Math 100 Final Exam PRACTICE TEST
Solve the equation.
5) -5 ≤ x - 5 ≤ 3
1) 9x + 7(-3x - 3) = -31 - 2x
A) 1
C)
A) [0, 8]
26
7
B)
-6
26
5
-4
-2
0
2
4
6
8
10
12
-4
-2
0
2
4
6
8
10
12
-12 -10
-8
-6
-4
-2
0
2
4
-8
-6
-4
-2
0
2
4
D) - 1
B) (0, 8)
Solve.
-6
2) 0.09y + 0.13(2000 - y) = 0.46y
A) {130}
B) {1300}
C) {520}
D) {1560}
C) [-10, -2]
-14
Solve the investment problem.
D) (-10, -2)
3) Mardi received an inheritance of
$60,000. She invested part at 8% and deposited
the remainder in tax-free bonds at 11%. Her total
annual income from the investments was $5100.
Find the amount invested at 8%.
A) $50,000
B) $49,000
C) $54,900
D) $25,000
-14
-12 -10
For the compound inequality, give the solution set in both
interval and graph forms.
6) x ≥ -2 or x ≤ 6
A) (-∞, ∞)
Solve the inequality, giving its solution set in both interval
and graph forms.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
4) -3x ≤ 9
B) (-∞, -2] ∪ [6,∞)
A) [-3, ∞)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
C) [-2, 6]
B) (- ∞, -3]
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
D) (-6, 2)
C) [3, ∞)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-2
-1
0
1
2
3
4
5
6
7
8
Express the set in simplest interval form.
D) (- ∞, -3)
-8
-7
7) (-8, 9] ∩ (-6, ∞)
-6
-5
-4
-3
-2
-1
0
1
2
A) (-8, ∞)
B) (-8, 9]
C) (-6, 9]
D) [-6, 9]
8) (-7, 4) ∪ [-3, 6]
1
A) (-7, -3]
B) [-3, 4)
C) [-3, 6]
D) (-7, 6]
Solve the given equation or inequality. If an equation is
given, then write the solution set in set notation. If an
inequality is given, then write the solution set in interval
notation.
D) (-4, 0); (0, 1)
y
10
9) |x + 8| + 7 = 15
5
A) no solution
B) 0, 16
C) 0
D) -16, 0
-5
-10
5
10
Find the x- and y-intercepts. Then graph the equation.
-5
10) 2x - 8y = 8
A) (4, 0); (0, -1)
-10
y
10
Find the slope of the line through the pair of points.
5
-10
-5
5
10
x
11) (9, -3) and (-2, 3)
11
A)
6
B) - 6
11
6
11
D) - 11
6
C)
-5
Find the slope of the line.
-10
12)
y
B) (-1, 0); (0, 4)
10
y
10
5
5
-5
-10
-10
-5
5
10
5
10
x
-5
-5
-10
-10
A) - 2
C) (1, 0); (0, -4)
C)
y
10
5
-10
-5
5
10
x
-5
-10
2
1
2
B) 2
D) - 1
2
x
x
Write the equation in slope-intercept form, state the slope
and y-intercept, and graph the equation.
13)
y
17) 4x - 5y = -20
4
A) y = - x - 4;
5
10
5
4
slope: - , y-intercept (0, - 4)
5
-10
-5
5
10
x
8
y
6
-5
4
2
-10
-8
-6
-4
-2
2
4
6
8 x
6
8 x
6
8 x
-2
3
A)
2
B) 0
C) -2
D) Undefined
-4
-6
-8
4
B) y = x - 4;
5
14)
4
slope: , y-intercept (0, - 4)
5
y
10
8
y
6
4
10
-10
2
x
-8
-6
-4
-2
2
4
-2
-4
-10
-6
-8
A) 0
B) 2
C) -2
D) Undefined
4
C) y = - x + 4;
5
4
slope: - , y-intercept (0, 4)
5
Decide whether the pair of lines is parallel, perpendicular, or
neither.
8
15) The line through (-20, 5) and (-4, 7) and the line
through (-5, 5) and (7, 4)
y
6
A) Parallel
4
B) Neither
2
C) Perpendicular
-8
-6
-4
-2
2
-2
-4
16) 9x + 3y = 12 and 24x + 8y = 36
-6
A) Perpendicular
-8
B) Neither
C) Parallel
3
4
4
D) y = x + 4;
5
B)
y
4
slope: , y-intercept (0, 4)
5
4
y
8
2
6
4
-4
2
-2
2
4
6x
2
4
6x
2
4
6x
-2
-8
-6
-4
-2
2
4
8 x
6
-2
-4
-4
-6
-6
-8
C)
y
Find an equation of the line satisfying the conditions. Write
the equation in slope-intercept form.
