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Worked Solutions to the 2022 HSC Mathematics Extension 1 Exam

I have completed the solutions to the 2022 HSC Mathematics Extension 1 exam.

UPDATE: Looking for the latest Extension 1 Exam solutions? Find the 2023 exam here: Worked Solutions to the 2023 HSC Mathematics Extension 1 Exam

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

I think the multiple choice overall was a bit on the difficult side. In particular, 3, 7, 8, and 9 were potentially most difficult for students. I found question 9 in particular fun to consider but I hope this one didn’t stress too many students out!

Questions 11 and 12 were relatively easy, as usual, and gave students an opportunity to show their mastery of the basics of the course.

I found most of Question 13 to be interesting and a decent challenge, although I’d say 13 (d) was probably the trickiest part. I had to try a couple different approaches to see what would work to get answer. I am not sure if the approach I went with in the end was the most efficient, and if anyone has a different way to work out the answer I’d be interested to know!

Question 14, of course, is where all the challenging questions are. 14 (a) would have easy for you if you were in Extension 2, but I can imagine many students getting stuck on the integration of the x side of the equation. 14 (b) was a really interesting question but I think was not too bad if you know your formulas for projection of vectors and thought to consider the cosine rule. I did hear 14 (c) was considered difficult by most, but if you practice a lot of projectile motion it shouldn’t have been too bad. I will say I thought I got stuck but I had just made a small error in my working out. 14 (d) was a good question but I can imagine it may have been tricky for many students to work with n as an unknown.

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.

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!

2022 HSC Mathematics Extension 1 Worked Solutions


  • Question 10 – Previously had the answer as D, but that has been corrected to B. This one stumped me for a minute when I learned what the correct answer was, but it makes sense due to the horizontal walls of 0 slop in the slope field, creating asymptotes.
  • Question 11d – At the end of the question I had accidentally factorised with the minus in the wrong factor. The correct answer is a = -2 or a = 1.
  • Question 13d – I made a calculation mistake near the end, this has been fixed up and the correct answer is -2.

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