Identify the following as an expression or an equation.
82)
8x +4
2=9 x
7–3
82)
A)
Equation
B)
Expression
Write the rational expression in lowest terms.
83)
a2– 3a
(a + 7)(a – 3)
83)
A)
1
a + 7
B)
a – 3
a + 7
C)
a2
a + 7
D)
a
a + 7
Solve the problem.
84)
A triangle drawn on a map has sides of lengths 9.0 cm, 10 cm, and 15 cm. The shortest of the
corresponding real–life distances is 138 km. Find the longest of the real–life distances. Round to the
nearest unit.
84)
A)
83 km
B)
230 km
C)
207 km
D)
153 km
Multiply. Write the answer in lowest terms.
85)
t – 7
t2– 3t –10
·t + 2
t2–12t +35
85)
A)
t
(t +5)(t +5)
B)
–1
5(t +5)
C)
1
(t –5)(t –5)
D)
(t – 7)
(t –5)(t –5)(t + 7)
19
Solve the equation.
86)
–2 x
2x +12 =2 x
4x +24 +6x –4
x +6
86)
A)
{16}
B)
–8
15
C)
1
30
D)
8
15
Find all values that make the expression undefined.
87)
–4
3z
87)
A)
0
B)
Never undefined
C)
3
D)
0.333
A
Write the rational expression in lowest terms.
88)
tx + t +5x +5
8x +8
88)
A)
t –8
5
B)
t –5
8
C)
t +8
8
D)
t +5
8
D
Determine whether the variation between the indicated quantities is direct or inverse.
89)
The number of hours worked by an hourly worker and the amount of her paycheck
89)
A)
Direct
B)
Inverse
A
Solve the problem.
90)
A machine can fill 5472 boxes of cereal in 0.9 hour. How many boxes of cereal can it fill per hour?
90)
A)
5473 boxes/hour
B)
6080 boxes/hour
C)
5472 boxes/hour
D)
4925 boxes/hour
B
D
Divide. Write the answer in lowest terms.
91)
3p – 3
p÷5p – 5
9p2
91)
A)
5
27p
B)
15p2+ 30p + 15
9p3
C)
27p3– 27p2
5p2– 5p
D)
27p
5
Simplify the complex fraction.
92)
8
y
6
y +7
92)
A)
3 y
4(y +7 )
B)
y +7
48 y
C)
48 y(y +7 )
D)
4(y +7 )
3 y
Find the numerical value of the expression for the given value.
93)
4– 9 x
5 x , x = 2
93)
A)
–7
5
B)
11
5
C)
7
5
D)
–89
10
Find the least common denominator (LCD).
94)
3
10xy , 3
4x2
94)
A)
20x2y
B)
20xy3
C)
20x3y
D)
20xy2
Perform the indicated operation and write the answer in lowest terms.
95)
6
15x+2
15x
95)
A)
8
15x
B)
1
C)
8
30x
D)
15x
8
Solve the equation.
96)
1
x –4+4
4x –16 =2
96)
A)
{40}
B)
{–3}
C)
{5}
D)
{1}
Find all values that make the expression undefined.
97)
x2– 81
x2– 10x + 21
97)
A)
9, –9
B)
–3, –7
C)
3, 7
D)
0
Divide. Write the answer in lowest terms.
98)
–4k3
4k6÷(4k)5
20k7
98)
A)
–5
256k
B)
1024k
C)
1024k
5
D)
–5
256k3
Perform the indicated operation and write the answer in lowest terms.
99)
–7x – 8
x+
–5x – 4
6x
99)
A)
–47x + 44
6x
B)
–47x – 52
6x2
C)
–47x – 52
6x
D)
–37x – 52
6x
100)
b
b2– 25
+5
b + 5 –6
b
100)
A)
25(b – 6)
(b + 5)(b – 5)
B)
25(b + 6)
b(b + 5)(b – 5)
C)
6b2– 25b + 150
b(b + 5)(b – 5)
D)
–25(b – 6)
b(b + 5)(b – 5)
Determine whether the variation between the indicated quantities is direct or inverse.
