Faking your way through Calculas

Imagine being most of the way through a year of math to realize you don't know symbols?

Jeff slouched in his chair at the back of the physics club room, a dimly lit corner of Westridge High where the after-school Calculus-Based Physics Club met every Tuesday. The club had been his refuge for most of senior year—a place to geek out over motion, forces, and energy with a dozen other kids who didn’t roll their eyes at equations. He wasn’t the loudest or the flashiest, but he always turned in his problem sets, and they were always right. No one asked how he got there; they just nodded and moved on.


Today, though, felt off. Mr. Holmes, the club’s advisor with a penchant for tweed and coffee stains, walked in without his usual grin. He grabbed a piece of chalk and scrawled five problems across the board, each bristling with symbols and integrals. “Solve these for today’s lesson,” he said, voice flat, then sat down to grade papers.


Jeff stared at the board. His stomach twisted. Four symbols—∂, ∮, ∇, and a weird squiggle he couldn’t even name—glared back at him like gatekeepers to a club he didn’t belong in. He raised his hand, tentative. “Uh, Mr. Holmes? I don’t know what those four symbols mean.”


The room went quiet. Mr. Holmes looked up, brow furrowed. “What do you mean, Jeff?”


“I mean… I don’t know them. Never seen ‘em before.” Jeff’s face burned. The other kids exchanged glances, some stifling smirks.


Mr. Holmes set down his pen, leaning forward. “Jeff, those are core calculus symbols. Partial derivatives, integrals, gradients… how have you been keeping up all year without knowing calculus?”


The room erupted in murmurs. Sarah, the club’s unofficial math prodigy, piped up, “We’ve known the whole time, Mr. Holmes. Jeff doesn’t know calc.”


“Yeah,” added Mike, grinning. “But he still gets the answers right. Always has. We just figured he was, like, vibing through it.”


“Vibing?” Mr. Holmes repeated, incredulous. He pinched the bridge of his nose. “You’re telling me Jeff’s been solving calculus-based physics problems all year… without knowing calculus?”


“Yup,” Sarah said, shrugging. “He just thinks about the problems differently. Like, he describes the motion or the forces in his head and lands on the answer.”


Jeff sank lower in his seat, bracing for the inevitable. He was done for—kicked out for sure.


Mr. Holmes clapped his hands. “Alright, everyone except Jeff, take a 15-minute walk around the school. Go.”


The other kids shuffled out, whispering. Jeff stayed glued to his chair, heart pounding. This was it. The boot. He stared at his sneakers, waiting for the verdict.


But Mr. Holmes didn’t yell or lecture. Instead, he grabbed a fresh piece of chalk and moved to the board. “Jeff,” he said, “you’re not in trouble. You’ve been pulling off something remarkable, and I didn’t even notice. Let’s fix the gaps.”


For the next 15 minutes, Mr. Holmes broke down the symbols Jeff didn’t know. He sketched ∂ and explained partial derivatives as rates of change in multiple directions. He drew ∮ and walked through integrals as tools for summing continuous quantities. ∇ was the gradient, a vector pointing to the steepest climb. The squiggle—∝—meant proportionality, a shortcut for relationships. Then he wrote two equations: the fundamental theorem of calculus and the chain rule. “These,” he said, “unlock most calculus problems you’ll see here. Memorize them. Play with them.”


Jeff nodded, scribbling notes, his mind racing to connect the symbols to the physics he’d been intuiting all year. It was like someone had handed him a map to a city he’d already been navigating blind.


The other kids trickled back in, eyeing Jeff like he was a dead man walking. They’d clearly expected him to be gone, maybe crying in the hallway. Instead, Mr. Holmes clapped his hands again. “Okay, Sarah, Mike, Priya—each of you put one of your calculus homework problems on the board. Let’s see what we’re working with.”


The three exchanged wary looks but complied, writing up problems involving integrals, derivatives, and vector fields. The rest of the club leaned back, expecting the usual slog.


Jeff stood, marker in hand, and tackled the first problem—a projectile motion with air resistance. He recognized the integral now, saw how it summed the forces over time. He applied the chain rule to the second, a related rates problem, and used the gradient for the third, a potential energy field. In under five minutes, he’d solved all three, steps neat and answers correct.


The room was silent. Sarah’s jaw hung open. Mike just said, “Dude.”


Mr. Holmes grinned, wiping chalk dust off his hands. “Alright, back to today’s problems. Jeff, you’re with us.”


The club resumed, kids scribbling and debating as if nothing had happened. Jeff sat back down, heart still racing, but now with a quiet fire. He wasn’t just vibing anymore. He had the map, and he was ready to run.