Solution

The total energy in each case is:

Top of the hill:

Bottom of the hill:

We'll need to compare the two energies to see if it was conserved:

So... if the energy was conserved would have to be 0, which means the quantity in brackets above would be zero (we know the mass isn't...)

The energy was not conserved... The skier had less total energy at the bottom of the hill than at the top. This would be due to a nonconservative force like friction acting on them.