Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the function with its graph.
1)
f(x) =1
x + 3
1)
A)
B)
C)
D)
1
2)
f(x) =-1
x + 3
2)
A)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the mistake, then find the correct answer.
3)
line 1 4
x–x
11
line 2 4 – x
x – 11
3)
2
4)
line 1 6
x+7
x + y
line 2 6 + (y)
x + (y) +7
(x + y)
line 3 6 + y + 7
x + y
line 4 13 + y
x + y
4)
5)
line 1 4y
x+11y
6x
line 2 4y + 11y
x + 6x
line 3 15y
7x
5)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve. Round to two decimal places unless otherwise noted.
6)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 300
x + 10 , what do
400 units cost?
6)
A)
$292.68
B)
$12,000.00
C)
$60.00
D)
$299.98
Simplify the complex fraction.
7)
12x + 18
7
16x + 24
4
7)
A)
1
7
B)
3
7
C)
4
7
D)
3
4
Solve.
8)
5z
z + 5 =9z
2z – 3
8)
A)
–60
B)
0, 30
C)
0, 60
D)
-30
3
Add or subtract. Simplify your answer to lowest terms.
9)
4p + 6
15p8q3+8p – 8
3p5q2
9)
A)
4p + 6 + 40p4q – 40p3q
15p8q3
B)
4p + 6 + 8p4q – 8p3q
15q3p8
C)
4p + 6 + 40 – 40p3q
15p8q3
D)
4p + 6 + 40p4q – 40
15p8q3
Solve.
10)
t
t + 8=6–48
t + 8
A)
–1
B)
5
C)
0
D)
No solution
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
11)
2
x2– 3x – 18 , 6
3x – 18
A)
3(x + 3)(x – 6); 6
3(x + 3)(x – 6), 6x + 18
3(x + 3)(x – 6)
B)
3(x – 3)(x + 6); 2x + 6
3(x – 3)(x + 6), 18
3(x – 3)(x + 6)
C)
3(x – 3)(x – 6); 6x + 18
3(x – 3)(x – 6), 6
3(x – 3)(x – 6)
D)
3(x + 3)(x + 6); 18
3(x + 3)(x + 6), 2x + 6
3(x + 3)(x + 6)
12)
x + 4
x2– 2x – 3 , x + 6
x2+ 4x + 3
A)
(x + 1)(x + 3); x2+ 7x + 12
(x + 1)(x + 3), x + 6
(x + 1)(x + 3)
B)
(x + 3)(x – 1)(x + 3); x2+ 7x + 12
(x + 3)(x – 1)(x + 3), x2+ 9x + 18
(x + 3)(x – 1)(x + 3)
C)
(x – 3)(x + 1); x + 4
(x – 3)(x + 1), x2+ 3x – 18
(x – 3)(x + 1))
D)
(x – 3)(x + 1)(x + 3); x2+ 7x + 12
(x – 3)(x + 1)(x + 3), x2+ 3x – 18
(x – 3)(x + 1)(x + 3)
Simplify the complex fraction.
13)
x + 4 + 4
x
x – 3 –10
x
A)
(x + 2)2
x – 5
B)
x + 2
x2– 5x
C)
x + 2
x – 5
D)
x2+ 4x + 4
x2– 3x – 10
4
14)
16
3
2
A)
8
3
B)
3
8
C)
8
D)
32
3
15)
2
8 + 3
6
3 + 2
7
A)
23
19
B)
252
23
C)
21
92
D)
3
92
Solve.
16)
1
x + 7+2
x + 3=-4
x2 + 10x + 21
A)
3
B)
–7
C)
0
D)
No solution
17)
Smallville and Big City are about 1950 miles apart. At 10:00 A.M. an airplane leaves Smallville for
Big City flying at 300 miles per hour. At the same time an airplane leaves Big City for Smallville
flying at 350 miles per hour. How long will it be before the two airplanes meet?
A)
6 hr
B)
8 hr
C)
4 hr
D)
3 hr
18)
1
p+6
p – 6=p
p – 6
A)
–2
B)
3
C)
–3, –2
D)
3, 2
Simplify the complex fraction.
19)
30m2
m – 2
5m8
m – 2
A)
6
m6(m – 2)2
B)
6
m6
C)
6m6
(m – 2)2
D)
6m6
Add or subtract. Simplify your answer to lowest terms.
20)
8
4 – 5x –2
5x – 4 +x – 4
5x2 + 16x – 16
A)
7x + 20
(5x – 4)(x + 4)
B)
-9x – 44
(5x – 4)(x + 4)
C)
-5x – 28
(5x – 4)(x + 4)
D)
None of these
21)
a2
a2 + 10a + 24 –36
a2 + 10a + 24
A)
a + 6
a – 4
B)
a – 6
a – 4
C)
a – 6
a + 4
D)
a + 6
a + 4
5
Solve.
22)
If the temperature is held constant, the pressure that a gas exerts against the walls of a container is
inversely proportional to the volume of the container. A gas is inside a cylinder with a piston at one
end that can vary the volume of the cylinder. When the volume of the cylinder is 240cm3, the
pressure inside is 21 kg/cm2. At what volume will the pressure inside be 36 kg/cm2?
A)
411cm3
B)
140cm3
C)
154cm3
D)
391cm3
Find the product.
23)
–21p7q2
16pq5·12pq5
7p3q7
A)
–3p4
4q5
B)
–9p4
4q7
C)
–3p4q5
4
D)
–9p7
4q5
Solve.
24)
The intensity I of light varies inversely as the square of the distance D from the source. If the
intensity of illumination on a screen 5 ft from a light is 2 foot–candles, find the intensity on a screen
20 ft from the light.
A)
2 foot–candles
B)
1
8 foot–candle
C)
11
8 foot–candles
D)
50
401 foot–candle
Solve and check. Identify any extraneous solutions.
25)
7
u – 3–42
u2 – 9= 1
A)
4, 3
B)
4 (3 is extraneous)
C)
No solution (3 is extraneous)
D)
4 (-3 is extraneous)
Find the indicated value of the given function.
26)
f(x) =x – 8
8x + 2 , f(-4)
A)
– 6
5
B)
3
10
C)
3
8
D)
2
5
Solve.
27)
The distance an object falls when dropped from a tower varies directly as the square of the time it
falls. If the object falls 144 feet in 3 seconds, how far will it fall in 12 seconds?
A)
2592 ft
B)
2304 ft
C)
2016 ft
D)
192 ft
Simplify the complex fraction.
28)
1
a – 12
a2
1 – 21
a + 108
a2
A)
1
a – 12
B)
1
(a – 9)(a – 12)
C)
1
a – 9
D)
a – 12
a – 9
6
Simplify the rational expression.
29)
36a6b4c2
-32a2b4c6
A)
–9a4c4
8
B)
–9a4
8c4
C)
–9a4b
8c4
D)
9a6b
8c4
Add or subtract. Simplify your answer to lowest terms.
30)
z + 12
8z –z – 9
3z
A)
-5z + 108
24z
B)
-5z + 108
24
C)
-5z + 108
8z
D)
-5z + 108
z
31)
13xy
x2 – y2–x – y
x + y
A)
x2+ 11xy + y2
(x + y)(x – y)
B)
–x2+ 11xy – y2
(x + y)(x + y)
C)
x2 + 15xy + y2
(x + y)(x – y)
D)
–x2 + 15xy – y2
(x + y)(x – y)
Find the indicated value of the given function.
32)
f(x) =4x2+ 9
7x , f(–3)
A)
– 3
B)
3
C)
– 3
7
D)
3
7
Solve.
33)
From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and
the other at 5 miles per hour. In how many hours will they be 30 miles apart?
A)
10 hr
B)
2 hr
C)
6 hr
D)
4 hr
Add or subtract. Simplify your answer to lowest terms.
34)
7a – 4b
a – b –4a + 9b
b – a
A)
11a + 5b
a – b
B)
–11a – 5b
a – b
C)
3a + 13b
a – b
D)
11a – 5b
a – b
Find the quotient.
35)
2x3y3
3xy ÷x2y4
6xy3
A)
4xy
B)
4x
y
C)
xy
4
D)
4y
x
Solve for the indicated variable.
36)
I =nE
nr + R, for n
A)
n =IR
Ir – E
B)
n =IR
E – Ir
C)
n = IR – E + Ir
D)
n =I(nr + R)
E
7
Find the product.
37)
2x2 – 11x + 14
2x2 + 3x – 3·3x2 + 13x – 10
2 – x
A)
–(3x –2)
B)
–(3x –2)(x +5)
C)
3x +2
D)
3x – 2
2 – x
Solve.
38)
If 2 sandwich rolls cost $0.56, how much will 12 rolls cost?
A)
$4.36
B)
$3.12
C)
$1.12
D)
$3.36
39)
The Epson Stylus 850 can print Helen’s class project in 12 minutes. The Epson Stylus 500 can print
the project in 42 minutes. If the two printers work together, how long would they take to print out
the project?
A)
84 min
B)
9 min
C)
91
3 min
D)
3
28 min
Find the quotient.
40)
x2+ 14xy + 48y2
x2+ 17xy + 72y2÷x2+ 6xy
x2+ 3xy – 54y2
A)
x – 6y
x
B)
x – 6y
x + 6y
C)
x – 6y
D)
x + 6y
x
Solve and check. Identify any extraneous solutions.
41)
1
x + 4+2
x + 3=-1
x2 + 7x + 12
A)
0, 4
B)
3
C)
No solution (–4 is extraneous)
D)
–4
Rewrite as a complex fraction and simplify.
42)
1 – 49x-2
1 + 7x-1
A)
x – 7
x2
B)
x2 – 49
x2 + 7
C)
x + 7
x
D)
x – 7
x
Find the domain of the rational function.
43)
h(x) =15x
6x2– 24
A)
{x|x -2, 2}
B)
{x|x -2, 0, 2}
C)
{x|x 0}
D)
{x|x -2}
Solve.
44)
8
x – 3 =9–1
x – 3
A)
1
B)
–2
C)
5
D)
4
8
Simplify the complex fraction.
45)
5
x + 1 – 2
x – 1
11
x + 1 + -8
x – 1
A)
3x – 7
3x – 19
B)
3x – 7
19x + 3
C)
3x + 7
3x + 19
D)
7x – 3
3x – 19
Solve.
46)
According to Ohm’s law, the electric current I, in amperes, in a circuit varies directly as the voltage
V. When 18 volts are applied, the current is 2 amperes. What is the current when 12 volts are
applied?
A)
32 amps
B)
108 amps
C)
9 amps
D)
1.33 amps
47)
If the height of a rectangular solid is held constant, the volume varies jointly with the length and
the width. If the volume is 128 cubic inches when the length is 8 inches and the width is 4 inches,
find the volume when the length is 7 inches and the width is 5 inches.
A)
105in.3
B)
140in.3
C)
112in.3
D)
160in.3
Find the indicated value of the given function.
48)
f(x) =7x + 4
2x , f(3)
A)
77
23
B)
19
23
C)
17
6
D)
25
6
Solve.
49)
r – 11
7+5
r=1
7
A)
7
B)
6
C)
7, 5
D)
–7, –5
50)
The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and
the square of the car’s speed, and inversely as the radius of the curve. If a force of 3600 pounds is
needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet,
what force would be required to keep the same car from skidding on a curve of radius 630 feet at
40 mph? Round your answer to the nearest pound of force?
