Provided you have a reasonable knowledge of 2-unit HSC maths, you should be alright. If you only have general maths, you will probably struggle in some courses, especially in later years (before you have free-reign on picking 3rd year electives). If you have not done any maths for HSC, or completely disregarded it and learnt nothing, reconsider your degree choice to something like arts/law (political economy major?). Arithmetic alone will not get you through. First year micro & macro do not have difficult maths, but they are calculation-oriented, and understanding basic algebra is essential. Stats A is trivial. Stats B is considerably harder, but is very rote-learning oriented, and provided you go to all lectures and do the work, you can probably at least pass. However, even I (as a maths major) found these courses (while relatively easy technically) very disgusting for their total lack of any real explanation. For example, in my experience, you will spend almost all of Stats B memorising many statistical tests and their layout/assumptions/etc, with only "intuitive" explanation (i.e. almost no explanation), unless you consult some other texts. It really is largely a test of your memory. What I found most disgusting was how systemised the teaching was towards this incorrect way of learning and thinking, but you may very well like this.
The upshot is that after you're done with the relatively few core units, you have quite a lot of freedom in a BEc, and so should in principle at least be able to pick courses you can do well at. However, in further years be very careful with your economics electives. Be sure to check the unit of study outlines (before beginning your courses), as some economics courses are very mathematical. Do not do economics honours units and their associated corequisites, even if you did "well" in first year, without a sound knowledge of maths. Many have regretted this. If you are not confident with at least 2-unit, definitely avoid microeconomics, except the obvious compulsory Intermediate Micro for an eco major, which tends to be quite mathematical. Though I have not taken these units, there are many (so I hear) non-mathematical 3rd year electives such as Development Economics, History of Economic Thought, Monetary Economics, which have large amounts of readings & essays, etc. Even so, your ability to properly understand things may be impaired if your knowledge is really weak, as this appreciatory knowledge is still often based on mathematical models/analysis. Economics as an academic discipline is very mathematical, however not all career paths require this level of knowledge.
As far as I know, bridging courses at USyd are not free. There is a "mathematics learning centre" which anybody can go to for help throughout semester, but I can't vouch for how good they are.
