# 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.

1. Simplify the following expression: (23 x 32)2
2. Find the product of (3x-5)(2x+1)
3. Factor the following trinomial: 5x2 + 26x + 5
4. Use the quadratic formula to solve: x2 + 8x - 4 = 0
5. Find all solutions to the following equation: x4 - 13x2 + 36 = 0
6. Find all solutions to the following equation: | 2x - 1 | = 5
7. Solve the inequality and sketch the solution on the real number line: 4 - 2x < 3
8. Plot the points and find the slope of the line passing through (-3, -2) and (1, 6)
9. Sketch the graph of the quadratic function.  Identify the vertex and intercepts:  f(x) = -x2 + 2x + 8
10. Divide by long division:  4x3 - 7x2 - 11x + 5 ¸ 4x + 5
11. Divide by synthetic division:  (3x3 - 17x2 + 15x - 25) ¸ (x - 5)
12. Evaluate the following expression: log2(83)
13. Write the following expression as the logarithm of a single quantity: 3 log7x - 4log7y + 2log7z
14. Solve the following system of equations
3x - 4y = 13
2x + 4y = 7
15. Solve the following system of equations
3x - 5y = 21
4x + 2y = 2
16. Find the midpoint of the interval with endpoints -2 and 3
17. Suppose in the interval [a, b], a = 2.  Find b if the midpoint of the interval is 7.
18. Find the point that is three-fourths of the way from -2 to 10.
19. If 5 is midway between a and b and 4 is one-third of the way from a to b, what are a and b?
20. What is the set of letters in the state name MISSISSIPPI?  How many elements are in that set?
21. What is the power set of {1, 2, 3}?
22. What is the power set of the empty set?  What is the power set of { q }?
23. Let A = {a, b, c, d} and B = { c, d, e, f}.  What is A Ç B?  A È B?  A - B?