A)
13,582 lb
B)
13,746 lb
C)
14,284 lb
D)
13,714 lb
Simplify the rational expression.
51)
4x2 – 25y2
6x2 – 25xy + 25y2
A)
2x + 5y
2x – 5y
B)
2x – 5y
3x – 5y
C)
2x + 5y
3x – 5y
D)
2x + 5y
3x + 5y
9
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
52)
9x – 5
x2+ 14x + 48 , x – 4
x2– 36
A)
(x + 6)(x + 1)(x + 8); 9x2+ 4x – 5
(x + 6)(x + 1)(x + 8), x2+ 4x – 32
(x + 6)(x + 1)(x + 8)
B)
(x + 6)(x – 6)(x + 8); 9x2– 59x + 30
(x + 6)(x – 6)(x + 8), x2+ 4x – 32
(x + 6)(x – 6)(x + 8)
C)
(x + 6)(x + 8); 9x – 5
(x + 6)(x + 8), x2– 10x + 24
(x + 6)(x + 8)
D)
(x + 6)2(x – 6)(x + 8); 9x3– 59x + 30
(x + 6)2(x – 6)(x + 8), x3+ 4x – 32
(x + 6)2(x – 6)(x + 8)
Add or subtract. Simplify your answer to lowest terms.
53)
15
8x2+7
8x2
A)
11
2x4
B)
4
11x2
C)
11
D)
11
4x2
Simplify the rational expression.
54)
12x2 + 18x
16x2 + 24x
A)
4
3
B)
3
C)
3
4
D)
1
55)
x3 + 1
4x2 – 3x – 7
A)
x2 + x + 1
3x – 7
B)
x2 – x + 1
3x – 7
C)
x2 – x + 1
4x – 7
D)
x2 + x + 1
4x – 7
Add or subtract. Simplify your answer to lowest terms.
56)
12a
9b +9a
9b
A)
7a
3b
B)
3a
7b
C)
7ab
3
D)
7a2
3b2
57)
2x
x + 4+9x – 9
x + 4–9x
x + 4
A)
2x – 9
3x + 12
B)
20x + 9
x – 4
C)
2x – 9
x + 4
D)
20x – 9
x + 4
10
Simplify the complex fraction.
58)
c
a6
b
a2
A)
c
a8b
B)
bc
a4
C)
c
a4b
D)
a4c
b
Solve.
59)
7
8w –4
7w =1
28
A)
81
B)
17
C)
81
2
D)
17
2
60)
The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of
5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 15 inches?
A)
708.9 in.2
B)
47.1 in.2
C)
94.2 in.2
D)
706.5 in.2
61)
The weight of a person on or above the surface of the earth varies inversely as the square of the
distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of
the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 200
miles above the earth‘s surface? Round your answer to the nearest hundredth of a pound.
A)
162.37 lb
B)
162.87 lb
C)
163.27 lb
D)
164.27 lb
Add or subtract. Simplify your answer to lowest terms.
62)
x
x – 5+10
x+ 5–50
x2 – 25
A)
1
B)
x + 20
x + 5
C)
x + 20
x2 – 25
D)
x – 20
x – 5
63)
17x – 2y
2x – 3y +-3x + 6y
3y – 2x
A)
20x – 8y
2x – 3y
B)
20x + 4y
2x – 3y
C)
14x + 4y
2x – 3y
D)
14x – 8y
2x – 3y
Simplify the rational expression.
64)
y2+ 5y + 6
y2+ 9y + 14
A)
5y + 6
9y + 14
B)
y + 3
y + 7
C)
5y + 3
9y + 7
D)
–y2+ 5y + 6
y2+ 9y + 14
11
Find the LCD for the list of fractions. Write the list as equivalent fractions with the LCD as their denominators.
65)
5
y7, y
7y + 28, 3y
y2 – 16
A)
7y7(y + 4)2(y –4); 35y3 – 560y
7y7(y + 4)2(y – 4), y8 – 4y7
7y7(y + 4)2(y – 4), 21y9 – 4y7
7y7(y + 4)2(y – 4)
B)
y7(7y +28)(y +4)(y –4); 5y3 – 560y
y7(7y + 28)(y + 4)(y – 4), y2 + 4y
y7(7y + 28)(y + 4)(y – 4),
21y8
y7(7y + 28)(y + 4)(y – 4)
C)
7y7(y +4)(y –4); 35y2 – 560
7y7(y + 4)(y – 4), y9 – 4y8
7y7(y + 4)(y – 4), 21y8
7y7(y + 4)(y – 4)
D)
7y(y +4)(y –4); 35y – 560
7y(y + 4)(y – 4), y2 – 4y
7y(y + 4)(y – 4), 21y7
7y(y + 4)(y – 4)
Simplify the complex fraction.
66)
3
8 – 4
7
5
9 + 4
11
A)
– 1925
56
B)
–1089
5096
C)
– 1188
91
D)
–11
5096
Perform the indicated operations.
67)
2x2– 7x – 4
10x2+ 19x – 15 ·3x2 + 22x + 7
3x2– 14x – 5 ÷x2+ 3x – 28
2x2– 5x – 25
A)
1
B)
2x – 1
5x – 3
C)
(2x + 1)(x + 7)2
(5x – 3)(x – 5)2
D)
2x + 1
5x – 3
Find the product.
68)
5x + 30
5x – 5·6x – 6
6x + 36
A)
1
B)
1
6
C)
30(x + 6)
30(x – 1)
D)
42x
Find the domain of the rational function.
69)
g(a) =2a + 22
a2 – 9
A)
{a a 3, –3, –11}
B)
{a a is any real number}
C)
{a a 3, –3}
D)
{a a 3}
12
Solve.
70)
An object is 30 feet from a lens with a focal length of 5 feet. What will be the image’s distance from
the lens? Round the answer to the nearest tenth if necessary. Use the following formula which
describes how the image of an object is affected by a lens where o represents the object’s distance
from the lens, i represents the image’s distance from the lens, and f represents the focal length of the
lens. 1
o+1
i=1
f
A)
25 ft
B)
4.3 ft
C)
6 ft
D)
35 ft
Add or subtract. Simplify your answer to lowest terms.
71)
18
x2 + 3x +8
x+6
x + 3
A)
48
x
B)
6
x
C)
8
x
D)
14
x
Simplify the complex fraction.
72)
2 + 3
7
5 – 5
10
A)
22
63
B)
17
45
C)
34
63
D)
–34
63
Solve.
73)
1
x – 5+6
x=-30
x2 – 5x
A)
0
B)
0, 5
C)
–5
D)
No solution
Find the product.
74)
2xy2
7y4·56y3
x3
A)
16x2y
B)
16y
x2
C)
16y2
x
D)
x2y
16
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
75)
1
15a3b4, 11
20a2b5
A)
60a2b4; 4a
60a2b4, 44b
60a2b4
B)
300a3b5; 20b
300a3b5, 220a
300a3b5
C)
60a3b5; 4b
60a3b5, 33a
60a3b5
D)
300a5b9; 20a2b5
300a5b9, 220a3b4
300a5b9
13
Rewrite as a complex fraction and simplify.
76)
x–9 + y–9
x-1 + y-1
A)
y9 + x9
x8 + y8
B)
1
x + y
C)
1
x8 + y8
D)
y9 + x9
x8y9 + x9y8
Solve.
77)
40
x – 2 – 1 =42
x + 2
A)
–42, 14
B)
12, –14
C)
–12, 14
D)
No solution
Solve the direct variation.
78)
Suppose x varies directly as y. If x =8 when y =48, what is the value of y when x = 4 ?
A)
16
B)
36
C)
64
D)
24
Find the quotient.
79)
y2– 25
2y + 10 ÷y – 5
y – 1
A)
1
2
B)
(y – 1)(y – 5)
2(y – 5)
C)
y – 1
D)
y – 1
2
Solve.
80)
2
t=t
5t – 12
A)
0, 36
B)
0
C)
0, 24
9
D)
4, 6
81)
The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical
container 3 cm on a side is 54 g, find the weight of the liquid in a cubical container 5 cm on a side.
A)
10 g
B)
125 g
C)
110 g
D)
250 g
Solve for the indicated variable.
82)
A =h(B + b)
2 for b
A)
b=2A – Bh
h
B)
b= 2A –Bh
C)
b=2A + Bh
h
D)
b=A – Bh
h
Solve.
83)
The current I in an electrical conductor varies inversely as the resistance R of the conductor. The
current is 5 amperes when the resistance is 342 ohms. What is the current when the resistance is 864
ohms?
A)
2 amps
B)
0.51 amps
C)
12.6 amps
D)
0.08 amps
Simplify the rational expression.
84)
5x – m
m – 5x
A)
5
B)
1
C)
–1
D)
x–m
14
Simplify the complex fraction.
85)
18
7
3
A)
7
6
B)
54
7
C)
6
7
D)
6
Add or subtract. Simplify your answer to lowest terms.
86)
2
y2 – 2y + 1 +6
y3 – y
A)
2y2 + 8y – 6
y(y – 1)2(y + 1)
B)
2y2 + 2y + 6
y(y – 1)(y + 1)
C)
2y2 + 8y + 6
y(y + 1)2(y – 1)
D)
2y2 + 10y – 6
y(y – 1)2(y + 1)
87)
a + b
a – b –3ab + 3b2
a2 – b2
A)
a + 2b
a – b
B)
a2 – 2ab – 2b2
a2 – b2
C)
a – 2b
a + b
D)
a – 2b
a – b
88)
y + 1
y2 – 1 –y
y – 4 +y2 – 1
y2 – 3y – 4
A)
y
(y – 1)(y – 4)
B)
–3
(y – 1)(y – 4)
C)
–3
(y + 1)(y – 4)
D)
y – 3
(y – 1)(y + 1)
Simplify the rational expression.
89)
–12x – 18
16x + 24
A)
–3
4
B)
3
4
C)
–3
D)
–4
3
Add or subtract. Simplify your answer to lowest terms.
90)
7
x + 1 –x
x – 8 +x2+ 56
x2– 7x – 8
A)
8x
(x + 1)(x – 8)
B)
6x
(x + 1)(x – 8)
C)
6x
(x – 1)(x + 8)
D)
2x2+ 8x – 112
(x – 1)(x + 8)
Solve.
91)
The volume V of a given mass of gas varies directly as the temperature T and inversely as the
pressure P. If V =290.0 in.3 when T =290° and P =10 lb/in.2, what is the volume when T =190°
and P =10 lb/in.2?
A)
220.0 in.3
B)
190.0 in.3
C)
180.0 in.3
D)
160.0 in.3
15
Without solving the equation, find the value(s) of the variable that could result in an extraneous solution.
92)
7
x + 9=1
A)
–9
B)
–9, 7
C)
9
D)
None
Solve.
93)
x
x – 5–5=5
x – 5
A)
– 5
4
B)
5
C)
–5
D)
No solution
Find the product.
94)
k2+ 8k + 12
k2+ 11k + 30 ·k2+ 5k
k2– 2k – 8
A)
k
k – 4
B)
k2+ 5k
k – 4
C)
k
k2+ 11k + 30
D)
1
k – 4
95)
2t2– 13t – 24
3t2– 3t – 6·3t2+ 12t – 36
t2– 2t – 48
A)
(2t + 3)(t + 8)
(t + 6)(3t – 6)
B)
(2t + 3)
(t – 1)
C)
(2t + 3)
(t + 1)
D)
(2t + 3)(t + 6)
(t + 1)(t – 6)
Find the domain of the rational function.
