Pretty much the units you'll do in first year are:
ENGG1800 - Engineering Disciplines - They teach you about different streams and you do projects and stuff. You only really need some maths knowledge for this (maybe ext 1)
ENGG1801 - Engineering Computing - This is computation using MATLAB. You'll need basic maths knowledge and that's it.
ENGG1803 - Professional Engineering 1 - You don't really need anything but basic maths knowledge for this.
CHEM1001 - Chemistry 1A - You'll need HSC Chem and that's it.
CHEM1002 - Chemistry 1B - You'll need HSC Chem and CHEM1001 and that's it.
CHNG1103 - Material and Energy Transformations Introduction - You'll just need to know basic maths and CHEM1001 for this.
MATH1001 - Differential Calculus - You'll need to know Mathematics Extension One
MATH1002 - Linear Algebra - You'll need to know Mathematics Extension One
MATH1003 - Integral Calculus and Modelling - You'll need to know Mathematics Extension One
MATH1005 - Statistics - You'll need to know Mathematics Extension One (not really, since there's barely any statistics in extension one)
It's all here:
http://cusp.sydney.edu.au/students/view-degree-page/degree_id/3