Your quiz will be a constructive existence proof, and will involve rational/irrational numbers. Study appropriately (see your groupwork, and read Hammack 7.3-7.4). Here are a couple similar types of proofs appropriate to study by:

For every irrational x, there exists an irrational y such that xy = 1.

For every two rational numbers x and y, there is an irrational between x and y (we did this one before).

Every rational number can be written as a product of two rational numbers.