- Suppose we have a positive integer a. We subtract −a from it. The result is
(a) equal to 0.
(b) equal to a.
(c) equal to a+a.
(d) equal to −a−a.
(e) undefined.
- Fill in the blank to make the following statement true. “Suppose that a is a nonzero
number. Also suppose that m and n are rational numbers. If we raise a to the mth power
and then raise that quantity to the nth power, we get the same result as if we ____.”
(a) raise a to the power of (m+n)
(b) raise a to the power of (m−n)
(c) raise a to the power of mn
(d) raise a to the power of m/n
(e) raise a to the power of 1/(mn)
- Suppose we see two cubic functions. All of the coefficients and constants are real
numbers. As we solve these functions as a two-by-two system, we create a single-
variable equation by mixing the independent-variable parts of the functions. When we
factor that equation, we discover that it can be written in binomial-cubed form. Based
on that knowledge, what can we say about the multiplicities of the real solutions of
the original system?
(a) Nothing, because there are no real solutions at all.
(b) There are three different real solutions, each of which has multiplicity 1.
(c) There is one real solution with multiplicity 1, and a second, different real solution
with multiplicity 2.
(d) There is one real solution with multiplicity 3.
(e) There is one real solution with multiplicity 6.
- Which of the following sets is nondenumerable?
(a) The set of all natural numbers.
(b) The set of all negative integers.
(c) The set of all integers.
(d) The set of all rational numbers.
(e) The set of all irrational numbers.
- The intersection of the null set with any other set is always equal to
(a) that other set.
(b) the null set.
(c) the set containing 0.
(d) the set containing the null set.
(e) the universal set.
Final Exam 553
