The Chinese IMO team eat sequences like this for breakfast!* — When it comes to Olympiad Mathematics, China rules. The Chinese team has won the IMO (International Mathematical Olympiad) for the last 4 years, and has not finished outside the top 3 in the last 25 years. China runs its National Olympiad earlier than most countries. All countries run it early…

From Gauss and the birth of statistics to modern data science and machine learning — Ordinary least squares (OLS) regression is one of the first items on the menu in an introductory Statistics or Data Science course. But why do we need to square the errors? It’s a common question even high school students ask. …

Evaluate tan(100°) + 4sin(100°) — Can you evaluate tan(100°) + 4sin(100°)? Believe it or not, this expression can be simplified down a simple constant. Feel free to have a try yourself. Or, if you want, ask ChatGPT to try to solve the problem. I’m pretty sure it won’t be able to do it. BUT…

Investigating prime factors of 2ⁿ − 1 — When I scan the Art of Problem Solving Contest Collection Forum for nice math problems, I tend to be drawn to those with a short and simple problem statement. Problem 4 from the 2023 Korea Mathematical Olympiad certainly met this condition! Find all positive integers n such that (2ⁿ −…

A complex numbers question with a twist or two — One of my students asked me if I’d heard in the news about the crazy difficult HSC math exam question from last week. I had not, but of course now I was curious… what was this question and what’s so hard about it? For some context, in Australia high school…

From the 2023 Shanghai Gao Kao — You’ve probably heard that high school math in China is hard. This algebra problem from the 2023 Shanghai Gao Kao (college entrance exam) is not the hardest question on the paper, but I think it’s pretty nice. Here is the Chinese version of the question.

Did you ever learn “completing the rectangle”? — Problem 19 from the 2023 UK Senior Maths challenge asked about the rational expression (7n + 12)/(2n + 3). We are told this expression takes integer (whole number) values for certain integer values of n, and we’re asked to find the sum of all such integer values.

Top Asian universities are given more recognition — The Times Higher Education (THE) World University Rankings for 2024 were published on September 27, 2023. To me the THE Rankings (no that’s not a typo 😅) are the most rigorous of the popular university ranking systems, because they consider a broader range of relevant ranking metrics compared to QS…

Or does technology give students a deeper appreciation of mathematics? — In Melbourne, Australia, where I teach high school mathematics, students are allowed to use a CAS calculator in most of their mathematics exams. CAS stands for Computer Algebra System, and are capable of equation solving, graphing, differential and integral calculus, even programming! Let me show you how powerful they are…