On a cold Saturday morning in February, Maya stood outside a high school she had never visited before, clutching a sharpened pencil and an AMC 10 admission ticket. She had spent weeks working through past problems, timing herself, and reviewing solutions. But as she watched other students laughing and trading math puns, one thought kept looping in her head: “People like them become champions. I’m just hoping not to embarrass myself.”
Fast forward three years. Maya is standing on a different stage, this time under bright lights at the MATHCOUNTS Nationals Awards Ceremony. Her team just placed in the top 10. When someone asks her later how she did it, she doesn’t talk about “talent” or being a “genius.” She talks about a notebook full of mistakes, daily 30-minute practice sessions, and learning to stay calm when a problem looks impossible.
Stories like Maya’s are more common than you might think. Many math competition champions started as nervous first-timers, unsure if they “belonged” in contests like AMC, Math Kangaroo, or AIME. What changed wasn’t their IQ; it was their process, their mindset, and their support systems. In this ScholarComp guide, we step behind the scoreboards and talk about what champions really do differently—and what they wish they had known earlier.
This article is part of our “Inside Mathematics Competitions” series, which looks at contests from multiple angles. If you’re curious about event logistics, you might also like What Really Happens at Mathematics Competition Day. Here, we focus on something more personal: champion perspectives, candid stories, and concrete advice you can use to shape your own path.
Daniel didn’t take his first math competition seriously until ninth grade. He had heard about AMC 8 and MATHCOUNTS in middle school but never participated. By the time he learned what “AIME qualifier” meant, he assumed he was already behind students who had been training for years.
In his first AMC 10 attempt, Daniel scored solidly average for his school. He left several problems blank and misread one question he knew how to solve. Walking home, he felt the familiar story forming in his mind: “I’m just not a contest person. The real champions are born different.” But instead of quitting, he decided to treat his disappointment as data.
He opened the official AMC solutions, compared them to his scratch work, and started keeping a “mistake log.” For every missed problem, he wrote three sentences: what he tried, what went wrong, and what he should notice next time. That simple habit changed everything.
When asked to describe his practice routine, Daniel didn’t mention six-hour marathons or “grind culture.” Instead, he focused on sustainable habits.
He started with short, daily sessions—about 30 to 45 minutes after school. On Mondays and Wednesdays, he worked on old AMC 10 papers under timed conditions. On other days, he picked one or two problems just outside his comfort zone and dissected them slowly, writing full solutions even if he thought the step was “obvious.”
One evening, for example, he wrestled with a geometry problem involving three circles and a triangle. At first, he tried plug-and-chug computations. Nothing worked. He almost gave up. Then he remembered advice he’d read on platforms like ScholarComp: redraw the figure, label everything clearly, and look for patterns. After 40 minutes of trial and error, he spotted similar triangles and solved the problem with a single observation. That moment—when frustration turned into insight—became his favorite part of training.
Over time, Daniel shifted from “doing lots of problems” to “doing fewer problems more deeply.” When he met other high scorers, he noticed a pattern: they spent as much time reviewing and generalizing a problem as they did solving it. If a number theory problem used modular arithmetic in a clever way, he would summarize the idea in his notebook, then hunt for other problems where a similar trick might appear.
Daniel describes his biggest shift as “replacing identity with process.” At first, he was obsessed with labels like “AIME qualifier” or “top 10%.” He constantly compared his scores to others. Every test felt like a verdict on his talent.
Eventually, he tried a different approach: whenever he took a practice test, he asked himself one question afterward—“What did I learn about how I think?” If he rushed through easy problems and made careless errors, that was a thinking pattern to adjust. If he froze when a problem looked unfamiliar, that was a psychological habit to work on. Scores became feedback, not judgments.
He also learned to treat nerves as normal. On the morning of his second AMC 10, he felt that familiar stomach twist. Instead of trying to “get rid” of anxiety, he reframed it: “This means I care. Caring is good. I’ve done the work. Let’s see what happens.” He started the test by scanning and quickly doing the easiest problems, building early confidence before tackling the more challenging ones.
When younger students ask Daniel what they should do if they start “late” or feel behind, he offers three specific pieces of advice.