96)
g(c) =2c + 18
9c2+ 2c – 7
A)
c c – 7
9, 1
B)
c c 7
9, -1
C)
c c -9,-1, 7
9
D)
c c 9
7, -1
Add or subtract. Simplify your answer to lowest terms.
97)
r2
r + 9–81
r + 9
A)
r –81
B)
r +9
C)
r –9
D)
r – 9
r + 9
Simplify the complex fraction.
98)
6 – 7
n + 9
n + 9
A)
6n + 47
(n + 9)2
B)
6n + 47
n + 9
C)
6n + 61
(n + 9)2
D)
9n + 47
(n + 9)2
16
Rewrite as a complex fraction and simplify.
99)
x-2y-2
8x-1 + 3y-1
A)
1
8xy2 + 3x2y
B)
xy
8y + 3x
C)
x2y2
8y + 3x
D)
1
8x2y + 3xy2
Solve.
100)
The gravitational attraction A between two masses varies inversely as the square of the distance
between them. If the force of attraction is 2.25 lb when the masses are 4 ft apart, what is the
attraction when the masses are 6 ft apart?
100)
A)
2 lb
B)
1 lb
C)
3 lb
D)
4 lb
Simplify the rational expression.
101)
z2 – 16 – 3z – 12
2z + 8
101)
A)
z + 7
2
B)
z – 12
2
C)
z + 12
2
D)
z – 7
2
Solve.
102)
If x represents a number, write and simplify an expression for the sum of 16 times the number and
11 times its reciprocal.
102)
A)
16x + 11
x
B)
16x2 + x
11
C)
16 + 11x
x
D)
16x2 + 11
x
Simplify the rational expression.
103)
x2– 2x
x2+ 5x – 14
103)
A)
x
x + 7
B)
x2
x + 7
C)
x
x – 2
D)
x
x – 7
Find the domain of the rational function.
104)
f(x) =7
x + 2
104)
A)
{x|x is any real number}
B)
{x|x -2}
C)
{x|x -2, 2}
D)
{x|x -7}
Without solving the equation, find the value(s) of the variable that could result in an extraneous solution.
105)
2
x – 4–1
x + 6=2
7
105)
A)
–6, 0, 4
B)
–6, 1
2, 4
C)
–4, 6
D)
–6, 4
17
Simplify the complex fraction.
106)
a
a + 5 –4
a – 6
a
a + 5 –1
a – 6
106)
A)
a2+ 2a – 20
a2+ 5a – 5
B)
a2– 10a – 20
a2– 7a – 5
C)
a2– 10a + 20
a2– 7a + 5
D)
a2+ 10a + 20
a2+ 7a + 5
Add or subtract. Simplify your answer to lowest terms.
107)
6
r+7
r – 5
107)
A)
30r – 13
r(r – 5)
B)
13r – 30
r(5 – r)
C)
30r – 13
r(5 – r)
D)
13r – 30
r(r – 5)
Solve. Round to two decimal places unless otherwise noted.
108)
Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by
y = 62,500
x + 125. What is the cost per ton for x = 40?
108)
A)
$1437.50
B)
$1562.50
C)
$12.50
D)
$378.79
Solve the inverse variation.
109)
If n varies inversely as m and n is 6 when m is 11, what is m when n is 13.2?
109)
A)
0.37
B)
8.8
C)
2.73
D)
5
Solve for the indicated variable.
110)
S =H
mt1 – mt2, for m
110)
A)
m =H
St1 – t2
B)
m =SH
t1 – t2
C)
m =H
S(t1 – t2)
D)
m =H + St2
St1
Solve.
111)
The shadow cast by an object on a sunny day varies directly as the height of the object. If a person
82 inches tall casts a shadow 63 inches long, how tall is a tree which casts a shadow 32 feet in
length?
111)
A)
72.5 ft
B)
161.44 ft
C)
24.59 ft
D)
41.65 ft
Add or subtract. Simplify your answer to lowest terms.
112)
p3
p2 + 2p + 4–8
p2 + 2p + 4
112)
A)
p – 2
p2 + 2p + 4
B)
1
p – 2
C)
p +2
D)
p –2
18
Solve.
113)
The resistance of a wire varies directly as the length of the wire and inversely as the square of the
diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms.
What would the resistance be for a 43 foot length, with diameter 0.01 inch, of the same kind of wire
?
113)
A)
657 ohms
B)
638 ohms
C)
645 ohms
D)
642.5 ohms
Find the quotient.
114)
x2– 49
x2– 4x + 4 ÷8x + 56
x2– 3x + 2
114)
A)
x – 2
(x – 7)(x – 1)
B)
(x – 7)(x – 1)
x – 2
C)
(x + 7)(x + 1)
8(x + 2)
D)
(x – 7)(x – 1)
8(x – 2)
Simplify the complex fraction.
115)
s
y
a
115)
A)
sy
a
B)
s
ya
C)
sya
D)
sa
y
Solve.
116)
1
x – 1+4
4x – 4=2
116)
A)
1
B)
0
C)
2
D)
16
117)
The total current flowing through a particular circuit is given by
V
1
R + 1
R – 10
where V represents voltage and R represents resistance. Simplify this expression.
117)
A)
VR(R – 10)
2(R – 5)
B)
V
R(R – 10)
C)
V(R – 10)
2(R – 5)
D)
VR(R –10)
Find the product.
118)
2k2 + 17k + 21
9k2 – 18k + 8· 9k2 – 16
6k2 + 17k + 12
118)
A)
k + 7
3k – 2
B)
k + 8
2k – 3
C)
k + 1
3k + 2
D)
–1
Simplify the complex fraction.
119)
1 – 9
x
1 + 9
x
119)
A)
–1
B)
x – 9
x + 9
C)
9 – x
9 + x
D)
–4
5
19
Solve.
120)
y + 1
y + 6 –y
y2 – 36 =y – 3
y – 6
120)
A)
3
4
B)
1
C)
4
5
D)
4
3
Find the product.
121)
6u5v2
2v2+ 6v + 4 ·2v + 4
3u3v
121)
A)
2u2v(v + 1)
B)
2u2v
v + 1
C)
2uv
v – 1
D)
2u2v
2v – 1
Add or subtract. Simplify your answer to lowest terms.
122)
x
x2 – 16 –7
x2 + 5x + 4
122)
A)
x2– 6x + 28
(x – 4)(x + 4)
B)
x2– 6x + 28
(x – 4)(x + 4)(x + 1)
C)
x2– 6
(x – 4)(x + 4)(x + 1)
D)
x2+ 6x + 28
(x – 4)(x + 4)(x + 1)
Solve. Round to two decimal places unless otherwise noted.
123)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 600
x + 20 , what is the
unit cost for 10 units?
123)
A)
$40.00
B)
$20.00
C)
$60.00
D)
$3.00
Add or subtract. Simplify your answer to lowest terms.
124)
7x
x + 1 +8
x – 1 –14
x2 – 1
124)
A)
7x
x – 1
B)
7x – 6
x + 1
C)
7x – 6
x – 1
D)
x + 1
x – 1
Solve the direct variation.
125)
If s varies directly as the square of t and s =75 when t =5, what is the value of s when t =8 ?
125)
A)
40
B)
192
C)
120
D)
15
Simplify the rational expression.
126)
20a3 + 10a2 – 4a – 2
20a2+ 6a – 2
126)
A)
4a2 – 1
5a + 1
B)
5a2 – 1
5a + 1
C)
5a2 – 1
5a – 1
D)
5a2 – 1
4a + 2
20
127)
x3 + 27
3x2 – 27
127)
A)
x2 – 3x + 9
3(x – 3)
B)
x2 – 3x + 9
3(x + 3)
C)
x2 + 3x + 9
3(x – 3)
D)
x2 – 3x + 9
x – 3
Solve.
128)
The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 212
vibrations per second and a wavelength of 19.3 ft. Find the wavelength of another tone that has a
pitch of 219 vibrations per second.
128)
A)
0.000416 ft
B)
18.7 ft
C)
2405.6 ft
D)
0.05 ft
129)
y
y2– 11y + 28 +y
y2– 16 =y
y2– 3y – 28
129)
A)
8, 0
B)
–1, 0
C)
-8 , 0
D)
1, 0
Find the product.
130)
3a – 3b – ab + b2
25a2 – 10ab + b2·25a2 – b2
5a2– 4ab – b2
130)
A)
3– b
B)
3 – b
5a – b
C)
5a – b
3 – a – b
D)
3 + b
5a – b
Add or subtract. Simplify your answer to lowest terms.
131)
5c
d2+15c
d2
131)
A)
40c
d2
B)
20c2
d2
C)
20c
d4
D)
20c
d2
Solve.
132)
At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the
square of its diameter d. If the resistance is 0.48 ohm when the diameter is 1 mm and the length is
240 cm, what is the resistance when the diameter is 4 mm and the length is 2080 cm?
132)
A)
130 ohms
B)
62.4 ohms
C)
0.26 ohms
D)
1.04 ohms
Find the product.
133)
a3 + b3
a2 – b2·a2 – 2ab + b2
2a2 + 8ab – 10b2
133)
A)
a2 + ab + b2
2(a + 5b)
B)
a – b
2(a + 5b)
C)
a2 – ab + b2
2(a + 5b)
D)
a2 – ab + b2
2(a – b)
Add or subtract. Simplify your answer to lowest terms.
134)
9
2 – y –6
y – 2
134)
A)
-3
2 – y
B)
54
2 – y
C)
3
2 – y
D)
15
2 – y
21
Find the LCD for the list of fractions. Write the list as equivalent fractions with the LCD as their denominators.
135)
9
k2+ 2k– 8 , –5
k2– 8k+ 12 , 7
k2– 11k+ 18
135)
A)
(k+ 4)(k – 2)(k – 6);
9k – 54
(k+ 4)(k – 2)(k – 6), –5k – 20
(k+ 4)(k – 2)(k – 6), -14k – 168
(k+ 4)(k – 2)(k – 6)
B)
(k+ 4)(k – 2)(k – 6)(k – 9);
9k2– 135k + 486
(k+ 4)(k – 2)(k – 6)(k – 9), –5k2+ 25k + 180
(k+ 4)(k – 2)(k – 6)(k – 9), 7k2– 14k – 168
(k+ 4)(k – 2)(k – 6)(k – 9)
C)
(k+ 4)(k – 6)(k – 9);
9k2– 45k + 486
(k+ 4)(k – 6)(k – 9), –5k2+ 75k + 180
(k+ 4)(k – 6)(k – 9), 9k2+ 21k – 378
(k+ 4)(k – 6)(k – 9)
D)
(k+ 4)(k – 2)3(k – 6)(k – 9);
9k5– 135k3+ 486
(k+ 4)(k– 2)3(k – 6)(k – 9), –5k4+ 25k2+ 180k
(k+ 4)(k – 2)3(k– 6)(k – 9), 7k3– 14k – 168
(k+ 4)(k – 2)3(k – 6)(k – 9)
Find the quotient.
136)
z2+ 4z + 4
z2+ 7z + 10 ÷z2+ 2z
z2+ 10z + 25
136)
A)
z + 5
z
B)
z
z2+ 7z + 10
C)
z + 5
D)
z + 5
z2+ 5z
Find the indicated value of the given function.
