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Worked Solutions to the 2021 HSC Mathematics Advanced Exam

UPDATE: If you are looking for the latest worked solutions, you can find them here: Worked solutions to the 2023 HSC Mathematics Advanced 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 Advanced Exam here:

2021 HSC Mathematics Advanced Worked Solutions


  • Question 26b – Solution corrected to -10*sqrt(69). I originally missed cancelling the 2 in front of the square root. Thanks to Jeffrey for pointing it out!

Any further 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 Advanced maths!

Thoughts on the exam

I thought the 2021 Advanced had a lot of difficult questions. Most of the easier questions were the common marks between Standard and Advanced. Much of the Advanced-only content was on the harder side. I noticed there were a lot of questions on probability and probability distributions, which is often a weaker subject for many students. Luckily there was also plenty of calculus to go around.

I thought Question 32 was creative and challenging to solve efficiently. This was a common question with Standard in which they do not solve simultaneous equations algebraically. While Advanced students could find the mean and standard deviation with simultaneous equations, it is possible to find them without equations which saves time and working. Note that not a lot of working out space was provided.

I loved Question 33 because probability and statistics are kind of my jam, but I have a feeling many students would have struggled with part (d). In order to solve (d) you must realize that you need to use conditional probabilities.

Similarly, I thought Question 34 was fun but it may have been intimidating to some students. The trick is to work out the expected value and then use the fact that the sum of the probabilities equals one in order to get an expression to replace r^n.

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

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