It has now been seven years since the release of the current HSC Mathematics syllabuses in 2017, and the new 2024 syllabus is on the horizon. Prior to the introduction of the 2017 syllabus, Dr Bill Pender, a highly respected figure in Mathematics education and the author of widely-used Cambridge Mathematics textbooks, offered insightful observations… Continue reading 7 Years On: Revisiting Dr Pender’s 2017 Letter

## Recovering The Dot Product in Complex Numbers

In the pre-2017 syllabus, the only exposure students had to vectors was in the application of complex numbers to solve geometric problems. In the 2017 syllabus, and continuing into the newly released 2024 syllabus, the introduction of Euclidean vectors and their operations such as the dot product means that there is now a second framework… Continue reading Recovering The Dot Product in Complex Numbers

## My Solutions to 2024 HSC Mathematics Exams

Mathematics Advanced Mathematics Extension I Mathematics Extension II

## My Observations and Comments on the New 2024 Mathematics Syllabuses

Here are my observations, comments and opinions about the new syllabuses that NESA published recently. Schools are to plan for it in 2025, and implement it in 2026. The link to the syllabuses can be found here: https://curriculum.nsw.edu.au/learning-areas/mathematics

## ASTC Falls Short of Promoting Conceptual Understanding

The Prevalence of ASTC in Trigonometry Classrooms In classrooms around the world, the mnemonic ASTC (All Stations To Central) is widely used to help students remember the signs of trigonometric functions in each quadrant of the unit circle. On the surface, ASTC seems like an efficient tool, offering a simple way to recall which trigonometric… Continue reading ASTC Falls Short of Promoting Conceptual Understanding

## The Ideal Understanding of Divisibility

Divisibility is a fundamental concept in mathematics, seamlessly integrated into our daily experiences, such as dividing a cake into equal parts or determining if one number is a factor of another. Traditionally, we understand divisibility to mean that a number \(a\) divides another number \(b\) (notated as \(a | b)\) if there exists an integer… Continue reading The Ideal Understanding of Divisibility

## My Solutions to 2023 HSC Mathematics Extension II

Here’s a link to my solutions: https://www.dropbox.com/scl/fi/qwrq9e5ptz5wxgy7f76hi/2023-Ext-2-Solutions-Mok.pdf?rlkey=idnadofksn2n9ehpi3ogtefsh&dl=0 Here’s a video I quickly recorded explaining the solution to the last question in the 2023 HSC Mathematics Extension II paper. This question made the Sydney Morning Herald: https://www.smh.com.au/national/nsw/not-seen-a-question-like-it-the-most-difficult-problem-in-this-year-s-hsc-20231016-p5ecms.html News.com.au also featured my video here! https://www.news.com.au/lifestyle/parenting/school-life/sadistic-hsc-extension-2-maths-question-thats-too-hard-to-solve/news-story/16e1e8eafa486ac15fbf67fa8ffbc2a1

## I’ve Done It! Modules and Reps is done!

In my post I’ve Applied for a Master of Mathematics Degree! I shared that I was most scared of the course in Modules and Representation Theory as I bombed that course in my undergrad degree (I got a 62). The UNSW term ended in May and I got my results back and I got a… Continue reading I’ve Done It! Modules and Reps is done!

## Horology, Slide Rules and Logarithms

Mathematics is obviously one of my interests, but admiring wrist watches is another. There’s something beautiful about the way a mechanical, battery-less contraption built up from miniscule parts could keep time as long as the wearer stays alive (of course taking into account servicing, etc but I digress). Placing a tool such as a watch… Continue reading Horology, Slide Rules and Logarithms

## It’s All Sets

Set Theory underpins the foundations of Mathematics. When all of modern Mathematics is formulated axiomatically with sets, it baffles me how much the syllabus requires us to hide it away from students in the HSC Mathematics courses. At the moment it only rears its head when dealing with topics in Probability and Venn Diagrams, and… Continue reading It’s All Sets