137)
h(x) =x2+ 3x – 28
x2 – x + 11 , h(4)
137)
A)
–1
33
B)
0
C)
1
32
D)
Undefined
Rewrite as a complex fraction and simplify.
138)
a-2 – b-1
6a-1 + 3b-2
138)
A)
b2 – a2b
6b2 + 3a2
B)
b2 – a2
6ab2 + 3a2
C)
ab2 – a2
6b2 + 3a2b
D)
b2 – a2b
6ab2 + 3a2
Solve.
139)
If y varies directly with x and inversely as z and y =12 when x =6 and z =4, find y when x =7 and
z =14.
139)
A)
5
B)
2
C)
4
D)
8
Perform the indicated operations.
140)
r2 – s2
(r – s)2÷r2 – 2rs + s2
r2 – rs + s2·(r – s)4
r3 + s3
140)
A)
1
r2 – rs + s2
B)
r + s
C)
1
r3 + s3
D)
r – s
22
Find the domain of the rational function.
141)
h(x) =18
x2– 4x – 32
141)
A)
{x|x -8, 4}
B)
{x|x 0}
C)
{x|x 0, -4}
D)
{x|x -4, 8}
Simplify the complex fraction.
142)
–5
x + 5 + -3
x – 3
-3
x – 3 – –5
x – 4
142)
A)
-8x2+ 32x
2x2+ 7x – 15
B)
-(x – 4)
x + 5
C)
-8x2– 2x + 120
-8x2+ 43x – 15
D)
-8x2+ 32x
-8x2– 47x – 15
Add or subtract. Simplify your answer to lowest terms.
143)
6w
y+7w
5y
143)
A)
6wy + 7w
5y
B)
37w
5y
C)
37w
5y2
D)
13w
5y
144)
125x3
25x2 + 15xy + 9y2–27y3
25x2 + 15xy + 9y2
144)
A)
5x –3y
B)
3y –5x
C)
5x2 – 3y2
5x + 3y
D)
x – y
25x2 + 15xy + 9y2
Simplify the rational expression.
145)
y2+ 6y – 27
y2+ 4y – 45
145)
A)
6y – 3
4y – 5
B)
6y – 27
4y – 45
C)
y – 3
y – 5
D)
–y2+ 6y – 27
y2+ 4y – 45
Add or subtract. Simplify your answer to lowest terms.
146)
u2– 12u
u2– 24u + 144 +5
2u – 24
146)
A)
2u + 5
2(u – 12)
B)
2u + 5
u – 12
C)
u + 5
2(u – 12)
D)
u2– 12u + 5
2(u – 12)2
Find the product.
147)
4r – 12
12r2 + 24r·6r + 12
24 – 8r
147)
A)
–4
4(3 – r)
B)
–1
4r
C)
1
4
D)
r – 3
4r(3 – r)
23
Solve.
148)
Given the area A, and length l, of a rectangle, the width can be found using the formula w =A
l .
Suppose the area of a rectangle is 12x + 18
7 square inches and the length is 16x + 24
4 inches . Find
the width.
148)
A)
3
7 in.
B)
4
7 in.
C)
1
7 in.
D)
3
4 in.
Simplify the rational expression.
149)
-12x7y5z8
27x2y10z8
149)
A)
–4x5z
9y5
B)
–4x2
9y5
C)
–4x5
9y5
D)
–9y5
4x5
Solve.
150)
The portion of a house that Mike paints after t hours is represented by t
3, the portion that Dave
paints is represented by t
6, and the portion that Doug paints is represented by 2t
24. Find the portion
of the house painted by all three together after t hours.
150)
A)
252t
432
B)
7t
12
C)
t
6
D)
11t
24
151)
4x – 6
2x + 1 =2x -1
x + 4
151)
A)
27
10
B)
–5
2
C)
23
10
D)
No solution
Simplify the complex fraction.
152)
4
y2 + 8
xy + 4
x2
2
y2 + – 2
xy – 4
x2
152)
A)
2x + 2y
2x – 2y
B)
2x + 2y
x – 2y
C)
2x + 2y
x + 2y
D)
2xy + 2y
xy – 2y
Solve.
153)
Martha can rake the leaves in her yard in 3 hours. Her younger brother can do the job in 4 hours.
How long will it take them to do the job if they work together?
153)
A)
4 hr
B)
7
12 hr
C)
12
7 hr
D)
12 hr
24
Simplify the complex fraction.
154)
q + 2
q – 7
8 – 2
q – 7
154)
A)
q + 2
8q – 2
B)
q + 2
8q – 58
C)
q2 – 7q + 2
8q – 58
D)
q2 – 7q + 2
8q – 54
Solve.
155)
A plane flies 410 miles with the wind and 350 miles against the wind in the same length of time. If
the speed of the wind is 30 mph, what is the speed of the plane in still air?
155)
A)
385 mph
B)
380 mph
C)
405 mph
D)
370 mph
Simplify the complex fraction.
156)
12 + 25
w + 12
w2
4 + – 13
w – 12
w2
156)
A)
3w + 4
w + 4
B)
3w – 4
w + 4
C)
4w + 3
w – 4
D)
3w + 4
w – 4
Solve for the indicated variable.
157)
P =A
1 + rt, for t
157)
A)
t=A – P
Pr
B)
t=P – A
1 + r
C)
t=P – 1
Ar
D)
t= P – Ar
Solve.
158)
The width of Ashley’s house is 4
x + 2. An extension adds an extra x
x – 3 to the width. What is the
width of Ashley’s house after the extension?
158)
A)
x2 + 8x – 12
(x + 2)(x – 3)
B)
x2 + 8x – 7
(x + 2)(x – 3)
C)
x2 + 6x – 7
(x + 2)(x – 3)
D)
x2 + 6x – 12
(x + 2)(x – 3)
159)
Given the area and length of a rectangle, the width can be found using the formula w = A
l. Suppose
the area of a rectangle is described by 4n + 1
8 square feet and the length is described by n – 4
10 feet.
Find an expression for the width.
159)
A)
5(n – 4)
4(4n + 1)
B)
4(n – 4)
5(4n + 1)
C)
5(4n + 1)
4(n – 4)
D)
4(4n + 1)
5(n – 4)
160)
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a
5 foot length with diameter 2 inches costs $48.00 , how much will a 18 foot length with diameter
5 inches cost?
160)
A)
$432.00
B)
$429.60
C)
$437.57
D)
$437.30
25
Add or subtract. Simplify your answer to lowest terms.
161)
7x
x2 – 25 –x
x – 5
161)
A)
x2 + 12x
x2 – 25
B)
–x2 + 12x
x2 – 25
C)
x2 + 2x
x2 – 25
D)
–x2 + 2x
x2 – 25
Solve.
162)
If f(x) =x + 1
3x – 6 and g(x) =2
3x, find (f + g)(-2).
162)
A)
1
12
B)
– 1
12
C)
1
2
D)
– 1
4
Perform the indicated operations.
163)
x2+ 8x + 16
x – 3 ·x2– 5x + 6
x + 4 ÷x – 2
6x – 12
163)
A)
6(x – 2)
B)
6(x + 4)
x – 2
C)
6(x + 4)(x – 2)
x – 2
D)
6(x + 4)(x – 2)
Simplify the rational expression.
164)
ab + 6a – 5b – 30
bc – 4b + 6c – 24
164)
A)
b – 6
c + 4
B)
a + 5
c – 4
C)
a – 5
c + 4
D)
a – 5
c – 4
Find the indicated value of the given function.
165)
f(x) =3x + 8
6x2+ 4x – 9 , f(–4)
165)
A)
– 4
71
B)
– 20
71
C)
– 4
121
D)
20
71
Solve for the indicated variable.
166)
L =dR
D – d, for d
166)
A)
d = LD – R – L
B)
d =L(D – d)
R
C)
d =LD
R – L
D)
d =LD
R + L
Find the quotient.
167)
x2 – 4
x÷2x + 4
x – 2
167)
A)
2x
(x – 2)2
B)
(x – 2)2
x
C)
(x – 2)2
2x
D)
2(x + 2)2
x
26
Solve.
168)
7
y + 5 –4
y – 5 =11
y2– 25
168)
A)
42
B)
–22
C)
22
D)
No solution
169)
5
5x +1
2x = – 1
10
169)
A)
–16
B)
–15
C)
15
D)
No solution
170)
The speed of a stream is 4 mph. If a boat travels 40 miles downstream in the same time that it takes
to travel 20 miles upstream, what is the speed of the boat in still water?
170)
A)
14 mph
B)
15 mph
C)
12 mph
D)
8 mph
Add or subtract. Simplify your answer to lowest terms.
171)
7
s2 + 6s + 9+2s
s + 3
171)
A)
2s2 + 6s + 7
(s + 3)2
B)
2s2 – 6s + 7
(s + 3)(s – 3)
C)
2s + 7
(s + 3)(s – 3)
D)
2s + 7
(s + 3)2
Find the domain of the rational function.
172)
h(t) =t – 15
t3 + 125
172)
A)
{t t is any real number}
B)
{t t –5}
C)
{t t –5, 5}
D)
{t t –5, 15}
Solve.
173)
5 – x
x–7
x= – 3
4
173)
A)
–8
B)
8
C)
–4
D)
No solution
Rewrite as a complex fraction and simplify.
174)
16a-1 – ab-2
b-1 – 4a-1
174)
A)
(4b + a)(4b – a)
b2(a – 4)
B)
–4b + a
b
C)
4b – a
b
D)
16b2 – a
b(a – 4b)
Add or subtract. Simplify your answer to lowest terms.
175)
3x + 5
x2– 9x + 8 –x + 8
x2– 64
175)
A)
4x2+ 36x + 32
(x – 8)(x + 8)(x – 1)
B)
4x + 13
(x – 8)(x – 1)
C)
2x – 3
(x – 8)(x + 8)
D)
2x2+ 22x + 48
(x – 8)(x + 8)(x – 1)
27
Rewrite as a complex fraction and simplify.
176)
m-1 + z-1
m-1 – z-1
176)
A)
z – m
z
B)
z + m
m
C)
z + m
z
D)
z + m
z – m
Solve.
177)
Tom Quig traveled 210 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one
period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 6
hours, how many miles did he drive at the reduced speed?
177)
A)
25 mi
B)
50 mi
C)
40 mi
D)
30 mi
178)
The intensity of a radio signal from the radio station varies inversely as the square of the distance
from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the
intensity be at a distance of 12 miles? Round your answer to the nearest unit.
178)
A)
248 units
B)
222 units
C)
205 units
D)
186 units
Add or subtract. Simplify your answer to lowest terms.
179)
1
8x – 7+4
7 – 8x
179)
A)
-3
8x – 7
B)
5
8x – 7
C)
-5
8x – 7
D)
3
8x – 7
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
180)
1
r2 + 18r + 81, 1
r2 + 9r
180)
A)
(r + 9)2; 1
(r + 9)2, r + 9
(r + 9)2
B)
r(r + 1)(r +9); 1
r(r + 1)(r + 9), r + 1
r(r + 1)(r + 9)
C)
r(r +9); 1
r(r + 9), r
r(r + 9)
D)
r(r + 9)2; r
r(r + 9)2, r + 9
r(r + 9)2
Solve.
181)
If y varies jointly with x and z and inversely with n and y =49 when x =2, z = 7, and n = 4, find y
when x = 6, z =5, and n =10.
181)
A)
84
B)
35
C)
42
D)
21
Rewrite as a complex fraction and simplify.