First, he says, build a mistake log. After every contest or practice set, choose your top three “teachable mistakes” and write them down: the error, the correct idea, and how you might recognize a similar pattern next time. Over months, this becomes a personalized textbook of your growth.
Second, he recommends starting small and consistent. Instead of planning for three-hour weekend sessions that never happen, commit to brief daily practice blocks. He likes the structure of one timed set per week, one day focused on reviewing solutions, and a few days devoted to exploring new topics—perhaps using competition guides from ScholarComp or problems from math club.
Finally, he encourages students to define success in stages. For his first year, his goals were simple: attempt all problems, reduce careless errors, and improve relative to his past scores. It wasn’t until later that he wrote “qualify for AIME” on a sticky note above his desk. That progression kept his motivation grounded in improvement rather than pressure.
Alina’s journey began in a small school where “math club” was mostly a place to finish homework. In sixth grade, a new teacher introduced MATHCOUNTS problems. The first one Alina tried took up half a page of scratch work and still didn’t make sense to her. She left club that day certain of two things: these problems were hard, and she wanted to learn how to solve them.
By eighth grade, she was the anchor of her school’s MATHCOUNTS team, leading them to the state competition and earning an individual top-five finish. The transformation didn’t happen because she suddenly became a “natural leader.” In fact, Alina was quietly shy and rarely volunteered answers in regular class. What changed was how she saw practice—and her role in the team.
Alina’s coach scheduled weekly practices using past MATHCOUNTS Sprint, Target, and Team rounds. At first, Alina approached these sessions like solo exams. She tried to get as many answers as possible and keep them to herself until the coach called for solutions.
One day, during a team round, the group spent several minutes stuck on a combinatorics question about seating arrangements. Time was ticking down. Everyone was mumbling ideas, scribbling diagrams, and getting nowhere. Suddenly, Alina paused and said, “Let’s stop. Can someone explain what we’re actually counting?”
She didn’t propose a solution; she asked a clarifying question. That shift changed the conversation. Another teammate restated the problem in their own words. Someone else broke it into cases. They realized they had been double-counting certain configurations. With just seconds left, they arrived at the correct answer—and won that practice round.
Afterward, the coach pulled Alina aside and pointed out what she had done. She had guided the group not by having the best idea, but by organizing the thinking. From then on, she began to treat math as both an individual and a collaborative sport.
In later practices, when they encountered a difficult geometry problem, she would say, “Let’s list what we know for sure” or “Can we draw this in a simpler way first?” Her teammates began to mirror her habits, and their overall performance improved.
One of the most surprising challenges for Alina wasn’t solving problems; it was explaining them quickly and clearly during the Countdown Round. She remembers a regional competition where she solved a problem first but stumbled while explaining her reasoning, which almost led the judges to doubt her answer.
To fix this, she started practicing short, verbal explanations at home. After solving a problem, she would pretend she was on stage and had to explain her solution to a judge who had never seen the problem before. Her rule: use simple sentences, mention the key idea, and check that each step logically followed from the last.
For instance, if a problem involved recognizing a Pythagorean triple, she would say out loud, “I saw a right triangle with side lengths that match a 3-4-5 triangle. That told me the hypotenuse must be 5, so the perimeter is 3 + 4 + 5.” Practicing this kind of concise explanation made her more confident during live rounds and also sharpened her own understanding.
At state-level MATHCOUNTS, she encountered a Countdown problem involving patterns in a sequence. She solved it quickly, but instead of blurting out a half-explained method, she took a breath and summarized the core pattern in one sentence. The moderator nodded, accepted her answer, and she advanced another round.
When reflecting on what helped her team reach state-level success, Alina rarely talks about individual brilliance. Instead, she highlights three habits that strong teams share.
First, they practice like it’s real. Her team regularly simulated full competitions: timed Sprints, Target rounds with strict pacing, and actual team rounds where communication had to be fast and efficient. These rehearsals helped them develop routines and reduce stress on the real competition day.
