Chapter 10:
Spring 2012 Midterm Review
1. Write the partial fraction decomposition of
x3  8
3x  5
a.
b.
3
x3 1
x 2 x  1
c.
8 x 2  24 x  12
( x  1)( x 2  5 x  2)
( x  4) 2  ( y  2) 2  25
2. Solve by graphing 
4 y  8 x  24
x  0
y  0

 x  2 y  1
3. Graph the system of inequalities 
 x  2 y  10
x  y  2

 x  y  8
Chapter 3:
1. Write a polynomial whose zeros and degree are: Zeros: -3,-5, 5 degree 3
2. Find the x and y-intercepts of f(x) = (x + 4)(x – 2)(x +2)
3. Find the domain of the rational function f ( x) 
2x 2  4
.
3x 2  6 x  45
4. Find the domain of the rational function f ( x) 
 2 x ( x  2)
5 x 2  3x  8
5. Find the vertical, horizontal and/or oblique asymptotes.
x2  4
9x 2  6x  9
a. f ( x) 
b. h( x) 
3x  2
16  x 4
6. Find the x and y intercepts of f ( x) 
7. Solve the inequality a. x( x  3)  4
x 2  x  30
x2  5
b.
x  9x  4  0
c.
x 1
8. Use the given zero to find the remaining zeros of the function
a. f ( x)  x 3  6 x 2  14 x  16; zero : 1  i
b. f ( x)  x 3  7 x 2  19 x  13; zero :  3  2i
x 1
1
x2
9. Find all of the real zeros of the polynomial function. Then use the real zeros to factor f
over the real numbers.
f ( x)  x 3  3x 2  4 x  12
10. Determine whether each of the following functions have a maximum or minimum. Then
find that value.
a. 𝑓(𝑥) = 3𝑥 2 − 2𝑥 + 6
b. 𝑓(𝑥) = −4𝑥 2 + 8𝑥 − 1
11. Graph the following rational functions.
2𝑥 2 −14𝑥+24
𝑥 2 +2𝑥−3
a. ℎ(𝑥 ) =
b. 𝑔(𝑥 ) =
𝑥 2 +6𝑥−40
𝑥+1
12. The current i in a circuit is inversely proportional to its resistance R measured in ohms.
Suppose that when the current in a circuit is 30 amperes the resistances is 8 ohms.
Find the current in the same circuit when the resistance is 10 ohms.
13. The horsepower (hp) that a drive shaft can safely transmit varies jointly with its
speed (in revolutions per minute, rpm) and the cube of its diameter. If a drive shaft
of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what
diameter must the drive shaft have to transmit 45 hp at 125 rpm?