Central Carolina Technical College
MAT 110 - College Algebra
Exam Review
Midterm Exam will cover problems #1-39.
Final Exam will cover problems #1-90.
Add or subtract as indicated and write the
result in standard form.
1) (7 - 6i) + (7 - 5i) + (7 + 5i)
Use the graph of the function f, plotted with a
solid line,
to sketch the graph of the given function g.
7) g(x) = f(x) + 1
y = f(x)
Find the product and write the result in
standard form.
2) (6 + 3i)(4 - 3i)
3) (2 + 4i)2
Divide and express the result in standard
form.
8 + 3i
4)
7 - 4i
Perform the indicated operations and write the
result
in standard form.
5) 5 -49 + 4 -64
6)
Use the graph of the function f, plotted with a
solid line, to sketch the graph of the given
function g.
8) g(x) = - f(x) - 1
y = f(x)
-10 + -20
2
9) g(x) = f(x + 2)
y = f(x)
mat110ExamReview2013-2014.tst
10) g(x) = f(x + 2) + 1
y = f(x)
Determine which two functions are inverses of
each other.
x-3
17) f(x) =
3
g(x) = 3x - 3 h(x) =
x+3
3
Find the inverse of the one-to-one function.
18) f(x) = x + 5
Use the graph of f to draw the graph of its
inverse function.
19)
Find the domain of the function.
x
11) g(x) =
x2 - 25
12) f(x) =
21 - x
Given functions f and g, perform the indicated
operations.
13) Given f(x) = 5x - 5 and g(x) = 4x - 7,
find: f + g , f - g , and fg.
For the given functions f and g , find the
indicated composition.
14) f(x) = 5x + 15, g(x) = 5x - 1
(f g)(x)
15) f(x) = 4x 2 + 4x + 8,
g(x) = 4x - 7
(g f)(x)
Find the domain of the composite function f
g.
2
, g(x) = x + 2
16) f(x) =
x+7
2
Identify the vertex of the parabola.
20) f(x) = (x + 3)2 - 5
Find the coordinates of the vertex for the
parabola
defined by the given quadratic function.
21) f(x) = -x2 - 12x + 9
Determine the axis of symmetry of the
parabola.
22) f(x) = (x + 2)2 + 4
Determine the range of the quadratic function.
23) f(x) = 6 - (x + 2)2
Find the x-intercepts and the y-intercept for
the
graph of the quadratic function.
24) f(x) = (x + 9)2 - 14
mat110ExamReview2013-2014.tst
Graph the given quadratic function.
25) f(x) = -4(x + 6)2 - 2
Solve the problem.
26) An arrow is shot upward into the air
at a
speed of 64 feet per second from a
platform that is 14 feet high. The
height of the arrow is given by the
function h(t) = -16t2 + 64t + 14, where
"t" is the time in seconds. After how
many seconds does the arrow reach
its maximum height? Determine the
maximum height of the arrow.
31) A function of odd degree that has a
negative leading coefficent and three
distinct real roots.
A)
B)
Use the Leading Coefficient Test to determine
the
end behavior of the polynomial function.
27) f(x) = -3x4 + 5x3 + 4x2 - 2x + 4
28) f(x) = x3 - 5x2 - 3x - 5
C)
Find the zeros for the polynomial function and
give the multiplicity for each zero. State
whether the graph crosses the x-axis or
touches the x-axis and turns around, at each
zero.
29) f(x) = 5(x - 2)(x + 7)2
Sketch the graph of the polynomial function.
30) f(x) = x4 - 9x2
D)
Determine the graph of the polynomial
function.
3
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Divide using long division.
32) (4x5 - x3 + 3x2 - 180x - 21) ÷ (x2 - 7)
Divide using synthetic division.
x5 + x 3 + 5
33)
Find an nth degree polynomial function with
real coefficients satisfying the given
conditions.
39) n = 4; 2i, 4, and -4 are zeros; leading
coefficient is 1
x-2
Use synthetic division and the Remainder
Theorem to
find the indicated function value.
34) f(x) = x5 + 3x4 - 7x3 - 7; f(2)
Use the graph to determine a solution of the
equation.
Use synthetic division to verify that this
number is a solution of the equation. Then
solve the polynomial equation.