101)
The time it takes to drive 100 miles and the speed at which you drive
101)
A)
Inverse
B)
Direct
Solve the problem.
102)
A church steeple casts a shadow 118 ft long, and at the same time a 8.0–ft post casts a shadow 7.0 ft
long. How high is the steeple? Round to the nearest unit.
102)
A)
8 ft
B)
135 ft
C)
119 ft
D)
103 ft
Find the least common denominator (LCD).
103)
1
20x5y , 1
36x4y3 , 2
45x2y4
103)
A)
60x5y4
B)
36x5y
C)
90x20y12
D)
180x5y4
Simplify the complex fraction.
104)
4
3r – 1 –4
4
3r – 1 +4
104)
A)
3 r
2 –3 r
B)
2 – r
r
C)
2 +3 r
3 r
D)
2 –3 r
3 r
Solve the equation.
105)
y
y2+ 7y +10
+y
y2– 4
=y
y2+ 3y – 10
105)
A)
{1 , 0}
B)
{–4, 0}
C)
{4 , 0}
D)
{–1, 0}
Solve the problem.
106)
The number G of gears a machine can make varies directly as the time T it operates. If it can make
1420 gears in 12 hours, how many gears can it make in 17 hours?
106)
A)
0.1437 gears
B)
1449 gears
C)
118.33 gears
D)
2011.67 gears
107)
A quantity, its 2
3, its 1
2, and its 1
7, added together, become 16. What is the quantity?
107)
A)
672
97
B)
97
42
C)
42
97
D)
1552
42
Find all values that make the expression undefined.
108)
x2– 4
x2+ 19x + 90
108)
A)
2, –2
B)
0
C)
9, –10
D)
–9, –10
Solve for the specified variable.
109)
1
a+1
b= c for b
109)
A)
b=a
ac – 1
B)
b=1
c– a
C)
b=ac –1
a
D)
b=1
ac
Determine whether the variation between the indicated quantities is direct or inverse.
110)
The distance traveled by you in a car and the time taken to drive this distance
110)
A)
Direct
B)
Inverse
The two triangles below are similar. Find the missing length.
111)
10 15
6 9
12
111)
A)
x =25
B)
x =12
C)
x =20
D)
x =19
Write the rational expression as an equivalent expression with the indicated denominator.
112)
9
x2+ 2x
=x(x + 2)(x – 5)
112)
A)
9(x + 5)
x(x + 2)(x – 5)
B)
9
x(x + 2)(x – 5)
C)
9(x + 2)
x(x + 2)(x – 5)
D)
9(x – 5)
x(x + 2)(x – 5)
Solve the equation.
113)
2x
9– 4 = x
113)
A)
–36
7
B)
9
2
C)
–2
9
D)
7
36
A
Perform the indicated operation and write the answer in lowest terms.
114)
6x
x +5+3
x –5
114)
A)
6x2– 27x +15
x2+10x +25
B)
6x2– 27x +15
x2–25
C)
6x +3
(x +5)(x –5)
D)
6x2– 27x +15
x2–10x +25
B
Perform the indicated operation. Write the answer in lowest terms.
115)
15s2+ 8st +t2
2s2– 5st – 3t2·5s2– 16st + 3t2
t2+ 4st – 5s2÷15s2+ 2st –t2
2s2+ 3st +t2
115)
A)
1
B)
t + s
t – s
C)
(t + 3s)2(5s – t)2
(4s + t)2(t2–s2)
D)
(t + 3s)
(t + s)(t – s)
B
D
Write the rational expression in lowest terms.
116)
3x – 3y – bx + by
3x – 3y + bx – by
116)
A)
Already in lowest terms
B)
3– b
3+ b
C)
–1
D)
1
Add or subtract. Write the answer in lowest terms.
117)
2x –6
x2–9
–2x –6
9–x2
117)
A)
4
B)
4
x +3
C)
0
D)
4
x –3
B
Write the rational expression as an equivalent expression with the indicated denominator.
118)
5
2m =8m
118)
A)
2
8m
B)
4
8m
C)
5
8m
D)
20
8m
D
Find the numerical value of the expression for the given value.
