Worked Solutions to the 2021 HSC Mathematics Extension 2 Exam

Each year, as soon as the paper is officially published, I work through the solutions to the latest HSC exam while we wait for the official solutions to be published. You can find my complete handwritten solutions to all questions on the 2021 HSC Mathematics Extension 2 Exam here:

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Any corrections made to the answers will be posted here. If you find what you think may be an error, please let me know!

Very soon we will upload videos of detailed explanations for all questions on this latest test. You can subscribe to our YouTube channel to be notified when they are published, or check back here!

2021 students – congratulations on finishing Extension 2 maths! Amazing!


Thoughts on the exam

As I worked through up to Question 15, I felt the Extension 2 exam was relatively easy (for Extension 2, of course). The questions up to this point were generally well targeted towards testing students’ knowledge of the core syllabus content. Of course, the last multiple choice question and Questions 15 and 16 typically have some good challenges.

I thought Question 15 (a)(i) was one of the more challenging ones, although I usually do feel that way when it comes to these kinds of inequality proofs. It took me a few tries to get a setup that produced the required result. Question 15 (d) was an interesting one and had me pondering for a little bit on how the proof could be done. Another “show that” type question was Question 16 (a), which I thought was fun since it required working with vectors. I think my reasoning for part (iii) is sufficient, as I could not think of another way to come to the result. Finally, 16 (c) was also a really interesting question and had me really thinking about what the sketch would look like! Once I was thinking about it in the right way, drawing up the sketch was fun.

If you took the 2021 Mathematics Advanced exam, I’d love you hear your thoughts!