[ibmthrowaway271]

> You could always use a calculator but the whole 'show your own working' catch meant you had to do it all manually. Not any more!

You could often cheat (for equation rearrangement questions) if you knew the answer by simply working backwards towards the question, this is often easier than going from problem to solution but still provides all of the steps along the way.

I remember one maths teacher hinting at this trick, especially to understand the derivation of the quadratic formula:-

    ax^2 + bx + c = 0

by starting with:-

    x = ( -b +/- sqrt( b^2 - 4ac ) ) / 2a

and working backwards.

[Asooka]

There is also "solving by assuming the negative". It's a technique for problems like "Given X, prove Y", where you assume "Y is false" and use it to prove "X is false", but X is true, therefore Y has to be true. Sometimes it's easier to do it in that direction than X->Y.

[Tyr42]

Contrapositive is the fancy word for that technique.

A -> B iff not(B) -> not(A)