182)
y-1
6y-1 – 1
182)
A)
1
6 – y
B)
y
6 – y
C)
1
6y – 1
D)
y
6y – 1
28
Solve.
183)
The portion of a house that Sara paints after t hours is represented by 1
7t, and the portion that
Debbie paints is represented by 1
14t. Find the portion of the house painted by Sara and Debbie
together after t hours.
183)
A)
2
21 t
B)
3
14 t
C)
3
14
D)
1
7t
184)
Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 360 miles in the same
time that Dana travels 342 miles. If Chuck’s rate of travel is 3 mph more than Dana’s, and they
travel the same length of time, at what speed does Chuck travel?
184)
A)
60 mph
B)
56 mph
C)
57 mph
D)
64 mph
Simplify the rational expression.
185)
z3 + 64
z3 – 4z2 + 16z
185)
A)
z – 4
z
B)
z – 4
4
C)
z + 4
z
D)
z + 16
z
Solve.
186)
The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A
tire that has traveled 39,000 mi has 13
32 in. of tread left. How much tread will be left on a tire that
has traveled 83,000 mi?
186)
A)
96,000 in.
B)
507
2656 in.
C)
1
96000 in.
D)
2656
507 in.
Find the LCD for the list of fractions. Write the list as equivalent fractions with the LCD as their denominators.
187)
6
r2+ 9r, -4
7r + 63, -2
r2+ 18r+ 81
187)
A)
7r(r + 9)2; 42r + 378
7r(r + 9)2, -4r2– 36r
7r(r + 9)2, -14r
7r(r + 9)2
B)
r(r + 9)2; r+ 9
r(r + 9)2, -4r – 36
r(r + 9)2, -2r
r(r + 9)2
C)
7(r + 9)2; 7r + 63
7(r + 9)2, -4r – 36
7(r + 9)2, -14
7(r + 9)2
D)
7(r +9); 7
7(r + 9), -4
7(r + 9), -14
7(r + 9)
Add or subtract. Simplify your answer to lowest terms.
188)
y – 2
y + 5 –y + 6
y – 5 +y + 9
y2– 25
188)
A)
2y2+ 3y + 31
(y + 5)(y + 5)
B)
2y2+ 5y + 49
(y + 5)(y + 5)
C)
-17y – 11
(y + 5)(y – 5)
D)
2y2+ 5y + 49
(y + 5)(y – 5)
29
Simplify the complex fraction.
189)
1 – 36
w2
1 + 10
w + 24
w2
189)
A)
w – 6
w + 4
B)
1
(w – 6)(w + 4)
C)
w – 6
w – 4
D)
w + 6
w + 4
Solve.
190)
4–1
4t – 19 =67
4t – 19
190)
A)
10
B)
9
C)
11
D)
8
Graph.
191)
f(x) =1
x – 3
191)
A)
B)
30
C)
D)
Find the domain of the rational function.
192)
f(x) =x + 1
3x + 5
192)
A)
x|x 5
3
B)
{x|x is any real number}
C)
x|x – 5
3
D)
x|x – 5
3, -1
Find the product.
193)
36x2– 25y2
216x3+ 125y3·36x2– 30xy + 25y2
36x2– 60xy + 25y2
193)
A)
36x2– 30xy + 25y2
(6x – 5y)(6x – 5y)(6x – 5y)
B)
1
6x – 5y
C)
1
36x2– 30xy + 25y2
D)
1
Solve.
194)
10
x – 2 = 1 +12
x + 2
194)
A)
–12, 8
B)
–6, 8
C)
6, –8
D)
No solution
195)
Jim and Steve’s motorboats both travel at the same speed. Jim pilots his boat 75 miles before
docking. Steve continues for another 4 hours, traveling a total of 175 miles before docking. How
long did it take Jim to navigate the 75 miles?
195)
A)
5 hr
B)
25 hr
C)
7 hr
D)
3 hr
Add or subtract. Simplify your answer to lowest terms.
196)
7
5x – 1–5
1 – 5x
196)
A)
2
5x – 1
B)
-12
5x – 1
C)
-2
5x – 1
D)
12
5x – 1
31
Find the quotient.
197)
4xy2
3y4÷x3
18y3
197)
A)
24y
x2
B)
24x2y
C)
24y2
x
D)
x2y
24
Solve.
198)
1
x2– 3x + 2 +2
x2+ 2x – 3 = 3
x2+ 8x + 15
198)
A)
– 1
23
B)
11
23
C)
9
23
D)
No solution
Add or subtract. Simplify your answer to lowest terms.
199)
m
m2 – 16 –4
m2 – 16
199)
A)
1
m + 4
B)
1
m + 16
C)
m – 4
m + 4
D)
1
m – 4
Find the product.
200)
–36a6b4c3
40ab3c2·44abc2
27a2b4c9
200)
A)
–20a4c6
15b2
B)
–22a4
15bc6
C)
–20a6
15bc6
D)
–22a4
15b2c6
Solve the joint variation.
201)
If f varies jointly as h and the square of q, and f =96 when q =4 and h =3, find q when f =40 and h
=5.
201)
A)
3
B)
2
C)
4
D)
5
Solve.
202)
If f(x) =x2 – 2x + 7
x – 3 and g(x) =6x – 8
x – 3, find (f – g)(2).
202)
A)
7
B)
35
C)
-3
D)
– 35
203)
With both the cold water and hot water faucets open, it takes 6 minutes to fill a sink. The cold water
faucet alone takes 8 minutes to fill the sink. How long would it take to fill the sink using the hot
water faucet alone?
203)
A)
25 min
B)
191
4 min
C)
241
2 min
D)
24 min
32
Perform the indicated operations.
204)
16s2+ 8st + t2
3s2– 14st – 5t2·2s2– 11st + 5t2
t2+ 3st – 4s2÷8s2– 2st – t2
3s2+ 4st + t2
204)
A)
(t + 4s)
(t + s)(t – s)
B)
(t + 4x)2(2x – t)2
(4s + t)2(t2 – s2)
C)
1
D)
t + s
t – s
Simplify the rational expression.
205)
12x + 21
16x + 28
205)
A)
3
4
B)
4
3
C)
1
D)
3
Find the product.
206)
3p – 3
pq8·3p2q5
7p – 7
206)
A)
9pq3
7
B)
9p(p – 1)
7q3
C)
9p2
7q3
D)
9p
7q3
Find the quotient.
207)
–21p9q4
16pq4÷7p2q8
12pq4
207)
A)
–9p9
4q4
B)
–3p7
4q4
C)
–9p7
4q4
D)
–3p7q4
4
208)
12x + 18
x6÷16x3 + 24x2
x3
208)
A)
3
4x5
B)
4
3x5
C)
3
4x3
D)
4
3x3
Solve. Round to two decimal places unless otherwise noted.
209)
Suppose a cost–benefit model is given by y =8.8x
100 – x, where y is the cost in thousands of dollars for
removing x percent of a given pollutant. Find the cost of removing 25% to the nearest dollar.
209)
A)
$2200
B)
$2933
C)
$333
D)
$8800
Add or subtract. Simplify your answer to lowest terms.
210)
3
8x2+3
8x2
210)
A)
3
4x2
B)
4
3x2
C)
3
2x4
D)
3
33
Find the indicated value of the given function.
211)
f(x) =6x2– 3x + 6
5 – x , f(5)
211)
A)
891
10
B)
Undefined
C)
891
D)
– 891
10
Add or subtract. Simplify your answer to lowest terms.
212)
6
3m2– 8m – 3 +3
15m2+ 2m – 1 –4
5m2– 16m + 3
212)
A)
45m – 19
(3m + 1)(m – 3)(5m – 1)
B)
21m – 11
(3m + 1)(m – 3)(5m – 1)
C)
21m – 19
(3m + 1)(m – 3)(5m – 1)
D)
45m – 11
(3m + 1)(m – 3)(5m – 1)
Simplify the complex fraction.
213)
x + 5
18
x – 8
2
213)
A)
9(x +5)(x –8)
B)
(x + 5)(x – 8)
9
C)
(x + 5)
9(x – 8)
D)
9(x + 5)
(x – 8)
Add or subtract. Simplify your answer to lowest terms.
214)
y2
y2+ 14y + 45 +11y + 30
y2+ 14y + 45
214)
A)
y2+ 6
y + 9
B)
y + 6
y + 3
C)
11y + 30
y2+ 14y + 45
D)
y + 6
y + 9
215)
2ab
a2 – b2–b
a – b +4
215)
A)
4a + 5b
a2 – b2
B)
4a + 5b
a + b
C)
(a – b)(4a + 5b)
a2 – b2
D)
2ab – b + 4
a + b + 1
Solve.
216)
If x is Sam’s average speed when walking and x + 10 is his average speed when cycling, then the
total time, T, for a trip involving 12 miles of cycling and 8 miles of walking is given by
T =12
x + 10 +8
x
where T is in hours and x is in miles per hour. Find Sam’s average walking speed if the total time
for a trip is 5 hours.
216)
A)
4 mph
B)
3 mph
C)
3.5 mph
D)
2 mph
34
217)
Frank can type a report in 5 hours and James takes 7 hours. How long will it take the two of them
typing together?
217)
A)
35
2 hr
B)
7 hr
C)
12
35 hr
D)
35
12 hr
218)
The volume of wood in a tree varies jointly as the height of the tree and the square of the distance
around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the
distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 39 feet
tall having a measurement of 5 feet around the trunk?
218)
A)
82 ft3
B)
78 ft3
C)
70 ft3
D)
87 ft3
Add or subtract. Simplify your answer to lowest terms.
219)
7z + 18
z + 8+18z – 12
z + 8
219)
A)
6z + 10
17z + 20
B)
8z + 26
19z – 4
C)
-11z + 30
z + 8
D)
25z + 6
z + 8
Simplify the complex fraction.
220)
2 – t
9
7 + t
9
220)
A)
2 – t
7 + t
B)
18 – t
7 + t
C)
1 – 18t
1 + 63t
D)
18 – t
63 + t
Find the quotient.
221)
x3 – 64y3
x2 + 4xy + 16y2÷x2 – 16y2
x2 + 7xy + 12y2
221)
A)
1
x + 3y
B)
x +3y
C)
1
D)
(x +3y)(x –4y)
Solve the inverse variation.
222)
If x varies inversely as y2 and x =2 when y =15, what is x when y =5?
222)
A)
50
B)
18
C)
12
D)
3
Solve.
223)
m + 7
m2– 3m – 4 –7
m2+ 2m + 1 =m – 7
m2– 3m – 4
223)
A)
–42
B)
6
C)
–63
D)
–6
35
Simplify the complex fraction.
224)
8
p3 – 1
2
p – 1
224)
A)
p2+2p +4
B)
p2 – 2p + 4
p2
C)
p2 + 2p + 4
p2
D)
(p2 + 2p + 4)(2 – p)
2p2 – 1
Add or subtract. Simplify your answer to lowest terms.
225)
1
y2+ 4y – 5–7
y + 1
225)
A)
–3y +31
B)
–7y +36
C)
-7y + 36
(y + 1)(y – 5)
D)
-3y + 31
(y + 1)(y – 5)
Find the quotient.