4
18) Through (-3, 8); perpendicular to
-3x + 4y = -23
3
23
3
41
A) y = - x + B) y = x + 4
4
4
4
4
C) y = - x + 4
3
2
-4
-2
4
D) y = x + 12
3
-2
-4
Graph the compound inequality.
-6
19) 2x - y > 4 and x ≤ 4
D)
A)
y
y
4
4
2
2
-4
-2
2
4
-4
6x
-2
-2
-2
-4
-4
-6
-6
4
Decide whether the relation is a function.
20) 4x < y + 2 or y < -2
21) {(-4, -8), (-2, 9), (-1, -1), (-1, 7)}
A)
A) Function
y
B) Not a function
10
Give the domain and range of the relation.
5
-10
22) {(12, 6), (12, 5), (8, -5), (-7, 2), (4, -3)}
-5
5
10
A) Domain: {5, -5, -3, 2, 6}; Range: {12, 12, 8, 4,
-7}
x
B) Domain: {12, -12, 8, 4, -7}; Range: {5, -5, -3,
2, 6}
-5
C) Domain: {12, 12, 8, 4, -7}; Range: {5, -5, -3,
2, 6}
-10
D) Domain: {12, 8, 4, -7}; Range: {5, -5, -3, 2,
6}
B)
y
Decide whether the relation is a function, and give the
domain and range.
10
5
23)
y
-10
-5
5
10
10
x
-5
5
-10
-10
-5
C)
5
10
x
-5
y
10
-10
5
-10
A) Function; domain: (-∞, 3] ; range: (-∞, ∞)
-5
5
10
B) Not a function; domain: (-∞, 3] ; range: (-∞,
∞)
x
-5
24)
y
-10
10
D)
5
y
10
-10
-5
5
10
x
5
-5
-10
-5
5
10
x
-10
-5
A) Not a function; domain: (-∞, ∞); range: (0,
∞)
-10
B) Function; domain: (-∞, ∞); range: (0, ∞)
5
Solve the problem.
Apply the quotient rule for exponents, if applicable, and
write the result using only positive exponents. Assume all
variables represent nonzero numbers.
x-6
32)
x-17
25) Find f(-4) when f(x) = x2 - 2x + 6.
A) 18
B) 14
C) 30
D) 2
26) Find f(k) when f(x) = 3x 2 + 4x + 5
A) 3k2 + 4k + 5
B) 9k2 + 16k + 25
C) 3k2 + 4k + 25
D) 3k2 + 16k + 5
A)
C) -x11
Decide whether the ordered pair is a solution of the given
system.
B) No
Solve the system by substitution.
28) x + 7y = -2
3x + y = 34
A) {(-2, 3)}
B) {(3, 7)}
C) {(12, -2)}
D) {(7, 12)}
29) x + 7y = -30
2x + 6y = -28
B) -27x7
C) 27x12
D) -27x12
A)
11
4r10
B)
11r5
4
C)
11r10
4
D)
11
4r5
Combine terms.
B) {(2, -3)}
35) q3 - 10q4 + 5q2 + q4 - 11q3
C) {(-3, -3)}
A) -10q4 + q3 + 5q2
D) {(-2, -4)}
B) -9q8 - 10q6 + 5q2
Apply the product rule for exponents, if possible.
C) 9q4 + 10q3 - 5q2
30) (-3x4 y)(-1x4 y5 )
C) 3x8 y6
D) 3x16y7
D) -9q4 - 10q3 + 5q2
Add or subtract as indicated.
36) (-7x4 + 2x6 - 2 - 6x5 ) (6 - 4x5 + 6x6 - 3x4 )
Evaluate the expression. Assume all variables represent
nonzero numbers.
A) 8x6 - 10x5 - 10x4 + 4
31) 9 0 + 40
A) 0
B) 13
C) 1
D) x11
A) 27x7
A) Inconsistent: no solutions
B) -1x9 y6
1
x23
Simplify the expression so that no negative exponents appear
in the final result. Assume all variables represent nonzero
numbers.
11r3 (r5 )3
34)
4(r2 )4
Solve the system by elimination. If the system is inconsistent
or has dependent equations, say so.
A) -3x8 y5
B)
Simplify the expression. Write your answer with only
positive exponents. Assume that all variables represent
nonzero real numbers.
