My Solutions to 2023 HSC Mathematics Extension II

Here’s a link to my solutions: 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: also featured my video here!

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

What Are Random Variables?

Related Content Outcomes: MA-S1 Probability and Discrete Probability Distributions S1.2: Discrete probability distributions HSC, We Have A Problem The HSC Syllabus does not give a clear definition of what a random variable actually is – it rather describes what it does: know that a random variable describes some aspect in a population from which samples… Continue reading What Are Random Variables?

Thoughts About Some Mathematical Practices

Here are some of my thoughts about some miscellaneous mathematical practices – some words of advice, warning, interesting insights, contentious disagreements, or whatever else comes to mind. This might become a multipart series as more comments come to mind in the future… Notation of Domains of Functions The domain of a function is a set.… Continue reading Thoughts About Some Mathematical Practices

The Language of Proof in HSC

Related Content Outcome MEX-P1 The Nature of Proof This post will primarily look at the following dot-point from page 28 of the Extension II syllabus: use the formal language of proof, including the terms statement, implication, converse, negation and contrapositive (ACMSM024) –  use the symbols for implication (⇒), equivalence (⇔) and equality (=) , demonstrating a clear understanding of the… Continue reading The Language of Proof in HSC

Comments on the 2020 New HSC Syllabus Exams

It’s been a few weeks since the HSC 2020 Examinations concluded. Mathematics teachers and the students who sat the exam have had time to ruminate over what went into each paper. The Sydney Morning Herald printed a story about the Standard 2 Mathematics examination with a title that can only further scare future students from… Continue reading Comments on the 2020 New HSC Syllabus Exams

Dangerous Moivres

Related Content Outcomes: MEX-N2 Using Complex Numbers N2.1: Solving Equations with Complex Numbers Terrible Puns, Terrible Maths Excuse the terrible pun on “dangerous moves” in the title (I thought it was brilliant) but it’s to highlight the all too common mistake made by students (and teachers) of elementary high school mathematics of overlooking necessary assumptions… Continue reading Dangerous Moivres

The Incomplete Treatment of Functions in HSC Mathematics

Related Content Outcome: MA-F1 Working with Functions F1.2: Introduction to Functions What Does The Syllabus Say? The first port of call for all students and teachers when learning or teaching HSC Mathematics is of course the Syllabus. Here is the excerpt from the Syllabus (Page 31) about how a function is defined: define and use… Continue reading The Incomplete Treatment of Functions in HSC Mathematics