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You could have sin ( pi ) = 0, cos ( pi ) = -1, sin (pi / 2)  = 1, etc, asking basic questions about trig operations and identities and stuff.

But maybe if we had a geometry level, it could be done differently. Maybe the Geometry level is composed of different kinds of shapes - where you have an octagon room, a rectangle room, a triangle room, etc... And when you solve the notebooks, you have to answer "what is this shape?" Then it places the shape on a map of the Geometry level to help you navigate. The more notebooks you solve, the more of a complete map will appear in each notebook. If this makes the game too easy, maybe the Geometry level can be randomly generated each time and the map-building process is there to encourage you to find notebooks as quickly as possible.

But this whole idea of a Geometry level seems kind of redundant. We already have a Math level and Geometry is just a subset of Math. Why not explore the other subjects? Art, P.E., Music, Science. My opinion is that the 4th floor should be a Computer class. The teacher on this floor could be virtual and only appear on a screen, but will be able to influence the game in weird ways, such as flickering the lights and locking doors randomly.