The wall
clock in Class XII Science 1 showed 10:15 AM. The Sukabumi sun began to rise,
heating the school roof, but inside the air-conditioned room, the atmosphere
was frozen. Cold, rigid, and full of pressure.
Second
period: Advanced Mathematics with Mr. Arman.
Mr. Arman
wasn't just any teacher. He was a living legend at Rajawali High. Rumor had it
he used to be a guest lecturer at top universities before deciding to "descend
the mountain" to teach high school kids for reasons unknown to anyone. His
teaching style was unique; he disliked students who merely memorized formulas.
He liked students who thought.
And today,
Mr. Arman was in the mood to torture.
On the wide
whiteboard stretching across the front of the class, Mr. Arman had just written
a word problem about Related Rates combined with three-dimensional geometry.
The problem looked simple—a cone being filled with water—but the variables Mr.
Arman provided were minimal, as if he intentionally omitted half the crucial
information.
"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 water depth is 6 cm?"
Mr. Arman
put down his marker, then turned to face the 30 elite students before him.
"This is a
standard National Exam problem, perhaps even too easy for Olympiad level," Mr.
Arman said, his baritone voice calm yet intimidating. "But I want you to solve
it without using partial derivatives. Use pure geometric logic combined with
basic calculus. Who dares?"
Silence.
Nadia,
sitting in the front row, bit the end of her pen. Her forehead creased deeply.
She knew how to solve it using the quick formulas taught at her expensive cram
school, but Mr. Arman forbade "rat paths." Mr. Arman wanted a "highway" built
from scratch.
While the
whole class was racking their brains until smoke nearly came out, Salim Nur
Hidayah was busy with his own world in the back row.
His math
notebook was open, but he wasn't writing numbers. On the very last page, Salim
was sketching a rough drawing: a Corn Fritter with wings and a cape, fighting
against a Spicy Tofu Monster. He named his character "Captain Corn: The Oily
Avenger."
"Oy," Dani
whispered beside him. "What the hell are you doing drawing fried snacks? Mr.
Arman is in beast mode right now."
"I'm still
hungry, Dan. The fritters at the canteen ran out, I only got a piece of
half-cooked tempeh," Salim replied without looking up, still absorbed in adding
shading details to the corn kernels in his drawing. "Besides, the problem is
boring. It's a classic question. The answer is definitely going to be an ugly
fraction."
"Shhh! Don't
be arrogant. Look, even Nadia is sweating," Dani glanced to the front.
Sure enough,
Nadia finally raised her hand. Her ambition was indeed unstoppable. "I'll try,
Sir."
Mr. Arman
nodded. "Go ahead, Nadia."
Nadia walked
to the front. The black marker in her hand danced across the whiteboard. She
started by drawing a cone diagram, then wrote down the triangle similarity
ratios to find the relationship between the radius and the water height.
Then she
inputted the cone volume formula.
V = 1/3 pi
r^2 h
V = 1/3 pi
(h/3)^2 h
V = (pi/27)
h^3
Nadia's
steps were systematic, neat, and procedural. She derived it with respect to
time (t).
dV/dt =
(pi/27) * 3h^2 * (dh/dt)
2 = (pi/9) *
(6)^2 * (dh/dt)
Nadia kept
writing until the board was almost full of numbers and symbols. Cold sweat
trickled down her temple. She was extremely meticulous, afraid of missing a
single decimal or exponent. After nearly seven minutes, she finally reached the
final result.
Dh/dt = 1 /
(2pi) cm/second
Nadia took a
step back, looking at her work with satisfaction. She turned to Mr. Arman.
"Done, Sir. The answer is 1 over 2 pi."
Mr. Arman
observed the board without expression. He didn't praise her immediately. His
eyes traced every line of Nadia's writing.
"Good
process, Nadia. Neat. Very... procedural," Mr. Arman commented. There was a
hint of disappointment in the word 'procedural'. "The answer is correct. But
you spent seven minutes and half of my marker ink for something that could be
solved in three lines."
Nadia's face
turned bright red. She had done everything right, but it still felt like she
wasn't good enough in Mr. Arman's eyes.
"Does anyone
have another way? A more... elegant way?" Mr. Arman asked, his eyes sweeping
the class like a talent scout radar.
Mr. Arman's
eyes stopped at the back corner near the window. There, Salim was suppressing a
small chuckle looking at his silly Corn Fritter drawing.
"Salim," Mr.
Arman called. His voice wasn't loud, but it was enough to make the whole class
turn around.
Salim jolted
in surprise. He hurriedly closed his sketchbook. "Uh, yes, Sir? What is it,
Sir? Did the Tofu Monster attack?"
The class
chuckled. Rinto, a wealthy student sitting across the room, snorted cynically.
"What a hillbilly. Making kampong jokes in an elite class."
Mr. Arman
didn't laugh. He stared at Salim sharply. "It seems you have something more
interesting than Calculus on your desk. Come forward. Solve this problem using
a different method than Nadia's. If you can't, get out of my class and stand by
the flagpole until the final bell."
Dani looked
at Salim with a pale face. "You're dead, Lim. The sun is scorching right now."
Salim let
out a long sigh. His face shifted from shock to his usual lazy mode—his default
setting. He stood up, walking sluggishly toward the whiteboard. His sneakers
squeaked softly on the polished ceramic floor.
