some basic mental sums as you are going to have to do this while flying the aircraft at times
One thing they don't get you to do at school (well, they didn't get me to do it, and everyone says the maths teaching is getting worse rather than better
) is doing approximate trigonometric calculations in your head - whether you were brought up with tables, slide rules or calculators, nobody expected you to
remember more than about four sines and cosines.
The rule of thumb for approximating crosswind components (one sixth of the wind speed for each ten degrees off the runway) I can remember, and is just a ludicrously extreme version of the approximation you know anyway, that "sin x ~= x for small x". Whilst the result is seriously inaccurate, at least it's so in the right direction, that of safety - using that approximation you won't mistakenly try to land with a wind above your crosswind limit.
But the tricks for calculating wind correction angles in the hold (you won't need this for the PPL, it's IMCr stuff) and so on I have more trouble with. I can worth this out mathematically on the ground, but I have trouble remembering apparently random rules of thumb for approximating things in the air.