I don't think your mathematical knowledge will matter that much if you wish to study something related to medicine beyond year 12. In terms of taking Mathematics Standard or Mathematics Advanced, you should definitely consider your current mathematical ability/performance and make an informed decision based on that.
In terms of prerequisites, USyd's Bachelor of Nursing (Advanced Studies) doesn't seem to have any specific prerequisites. Have a look at their "Admission criteria" section on their degree's link:
The Bachelor of Nursing (Advanced Studies) contains advanced components that focuses on cultivating non-technical skills in leadership and decision making. Learn more about our nursing courses.
www.sydney.edu.au
Instead, USyd requires you to get an ATAR of 84, which is definitely achievable with, firstly, any combination of subjects, and secondly (and more importantly), regularly studying and staying up-to-date with content so that you can perform well in your assessment tasks and exams.
Similarly, UTS doesn't seem to have any specific prerequisites and requires a selection rank between 79 and 83, which again is definitely achievable and does not depend on the subjects you choose, but more on your efforts, determination and diligence in your studies. The only "prerequisite" is:
Participation in screening and vaccination against infectious diseases are prerequisites for students undertaking clinical placements in health facilities.
However, this is not an academic prerequisite and doesn't affect your chances of receiving an offer to study UTS's Bachelor of Nursing.
www.uts.edu.au
Biology and Chemistry definitely don't impose a light workload, but this perception can differ between students. Since they are not prerequisites, you might choose to study none, either or both subjects as the knowledge you gain by studying them will likely be relevant to your first-year university studies.
Since you want to help and interact with people, have you thought about taking Society and Culture? This is what this subject entails:
This course provides students with opportunities to develop social and cultural literacy and understand how interactions shape human behaviour. Drawing on cross-disciplinary concepts and social and cultural research methods, students undertake research in an area of particular interest to them and present their findings for external assessment in the Personal Interest Project (PIP).
This subject might give you a better understanding of different cultures within society, and hence assist you in communicating with people in the future.
I hope this helps!
