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MTH 100 Exam Review
Solve the equation.
1) -[7x + (6x + 7)] = 4 - (9x + 8)
2)
p 3p
=5
4
8
3)
6x
-7x + 6 5
+ =7
7
7
12)
5x + 9
49
<5
-8
13) 28a + 4 > 4(6a - 6)
4) (y - 4) - (y + 3) = 8y
Solve.
14)
5) -0.06y + 0.08(1100 - y) = 0.36y
Decide whether the equation is conditional, an identity, or
a contradiction. Give the solution set.
6) 4(24t + 12) = 16(4t + 5)
4
2
(3k + -1) > (4k - 3)
3
5
-8
-6
-4
-2
0
2
4
15) -2 ≤ x - 5 ≤ 4
Solve the percent problem.
7) Stevie bought a stereo for $205 and put it on
sale at his store at a 70% markup rate. What
was the retail price of the stereo?
-6
16) 6 ≤
Solve the investment problem.
8) Walt made an extra $9000 last year from a
part-time job. He invested part of the money at
8% and the rest at 7%. He made a total of $680
in interest. How much was invested at 7%?
-4
-2
0
2
4
6
8
10
12
14
3x - 1
≤9
2
For the compound inequality, give the solution set in both
interval and graph forms.
17) x ≤ -2 and x ≥ 7
Solve the mixture problem.
9) A chemist makes a mixture of concentrated
hydrochloric acid and distilled water so that
the ratio of acid to water is 9 to 7. If he starts
with 45 liters of acid, how much water is
mixed with the acid?
18) x - 1 > 2 or x + 2 < 1
Solve the inequality, giving its solution set in both
interval and graph forms.
10) -9x ≤ 90
Solve.
19) 4x - 6 = 3
Solve the inequality and graph the solution set.
20) x - 9 ≥ 8
11) -10y + 5 ≤ -11y + 13
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
1
2
4 6
8 10 12 14
21) 8x - 1 ≤ 7
-8
-6
-4
-2
0
2
4
Write the equation in slope-intercept form, state the slope
and y-intercept, and graph the equation.
30) 3x - 6y = -18
6
8
y
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.
22) |5k - 1| - 1 ≥ 6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
Solve the equation.
23) 2s + 3 = s - 2
-6
-8
Find the slope of the line through the pair of points.
24) (-6, -8) and (7, -1)
Write the equation in standard form of the line satisfying
the given conditions.
3
31) Through (4, 3); m = 5
Graph the line.
25) Through (0, 2); m =
1
4
y
32) Through (10, 7); horizontal
10
33) Through
5
-10
-5
5
10
1 8
,
; vertical
2 3
Write the equation in standard form of the line through
the given points.
34) (6, 1) and (-7, 4)
x
-5
-10
Find an equation of the line satisfying the conditions.
Write the equation in slope-intercept form.
35) Through (-3, 8); perpendicular to -3x + 4y =
-23
Decide whether the pair of lines is parallel, perpendicular,
or neither.
26) 3x - 6y = 19 and 18x + 9y = 14
27) 12x + 4y = 16 and 18x + 6y = 27
28) 4x - 3y = -13 and 3x + 3y = -13
Find the equation in slope-intercept form of the line
satisfying the conditions.
2
19
29) m = - ; y-intercept 0,
3
3
2
Graph the compound inequality.
36) x + y ≥ 2 and y ≤ 2
Decide whether the relation is a function, and give the
domain and range.
40)
y
y
10
4
5
2
-10
-4
-2
2
-5
5
10
x
6x
4
-5
-2
-10
-4
-6
Determine whether the relation defines y as a function of
x. Give the domain.
41) 3x = 13 - 5y
37) x - 5y ≤ 4 or 5x + y ≤ 3
y
Solve the problem.
10
42) Find f(1) when f(x) = x2 - 2x - 4.
5
43) Find g(a - 1) when g(x) = 2x - 5.
-10
-5
5
10
x
An equation that defines y as a function of x is given.
Solve for y in terms of x, and replace y with the function
notation f(x).
44) 5x - 6y = 5
-5
-10
Graph the linear or constant function. Give the domain
and range.
45) f(x) = -5x - 6
Decide whether the relation is a function.
38) {(-8, 7), (-4, -4), (-1, 3), (2, -1)}
6
Give the domain and range of the relation.
39) {(5, -3), (3, -5), (12, 5), (9, 6), (-6, 4)}
y
4
2
-6
-4
-2
2
-2
-4
-6
3
4
6 x
46) h(x) = 5
6
Use the FOIL method to find the product.
55) (x - 12)(4x - 3)
y
4
Find the product.
56) (12y + x)(12y - x)
2
-6
-4
-2
2
4
57) (w - 15)2
6 x
-2
Divide.
