If a test tube is put into a freezer so that all the water turns to ice, will the level of the ice be higher or lower than the level of water?

Materials expand on heating and contract when frozen. Water, on the other hand, is very unusual. It expands when frozen and contracts when melted. This means that if we keep a glass full of water in the freezer and wait for it to freeze, we will observe ice on its sidewall and around its base (from all the water that has overflown). Similar can be observed when we fill ice trays with water. If we fill them to the level, we can observe the ice to have risen above those levels.

If we place a test tube with some water (and water level marked) in the freezer, we will observe that ice would occupy more volume (because of expansion of water) and its level would be higher than that of the water. 

This expansion is due to the peculiar shape of water molecules. When water molecules link up with each, they do so by occupying a large volume, while leaving large empty spaces in between. This causes the expansion of the water when it converts from a liquid to a solid. 

Hope this helps.