226)
343y3+ 1
8y3+ 125 ÷49y2– 1
4y2– 10y + 25
226)
A)
7y + 1
2y + 5
B)
2y + 5
7y + 1
C)
49y2– 7y + 1
(2y + 5)(7y – 1)
D)
2y – 5
7y – 1
227)
3r – 9s
5r – 10s÷12s – 4r
2r – 4s
227)
A)
– 10
3
B)
– 3
10
C)
10
3
D)
– 1
10
228)
m2 + 11mn + 28n2
m + 4n ÷m2 – 49n2
4m – 28n
228)
A)
4(m + 7n)
m – 7n
B)
4
C)
m + 7n
4
D)
4(m – 7n)
m + 7n
Solve for the indicated variable.
229)
PV
T=pv
t for P
229)
A)
P=pvV
tT
B)
P=tvT
pV
C)
P=pvT
tV
D)
P=pv
tTV
Simplify the rational expression.
230)
a2 – 36
a2 + 10a + 24
230)
A)
a + 6
a + 4
B)
a – 6
a + 4
C)
a + 6
a – 4
D)
a – 6
a – 4
36
Add or subtract. Simplify your answer to lowest terms.
231)
m – 3
m2+ 14m + 48 +2m + 7
m2+ 6m – 16
231)
A)
3m + 4
2m2+ 20m + 32
B)
3m + 4
C)
3m2+ 14m + 48
(m + 8)(m + 6)(m – 2)
D)
3m2+ 14m + 48
(m – 8)(m – 6)(m + 2)
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
232)
10
9x – 90, x
18x – 108
232)
A)
18(x – 10); 2
18(x – 10), x2– 10x
18(x – 10)
B)
18(x – 10)(x – 6); 20x – 120
18(x – 10)(x – 6), x2– 10x
18(x – 10)(x – 6)
C)
9(x – 6); x – 6
9(x – 6), x2– 10x
9(x – 6)
D)
9(x – 10)(x – 6); x – 6
9(x – 10)(x – 6), x2– 10x
9(x – 10)(x – 6)
233)
t
t + 3 , 6
t – 5
233)
A)
(t + 3)(t – 5); t2– 5t
(t + 3)(t – 5), 6t + 18
(t + 3)(t – 5)
B)
6t; t2+ 3t
6t , t2– 5t
6t
C)
(t + 3); 1
(t + 3), t2+ 3t
(t + 3)
D)
(t – 5); t2– 5t
(t – 5), 1
(t – 5)
Solve.
234)
Amy can clean the house in 8 hours. When she works together with Tom, the job takes 5 hours.
How long would it take Tom, working by himself, to clean the house?
234)
A)
141
3hr
B)
131
3 hr
C)
3 hr
D)
132
3hr
Find the quotient.
235)
y2– 4y – 21
6y2÷y2– 6y – 27
y
235)
A)
y – 7
6y3(y – 9)
B)
y – 9
6y(y – 7)
C)
(y – 7)(y – 9)
6y3
D)
y – 7
6y(y – 9)
37
Simplify the complex fraction.
236)
5
12
2
9
236)
A)
8
15
B)
5
54
C)
15
8
D)
3
10
Add or subtract. Simplify your answer to lowest terms.
237)
8
m – n2+3
n2 – m
237)
A)
24
m – n2
B)
–5
m – n2
C)
5
m – n2
D)
11
m – n2
Find the quotient.
238)
25x2 – 4
x2 – 25 ÷5x – 2
x + 5
238)
A)
5x – 2
x + 5
B)
(5x – 2)(25x2 – 4)
(x2+ 5)(x + 5)
C)
x – 5
5x + 2
D)
5x + 2
x – 5
239)
–36a7b5c3
40ab3c2÷27a3b5c8
44abc2
239)
A)
–20a7
15bc5
B)
–22a4
15bc5
C)
–20a4c5
15b2
D)
–22a4
15b2c5
Simplify the rational expression.
240)
m2– 9m
9 – m
240)
A)
m
B)
–(m + 3)
C)
m + 3
D)
–m
Solve.
241)
3
x2 – 11x + 30 –1
x – 6 =1
9x – 45
241)
A)
27
5
B)
39
5
C)
6
D)
–4
3
Add or subtract. Simplify your answer to lowest terms.
242)
8
7x – 35 +1
28x + 224
242)
A)
33x + 251
28(x – 5)(x + 8)
B)
-31x – 261
(7x – 5)(4x + 8)
C)
31x + 261
28(x – 5)(x + 8)
D)
33x + 251
(7x – 5)(4x + 8)
38
243)
6z – 1
z + 7 –18z – 4
z + 7
243)
A)
24z + 3
z + 7
B)
-12z + 3
z + 7
C)
24z – 5
z + 7
D)
-12z – 5
z + 7
Rewrite as a complex fraction and simplify.
244)
4k-2 – 9m-2
2k-1 + 3m-1
244)
A)
2m + 3k
km
B)
2m – 3k
k2m2
C)
2k – 3m
km
D)
2m – 3k
km
Add or subtract. Simplify your answer to lowest terms.
245)
4
y2 – 3y + 2 +7
y2 – 1
245)
A)
11y – 10
(y – 1)(y + 1)(y – 2)
B)
56y – 10
(y – 1)(y + 1)(y – 2)
C)
11y – 10
(y – 1)(y – 2)
D)
10y – 11
(y – 1)(y + 1)(y – 2)
Solve.
246)
A contractor finds that it takes Sam Tockett 10 hours to construct a wall of a certain size. It takes Jim
Lowell 7 hours to construct the same wall. How long would it take if they worked together?
246)
A)
1 hr
B)
17
70 hr
C)
17 hr
D)
42
17 hr
Solve the joint variation.
247)
If m varies jointly with p and q, and m = 12 when p =4 and q =7, find m when p =6 and q =3.
247)
A)
54
7
B)
3
7
C)
27
7
D)
54
Solve.
248)
Two resistors are wired in parallel, one of which is 80 ohms. If the total resistance is to be 60 ohms,
what must be the value of the other resistor? Use the formula for the total resistance R in an
electrical circuit with resistors R1, R2, R3, …, Rn that are wired in parallel.
1
R=1
R1+1
R2+1
R3+ … +1
Rn
248)
A)
240 ohms
B)
140 ohms
C)
34.3 ohms
D)
20 ohms
Solve for the indicated variable.
249)
1
a+1
b=1
c, for c
249)
A)
c = a + b
B)
c = ab(a + b)
C)
c =ab
a + b
D)
c =a + b
ab
39
Solve.
250)
If 2.8 pounds of a certain grain cost $2.24, how much will 5.8 pounds of the grain cost?
250)
A)
$4.79
B)
$4.64
C)
$4.38
D)
$3.62
Find the product.
251)
7m2n2
3x – 18 ·6 – x
21m4n
251)
A)
–7n
m2
B)
–n
9m2
C)
–n(3 – x)
9m2(3 + x)
D)
m2n
Solve.
252)
Given the area A, and length l, of a rectangle, the width can be found using the formula w =A
l .
Suppose the area of a rectangle is 5x2– 12x – 32
36 square inches and the width is x – 4
9 inches . Find
the length.
252)
A)
8x + 5
4 in.
B)
5x – 8
4 in.
C)
5x + 8
4 in.
D)
4(5x –8) in.
Add or subtract. Simplify your answer to lowest terms.
253)
3
x + 3+x
x – 3
253)
A)
x2 + 9x – 6
(x + 3)(x – 3)
B)
x2 + 6x – 6
(x + 3)(x – 3)
C)
x2 + 9x – 9
(x + 3)(x – 3)
D)
x2 + 6x – 9
(x + 3)(x – 3)
Find the product.
254)
12x + 24y
x2y5·x4y
15x + 30y
254)
A)
4x2
5y5
B)
5x6y6
4
C)
5x2
4y4
D)
4x2
5y4
Solve.
255)
If the start–up costs for a small sandwich shop are $320 per day and it costs an average of $2 per
sandwich, the average cost per sandwich for making x sandwiches is given by,
C =320 + 2x
x
where C is in dollars. Find the number of sandwiches made if the average cost per sandwich is $6.
255)
A)
90 sandwiches
B)
160 sandwiches
C)
80 sandwiches
D)
8 sandwiches
Simplify the rational expression.
256)
4k – 20
35 – 7k
256)
A)
4
7
B)
–1
C)
–4
7
D)
1
40
Find the product.
257)
2x3y3
4xy ·8xy3
x2y4
257)
A)
4xy
B)
xy
4
C)
4y
x
D)
4x
y
Find the quotient.
258)
xy – 6x + 7y – 42
xy + 4x – 6y – 24 ÷xy + 5x + 7y + 35
xy + 5x – 6y – 30
258)
A)
y + 6
y – 4
B)
y – 6
y + 4
C)
x – 6
x + 4
D)
(y – 6)(y + 5)
y + 4
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
259)
7
6a – 48 , 4
a2– 8a
259)
A)
6a2– 48; 24
6a2– 48, 4a
6a2– 48
B)
6a(a – 8); 7a
6a(a – 8), 24
6a(a – 8)
C)
6a2– 8; 7a
6a2– 8 , 24
6a2– 8
D)
6a – 8; 24
6a – 8 , 4a
6a – 8
Simplify the complex fraction.
260)
x6
5y4
x2
y2
260)
A)
x4
5y2
B)
x8
5y6
C)
x4
5y6
D)
x4
y2
Find the indicated value of the given function.
261)
h(x) =x2 – x + 15
x2+ 5x – 36, h(4)
261)
A)
0
B)
15
37
C)
15
D)
Undefined
Simplify the complex fraction.
262)
1
x – 49
x3
1 + 10
x + 21
x2
262)
A)
x – 7
x(x + 3)
B)
x(x – 7)
(x + 3)
C)
x + 7
x(x + 3)
D)
x(x – 7)
(x – 3)
41
263)
m
b
r
t
263)
A)
mrt
b
B)
mr
bt
C)
mt
br
D)
m
brt
Find the indicated value of the given function.
264)
f(x) =3– 4x
6x2– 3x – 9 , f(–3)
264)
A)
5
18
B)
– 1
4
C)
– 1
6
D)
5
12
Simplify the complex fraction.
265)
s
w
b
265)
A)
s
wb
B)
swb
C)
sb
w
D)
sw
b
Solve.
266)
The distance D that a spring is stretched by a hanging object varies directly as the weight W of the
object. If a 12–kg object stretches a spring 82 cm, find the distance when the weight is 8–kg.
266)
A)
102 cm
B)
1 cm
C)
7 cm
D)
55 cm
Simplify the complex fraction.
267)
a8b4
c9
a2b
c2
267)
A)
a6b3
c7
B)
a6b3c7
C)
a6b5
c7
D)
b3
a6c7
Solve.
268)
x +-12
x=-4
268)
A)
–2, 6
B)
-12
C)
-4, -12
D)
2, -6
Find the quotient.
269)
4y2 – 16z2
2y2 + 0yz – 8z2÷2y2– 3yz – 2z2
y2 – 4z2
269)
A)
2y + 4z
2y + z
B)
2y + 4z
2y – z
C)
2y – 4z
2y + z
D)
1
42
Add or subtract. Simplify your answer to lowest terms.
270)
12
x+7
6x
270)
A)
79x
6
B)
–79
x
C)
79
6x
D)
19
x2
Simplify the complex fraction.
271)
rs
t3
rs
t7
271)
A)
1
t4
B)
1
t10
C)
t4
D)
t4
rs
Add or subtract. Simplify your answer to lowest terms.
