I don't think there is anything wrong with using Ext1 methods in the Adv paper. However, if you do end up using it to solve a question then that is usually a sign that the question is poorly designed.
Ideally, all questions in Adv would be restrictive and targeted enough such that no one is advantaged by knowing additional stuff in Ext1. For example, a number of integration questions which can be solved by substitution in Ext1 can actually be solved more quickly in Adv by using the reverse chain rule formulas on the reference sheet.
I agree strongly with
@Trebla that questions
should not advantage MX1 students in the Advanced paper, nor similarly for MX2 students in the MX1 papers. For the HSC examinations, with the huge amount of time and effort that goes into their preparation, this really really should not happen. But then, mistakes in questions shouldn't happen, and yet they do.
However, trials and internally written papers have far less checking and while it should not happen, it does happen at times, as do mistakes in questions and in solutions..
I also would like to echo Trebla's advice, that if you are considering using an MX1 approach for an Advanced question, stop and ask yourself if this is really the most efficient way to solve the problem. If you can see no non-MX1 approach then giving a solution is better than leaving a page blank (obviously) but avoid complicated methods when simple ones will suffice. As a simple example, if I needed to show that
, I could use calculus to find the stationary point and prove that it is a global minimum... or I could complete the square
and note that the sum of a positive-or-zero term and a positive term is positive.