Admission requirements will vary, depending on whether you intend to undertake honours in the Faculty of Science, or in the Faculty of Arts and Social Sciences.

To qualify for admission to the Bachelor of Liberal Arts and Science (Honours), you must

Have qualified for or be a graduate with a Bachelor of Liberal Arts and Science from the University of Sydney or equivalent qualification from another tertiary institution,
Have completed a relevant major relating to the intended Honours discipline,
For Science Honours

Have achieved a Weighted Average Mark (WAM) of at least 65.00 or have a credit average (65.00) in 48 credit points of relevant 2000-level and 3000-level units of study, or (for Honours in the Arts Area) Have achieved an average of 70 or higher across the major, and
Satisfy any additional criteria set by the relevant Head of School or Discipline or Department.
For Arts and Social Sciences Honours:

Have achieved an average of 70 or higher across the major, and
completed the prerequisites, including advanced senior units of study
IELTS - A minimum result of 6.5 overall and a minimum result of 6.0 in each band
TOEFL IBT - A minimum result of 85 overall including a minimum result of 17 in Reading, Listening and Speaking and 19 in Writing
Pearsons Test of English- A minimum result of 61 overall and a minimum result of 54 in each band