It's not as hard as you make it out to be. Problem with most people is that they've become too calculator dependent, which in itself isn't that bad, but I just don't want to fall into that category
And I make stupid mistakes on a calculator sometimes, which is eliminated if I don't use one.
I give my answer to 1 sig fig most of time (sometimes to 2 sig fig, if I am certain that it is correct)... and I can do most square roots correct to 1 d.p. And plus, in Physics at HSC level you can be 1 decimal place off and still get the marks, unlike Maths, given that you've shown all working.
Again, it's not as hard as you make it out to be. You've probably been using a calculator all your HSC so you probably are not used to it. The only time I use a calculator in Physics is for irregular angles (ie. not 30, 60 or 45 deg). I just remember that sin60 deg = 0.866 to 3 d.p etc. Works most of the time