272)
y2
y2– 4y – 32 +–2y – 24
y2– 4y – 32
272)
A)
y – 6
y – 8
B)
y – 6
y2– 4y – 32
C)
y – 6
y – 32
D)
–2y – 24
–4y – 32
Simplify the complex fraction.
273)
4
x2 – 16 + 1
x – 4
7
x2 – 16 + 6
x + 4
273)
A)
x – 8
6x + 17
B)
x + 8
6x – 17
C)
x + 8
13
D)
x + 8
6x + 31
274)
6n
n + 7 + 1
n
4n – 8
n + 7
274)
A)
6n + 7
4n3 + 28n2 – 8n
B)
6n2 + n + 7
4n2 + 28n – 8
C)
6n2 + n + 7
4n3 + 28n2 – 8n
D)
6n2 + 7n + 1
4n3 + 7n2 – 8n
Solve.
275)
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112
feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles
per hour?
275)
A)
141.75 ft
B)
154.05 ft
C)
121.5 ft
D)
142.09 ft
43
276)
Suppose the velocity of an automobile starting from rest is given by
v =200t
2t + 6
where v is the velocity in miles per hour and t is the time in seconds. Find the number of seconds
when the velocity is 50 miles per hour.
276)
A)
4 sec
B)
1.5 sec
C)
5 sec
D)
3 sec
Find the quotient.
277)
2k2 + 9k + 9
9k2 – 18k + 8÷6k2 + 17k + 12
9k2 – 16
277)
A)
k + 1
3k + 2
B)
k + 3
3k – 2
C)
–1
D)
k + 4
2k – 3
Solve the direct variation.
278)
If y varies directly as z and y =270 when z =18, what is the value of y when z =16?
278)
A)
225
B)
324
C)
256
D)
240
Find the LCD for the list of fractions. Write the list as equivalent fractions with the LCD as their denominators.
279)
5
x, 8x – 7
4x4+ 4x2, 7
x2– 3x – 4
279)
A)
4x2(x + 1)(x + 1); 20x3– 60x2– 80x
4x2(x + 1)(x + 1), 8x2– 31x – 11
4x2(x + 1)(x + 1), 28x2
4x2(x + 1)(x + 1)
B)
4x(x2+ 1)(x + 1)(x + 1); 20x6– 60x5– 60x4 + 20x3– 3x2– 80x
4x(x2+ 1)(x + 1)(x + 1), 8x4– 31x3 + 1x2– 11x + 28
4x(x2+ 1)(x + 1)(x + 1),
28x2
4x(x2+ 1)(x + 1)(x + 1)
C)
4x2(x + 1)2(x + 1); 20x4– 60x2– 60x – 80
4x2(x + 1)2(x + 1), 8x2– 31x – 11
4x2(x + 1)2(x + 1), 28x2– 28x
4x2(x + 1)2(x + 1)
D)
4x2(x2+ 1)(x + 1)(x – 4); 20x5– 60x4– 60x3– 60x2– 80x
4x2(x2+ 1)(x + 1)(x – 4), 8x3– 31x2– 11x + 28
4x2(x2+ 1)(x + 1)(x – 4),
28x4+ 28x2
4x2(x2+ 1)(x + 1)(x – 4)
Add or subtract. Simplify your answer to lowest terms.
280)
3
10x+9
14x2
280)
A)
12
10x + 14x2
B)
12
140x2
C)
108
70x2
D)
21x + 45
70x2
Solve.
281)
A ship leaves port traveling at 25 miles per hour. Three hours later a speedboat leaves the same
port traveling at 45 miles per hour. How long will it take for the speedboat to overtake the ship?
281)
A)
11
14 hr
B)
3
4 hr
C)
12
3 hr
D)
33
4 hr
44
Solve the direct variation.
282)
If n varies directly as the square of m and n =48 when m =4, what is the value of n when m = –
5?
282)
A)
–60
B)
60
C)
–75
D)
75
Solve the inverse variation.
283)
If x varies inversely as v and x =6 when v =8, what is x when v =16?
283)
A)
3
B)
24
C)
64
D)
2
Solve.
284)
x + 2
x2 – 9+x – 3
x2– 2x – 3 =2x – 3
x2+ 4x + 3
284)
A)
17
12
B)
5
3
C)
4
3
D)
No solution
Solve and check. Identify any extraneous solutions.
285)
x
x – 5=5+5
x – 5
285)
A)
5
B)
–5
C)
– 5
4
D)
No solution (5 is extraneous)
Add or subtract. Simplify your answer to lowest terms.
286)
1
9u –1
11u
286)
A)
2
99u
B)
2
9u
C)
1
99u
D)
2u
99
Solve the inverse variation.
287)
If m varies inversely as n and n is 6 when m is 11, what is n when m is 5?
287)
A)
13.2
B)
2.73
C)
8.8
D)
0.37
Simplify the complex fraction.
288)
25r2– 9s2
tu
5
u – 3
t
288)
A)
3t + 5u
tu
B)
3t + 5u
C)
5t + 3u
D)
tu
5t + 3u
Solve. Round to two decimal places unless otherwise noted.
289)
In the following formula, y is the minimum number of hours of studying required to attain a test
score of x: y = 0.35x
100.5 – x. How many hours of study are needed to score 89?
289)
A)
27.10 hr
B)
101.10 hr
C)
2.71 hr
D)
7.15 hr
45
Solve.
290)
A commuter travels to work, driving a distance d at speed r. At the end of the day, she returns
home and drives the same distance 4 mph faster, at a speed r +4. Her average speed for the round
trip can be represented by the expression
2d
d
r + d
r + 4
Simplify this expression.
290)
A)
dr(r + 4)
dr + 2
B)
r(r + 2)
r + 4
C)
1
r + 2
D)
r(r + 4)
r + 2
Perform the indicated operations.
291)
2x2– 5xy – 3y2
y2+ 4xy – 5x2·y2+ 2xy – 3x2
6x2+ 5xy + y2÷3x2– 8xy – 3y2
15x2+ 2xy – y2
291)
A)
1
B)
x – 3y
y + 5x
C)
5x – y
5x + y
D)
(y + 3x)2
2x – y
Find the product.
292)
z2– 12z + 36
z2– 49 ·z2– 7z
z – 6
292)
A)
(z – 6)
z + 7
B)
z(z – 6)
z – 7
C)
z
z – 7
D)
z(z – 6)
z + 7
Solve.
293)
If y varies directly as the square of x and inversely as m, and y =3 when x =2 and m =10, find y
when x = 8 and m = 6.
293)
A)
0.83
B)
1.25
C)
80
D)
20
Add or subtract. Simplify your answer to lowest terms.
294)
x3 – 7
x – 7+x
x – 7–7x2
x – 7
294)
A)
x2
B)
x2+ x –7
C)
x3–7x2
D)
x2+ 1
Solve the joint variation.
295)
If y varies jointly with x and z, and y =30 when x =3 and z =2, find y when x =4 and z =1.
295)
A)
4
B)
5
4
C)
20
D)
5
Add or subtract. Simplify your answer to lowest terms.
296)
b
b2 – 25 +5
b + 5 –6
b
296)
A)
25(b – 6)
(b + 5)(b – 5)
B)
6b2 – 25b + 150
b(b + 5)(b – 5)
C)
-25(b – 6)
b(b + 5)(b – 5)
D)
25(b + 6)
b(b + 5)(b – 5)
46
Find the quotient.
297)
12u5v2
4v2+ 4v – 8 ÷3u3
4v2– 4v
297)
A)
4u2v3(v + 2)
B)
4uv3
v – 2
C)
4u2v3
v + 2
D)
4u8v2
v + 2
Solve.
298)
y
y + 4 +8y + 28
y2 + 7y + 12 =4
y + 3
298)
A)
–3, –4
B)
4, 3
C)
–6, 5
D)
No solution
Add or subtract. Simplify your answer to lowest terms.
299)
8x – 5y
4x2y–5x – 7y
xy2
299)
A)
20x2– 20xy – 5y2
4x2y2
B)
8x2y2 + –5xy3– 20x3y + 28x2y2
4x3y3
C)
-20x2 + 36xy – 5y2
4x2y2
D)
3x + 2y
4x2y2
Simplify the complex fraction.
300)
3 – 4
9
8
10 + 4
7
300)
A)
1373
432
B)
31
864
C)
1637
48
D)
23
864
Graph.
301)
f(x) =-1
x + 1
301)
47
A)
B)
C)
D)
Add or subtract. Simplify your answer to lowest terms.
302)
m2– 11m
m – 6 +30
m – 6
302)
A)
m2– 11m + 30
m – 6
B)
m + 5
C)
m – 6
D)
m – 5
Solve.
303)
The weight W of an object on the Moon varies directly as the weight E on earth. A person who
weighs 119 lb on earth weighs 23.8 lb on the Moon. How much would a 193–lb person weigh on
the Moon?
303)
A)
38.6 lb
B)
335.8 lb
C)
965 lb
D)
0.2 lb
Solve. Round to two decimal places unless otherwise noted.
304)
Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by
y = 312,500
x + 625 . What is the cost per ton for x =200?
304)
A)
$100,000.00
B)
$937.50
C)
$378.79
D)
$75,757.58
48
Add or subtract. Simplify your answer to lowest terms.
305)
4
x – 9+6
9 – x
305)
A)
24
x – 9
B)
10
x – 9
C)
–2
x – 9
D)
2
x – 9
Solve.
306)
The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose
that a 10–m beam can support 800 kg. How many kilograms can a 10–m beam support?
306)
A)
8 kg
B)
0.0013 kg
C)
800 kg
D)
0.125 kg
Add or subtract. Simplify your answer to lowest terms.
307)
–2
27 –5
6x
307)
A)
4x – 45
54x
B)
–4x – 45
54x
C)
–4x + 45
54x
D)
-9
54 – 6x
Solve and check. Identify any extraneous solutions.
308)
1
y – 3 –5
y2 – 1 =10
y3 – 3y2 – y + 3
308)
A)
1, 4
B)
1
C)
4 (1 is extraneous)
D)
1 (4 is extraneous)
Add or subtract. Simplify your answer to lowest terms.
309)
3x + 4
5x5–6x – 5
10x
309)
A)
-3x + 9
10x5
B)
-3x5+ 2.5x4 + 3x + 4
5x5
C)
-6x6+ 5x5 + 6x2+ 8x
10x6
D)
-6x5+ 5x4 + 6x + 8
10x5
Solve.
310)
Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies
jointly as an object’s surface area A and velocity v. If a car traveling at a speed of 30 mph with a
surface area of 37 ft2 experiences a drag of 166.5 N (Newtons), how fast must a car with 44 ft2 of
surface area travel in order to experience a drag force of 495 N?
310)
A)
75 mph
B)
72 mph
C)
77 mph
D)
80 mph
Solve for the indicated variable.
311)
S =H
m(t1 – t2), for t2
311)
A)
t2=Smt1 – H
m
B)
t2=mt1 – SH
Sm
C)
t2=H – Smt1
Sm
D)
t2=Smt1 – H
Sm
49
Find the product.
312)
vw – vx + wz – xz
kv + nv – kz – nz ·vw + vx – wz – xz
vw + vx + wz + xz
312)
A)
w + x
n + k
B)
(v + z)
(n + k)(v – z)
C)
w – x
n + k
D)
(w – x)(v + z)
(n + k)(v – z)
Solve.
313)
45 – 9r
81 – r2+r
r – 9=7
r + 9
313)
A)
9, 2
B)
–9, –2
C)
–2
D)
2
Find the quotient.