33) (-3x4 )3
27) (-4, -2)
3x + y = -10
4x + 3y = -10
A) Yes
1
x11
B) -4x6 - 2x5 - 4x4 - 8
D) 2
C) 8x6 - 10x5 - 10x4 - 8
D) -4x6 - 10x5 - 10x4 + 4
6
For the given polynomial function, find the requested value.
43) Use long division to find
(9z 4 - 6z 3 + 14z 2 + 6z + 7) ÷
37) f(x) = 6x3 + 3x2 + 30; find f(-2)
A) -18
B) -16
C) -6
(z 2 - z + 2)
D) -15
A) 9z 2 - 3z + 1 + Find the product.
38) 2x(x2 - 9x + 2)
B) 9z 2 + 3z - 1 + A) 2x3 - 9x2 + 2x
B) 2x3 - 18x + 4
C) 2x2 - 18x + 4
D) 2x3 - 18x2 + 4x
z - 9
z 2 - z + 2
-z + 9
z 2 - z + 2
C) 9z 2 + 3z - 1
D) 9z 2 + 3z - 1 + 39) (-7y + 1)(-5y2 - y + 5)
A) 35y3 - 12y2 - 36y + 5
z - 9
z 2 - z + 2
Factor out the greatest common factor.
B) 35y3 - 36y + 5
44) 24x8 y8 - 18x2 y4 - 18x5 y2
C) 2y2 - 36y + 5
A) 6(4x8 y8 - 3x2 y4 - 3x5 y2 )
D) 35y3 + 2y2 - 36y + 5
B) x2 y2 (24x6 y6 - 18y2 - 18x3 )
C) 6x2 y2 (4x6 y6 - 3y2 - 3x3 )
40) (7x - 11y) 2
D) 6x2 (4x6 y8 - 3y4 - 3x3 y2 )
A) 7x2 - 154xy + 121y2
B) 49x2 + 121y2
45) 5m(2 - m) + 7n(2 - m)
C) 7x2 + 121y2
A) m(5 + 7n)(2 - m)
B) (5m - 7n)(2 - m)
D) 49x2 - 154xy + 121y2
C) (5m + 7n)(2 - m)
D) 5(m + n)(2 - m)
Divide.
Factor by grouping.
18x7 - 21x2 + 30x
41)
3x
46) 40r2 + 45ry - 8xr - 9xy
A) 6x7 - 7x2 + 10x
B) 6x6 - 7x + 10
C) 6x7 - 21x2 + 30x
D) 18x6 - 21x + 30
8
y + 8
C) y2 + 8
B) (8r + 9y)(5x - r)
C) (8r + 9y)(5r - x)
D) (9r + 8y)(5r - x)
Factor the trinomial completely.
y2 + 16y + 64
42)
y + 8
A) y + A) (8r + 9y)(x - 5r)
47) y2 + 5y - 66
B) y + 8
A) (y - 11)(y + 6)
B) (y + 11)(y - 6)
C) (y - 11)(y + 1)
D) Prime
D) y - 8
48) 12y2 + 25y + 12
A) (3y - 4)(4y - 3)
B) (3y + 4)(4y + 3)
C) (12y + 1)(y - 12)
D) (12y + 4)(y + 3)
Factor the polynomial completely.
49) 36k2 - 25m 2
A) (6k + 5m)(6k - 5m)
B) (6k - 5m)2
C) (36k + m)(k - 25m)
D) (6k + 5m)2
7
Write the rational expression in lowest terms.
m 2 - 9m
57)
9 - m
50) m 2 + 10m + 25
A) (m - 5)2
B) (m + 5)(m - 5)
C) (m + 5)2
D) Prime
A) Already in lowest terms
B) m + 3
51) 216x3 + y3
C) -m
A) (6x + y)(36x2 + y2 )
D) m
B) (6x - y)(36x2 + 6xy + y2 )
C) (6x + y)(36x2 - 6xy + y2 )
Perform the indicated operation and express in lowest terms.
k2 + 6k
k2 + 9k + 14
· 58)
2
2
k + 13k + 42 k - 5k - 14
D) (216x + y)(x2 - 6xy + y2 )
52) 8a 3 - 27b3
A)
k2 + 6k
k - 7
B)
k
k2 + 13k + 42
C)
1
k - 7
D)
k
k - 7
B)
z + 8
z
D)
z + 8
z 2 + 8z
A) (2a + 3b2 )(4a 2 - 6ab + 9b2 )
B) (2a - 3b)(4a 2 + 6ab + 9b2 )
C) (2a - 3b)(4a 2 + 9b2 )
D) (2a + 3b)(4a 2 - 6ab + 9b2 )
59)
Find all solutions by factoring.