35) x3 + 6x2 + 11x + 6 = 0
*** Stop Here for the Midterm ***
Find the domain of the rational function.
x+8
40) g(x) =
x2 + 49x
Find the vertical asymptotes, if any, of the
graph of
the rational function.
x - 64
41) f(x) =
x2 - 11x + 18
Find the horizontal asymptote, if any, of the
graph of
the rational function.
5x
42) f(x) =
5x + 3
Use the Rational Zero Theorem to list all
possible
rational zeros for the given function.
36) f(x) = -2x3 + 2x2 - 3x + 8
Find the slant asymptote, if any, of the graph
of the rational function.
x2 + 7x - 9
43) f(x) =
x-8
44) f(x) =
Find a rational zero of the polynomial function
and
use it to find all the zeros of the function.
37) f(x) = x3 + 8x2 + 18x + 12
x2 + 16
x
38) f(x) = x3 + 7x2 + 24x + 18
4
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D)
Graph the rational function.
4x
45) f(x) =
x2 - 4
Determine the graph of the function.
46) A rational function has a denominator
of
x2 + x - 30. The numerator is first
degree
monomial with a positive leading
coefficent.
Solve the polynomial inequality and graph the
solution set on a number line. Express the
solution set in interval notation.
47) (x + 1)(x - 4) 0
A)
48) x2 + 7x + 10 > 0
Solve the rational inequality and graph the
solution set
on a real number line. Express the solution set
in interval notation.
x-7
>0
49)
x+5
B)
C)
50)
4 <
1
x-5
51)
x
x+4
2
Graph the functions by making a table of
coordinates.
52) f(x) = 4x
53) f(x) = 4-x
5
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Use the compound interest formulas
r nt
A=P1+
n
and A = Pert to solve.
54) Find the accumulated value of an
investment of $1000 at 9%
compounded continuously for
5 years.
55) Find the accumulated value of an
investment of $5000 at 5%
compounded monthly for
8 years.
Write the equation in its equivalent
exponential form.
56) log 4 x = 3
Write the equation in its equivalent
logarithmic form.
3
57) 216 = 6
Evaluate the expression without using a
calculator.
1
58) log 4
16
Graph the function.
59) Use the graph of f(x) = log x to obtain
the graph of g(x) = log x - 1.
Graph the logarithmic function. Find the
domain.
62) f(x) = log (x + 3)
4
Solve the equation by expressing each side as
a power of the same base and then equating
exponents.
63) 1024x = 64
Solve the exponential equation. Express the
solution set in terms of natural logarithms.
64) e 5x = 3
65) e
66) 5
x+3
x+8
=8
=4
Solve the logarithmic equation. Be sure to
reject any value that is not in the domain of
the original logarithmic expressions. Give the
exact answer.
67) log 3 (x + 2) = 2
68) log 5 (x + 3) = -3
69) log (x + 2) - log x = 2
7
7
70) log x + log (x +1) = log 56
Use properties of logarithms to condense the
logarithmic expression.
60) 4 log b t - log b s + 3log b z
Use common logarithms or natural logarithms
and
a calculator to evaluate to four decimal places.
61) log 27 362
6
Solve the system by the method of your choice.
71) y = 24 - 8x
8x + y = 64
72)
3x + y = 11
9x + 3y = 33
mat110ExamReview2013-2014.tst
73) x - 5y = 21
-3x - 6y = 42
Solve the problem.
74) A vendor sells hot dogs and bags of
potato chips. A customer buys 3 hot
dogs and 5 bags of potato chips for
$9.75. Another customer buys 2 hot
dogs and 3 bags of potato chips
for $6.25. Find the cost of each item.
Find the maximum or minimum value of the
given objective function of a linear
programming problem.
The figure illustrates the graph of the feasible
points.
79) Objective Function: z = 3x + 8y
Find maximum and minimum.
Solve the system of equations.
75) x + y + z = 1
x - y + 4z = -22
3x + y + z = 5
Solve the nonlinear system by the substitution
method.
76) x + y = 14
y = x2 - 4x + 4
Graph the solution set of the system of
inequalities.
77) 3x - y -6
x + 3y -12
Graph the solution set for the following system
of inequalities.
6
78) 2x + 3y
x-y 3
y 2
Solve the problem.
80) Mrs. White wants to crochet hats and
afghans for a church fundraising
bazaar. She needs
5 hours to make a hat and 4 hours to
make an afghan, and she has no more
than 55 hours available. She has
material for no more than
13 items, and she wants to make at
least two afghans. Let x = the number
of hats she makes and y = the number
of afghans she makes. Write a system
of inequalities that describes these
constraints.