-4
58) (5z4 - 3z 3 + 7z2 + 4z + 2) ÷ (z2 - z + 2)
-6
Factor the polynomial.
59) 27x9 - 12x7 - 12x5
Solve the system by substitution.
47) 3x - 13 = -y
2x + 9y = -8
60) 27a 3 - 64
Solve the system by elimination. If the system is
inconsistent or has dependent equations, say so.
48) 9x + 37 = 8y
-4x + 5y = 15
61) x3 + 8
62) x4 - 16
Solve the system.
7x
49)
- y = 10
12
63) 25p2 - 16q2
5x
+ 2y = 11
9
64) 8x2 - 10xy - 25y2
65) 27m 2 + 144mn + 192n 2
Evaluate the expression. Assume all variables represent
nonzero numbers.
50) (-10)0 + (-12)0
66) 5z4 - 17z2 - 40
67) ay + 6y - at - 6t
Evaluate the expression.
1 -4
51)
3
Find all solutions by factoring.
68) (2x + 3)(x + 3) = 20x - 3
Simplify the expression so that no negative exponents
appear in the final result. Assume all variables represent
nonzero numbers.
52) m -10m 5 m -1
69) 2x2 + 15x = -25
Solve the equation.
70) 3x3 + 17x2 + 20x = 0
53) (x-4 y5 )-2
Find all numbers that are not in the domain of the
function. Then give the domain using set notation.
x+1
71) f(x) =
4x + 6
2x3 y-3 -5
54)
x-2y4
4
Express the rational expression in lowest terms.
y2 + 2y - 8
72)
y2 + 8y + 16
83)
Solve the formula for the specified variable.
A
84) P =
for r
1 + rt
Write the rational expression in lowest terms.
m 2 - 25m
73)
25 - m
Find the root if it is a real number.
3
85) - 216
Perform the indicated operation and express in lowest
terms.
k2 + 13k + 36
k2 + 8k
74)
·
k2 + 17k + 72 k2 - 3k - 28
75)
x3 - 64y3
x2 + 4xy + 16y2
÷
86)
x2 + 6xy + 8y2
2
6
+
y2 - 3y + 2 y2 - 1
77)
6x
24
2
2
x - 5x + 6 x - 6x + 8
78)
6
3
162
+
x+3
2
3
x - 3x+ 9
x + 27
88) -
81)
- 81
8 - 4/3
125
Use the rules of exponents to simplify the expression.
Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
a 3 b-5 1/4
89) 256
a -1 b3
90) (64h 16k18)3/2
Simplify the complex fraction.
5
1x
79)
5
1+
x
80)
4
Evaluate the exponential.
81 1/2
87) 64
x2 - 16y2
76)
5
3
-21
+
=
x-7
x
x2 - 7x
91)
x3/5
6/5
x
· x-5
Express the radical in simplified form.
3
92) 54
y
7+y
+
7-y
y
7-y
y
+
y
7+y
Express in simplified form. Assume that all variables
represent positive real numbers.
3
93) - 512x4 y5
x-2
-2
x - y-2
94)
Solve the equation.
1
3
2
82)
=
y + 2 y - 2 y2 - 4
5
3 y22
64
Simplify the radical. Assume that all variables represent
positive real numbers.
4
95) 482
Solve the given equation by completing the square.
107) z 2 + 12z + 24 = 0
Find the complex solutions of the given equation.
108) -5x2 + 3x - 5 = 0
Find the distance between the pair of points.
96) (4, -3) and (6, -7)
Use the quadratic formula to solve the given equation.
(Solutions are real numbers.)
109) 6n 2 = -12n - 4
Perform the indicated operations and simplify. Assume
that all variables represent positive real numbers.
97) 5 72 + 6 162 + 7 200
110)
Simplify. Assume that all variables represent positive real
numbers.
3 5
98)
3
99)
Use the quadratic formula to solve the given equation.
111) x2 + x + 1 = 0
4 81
y
112) 7x2 - 5x = -1
Rationalize the denominator. Assume that all variables
represent positive real numbers and that the denominator
is not zero.
7- 2
100)
7+ 2
Solve this equation.
101) 3x + 10 = 5 - 2x
Solve the equation.
102) 2x + 3 -
3 2 1
1
s + s+
=0
4
2
12
x+1=1
Add or subtract as indicated. Write your answers in
standard form.
103) (4 + 9i) - (3 + 5i) + (3 + 10i)
Write the quotient in the form a + bi.
6 + 2i
104)
9 - 3i
Multiply or divide as indicated.
105) -49 · -9
Use the square root property to solve the given equation.