119)
4x + 4
3 x2– 9 x – 4 , x = – 4
119)
A)
–1
4
B)
–3
20
C)
1
4
D)
–3
4
B
B
Simplify the complex fraction.
120)
1
k +2
5
k2–4
120)
A)
k +2
5
B)
5
k –2
C)
k –2
D)
k –2
5
Write the expression in lowest terms.
121)
r2–s2
s–r
121)
A)
–r–s
B)
–r+s
C)
r+s
D)
–1
Find the reciprocal.
122)
x2+5xy –y2
x2–6xy +y2
122)
A)
x2–6xy +y2
x2+5xy –y2
B)
1
x2–6xy –y2
C)
x2–5xy +y2
x2+6xy –y2
D)
x2+6xy +y2
x2–5xy –y2
Perform the indicated operation and simplify.
123)
5
2m2– 9mp – 5p2+4
8m2+ 2mp –p2–2
4m2– 21mp + 5p2
123)
A)
28m – 27p
(2m + p)(m – 5p)(4m – p)
B)
20m – 27p
(2m + p)(m – 5p)(4m – p)
C)
20m – 23p
(2m + p)(m – 5p)(4m – p)
D)
28m – 23p
(2m + p)(m – 5p)(4m – p)
Find the least common denominator (LCD).
124)
1
r2+ 10r + 25 , 1
r2+ 5r
124)
A)
r(r + 5)2
B)
(r + 5)2
C)
r(r + 1)(r + 5)
D)
r(r + 5)
Determine whether the variation between the indicated quantities is direct or inverse.
125)
The balance on your credit card and the amount of available credit
125)
A)
Inverse
B)
Direct
Add or subtract. Write the answer in lowest terms.
126)
2
5x –8–6
8–5 x
126)
A)
–8
5x –8
B)
–4
5x –8
C)
8
5x –8
D)
4
5x –8
Solve the equation.
127)
2
t=t
4t – 6
127)
A)
{6, 2}
B)
0, 6
4
C)
D)
{0, 4}
Write the rational expression in lowest terms.
128)
9x +18
12x +24
128)
A)
3
4
B)
1
C)
3
D)
4
3
Solve for the specified variable.
129)
1
a+1
b=1
c for c
129)
A)
c = a + b
B)
c = ab(a + b)
C)
c =ab
a + b
D)
c =a + b
ab
130)
I =E
R + r for r
130)
A)
r =E
I– IR
B)
r =E – IR
I
C)
r =E – R
I
D)
r =IR
E
Perform the indicated operation and write the answer in lowest terms.
131)
2m
m – 4 +
–8
m – 4
131)
A)
0
B)
2
C)
2(m + 4)
m – 4
D)
2
m – 4
Write the rational expression as an equivalent expression with the indicated denominator.
132)
–7m
4m –4=20 –20m
132)
A)
–35m
20 –20m
B)
35m
20 –20m
C)
–5
20 –20m
D)
5m
20 –20m
Provide an appropriate response.
133)
If a fraction with denominator x – 4 must be written as an equivalent fraction with denominator
(x – 4 )3, then the original fraction must be multiplied by (x + 4 )2 in both the numerator and the
denominator.
133)
A)
True
B)
False
Simplify the complex fraction.
134)
8+8
8+8
8+8
134)
A)
104
17
B)
152
15
C)
–152
17
D)
152
17
Solve the problem.
135)
The difference of the reciprocals of two consecutive integers is 1/12. Find the integers.
135)
A)
3 and 4 or –3 and –4
B)
6 and 7 or –6 and –7
C)
2 and 3 or –2 and –3
D)
4 and 5 or –4 and –5
Simplify the complex fraction.
136)
1
15
2
5
136)
A)
2
75
B)
1
6
C)
6
D)
7
30
Solve the problem.
137)
The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical
container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 3 cm on a side.
137)
A)
27 g
B)
15 g
C)
6 g
D)
54 g
Answer Key
Testname: C14
Answer Key
Testname: C14
Answer Key
Testname: C14