Second, they assigned roles during team rounds. One teammate might be in charge of writing final answers neatly, another focused on checking arithmetic, and someone else specialized in organizing the approach to multi-step problems. Alina often took the role of “strategy coordinator,” asking questions like, “Who’s working on which problems?” and “Do any of these problems share a common trick?”
Third, they learned from each other after every practice. If someone found a clever shortcut, they took a few minutes to explain it to the group. This way, a single insight became a shared team resource. Over time, their collective toolkit grew much richer than any one member’s.
Alina urges new competitors not to underestimate the power of explaining ideas to others. She points out that teaching a problem to a teammate forces you to clarify your own reasoning. If you can’t explain a solution simply, it’s often a sign that something is still fuzzy in your understanding.
She also encourages shy students to find small ways to contribute in team settings. You don’t have to be the loudest voice to make a difference. Ask clarifying questions, suggest organizing strategies, or volunteer to double-check calculations. These contributions often matter as much as coming up with the initial idea.
Finally, she reminds students that team results aren’t the only measure of success. Some competitions, like MATHCOUNTS or certain regional contests, have a strong team component, while others like AMC and AIME are strictly individual. Learning to collaborate deeply in one setting can still make you a better solo competitor in another, because you’re essentially collaborating with your “future self” every time you write down a clear solution that you’ll review later.
Ravi’s story is different from Daniel’s and Alina’s. He started doing math competitions early—AMC 8 in sixth grade, Math Kangaroo in elementary school, and local problem-solving contests. But what set him apart wasn’t early specialization; it was an almost playful attitude toward hard problems.
When he first encountered proof-based Olympiad questions, such as those on USAMO or USAJMO, he didn’t see them as intimidating walls. He saw them as puzzles that might take days to unlock. While many students grow frustrated when a problem doesn’t yield to a standard trick, Ravi became curious: “Why is this problem hard? What is it hiding?”
By the time he qualified for USA(J)MO, his routine looked very different from the multiple-choice practice many students focus on. He spent long stretches of time exploring fewer problems, writing detailed proofs, and comparing his solutions with official ones and with those shared in math circles.
In early years, Ravi fell into the same trap many AMC students do: he treated problems like boxes to check off. If he arrived at the correct numeric answer, he moved on. However, when he began preparing for contests like AIME and Olympiad, he discovered that this approach left gaps in his understanding.
He recalls a turning point during preparation for his first AIME. He had solved a challenging geometry problem, obtained the correct final integer, and congratulated himself. Later, in a training session, a mentor asked him to explain his solution. Within two minutes, Ravi realized he had no coherent narrative. He’d made several leaps of intuition that he couldn’t justify clearly.
From then on, he imposed a new rule on himself: for any interesting problem, especially in areas like geometry or number theory, he would write a complete, clean solution as if someone else would read it. That meant defining variables carefully, structuring proofs logically, and ending with a clear conclusion.
Take a functional equation problem he tackled in ninth grade. Instead of celebrating as soon as he guessed the function, he wrote, “We claim that f(x) = 2x + 1 for all real x,” and then built a step-by-step argument showing how the given equation forced that form and why no other solution was possible. That process took time, but it trained him to think like a mathematician, not just a contest solver.
Ravi’s Olympiad training introduced him to a slower, more reflective style of practice. Instead of solving 20 short problems in an evening, he might spend over an hour on one or two long problems, sometimes returning to them with fresh eyes the next day.
One problem, involving inequalities and symmetric expressions, sat on his desk for three days. The first evening, he tried common tools and got nowhere. The second day, he reread the problem, searched for invariants, and made progress on a partial inequality but couldn’t complete the proof. On the third day, while walking home from school, he suddenly realized he could apply the rearrangement inequality—a technique he had encountered months earlier but never used in this context.
He likes to say that he “lived with” that problem for a while. He thought about it in the shower, at lunch, and during quiet moments. Instead of seeing this as wasted time, he viewed it as part of the creative process. Olympiad-level problems often require this kind of incubation, where your subconscious continues working on the puzzle even when you’re not actively writing.
Ravi also drew on resources like math circles, problem books, and curated collections on platforms like ScholarComp. He categorized problems by theme—functional equations, inequalities, geometry, combinatorics—and tried to identify common strategies. When he recognized a familiar structure in a new problem, it felt like meeting an old friend in a new city.
