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Worked Solutions to the 2023 HSC Mathematics Extension 2 Exam

I have completed my worked solutions to the 2023 HSC Mathematics Extension 2 exam, and will complete the video walkthrough soon.

Thoughts on this year’s exam (link to the solutions is at the bottom of the post):

I felt that the test covered the Extension 2 content well, but had a bit of a difficulty jump near the end. The last few questions are always difficult, however the test felt very doable until some of Question 15 and especially Question 16.

With Question 16 (c), the famously difficult one, I wanted to try a purely geometrical approach first, by which I was able to get the solution. After completing it, I saw most others’ solutions were more algebraic, so hopefully the slightly different approach I took will help some students who didn’t click with the other approaches. I included a lot of diagrams and working here that aren’t necessary to show, but included them in hopes that it’ll help students follow the solution better.

My personal favourite question was Question 15(c). That’s because I’ve always enjoyed 3d graphs and 3d calculus, and I’ve never graphed a function like this one before, so I thought it was fun. The question was also well put together, with the initial set up and the graphs to consider, which hopefully led you to the correct solution, as well!

Honourable mentions: I was also a fan of Question 16(b). Maybe because the approach I took on my first try worked out swimmingly. And I also liked 13(c). I thought the inclusion of the graph in part (iv) was interesting.

My personal least favourite question was Question 15(b). I usually find vector geometry proofs stressful but I typically work them out just fine. I got stuck on this one, though, and the approach was one I had just used on another problem (not on this test) and kind of obvious once I got a hint from my answer checker Nick. So I was frustrated with myself on that one, but I’m redirecting that anger and now I’m just mad at 15(b). Still, I have to admit when you look at what the question was about, it was pretty cool, which was that the sum of the squares of the lengths of the edges of a triangular pyramid are equal to four times the sum of the squares of the lengths of those midpoint diagonal things. Who knew?

Dishonourable mentions: Question 12(c) because these kinds of physics questions always do my head in, and this one especially so. For some reason the presentation of everything as a vector, including g, was just giving me a headache. Also Question 10, because I had narrowed it down to B and C, and it took me forever to realise the zero vector was on the table, unlike the others, for option C. So I was just sitting there for too long thinking, “They both can be true!!!” So I’m mad at that question too!

How did you all go with this exam? Which questions did you find the most difficult or interesting? Drop a comment or email me and let me know!

You can now watch a video of the worked solutions on your YouTube channel! Otherwise, see the link to the PDF of the worked solutions below.

Video coming soon. Check back!

My worked solutions can be found at the following link. If any errors are found, I will correct them and keep a log below. Please comment or email me if you find a mistake!

2023 HSC Mathematics Extension 2 Worked Solutions


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