Ateacher announces that a test will be given on one of the five weekdays of next week, but tells the class, "you will not know which day it is until you are informed at 8 a.m. of your 1 p.m. test that day." why isn't the test ever going to be given?

Maybe the week their in is the last week of school for the year.

8 + 0 = 8: identity- addition (any number + 0= that number) 
a(b + c) = ab + ac: distributive (multiplying a on the left-hand side of the equation by the numbers in parenthesis gives you the right-hand side of the equation) 
b + a = a + b: commutative- addition (numbers can be added in any order and still produce the same answer) 
If 2 = x, then x = 2: symmetric (if a = b then b = a) 
x(10) to be written 10x: commutative- multiplication (numbers can be multiplied in any order and still produce the same result)