Download Exam # 3

Math112
125Fall 2009 Instructor: Tigran
Exam
3 – Chapters
8 and 9
Summer 2013
MATH
Mkrtchyan,
NAME:____________________________Date:_________
Name:
Date: 07/10/2013
Score:
YOU MUST SHOW ALL OF YOUR WORK to receive full credit for the problem. The more work you show on
your paper leading to your solution will give me more opportunity to award partial credit. Clearly indicate your
solution to the problem.
1. (5 points) Express in simplest radical form. Assume variables represent positive real numbers.
4
48x 5 y 6
2. (5 points) Rationalize and simplify
3
8
27 y
3. (5 points) Rationalize and simplify
3− 2
1+ 2
4. (5 points each) Simplify
a)
 1 
 
 27 
−
2
3
1
b)
c)
9
 −6

x  x − x2 


2
3


6
 x 
 − 23 −3 
4 y 
1
3
5. (5 points each) Solve the equations
x+6 −6=
x
6. (5 points) Solve the equation for
=
1
a
x
−1
3a
2
7. (5 points) Divide and write the answer in the standard form a + bi .
1 − 2i
3+ i
8. (5 points) Solve the equation by completing the square.
x 2 + 3x − 5 =
0
9. (5 points) Solve using the quadratic formula.
2
( y + 1)( y − 2 ) =
3
10. (5 points) Solve the equation.
2
3
1
3
2 x − 11x + 12 =
0
11. (5 points each) Solve the inequalities.
2
a) x > 25
4
b)
x −1
≥0
x+2
12. (5 points) Given f ( x ) =
−x + 4x − 4
2
a) Determine the shape of the graph.
b) Find the vertex
c) Find the y-intercept and x-intercepts if any
d) Graph the function labeling the vertex and intercepts
5
13. (10 points) A projectile on Earth is fired straight upward so its height s (t ) (in feet) after t seconds
is given by the function s (t ) =
−16t + 400t .
2
a) Find the maximum height of the projectile.
b) What will be the height after 1 second?
c) After how many seconds will the projectile reach the ground?
6