The most difficult math problem in this year’s HSC

The “HSC” in Australia is the “High School Certificate” which you get when you graduate high school. In order to do that you have to take the final exam, known as the “HSC exam”, or simply the “HSC”.

When I did the HSC 24 odd years ago the top level maths course (which I took) was called “4 Unit Maths”, whereas these days the top level course is now called “Maths Extension 2”. I expect the difficulty increased over the decades too.

Here’s the hardest question from this year’s Maths Extension 2 HSC paper:

There’s an article about it all in the newspaper today: ‘Not seen a question like it’: The most difficult problem in this year’s HSC.

I don’t remember enough about complex numbers, geometry, and trigonometry to answer this question, it is quite beyond me.

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