106) (6t + 4)2 = 6
6
Answer Key
Testname: EXAM REVIEW
1) -
3
4
17) φ
2) {-40}
3) 11
7
4) 8
5)
6)
7)
8)
9)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
18) (-∞, -1) ∪ (3, ∞)
-7 -6 -5 -4 -3 -2 -1 0
{176}
Conditional; {1}
$348.50
$4000
35 liters
19)
1
2
3
4
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
2
4 6
5
6
7
3 9
,
4 4
20) (-∞, 1] ∪ [17, ∞)
10) [-10, ∞)
-15 -14 -13 -12 -11 -10 -9
-8
-7
-6
8 10 12 14 16 18
3
21) - , 1
4
-5
11) (-∞, 8]
-8
1
2
3
4
5
6
7
8
9
-6
10 11 12 13 14 15
347
12)
,∞
25
-2
22) -∞, -
6
8
∪ ,∞
5
5
23) - 5, -
1
3
24)
347
25
-4
0
2
4
7
13
25)
13) (-7, ∞)
y
10
-14 -13 -12 -11 -10 -9
14)
-8
-7
-6
-5
-4
-3
-2
-1
0
5
1
,∞
18
-10
-5
5
-5
-8
-6
-4
-2
0
2
4
6
15) [3, 9]
-6
16)
-10
-4
-2
0
2
4
6
8
10
12
26) Perpendicular
27) Parallel
28) Neither
2
19
29) y = - x +
3
3
14
13 19
,
3 3
13
3
19
3
7
10
x
6
8
Answer Key
Testname: EXAM REVIEW
30) y =
1
x + 3;
2
slope:
37)
y
10
1
, y-intercept (0, 3)
2
8
5
y
6
-10
4
-5
5
2
-8
-6
-4
10
x
-5
-2
2
4
8 x
6
-10
-2
-4
38) Function
39) Domain: {3, -6, 9, 5, 12}; Range: {-3, -5, 5, 6, 4}
40) Not a function; domain: (-∞, 2] ; range: (-∞, ∞)
41) Function; domain: (-∞, ∞)
42) -5
-6
-8
31) 3x + 5y = 27
32) y = 7
1
33) x =
2
43) 2a - 7
44) f(x) =
34) 3x + 13y = 31
4
35) y = - x + 4
3
5 - 5x
-6
45) domain: (-∞, ∞); range: (-∞, ∞)
y
6
36)
y
4
2
4
-6
-4
-2
2
2
4
6
x
6
x
-2
-4
-4
-2
2
4
6x
-6
-2
46) domain: (-∞, ∞); range: {5}
-4
y
6
-6
4
2
-6
-4
-2
2
-2
-4
-6
47) {(5, -2)}
48) {(-5, -1)}
8
4
Answer Key
Testname: EXAM REVIEW
49) (18,
1
)
2
50) 2
51) 81
1
52)
m6
53)
x8
y10
54)
y35
32x25
6x - 33
x2 - 3x + 9
79)
x-5
x+5
80)
7+y
7-y
81)
y2
y2 - x2
82) {-5}
83) ∅
A- P
84) r =
Pt
55) 4x2 - 51x + 36
56) 144y2 - x2
85) -6
86) Not real
9
87) 8
57) w2 - 30w + 225
58) 5z2 + 2z - 1 +
78)
-z + 4
z2 - z + 2
59) 3x5 (9x4 - 4x2 - 4)
60) (3a - 4)(9a 2 + 12a + 16)
88)
625
16
61) (x + 2)(x2 - 2x + 4)
62) (x2 + 4)(x + 2)(x - 2)
89)
4a
b2
90) 512h 24k27
91) x22/5
63) (5p + 4q)(5p - 4q)
64) (2x - 5y)(4x + 5y)
65) 3(3m + 8n)2
92) 3
66) (5z2 + 8)(z 2 - 5)
67) (a + 6)(y - t)
3
68)
,4
2
71) 72)
2
93) -8xy
94)
5
69) - , -5
2
70) -4, -
3
3
y7
3
xy2
y
4
95) 4 3
96) 2 5
97) 154 2
3
45
98)
3
5
,0
3
3
3
; x|x ≠ 2
2
y- 2
y+ 4
99)
73) -m
k
74)
k- 7
100)
75) x + 2y
3
4
y3
y
51 - 14 2
47
3
4
76)
8y - 10
(y - 1)(y + 1)(y - 2)
101)
77)
6(x - 6)
(x - 3)(x - 4)
102) {3, -1}
103) 4 + 14i
8
2
104)
+ i
15 5
9
Answer Key
Testname: EXAM REVIEW
105) -21
-4 + 6 -4 - 6
106)
,
6
6
107) - 6 + 2 3, - 6 - 2 3
3
91 3
91
108)
i,
i
+
10
10
10
10
109)
-3 + 3 -3 - 3
,
3
3
110) -
1
3
111)
-1 + i 3 -1 - i 3
,
2
2
112)
5+i 3 5-i 3
,
14
14
10