Salim
stopped in front of the board, right next to Nadia's crowded writing. He
glanced at the problem briefly, then turned to Mr. Arman.
"Sir, can I
borrow the red marker? Just to be different. I'm bored of seeing black, it
looks like the future of my wallet," Salim qupped dryly.
Mr. Arman
tossed the red marker. Salim caught it with one hand without looking.
Salim didn't
erase Nadia's work. Instead, he drew a small line next to Nadia's cone diagram.
"Nadia was
too focused on the volume formula," Salim mumbled, his voice loud enough for
the silent class to hear. "Even though the rate of height change is just a
matter of the water's surface area at that exact moment."
Salim wrote
quickly. His handwriting was chicken scratch, a stark contrast to Nadia's
computer-like script.
Line 1:
Water Surface Area (A) = pi r^2
When h = 6,
since r = h/3, then r = 2.
So A = 4 pi.
Line 2: Flow
Rate (Q) = A * Rising Velocity (v)
2 = 4 pi * v
Line 3: v =
2 / 4 pi = 1 / 2 pi
Done.
Time taken:
15 seconds.
Salim capped
the marker. "Done, Sir."
The silence
in the class was different this time. If before it was the silence of thinking,
now it was the silence of shock. Nadia gaped at the three lines of red writing.
The long-winded formula she had painstakingly derived was completely slashed by
Salim's simple logic.
"Wait,"
Rinto interrupted, refusing to accept it. "Where did that formula come from?
Flow Rate = Area * Velocity? That's a physics formula for a cylindrical pipe!
This is a cone, Lim! The surface area changes with height. You can't use a
static formula!"
Nadia nodded
in agreement with Rinto. "Yes, Sir. That's just a lucky coincidence.
Conceptually in calculus, it's wrong because he assumed the cross-sectional
area is constant."
Salim turned
around, looking at Rinto and Nadia with a bored gaze. His cold nature surfaced.
"You guys
are overthinking it," Salim said. "I didn't assume the area was constant. I
calculated the area at that exact second. At the second where h=6, the
cross-sectional area is 4 pi. The incoming water is 2 cubic cm. Imagine that
water as a thin plate placed on top of that 4 pi surface. The thickness of that
plate is the height increase. So just divide the incoming volume by the base
area at that moment. That's the basic principle of integrals, Nad. Integrals
are just stacks of thin plates. You were busy deriving the volume formula, when
you only needed to look at the cross-section slice."
Salim
pointed at the board with the marker tip. "Math isn't about memorizing which
road to take. It's about knowing where your destination is, then finding a
shortcut so you don't get tired. I'm hungry, I want to save energy."
Mr. Arman
smiled. A wide smile that was rarely seen.
"Infinitesimal
logic," Mr. Arman murmured. "You used Leibniz's basic concept. Seeing change as
instantaneous thin slices. Rinto, Nadia, what Salim did is valid. That is the
core of differential calculus. He dissected the instantaneous phenomenon, not
the whole phenomenon."
Mr. Arman
patted Salim's shoulder. "Sit down, Salim. And... that fritter drawing of
yours, add some chili sauce to make it tastier."
The class
erupted in laughter. The tension melted away. Salim walked back to his seat
with an expressionless face, as if he had just taken out the trash, not solved
a complex problem in front of a killer teacher.
As he sat
down, Dani shook his head. "You're crazy. I swear, what's inside your brain?
Fiber optic cables?"
"It's filled
with electricity bills and plans to buy internet data, Dan," Salim answered
while reopening his sketchbook.
In the
opposite row, Maya turned back. She smiled sweetly at Salim, a look of
admiration she couldn't hide. Salim, realizing this, just nodded awkwardly,
then pretended to be busy looking for an eraser.
However, not
everyone was impressed.
In the
middle row, Rinto clenched his fist. He hated seeing Salim. He hated how
Salim—who was poor, whose bike was junk, whose shoes were filthy—could shine so
brightly in front of everyone—especially in front of Maya.
"Just a
fluke," Rinto muttered to his seatmate. "Just wait for the exams. He's just
lucky."
Meanwhile,
Salim had resumed his drawing. He added details to the Spicy Tofu Monster
character. This time, he gave the monster a face that slightly resembled the
pouting Nadia.
"Lim," Rizki
whispered from the seat in front of Salim, turning his body slightly.
"What, Ki?"
"Do you
realize, the way you thought just now... that wasn't how a high schooler
thinks," Rizki said softly, his eyes sharp, as if analyzing his own best
friend. "You cut the logic compass. You eliminated the time variable. It was...
extremely efficient. Too efficient."
"That's what
lazy people do, Ki. Lazy people always look for the fastest way to finish a
job," Salim answered lightly.
"Or maybe
you just have a talent for being a strategist," Rizki replied. "It's just a
shame you only use your talent to calculate discounts on fried snacks."
Salim fell
silent for a moment. He stared at the whiteboard in front, seeing his red
writing standing next to Nadia's black writing.
Strategy,
huh? Salim thought. What's the use of strategy if my enemy is just poverty?
Poverty can't be calculated with integrals. It just arrives, like a constant
variable that can't be eliminated.
The bell for
the next period rang. Salim closed his book. Math was over. Now it was time to
face another reality: History class, where he had to memorize the past, even
though he was more dizzy thinking about his own future.