53) 2x2 - 24x = -64
A) -8, - 4
C) 4, 8
A) z + 8
B) -8, 4
C)
D) {8, 16}
54) (x + 10)(x + 6) = -3
60)
A) {-9, -10}
B) {-7, -9}
C) {-10, -6}
D) {-6, -13}
Find all numbers not in the domain of the function.
x2 - 64
55) f(x) = x2 + 4x - 21
A) 8, -8
B) 7, -3
C) 0
D) -7, 3
61)
Express the rational expression in lowest terms.
y2 + 6y - 27
56)
y2 + 5y - 36
A)
6y - 3
5y - 4
6y - 27
C)
5y - 36
z 2 + 14z + 49
z 2 + 7z
÷ z 2 + 15z + 56 z 2 + 16z + 64
B)
62)
y - 3
y - 4
z 2 + 15z + 56
3
4
+ r r + 2
A)
7r + 6
r(r + 2)
B)
7r + 6
r(-2 - r)
C)
-6r - 7
r(r + 2)
D)
-6r - 7
r(-2 - r)
2
8
- 5 x - 5
5 - 5 x
A)
-6
5 x - 5
B)
10
5 x - 5
C)
6
5 x - 5
D)
-10
5 x - 5
B)
x - 24
x - 6
D)
x + 24
x2 - 36
x
12
72
+ - x - 6 x + 6 x2 - 36
A)
y2 + 6y - 27
D) - y2 + 5y - 36
z
x + 24
x + 6
C) 1
8
Simplify the complex fraction.
2
4 + x
63)
x 1
+ 4 8
16
A)
x
B) 1
Simplify the root.
4
69)
x28
x
C)
16
A) - x7
B) x7
C) -x7
D) x7
D) 16
Simplify the expression involving rational exponents.
70) 125 4/3
Solve the equation.
1
1
5
+ = - 64)
10
5x 2x
A) {-15}
B) {15}
C) {-16}
D) ∅
71)
-2y2 - 18y - 3 2y + 2
-6y - 93
= + 65)
y - 5
y2 - 25
y2 - 25
2
A) -5, 5, - , 1
31
A) 78,125
B) 625
C) 15,625
D) 3125
25 -1/2
81
A)
5
9
B)
9
5
C)
25
162
B) { y y is a real number }
D) Not a real number
C) { y y ≠ -5, y ≠ 5 }
D) ∅
Write with radicals. Assume that all variables represent
positive real numbers.
72) (5m 4 + 4k2 )2/5
Solve the problem.
66) A formula for electric circuits is
1 1 1
= + . If a = 18 and b = 19, find c.
a b c
A) 342.000
B) 1.056
C) 0.003
D) 0.947
A)
C)
5
2
5m 4 + 4k2
5m 4 + 4k2
A) P = pvV
tT
B) P = pvT
tV
A) 5km 2
C) P = pv
tTV
D) P = tvT
pV
C)
68) S = 2πrh + 2πr2 for h
C) h = S
- 1
2πr
74)
B) h = hS - r
D) h = 5
D)
5
5
2
5m + 4k
5m 4 + 4k2
2
Use the rules of exponents to simplify the expression. Write
the answer with positive exponents. Assume that all
variables represent positive real numbers.
73) (243k5 m -10)1/5
Solve the formula for the specified variable.
PV pv
67)
= for P
T
t
A) h = 2π(S - r)
B)
5k
m2
C)
9
D)
3k
m2
B)
1
17/4
x
x1/2
3/4
x · x-3
A) x17/4
S - 2πr2
2πr
B) 3km 2
1
x11/4
D) x11/4
Multiply using the product rule. Assume all variables
represent positive real numbers.
3
3
75) 25xy · 4xy
3
A) 29x2 y2
B) 10xy
3
D) 7xy
C) 100x2 y2
Simplify. Assume that all variables represent positive real
numbers.
5
5
82) 3 x6 y - 2x xy
5
A) (3 - 2x) xy
5
B) x xy
5
C) 2x xy
Express the radical in simplified form.
4
76) 768
D) Cannot be simplified
A) 5
B) 3
C) 27
D) 4
4
4
4
83)
3
343 4 7
7
- + 5
5
25
336
5
A) - Express in simplified form. Assume that all variables
represent positive real numbers.
77)
C)
4 7
25
D)
6 7
5
108x2
A) 6x 3
B) 3x2 6
C) 108x
D) 6 3x
3
78) - 1000x4 y5
3
A) -10xy xy2
C) -10xy
3
xy
B) 10xy
D) 2xy
2
3
Multiply, then simplify the product. Assume that all
variables represent positive real numbers.