High-level auditions like USA(J)MO often come with significant pressure. Ravi remembers the morning of his first Olympiad as strangely quiet. Unlike AMC or AIME, which are full of multiple-choice or short-answer problems, USA(J)MO offers a few deep problems over several hours. That format can feel both liberating and terrifying.
To manage his nerves, he reminded himself that his worth didn’t depend on the outcome of a single contest. He also followed a strategy he had practiced many times: read all the problems first, choose one that felt most accessible, and try to secure a full solution there before moving on. This gave him an early sense of progress and calm.
On that exam, he quickly found a combinatorics problem that resonated with techniques he had studied. He spent nearly two hours crafting a careful proof, writing slowly and checking each step. Knowing he had one strong solution allowed him to experiment more freely with the other problems without panicking about “zero score.”
Ravi emphasizes that Olympiad-style success is built on three pillars: strong fundamentals, patience with hard problems, and joy in the process.
He urges students not to skip foundational material. Contest math may feel advanced, but it still rests on algebraic fluency, Euclidean geometry basics, and comfort with proof techniques. Free resources like Khan Academy can help solidify these building blocks, while competition-focused resources can push you beyond school curricula.
He also suggests embracing the idea that some problems will take hours or even days. This isn’t a sign of weakness; it’s what serious problem solving looks like. Keeping a “long problem journal” where you record your attempts, partial ideas, and breakthroughs can show you how much your thinking evolves over time.
Finally, he encourages students to seek out community—math circles, school clubs, online forums, and peer study groups. Many of his biggest leaps came from seeing how others approached the same problem differently. Even for individual contests, math is rarely a solitary journey.
Although Daniel, Alina, and Ravi have very different stories, they share some striking similarities. None of them describe themselves as “the smartest in the room.” Instead, they talk about specific habits and support systems that, over time, compounded into high achievement.
For one, all three built regular practice routines that fit their lives. Daniel’s short daily sessions, Alina’s structured team practices, and Ravi’s long-form problem exploration might look very different on the surface, but each reflects a deliberate, consistent pattern. Rather than cramming before a contest, they treated preparation as part of their weekly rhythm.
They also took reflection seriously. Daniel’s mistake log, Alina’s habit of explaining solutions out loud, and Ravi’s written proofs all serve the same function: they turn each problem into a learning experience, not just a score. Champions don’t just count how many problems they solved; they analyze how they solved them and what they could do better next time.
Another shared trait is how they respond to setbacks. None of them have perfect records. Daniel missed early AIME cutoffs. Alina has lost tight Countdown battles. Ravi has stared at Olympiad problems for hours and written nothing he felt proud of.
What distinguishes them is not the absence of failure, but their interpretation of it. They see a low score as a snapshot, not a permanent label. When Ravi once scored significantly below his expectation on a mock Olympiad, he spent time dissecting why—he had rushed his first solution and written too informally, leading to lost points. That experience led him to adopt a slower, more deliberate writing style, which later helped him on actual exams.
Alina recalls leaving a competition one year feeling crushed. Her team had narrowly missed advancing. After a week away from contest prep, she returned with a renewed resolve. In hindsight, she sees that disappointment as a key turning point, pushing her to seek better resources, attend a summer math program, and help organize more serious practices for the following year.
Each champion also found a way to connect math competitions to something deeper than medals. For Daniel, it became about self-improvement and proving to himself that he could grow in an area that once intimidated him. For Alina, competitions opened doors to friendships and a sense of belonging to a community that loved challenges. For Ravi, problem solving itself became a source of joy—an intellectual playground where creativity and rigor met.
This perspective matters. Students who tie their self-worth only to scores often burn out or lose confidence after a single bad result. Champions, by contrast, usually care deeply about performing well, but they also see contests as part of a longer journey in learning, discovery, and personal growth.
Platforms like ScholarComp can support this mindset by framing competitions as opportunities to explore, learn, and connect—not just as tests. Guides, interviews, and resource collections help students see the broader landscape: how different contests compare, how scoring works, and how to plan a sustainable path forward.