314)
2a – 2b – ab + b2
16a2 – 8ab + b2÷4a2– 3ab – b2
16a2 – b2
314)
A)
4a – b
2 – a – b
B)
2 + b
4a – b
C)
2– b
D)
2 – b
4a – b
Solve.
315)
The thickness of a board is given by 2
x – 5 . The board is run through a planar, which removes a
layer whose thickness is 6
x. What is the new thickness of the board?
315)
A)
-4x – 30
x(x – 5)
B)
-4x + 30
x(x – 5)
C)
8x – 30
x(x – 5)
D)
-4x + 5
x(x – 5)
Find the LCD for the pair. Write the fraction pair as equivalent fractions with the LCD as their denominators.
316)
m + 3
m3+ 10m2+ 16m, 3m + 7
m4+ 5m3+ 6m2
316)
A)
m2(m + 2)(m + 8)(m + 3); m3+ 6m2+ 9m
m2(m + 2)(m + 8)(m + 3), 3m2+ 31m + 56
m2(m + 2)(m + 8)(m + 3)
B)
m3(m + 2)2(m + 8); m5+ 6m3+ 9m
m3(m + 2)2(m + 8), 3m4+ 31m2+ 56
m3(m + 2)2(m + 8)
C)
m2(m + 2)2(m + 8)(m + 3); m4+ 6m3+ 9m2
m2(m + 2)2(m + 8)(m + 3), 3m3+ 31m2+ 56m
m2(m + 2)2(m + 8)(m + 3)
D)
m(m + 2)(m + 8)(m + 3); m2+ 6m + 9
m(m + 2)(m + 8)(m + 3), 3m2+ 31m + 56
m(m + 2)(m + 8)(m + 3)
Add or subtract. Simplify your answer to lowest terms.
317)
8x
x2 – 5x + 6 –32
x2 – 6x + 8
317)
A)
8
(x – 2)(x – 3)
B)
8x – 32
(x – 2)(x – 3)(x – 4)
C)
x – 6
(x – 3)(x – 4)
D)
8(x – 6)
(x – 3)(x – 4)
50
318)
3x + 22
x2– 2x – 24 –x + 14
x2– 2x – 24
318)
A)
2x + 36
x2– 2x – 24
B)
1
x – 3
C)
2x + 8
D)
2
x – 6
Simplify the rational expression.
319)
a2– b2– 3a + 3b
2a + 2b – 6
319)
A)
b – a
2
B)
a – b
2
C)
a2– b2
6
D)
a + b
6
320)
–42m4p2
3m9p
320)
A)
–14m5p2
B)
–14mp
C)
–14p
m5
D)
–14m5
p
Solve.
321)
A person travels 15 miles in 1
3 of an hour, then returns by traveling that same 15 miles in 1
7 of an
hour. What is that person’s average rate for the trip?
321)
A)
71.4 mph
B)
7.14 mph
C)
63 mph
D)
75 mph
322)
A water tank can be filled in 5 minutes and emptied in 8 minutes. If the drain is accidentally left
open when the tank is being filled, how long does it take to fill the tank?
322)
A)
26 min
B)
15 min
C)
3 min
D)
13.33 min
Solve and check. Identify any extraneous solutions.
323)
1
w + 4+1
3w – 8 =-20
3w2 + 4w – 32
323)
A)
–4
B)
–3
C)
No solution (–4 is extraneous)
D)
8
3, –4
Solve.
324)
From a point on a straight road, two cars are driven in opposite directions, one at 50 miles per hour
and the other at 69 miles per hour. In how many hours will they be 595 miles apart?
324)
A)
Not enough information
B)
6 hr
C)
4 hr
D)
5 hr
Solve the joint variation.
325)
If f varies jointly as h and the square of q, and f = 54 when q = 3 and h = 2, find f when q = 2 and
h = 5.
325)
A)
60
B)
30
C)
15
D)
12
51
Find the domain of the rational function.
326)
h(x) =x – 140
x3– 7x2– 18x
326)
A)
{x|x 0, -2, 9}
B)
{x|x -2, 9}
C)
{x|x 0, -2, 9, 140}
D)
{x|x 0, -9, 2}
Solve the direct variation.
327)
If m varies directly as p and m =20 when p =4, what is the value of m when p = 7?
327)
A)
25
B)
35
C)
49
D)
16
Simplify the complex fraction.
328)
m + 8
m – 8 – m – 8
m + 8
m + 8
m – 8 + m – 8
m + 8
328)
A)
16m
(m + 8)2
B)
16m
2m2 + 64
C)
16m
m2 + 64
D)
8m
m2 + 64
Solve and check. Identify any extraneous solutions.
329)
3
x – 6+9
x=-54
x2 – 6x
329)
A)
0, 6
B)
–6
C)
0
D)
No solution (0 is extraneous)
Solve.
330)
For a fixed amount of principal, the simple interest varies jointly with the rate and the time. If the
simple interest is $1750 when the rate is 5% and the time is 7 years, find the simple interest when
the rate is 6% and the time is 10 years.
330)
A)
$300
B)
$6000
C)
$3000
D)
$3300
Rewrite as a complex fraction and simplify.
331)
x-2
x-2 – y-2
331)
A)
y
y2 – x2
B)
y2
y2 – x2
C)
y2 – x2
y2
D)
y2
y2 + x2
Simplify the complex fraction.
332)
y
7 – y + 7 + y
y
7 – y
y + y
7 + y
332)
A)
7 + y2
y2 – 7
B)
7 + y
7 – y
C)
–1
D)
7 – y
7 + y
52
Solve for the indicated variable.
333)
1
a+1
b= c, for a
333)
A)
a=b
bc – 1
B)
a=bc –1
b
C)
a=1
bc
D)
a=1
c–b
Solve.
334)
Sandi can make a quilt in 10 days and Eva can make a quilt in 6 days. In how many days can they
make a quilt working together?
334)
A)
34
15 days
B)
33
4 days
C)
52
9 days
D)
41
2 days
Simplify the rational expression.
335)
12x2 + 25xy + 12y2
3x2– 5xy – 12y2
335)
A)
4x + 3y
x – 3y
B)
4xy + 3y
xy – 3y
C)
3x + 4y
3x – 4y
D)
4x + 3y
x + 3y
Add or subtract. Simplify your answer to lowest terms.
336)
x
x2– 5x – 24 –6
x + 3
336)
A)
x – 6
(x + 3) (x – 8)
B)
-6x + 48
(x + 3) ( x – 8)
C)
-5x + 48
(x + 3) (x – 8)
D)
x2 – 8x – 6
(x + 3) (x – 8)
337)
-7x – 4
x+6x + 5
3x
337)
A)
-15x – 7
3x
B)
-15x – 7
3x2
C)
-27x – 7
3x
D)
-15x + 17
3x
Solve the inverse variation.
338)
If y varies inversely as x and y is 4.5 when x is 6, what is y when x is 4?
338)
A)
13.5
B)
3
C)
0.19
D)
6.75
Without solving the equation, find the value(s) of the variable that could result in an extraneous solution.
339)
4y
y2+ 8y – 9 –3
y2+ 2y – 3=6y
y2 + 12y + 27
339)
A)
–1, 3, 9
B)
–9, –3, 1
C)
–9, –3
D)
–1, 0, 3, 9
Simplify the rational expression.
340)
y2– 4y – 12
y2+ 3y – 54
340)
A)
–4y – 12
3y – 54
B)
y + 2
y + 9
C)
–4y – 2
3y – 9
D)
–y2– 4y – 12
y2+ 3y – 54
53
Solve.
341)
4
m – 4 –7
m + 4 =11
m2– 16
341)
A)
33
B)
7
C)
11
D)
-11
Simplify the rational expression.
342)
tx + t + 6x + 6
8x + 8
342)
A)
t + 6
8
B)
t + 8
8
C)
t – 6
8
D)
t – 8
6
Add or subtract. Simplify your answer to lowest terms.
343)
4z – 9
z – 20 +15z + 12
20 – z
343)
A)
19z – 21
z – 20
B)
-11z + 3
z – 20
C)
19z + 3
z – 20
D)
-11z – 21
z – 20
344)
y + 2
y – 3+y – 1
y + 4
344)
A)
2y + 1
(y – 3)(y + 4)
B)
2y + 1
2y + 1
C)
2y2 + 11
(y – 3)(y + 4)
D)
2y2 + 2y + 11
(y – 3)(y + 4)
Find the quotient.
345)
y3– 9y
y2– 81 ÷y2– 5y – 6
y2+ 3y – 54
345)
A)
(y + 9)(y – 1)
y(y2– 9)
B)
(y – 9)(y + 1)
y(y2– 9)
C)
y
y + 1
D)
y(y2– 9)
(y – 9)(y + 1)
Solve.
346)
x
2x + 2 =-2x
4x + 4 +2x – 3
x + 1
346)
A)
–12
5
B)
3
C)
–3
D)
3
2
Solve the joint variation.
347)
If m varies jointly as x and y, and m = 24 when x = 6 and y = 9, find m when x = 15 and y = 8.
347)
A)
160
3
B)
140
3
C)
64
3
D)
60
Add or subtract. Simplify your answer to lowest terms.
348)
2x + 6
x2+ 6x + 5 –x + 1
x2+ 6x + 5
348)
A)
x + 7
x2+ 6x + 5
B)
x + 5
C)
7
x2+ 6x + 5
D)
1
x + 1
54
Rewrite as a complex fraction and simplify.
349)
2x-1 +7x-2
7x-3 – 8x-1
349)
A)
2x +7
7 – 8x
B)
2x2+7x
7 + 8x2
C)
2x2+7x
7 – 8x2
D)
2x +7
7 – 8x2
Simplify the rational expression.
350)
4x + 4
20x2+ 28x + 8
350)
A)
4x + 5
5x + 28
B)
4x
5x + 2
C)
1
5x + 2
D)
4x + 4
20x2+ 28x + 8
Solve.
351)
The volume of a gas varies inversely as the pressure and directly as the temperature (in degrees
Kelvin). If a certain gas occupies a volume of 2.3 liters at a temperature of 320 K and a pressure of
24 newtons per square centimeter, find the volume when the temperature is 352 K and the pressure
is 12 newtons per square centimeter.
351)
A)
1.0 L
B)
30.7 L
C)
5.1 L
D)
50.2 L
Find the domain of the rational function.
352)
h(t) =10t2 – 2t + 1
100t2 – 49
352)
A)
t t 7
10
B)
t t 10
7, – 10
7
C)
t t 49
100, – 49
100
D)
t t 7
10, – 7
10
Solve for the indicated variable.
353)
I =E
R + r for r
353)
A)
r=IR
E
B)
r=E
I– IR
C)
r=E – R
I
D)
r=E – IR
I
Find the product.
354)
x3– 64
x2 – 16 ·x2– 8x + 16
x2+ 4x + 16
354)
A)
x – 4
B)
(x – 4)
x + 4
C)
(x – 4)(x – 4)
x + 4
D)
x2+ 4x + 16
x + 4
355)
y2– 25
6y – 30 ·y – 3
y + 5
355)
A)
y – 3
6
B)
(y – 3)(y + 5)
6(y + 5)
C)
1
6
D)
y – 3
55
Answer Key
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Answer Key
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Answer Key
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Answer Key
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Answer Key
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Answer Key
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Answer Key
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Answer Key
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