so if I did maths as a single degree at uni, how broad would my job prospects be?
That depends on your major. Doing a 3-year advanced mathematics degree means you can have up to two majors. And even your compulsory mathematics major can be pure/applied mathematics (at USYD, we don't distinguish between undergraduate pure/appled maths majors), financial mathematics or mathematical statistics. Your second major can also be one of the above, or something else from science (computer science is a popular second major for maths students).
Thus your job prospects depend on the majors you choose, which is very broad. Doing pure mathematics of course is probably the least employable of the other core maths majors outside of academia. However, you could argue that employers will see it as a massive IQ test, and give you a shot at that, but most people who do pure maths do it because they enjoy it, not for the employability. Applied maths is better in this aspect; there are good prospects for applied mathematics majors (especially in the finance industry) and you'd really want to consider pairing computer science with this one.
Financial maths (at USYD at least) is a bit of applied maths with mathematical statistics. It's obviously useful for getting into the finance/trading industry, but you're not limited to that, as statistics is very broad.
Mathematical statistics is the most employable of the core maths majors for the reason mentioned above; it can be used to getting into most industries, since pretty much every industry requires analysis of data.
A huge prospect for people with maths degrees is data analysis/science. You can get into it with applied maths or statistics, and computer science really helps with this one.
I'm not an expert when it comes to understanding job prospects, and I'm sure someone else can answer your question better. Try looking up those keywords in Seek.