84) (3 + 3)2
6 + 6
A) -2
C) 4
B) 12 + 3 3
C) 6 + 6 3
D) 12 + 6 3
Rationalize the denominator. Assume that all variables
represent positive real numbers.
100
85)
3
xy2
A)
10
6
B) 10
6
D) -4
6
A)
C)
6x + 4 216x + 2 24x
A) 29 6x
B) 6 246x
C) 7 246x
D) 28 6x
B) 10
D)
3
100 3
3
Simplify. Assume that all variables represent positive real
numbers.
4 16
86)
y
24
6
3
3
C) 19
Perform the indicated operations and simplify. Assume that
all variables represent positive real numbers.
80) -8
A) 9 + 6 3
xy2
Simplify the radical. Assume that all variables represent
positive real numbers.
10
79)
x31
10
10
A) x3 + x
B) x x3
10
C) x3
x
D) x x3
81)
4 7
5
B)
10
2
2
4
y3
y
4
y
y
B)
D)
2
2
4
y2
y
4
y3
y2
Rationalize the denominator. Assume that all variables
represent positive real numbers and that the denominator is
not zero.
6
87)
6 7 - 6
A)
C)
42 + 1
41
B)
42 - 1
41
D)
Multiply or divide as indicated.
94)
42 + 1
43
95)
7 + 1
41
5 - 8 50
6
B)
5 - 40 2
6
C)
15 - 48 50
6
D)
15 - 120 2
12
B) 72i
C) -72i
D) -72
-40
-10
B) 2
C) 2i
D) -2i
Add or subtract as indicated. Write your answers in standard
form.
96) (7 - 4i) + (6 + 2i)
A) 1 + 6i
B) 13 - 2i
C) 13 + 2i
D) -13 + 2i
97) (4 + 6i) - (-5 + i)
Solve the equation.
89)
A) 72
A) -2
Write the expression in lowest terms. Assume that all
variables represent positive real numbers.
30 - 48 50
88)
36
A)
-81 · -64
A) -9 - 5i
B) -1 + 7i
C) 9 - 5i
D) 9 + 5i
4x - 3 - 6 = 0
A) {36}
C)
39
4
B) ∅
D)
Multiply.
98) (6 + 2i)(3 - 7i)
9
4
A) 32 - 36i
B) 4 + 48i
C) 32 + 36i
D) -14i2 - 36i + 18
Solve this equation.
90)
Use the square root property to solve the given equation.
x + 3 = x - 3
A) {6}
B) {1, 13}
C) {1, 6}
D) {6, 13}
99) -2k2 + 18 = 0
Solve the equation.
3
91) x + 5 = 4
A) {6, -6}
B) {3}
C) {3, -3}
D) {-11.5}
100) (p + 8)2 = 11
11 - 8
A) {64}
B) {59}
A)
C) {11}
D) {-1}
B) -8 + 11, -8 - 11
C) -8 + 11
Write the number as a product of a real number and i.
Simplify the radical expression.
92)
D)
-49
A) i 7
B) -7i
C) 7i
D) ± 7
93) - -212
A) 2 53
B) -2i 53
C) -2 53
D) 2i 53
11
11 + 8, - 11 + 8
Find the imaginary solutions of the given equation.
101) 4x2 - 3x + 4 = 0
3 + i 55 3 - i 55
A)
, 8
8
B)
3 + 55 3 - 55
, 8
8
C)
-3 + 55 -3 - 55
, 8
8
D)
-3 + i 55 -3 - i 55
, 8
8
Use the quadratic formula to solve the given equation.
(Solutions are real numbers.)
102) 3n 2 = -8n - 2
-8 + 10 -8 - 10
A)
, 3
3
B)
-4 + 10 -4 - 10
, 3
3
C)
-4 + 10 -4 - 10
, 6
6
D)
-4 + 22 -4 - 22
, 3
3
12
Answer Key
Testname: MTH100PRACTICETESTFINAL
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A
C
A
A
A
A
C
D
D
A
B
B
D
A
B
C
D
C
D
D
B
D
B
B
C
A
B
C
D
C
D
D
D
C
D
B
C
D
D
D
B
B
B
C
C
C
B
B
A
C
C
B
C
54)
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13
B
D
B
C
D
B
A
B
A
A
A
D
A
B
D
D
B
B
D
D
D
C
D
A
A
C
C
A
B
C
D
A
A
A
B
C
A
B
C
B
D
B
B
D
A
C
B
A
B