2022 HSC ADV exam … a few observations


We’ve been working hard to get our past HSC question database up to date.

The 2022 Advanced HSC exam is now fully integrated into the SmarterMaths database, joining the Std2 paper, with Std1, Ext1 and Ext2 to follow in the next week or so.

For those interested, some observations as I went through this exercise are summarised below (these will be available in topic analyses in the SmarterMaths database later):

How hard was the paper?

  • Since multiple choice was introduced in 2012, the ADV exam has produced State raw marks with a mean of 60.7 marks and a standard deviation of 4.1.
  • On a brief tangent, if you thought the 2021 ADV exam was difficult, you are correct! It produced a raw mark result of 1.9 standard deviations below the mean.
  • After reviewing and writing solutions to all questions, my expectation for the 2022 exam (for what it’s worth) is a raw mark above the historical mean.


  • Composite Functions: This topic is consistently being tested to a very high difficulty, albeit in multiple choice questions. While we expected standard questions to involve finding the domain and range of composite functions, significantly more difficult questions looking at differentiation and graph interpretation (2022) have been notable to date.
  • AP’s and GP’s: Our initial thoughts on the new syllabus absorption of AP’s and GP’s within Financial Maths was that mark allocations would be meaningfully reduced due to “Modelling Investments and Loans” cannibalising it. This has not been the case, emphatically so in 2022, with a 5-mark allocation given to AP’s. Good luck to students. A great area to score highly!
  • Conditional Probability: The 2022 question required the use of probabilities within the conditional probability formula in part ii. We wait with anticipation to see how students performed here as we see this aspect of probability as important moving forward.
  • Exponential Growth and Decay: You could be forgiven for thinking that syllabus changes would have seen this topic area appearing less often in ADV. Not the case! Exponentials with base “a” saw high mark allocations within G&E in 2020-21 and again in 2022, G&D with its old school base “e” equation received a hefty 4 marks.
  • Curve Sketching: We note Q22 was defined within a range and required students to find global max/min by evaluating local max/min against the range extremes … great variation that will be repeated in our view (similar questions to be added to the database).
  • Trapezoidal Rule, Trig Graphs and Area Under Curves: Each individual area examined in a low band (show us your knowledge) question and followed up later in the exam with a significantly more challenging test of the topic area. This was notable in my mind.
  • Area Under Curves: Involved a circle for the first time in 17 years!
  • CDF’s and PDF’s: Examiners making it very, very clear that students need a deep understanding of this topic area and in particular, the link between these two functions. Already a key area where the best students can differentiate their paper in my view.
  • Max/Min: Q31i confusingly required the expression of a relationship and not the equation of a line. We expect this to result in the initial “Show the relationship” part of a max/min problem having a much lower mean mark than the later part(s) of the question.

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All the best!