It’s one thing to read inspiring stories; it’s another to turn them into action. You don’t have to copy any champion’s routine exactly. Instead, borrow their principles and adapt them to your level, goals, and schedule.
If you’re just starting out, pick one or two competitions to target, such as AMC 8, Math Kangaroo, or a regional middle school contest. Learn the format and scoring rules—our series article How Mathematics Competitions Are Scored and Judged can give you an overview of what different scoring systems reward. Then set modest goals: attempt every problem, reduce careless mistakes, and practice steady timing.
Plan for consistent weekly practice. For example, you might designate two days for working through past papers under loose time constraints, one day for reviewing mistakes and reading detailed solutions, and one day for exploring new topics or challenge problems from problem banks or competition-focused books. Keep sessions manageable; 30–60 minutes of focused work often beats multi-hour sessions of distracted effort.
One of the clearest lessons from champions is the value of reflection. After each test or serious practice set, take 10–15 minutes to review—not just what you missed, but why.
Try a simple three-part reflection:
Over time, these reflections help you design smarter practice. If you repeatedly struggle with geometry, you might focus a week on that topic, using targeted problems and video explanations. If you notice recurring time pressure, practice timed sets with strict pacing, gradually learning how to gauge when to move on from a stuck problem.
Every champion in this article benefited from some mix of independent work and community support. Solo practice builds concentration and personal problem-solving skills. Community—through math circles, school clubs, online groups, or coaching—provides motivation, feedback, and exposure to different perspectives.
If your school doesn’t have a math team, consider starting an informal group. Gather a few classmates, choose a set of problems each week, and meet to discuss solutions. Rotate who explains problems. Use competition guides and problem sets from resources like ScholarComp to structure your sessions. You may be surprised by how quickly your group’s collective skill grows.
Online practice platforms and adaptive learning tools can also supplement your preparation. These resources often offer problem banks categorized by topic and difficulty, which can help you address specific weaknesses identified in your reflections. Just remember that clicking through problems quickly is less valuable than deeply understanding a smaller set.
Champions often recommend setting layered goals: process goals, performance goals, and long-term aspiration goals. For example, your process goals might include “practice three times per week” and “write out full solutions for at least two problems each session.” Performance goals could be “increase AMC score by 5 points” or “solve at least half of the Target round questions.” Long-term aspirations might involve qualifying for AIME or reaching state-level in MATHCOUNTS.
By focusing primarily on process goals, you ensure that success remains largely under your control. You can’t guarantee a specific ranking in a given year, but you can control how you prepare, how you review, and how you respond to setbacks.
Also, recognize that your path may not look like anyone else’s. Some students reach high scores quickly, then plateau. Others, like Daniel, steadily improve over several years, eventually surpassing peers who seemed “naturally gifted” early on. Your timeline is your own; the key is to keep learning and adjusting.
The champions in this article didn’t start as legends. They began as curious, anxious, hopeful students, just like thousands of others walking into competition rooms each year. What distinguished them over time were not superhuman abilities, but deliberate habits, resilient mindsets, and a willingness to treat every competition—win or lose—as a stepping stone.
Daniel shows that you can start later than others and still reach high levels if you build consistent practice and learn from your mistakes. Alina demonstrates that teamwork, communication, and leadership can transform both your scores and your confidence. Ravi illustrates how deep curiosity and a love for hard problems can carry you into advanced, proof-based competitions like USA(J)MO.
Your journey might lead to national stages, local trophies, or simply a deeper appreciation for mathematical thinking. All of these outcomes are valuable. Competitions are not just about ranking; they’re about discovering how you think, how you learn, and how you respond when a problem refuses to yield easily.
As you move forward, consider borrowing one habit from each champion: keep a mistake log like Daniel, explain your solutions aloud like Alina, and occasionally “live with” a problem for days like Ravi. Layer these practices onto your own routine, at your own pace. Explore more competition stories, guides, and preparation resources on ScholarComp, and when you walk into your next contest room, remember—you’re not just chasing a score; you’re writing a story of growth that will stay with you far beyond any single test.
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