For animal & vet bioscience:
Admission to this course is on the basis of a secondary school leaving qualification such as the NSW Higher School Certificate (including national and international equivalents), tertiary study or an approved preparation program. English language requirements must be met where these are not demonstrated by sufficient qualifications taught in English. Special admission pathways are open for domestic mature aged applicants who do not possess a school leaving qualification, educationally disadvantaged applicants and for Aboriginal and Torres Strait Islander people. Applicants are ranked by merit and offers for available places are issued according to the ranking.
A limited number of applicants may be eligible for admission to the course under the Rural Entry Scheme
http://sydney.edu.au/vetscience/avb/rural.shtml
For vet science:
Admission to this course is on the basis of a secondary school leaving qualification such as the NSW Higher School Certificate (including national and international equivalents) or tertiary study. English language requirements must be met where these are not demonstrated by sufficient qualifications taught in English. Special admission pathways are open for educationally disadvantaged applicants and for Aboriginal and Torres Strait Islander people. Applicants are ranked by merit and offers for available places are issued according to the ranking.
A limited number of applicants may be eligible for admission to the course under the Rural Entry Scheme
http://sydney.edu.au/vetscience/bvsc/rural.shtml
In addition, admission to this course requires all applicants to sit the Multi-choice STAT and submit a "Commitment to Veterinary Science" Form. The results of this process will form part of the ranking of non-year 12 applicants and be applied as a filter for year 12 applicants.
http://sydney.edu.au/courses/Bachelor-of-Animal-and-Veterinary-Bioscience
I think you're safe without STAT for bioscience. If in doubt, email the faculty