Version B
College Algebra
Fall Midterm Final Exam
Name
Part 1: Multiple Choice
(NO Calculator – 2 points each)
Choose the one alternative that best completes the statement or answers the question.
Question 0 (1 point): What is your favorite thing about the Christmas/Hanukah/Kwanza/Holiday season?
(answer on your answer sheet)
1) Find and simply the difference quotient of f,
f ( x h) f ( x)
, h 0 , for the function f ( x ) x 2 3x 5 .
h
a) 1
b)
2 x 2 2 x 2 xh h 2 h 10
h
c) 2 x h 3
d) 2 x h 5
2) Determine the domain of the function: f ( x) 3 2 x
3
a) ,
2
3
b) ,
2
3
c) ,
2
3 3
d) , ,
2 2
3) Determine the domain of the function: h( x)
a) , 2
2,
b) ,
c) , 8
d) ,0
8,0 0,8 8,
0,
x2
x 64 x
3
4) Divide 6 x 3 21x 2 11x 4 by 2x 5 .
a) 3x 2 3x 2
6
2x 5
b) 3 x 2 3 x 2
6
2x 5
c) 3 x 2 3 x 2
14
2x 5
d) 3 x 2 3 x 2
14
2x 5
5) Given the function g ( x)
a)
n2 8
2n 4
b)
n 2 4n 2
2n 2
c)
n 2 4n 2
2n 4
d)
n2 6
2
2n
x2 6
, find g (n 2) . Simplify completely.
2x
x 4, x 0
6) Determine the graph of the function f ( x)
4 x 1, x 0
a)
b)
c)
d)
7) Find the slope-intercept form of the equation of the line that passes through (2, 2) and is
perpendicular to the line x 4 y 24 .
1
5
a) f ( x) x
4
2
b) f ( x) 4 x 10
c) f ( x) 4 x 6
d) f ( x)
1
x6
4
8) Solve x 2 5 x 6 0 for x.
a) x = -6, x = 1, x = -2, x = -3
b) x = -6, x = 1
c) x = 6, x = -1, x = 2, x = 3
d) x = 6, x = -1
9) Divide
6 2i
and write the result in the standard form a bi .
5 4i
a)
22 14i
41
41
b)
38 14i
41
41
c)
22 34i
41
41
d)
38 34i
41
41
10) What is the equation that yields the graph at right?
a) ( x 3) 2 ( y 4) 2 16
b) ( x 4) 2 ( y 3) 2 4
c) ( x 3) 2 ( y 4) 2 4
d) ( x 4) 2 ( y 4) 2 16
11) A model for the demand of wood saws is d 2 p 2 316 p 160 where d is the number of saws a
manufacturer can sell at a price of p dollars each. Find the price that will yield the maximum demand for
saws.
a) $40
b) $79
c) $158
d) $12,322
12) Perform the indicated operation and simplify the result. Leave the answer in factored form.
x 2 12 x 35
x2 9x
x 2 16 x 63 x 2 2 x 35
a)
x
x 16 x 63
b)
1
x7
c)
x ( x 9)
x7
d)
x
x7
2
13) Find the real solutions of the equation:
x2
3
.
x
x2
a) 4, 1
b) 2, 1
c) 4,1
d) 2,1
14) Perform the indicated operation and simplify the result. Leave the answer in factored form.
4
6
2
x 3x 2 x 1
2
a)
48 x 8
( x 1)( x 1)( x 2)
b)
10 x 8
( x 1)( x 2)
c)
10 x 8
( x 1)( x 1)( x 2)
d)
8 x 10
( x 1)( x 1)( x 2)
15) Solve the inequality. Express your answer by graphing the solution set on a number line.
7x 6 4 0
a)
b)
c)
d)
16) Identify the equation for the function graphed at right.
a) f ( x )
1
( x 3) 2 4
2
1
b) f ( x) ( x 3) 2 4
8
c) f ( x)
1
( x 3) 2 4
2
1
d) f ( x) ( x 3) 2 4
2
17) For the function f ( x ) 2 x 2 3x , find the average rate of change from 1 to x.
a) 2
b) 2 x 1
c)
2 x 2 3x 1
x 1
d) x 1
Version B
College Algebra
Fall Midterm Final Exam
Name
Part 2: Problem Exercises
(YES Calculator)
You must show ALL work and reasoning to receive full credit.
Solve the following equations in the complex number system (4 points each):
18) 12 x4 10x3 12 x2 0
19) 16 x3 12 x 2 4 x 3
20) x 2 x 3 0
21) Determine the standard form of the equation of a circle with endpoints of a diameter
at (6, -8) and (-4, -4). (6 points)
22) Determine the standard form of the equations of the circle with equation x 2 y 2 6 x 4 y 12 0
and graph the equation on the coordinate plane provided. (4 points)
1
1
23) For the polynomial f ( x ) 0.02( x 1)( x 5) 2 ( x 3)3 :
a) Determine the degree of the polynomial. (1 point)
b) Determine the x- and y-intercepts of the graph. (3 points)
c) Graph f using a graphing utility.
d) Determine the local maxima and local minima, if they exist, rounded to two decimal places. (2 points)
e) Determine the intervals where f is increasing and where f is decreasing. (2 points)
f) Determine the domain and range of f . (2 points)
0
