You'd need higher than general maths for any engineering major. The math subjects you will encounter in your first year will have 3 and 4 unit content. If you put in a little effort and maybe did a 3u bridging course, 2unit maths is a decent base to start on. But general, not so much. First year science or engineering maths is almost entirely calculus and linear algebra - linear algebra isn't covered in the HSC and general maths calculus isn't good enough. It could be a good idea to self study 2unit (focus on calculus, maybe a bit of trig) in any free time before doing a 2 and 3 unit bridging course.
If you can't be bothered with that or still aren't confident it would be worth looking into something like "fundy maths" at the university you plan on going to (most unis call it something along the lines of fundamental maths or foundation maths). It's essentially a slow paced bridging course that you take during your first semester that will prepare you for maths. You can usually catch up by doing second sem maths over summer, but even if you don't things will even out down the line as you can count fundy maths as on of your electives.
Not sure about other universities but UTS have a quiz before you start, it's not hard, but you would fail having only done general without a bridging course or self study. If you fail the quiz they will restrict you from enrolling into Mathematical Modelling 1 and make you do foundation maths instead. For 2012 entry the quiz was online and their attitude was that if you cheated you are only cheating yourself and might struggle with MM1, but 2013 entry the quiz was done in exam conditions at the university.