Give the order of the matrix, and identify the
given element of the matrix.
81) A =
7
15 6
10 7 ; a
12
-3 -13 2 -9
mat110ExamReview2013-2014.tst
Solve the matrix equation for X.
2 -2
3 0
82) Let A = -8 0 and B = 0 -3 ;
3 -9
2 -9
Solve for "x" using the definition of
determinants.
x -5 = 38
88)
2 -7
4X + A = B
89)
Find the product AB, if possible. If AB
=[(ab)ij], then identify the entry (ab)23.
3
0
1
5
83) A = -2
0
-9
3
x
3
= -24
Evaluate the determinant using a graphing
calculator.
3 1 -4
90)
4 0
5
-4 0 -3
and B = 1 3 -2
4 0 5
Find the product AB, if possible. If AB
=[(ab)ij], then identify the entry (ab)32.
9 -2 9
84) A =
7 2 3 , B=
-4 1 -4
2 -4
1 3
8 -2
8
3
3
Find the product AB using row by column
multiplication.
85) A =
-1
3
3
2
and B = -2a 3b
-a -2b
Evaluate the determinant.
-4 1
86)
-9 -3
87)
8
1
12
1
7
8
3
5
11
-
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
1) 21 - 6i
2) 33 - 6i
3) -12 + 16i
44 53
i
+
4)
65 65
5) 67i
6) -5 + i 5
7)
8)
9)
9
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
10)
11) (- , -5)
12) (- , 21]
(-5, 5)
(5, )
13) a) 9x-12 b) x + 2 c)20x 2 - 55x + 35
14) 25x + 10
15) 16x 2 + 16x + 25
16) (- , -9) or (-9, )
17) g(x) and h(x)
18) f-1 (x) = x2 - 5
19)
20)
21)
22)
23)
24)
25)
(-3, -5)
(-6, 45)
x = -2
(- , 6]
(-9 ± 14, 0); (0, 67)
26) 2 sec; 78 ft
27) falls to the left and falls to the right
10
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
28) falls to the left and rises to the right
29) 2, multiplicity 1, crosses x-axis;
-7, multiplicity 2, touches x-axis
and turns around
30)
31) C
32) 4x 3 + 27x + 3 +
9x
2
x -7
33) x4 + 2x 3 + 5x 2 + 10x + 20 +
45
x-2
34) 17
35) -1; The remainder is zero; -1, -2, and -3, or {-3, -2, -1}
1
36) ± , ± 1, ± 2, ± 4, ± 8
2
37) {-2, -3 + 3, -3 - 3}
38) {-1, -3 + 3i, -3 - 3i}
39) f(x) = x 4 - 12x 2 - 64
40)
41)
42)
43)
44)
45)
{x|x 0, x -49}
x = 9, x = 2
y=1
y = x + 15
y=x
46) C
11
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
47) [-1, 4]
48) (- , -5)
(-2, )
49) (- , -5) or (7, )
50) (- , 5) or (9, )
51) [-8, -4)
52)
53)
54) $1568.31
55) $7452.93
56) 43 = x
57) log
216
6=
1
3
58) -2
12
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
59)
60) log
t4 z 3
b
s
61) 1.7876
62)
D: (-2, )
3
63)
5
ln 3
5
64)
65) {ln 8 - 3}
ln 4
-8
66)
ln 5
67) {7}
68) 69) {
70)
71)
72)
73)
74)
374
125
1
}
24
{7}
{(x, y) 3x + y = 11}
{(-4, -5)}
$2.00 for a hot dog;
$0.75 for a bag of potato chips
75) {(2, 4, -5)}
76) {(5, 9), (-2, 16)}
13
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
77)
78)
79) maximum value: 82;
minimum value: 9
80) 5x + 4y 55
x + y 13
y 2
81) 2 × 4; 6
82)
1
1
4
2
X=
-
2 -
3
4
1
4
0
3 9 -6
83) AB = 2 -6 9 ; (ab) 23 = 9
20 0 25
84)
88 -60 93
40 -28 71 ; (ab)32 = 27
-39 27 -41
85)
AB = -a -9b
-8a
5b
86) 21
14
mat110ExamReview2013-2014.tst
Answer Key
Testname: MAT 110 COURSE REVIEW
87)
129
308
88) x = -4
89) x = -1
90) -8
15
mat110ExamReview2013-2014.tst