Math 150B
Final Exam
Spring 2014
Name ______________________________________
Score:________/200
Work each problem in the space provided on the exam page. Full or partial credit will be given only if all work has
been shown and the answers are clearly indicated.
y
1. (8 pts) Solve the following system by graphing.
x
2. (7 pts each) Solve the following systems.
a)
b)
3. (6 pts) A theatre can seat a total of 360 people. They take in $15,150 when every seat is sold. Orchestra
section tickets cost $45 and balcony tickets cost $35. Set up a system of equation whose solution gives you the
number of seats in each section. Do not solve the system.
4. (8 pts each) Simplify:
a)
b)
5. (7 pts each) Perform each indicated operation and simplify.
a)
b)
6. (8 pts) Solve the following equation.
7. (7 pts each) Simplify.
a)
b)
8. (8 pts each) Simplify using positive exponents only.
a)
b)
9. (7 pts each) Perform each indicated operation.
a)
c)
b)
10. (7 pts) Solve the following radical equation.
11. (7 pts each) Rationalize each denominator.
a)
b)
12. (7 pts each) Solve by the most appropriate method.
a)
b)
c)
13. (7 pts) Solve by completing the square.
14. (6 pts each) Use the discriminant to determine the number of solutions to the following quadratic
equations. Do not solve.
a)
b)
15. (7 pts) Graph the following quadratic equation by first finding the vertex and any intercepts.
y
x
16. (8 pts) An inlet pipe can fill a tank in 4 hours. A second pipe can fill the tank in 3 hours. If both pipes are
used, find how long it takes to fill the tank. Set up an equation, then solve.
17. (7 pts) A balloon is secured by a rope that is staked to the ground. A breeze blows the balloon so that the
rope is taut while the balloon is directly above a flag pole that is 30 feet from where the rope is staked down.
Find the altitude of the balloon if the rope is 90 feet long. Give your answer as a simplified radical and also as
an approximation to two decimal places.