INSTRUCTIONS: PLEASE READ THIS FIRST:
1. Make sure you have a complete exam. The exam has 10
pages, counting this cover
page.
2. Show all your work. Use the back of an adjacent page if
you need more space.
3. You are not al lowed to use a calculator of any kind.
4. If you have questions, raise your hand and I will
assist you as soon as possible.
5. The quadratic formula is
Good Luck.
| Problem |
Total Points |
Score |
| 1 |
21 |
|
| 2 |
6 |
|
| 3 |
11 |
|
| 4 |
15 |
|
| 5 |
4 |
|
| 6 |
6 |
|
| 7 |
10 |
|
| 8 |
6 |
|
| 9 |
5 |
|
| 10 |
6 |
|
| 11 |
10 |
|
| Total |
100 |
|
1. Solve each inequality . State the solution set using
interval notation, and graph it on a
number line .
(b) (5 pts) y2− 3y > 10
(c) (5 pts) 2z − 3z2≥ 0
(d) (6 pts) x3 − 3x2− 4x + 12 ≤ 0
2. (5 pts) Reduce the fraction
3. Solve each quadratic and state the solution set,
including complex solutions . You may
use any method except the quadratic formula. Complex solutions should be written
using i; radicals should be simplified .
(b) (6 pts) 2x2+ 12x = −26
4. Solve and state the solution set. You may use any
method to solve quadratic equations
you encounter, including the quadratic formula. Check for extraneous solutions
to
receive full credit.
5. (4 pts) Using a graph, find the solution set for the
system of equations
3x − 3y = 9
5y − 5x = 10.
Is this system dependent, independent, or inconsistent?
6. (6 pts) Graph the solution set to the system of
inequalities x −4y < 0 and 3x+2y ≥ 6
on the axes provided. Clearly indicate which region is the solution set.
7. (5 pts each) De termine the solution set to each system
of equations. Classify each
system as independent, dependent, or inconsistent.
(a)
(b)
2(y − 5) + 4 = 3(x − 6)
3x − 2y = 12
8. (6 pts) Simplify the complex fraction
9. (5 pts) Rewrite
as
10. (6 pts) Set up an equation for the following word
problem, but do not solve it :
Homer can row his boat 17 miles in the same time it takes Marge to cover 42
miles in
her motorboat. If Marge’s boat travels 15 mph faster than Homer’s, how fast is
Homer
rowing his boat? (Stop once you have the equation to solve!)
11. (5 pts each) Perform the indicated operations . Your
final answers must be a single
fraction in lowest terms.
Extra Credit: Starting from ax2+bx+c = 0, derive the
quadratic formula by completing
the square . Alternatively, provide a proof (with picture) of the Pythagorean
Theorem.
