In 2021, I achieved 1st place in NSW for Mathematics Extension 1 (3 Unit) and 8th place for Mathematics Extension 2 (4 Unit).
On paper, these results look clean and impressive. Most people think I had some natural talent or discovered some hidden trick. In reality, this came as a product of a long, sometimes frustrating and constantly fluctuating process that involved a lot of self-doubt, adjustment, and learning how to study mathematics properly.
What mattered most was the way I approached maths day after day, especially when progress wasn't obvious. Looking back now, everything that worked for me fits into three broad principles.
Understanding the Maths — Not Just Doing the Maths
One of the biggest mistakes I see students always make that honestly drives me crazy is equating success in maths with getting the right answer as quickly as possible. Yes, in hindsight this seems like a logical thought process. However, at Extension level, speed alone doesn't get you far. What matters is understanding, justification, and the ability to adapt when a question doesn't look familiar.
"I established a rule that I didn't truly understand something if I couldn't explain why it worked."
This required me to slow down, revise definitions again, and occasionally sit in perplexity for longer than I wanted to while others made "advances" on me. Although it wasn't always effective right away, it fundamentally altered my attitude to problem-solving.
Math becomes versatile after you grasp the fundamental concepts. When a question is phrased differently or incorporates topics in novel ways, you cease freaking out. You reason your way through rather than looking for a method that you have committed to memory.
Additionally, depth was significantly more important than quantity. I purposefully looked for challenging problems—those that make you consider, defend, and occasionally fail before achieving. Those questions trained my ability to stay calm under pressure and taught me how to break complex problems into manageable parts.
Over time, this approach made maths feel less like memorisation and more like logical problem-solving, which is exactly what Extension exams are designed to reward.
Consistency and Discipline Beat Talent Every Time
Nearly everyone in the room is competent at the Extension level. If most students weren't already proficient in maths, they wouldn't be enrolled in 3U or 4U. It's not intelligence that sets pupils apart; rather, it's what they do when the job becomes difficult. Those quiet moments no one notices.
Early on, I deliberately chose to approach math as a subject that required constant focus rather than spurts of inspiration. On certain days, this meant concentrated, productive sessions where everything came together. On other days, it meant feeling as though nothing was happening while staring at an issue for an excessive amount of time. I discovered that I shouldn't overreact to either. I came to understand that mathematics progression is rarely linear.
"There was a quiet assurance that came with always showing up, no matter how I felt. Difficult subjects eventually ceased to be so daunting just by virtue of their familiarity. Even 'math anxiety' is frequently caused by unfamiliarity rather than difficulty."
Exams were coming up, and I wasn't attempting to "get serious" all of a sudden. I was already accustomed to math. Because of this constancy, there were fewer surprises, less stress, and far greater confidence when taking tests.
Training Like It Was an Exam, Not Just Studying for One
Understanding and perfecting your knowledge of the content is obviously crucial. However, most people miss that it's just one aspect of doing well on an exam. Exams need to be approached as though they were their own skill set.
My preparation was greatly aided by past papers, but not in a passive manner. I rigorously graded them while I seated them under time constraints. More significantly, I took the time to analyze errors. Not only did I want to know what went wrong, but also why.
Key Questions I Asked After Every Practice Exam
- 1
Time management – Did I spend too long on certain questions?
- 2
Careless algebra – Were there simple calculation errors I could have avoided?
- 3
Misreading – Did I misinterpret what the question was actually asking?
- 4
Understanding gaps – Was there a fundamental concept I didn't fully grasp?
Patterns began to appear, and if you recognize them, you can correct them. That procedure was significantly more beneficial than continuously posing fresh queries.
I also focused heavily on how I communicated solutions. Clear structure, logical sequencing, and neat working matter much more than most students realize. Even when I wasn't completely confident in an answer, good communication often secured method marks. Those marks add up quickly at the top end.
By repeatedly simulating exam conditions, the real exams felt familiar rather than intimidating. I wasn't just prepared academically — I was comfortable with the process, the pressure, and the pacing.
Final Thoughts
Ranking first wasn't the result of a single moment or a clever trick. It was the outcome of consistent effort, deep understanding, and deliberate preparation over time.
"If there's one thing I'd tell students aiming high in maths, it's to stop searching for shortcuts."
Focus on building strong habits, invest in understanding rather than memorisation, and treat exams as a skill that can be trained. Progress might feel slow at times, but it compounds.
High-level maths is challenging, but it's also one of the most rewarding subjects when approached properly. With the right mindset and approach, exceptional results are far more achievable than they might initially seem.
