks."
Salim fell silent for a moment. He stared at the board, seeing his red ink standing beside Nadia's black script.
Strategy, huh? Salim thought. What use is strategy when my only enemy is poverty? You can't calculate poverty with an integral. It just exists, like a constant variable that you can never quite eliminate.
The bell for the next period rang. Salim closed his book. Mathematics was over. Now it was time to face a different reality: History class, where he would be forced to memorize the past, even as he struggled to figure out his own future.