Sample Examination I
Discrete Mathematics
The first major examination in Discrete Mathematics will be given on February
8. It will cover a review of College Algebra plus Section I in the
textbook. The following is a sample of what might be on the examination.
None of these questions will be on the examination. However most
of the questions on the examination will be similar to these.

Simplify the following expression: (2^{3} x 3^{2})^{2}

Find the product of (3x5)(2x+1)

Factor the following trinomial: 5x^{2} + 26x + 5

Use the quadratic formula to solve: x^{2} + 8x  4 = 0

Find all solutions to the following equation: x^{4}  13x^{2}
+ 36 = 0

Find all solutions to the following equation:  2x  1  = 5

Solve the inequality and sketch the solution on the real number line: 4
 2x < 3

Plot the points and find the slope of the line passing through (3, 2)
and (1, 6)

Sketch the graph of the quadratic function. Identify the vertex and
intercepts: f(x) = x^{2 }+ 2x + 8

Divide by long division: 4x^{3}  7x^{2}  11x +
5 ¸ 4x
+ 5

Divide by synthetic division:
(3x^{3}  17x^{2} + 15x  25)
¸ (x  5)

Evaluate the following expression: log_{2}(8^{3})

Write the following expression as the
logarithm of a single quantity: 3 log_{7}x  4log_{7}y
+ 2log_{7}z

Solve the following system of equations
3x  4y = 13
2x + 4y = 7

Solve the following system of equations
3x  5y = 21
4x + 2y = 2

Find the midpoint of the interval with
endpoints 2 and 3

Suppose in the interval [a, b], a =
2. Find b if the midpoint of the interval is 7.

Find the point that is threefourths
of the way from 2 to 10.

If 5 is midway between a and b and 4
is onethird of the way from a to b, what are a and b?

What is the set of letters in the state
name MISSISSIPPI? How many elements are in that set?

What is the power set of {1, 2, 3}?

What is the power set of the empty set?
What is the power set of { q }?

Let A = {a, b, c, d} and B = { c, d,
e, f}. What is A Ç
B? A È
B? A  B?