Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the expression that is equivalent to the given rational expression.
1)
–x –7
x +11
1)
A)
–x –7
x –11
B)
–x –7
– x –11
C)
–(x –7)
x +11
D)
–– x +7
x +11
2)
–3t –14
14t +13
2)
A)
3t –14
14t –13
B)
3t –14
–(14t +13)
C)
3t –14
14t +13
D)
–3t +14
14t –13
3)
–6x –10
15x +11
3)
A)
–6x +10
15x –11
B)
6k –10
–15x +11
C)
––6x –10
15x –11
D)
–6x +10
15x +11
4)
–x +4
x –12
4)
A)
–x +4
x +12
B)
–x +4
– x +12
C)
– x –4
x –12
D)
–– x –4
x –12
1
5)
–15x +10
7x –9
5)
A)
15x –10
7x –9
B)
–15x –10
7x –9
C)
–(15x – 10)
7x +9
D)
15x –10
9+7x
6)
–11k +5
12k +15
6)
A)
––11k – 5
12k –15
B)
–11k +5
12k –15
C)
11k – 5
–12k +15
D)
11k +5
–(12k +15)
7)
–12t –4
t +6
7)
A)
–(12t –4)
t +6
B)
–12t +4
t –6
C)
12t –4
t –6
D)
12t –4
t +6
8)
–11k +3
13k +6
8)
A)
––11k +3
13k –6
B)
–11k –3
13k –6
C)
11k –3
–13k –6
D)
11k +3
–13k +6
9)
–10k –4
15k –13
9)
A)
–10k –4
15k +13
B)
10k +4
–15k –13
C)
––10k +4
15k +13
D)
10k –4
–15k +13
10)
–10x +8
8x –4
10)
A)
10x –8
8x –4
B)
–10x +8
–(8x –4)
C)
10x +8
–(8x –4)
D)
10x –8
4+8x
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
11)
Explain in your own words how to multiply rational expressions. (How would you explain
this to a student in this class who was absent from class?).
11)
Provide an appropriate response.
12)
State whether the following situation represents direct variation, inverse variation, or
neither, and explain why: The cost of mailing a letter in the United States and the distance
that it travels.
12)
Provide an appropriate response.
13)
If 9 is substituted for x in the rational expression x –9
x2–81 , the result is 0
0. An often–heard
statement is “Any number divided by itself is 1.” Does this mean that this expression is
equal to 1 for x =9? Explain why or why not.
13)
Provide an appropriate response.
14)
State whether the following situation represents direct variation, inverse variation, or
neither, and explain why: A runner’s speed in a race and the time it takes to run the race
14)
15)
State whether the following situation represents direct variation, inverse variation, or
neither, and explain why: The weight of a roast and the number of servings obtained from
it.
15)
16)
For x 5, the rational expression 6(x –5 )
x –5 is equal to 6. Can the same be said for
6x –5
x –5? Explain why or why not.
16)
17)
Without multiplying by the least common denominator and solving, explain why the
rational equation x
x – 3 =3
x – 3 has no solution. (Hint: Examine both numerators and
denominators carefully.)
17)
18)
What are two possible LCDs which could be used for the sum 7
x – 5 +3
5– x?
18)
19)
Explain how to subtract rational expressions with different denominators.
19)
20)
Describe, in words, how to simplify a complex fraction by using the method of multiplying
by the LCD of the parts (Method 2).
20)
Write four rational expressions equivalent to the given expression.
21)
–12x +11
13x –13
21)
Provide an appropriate response.
22)
Describe, in words, how to simplify a complex fraction by using the method of writing it as
a division problem (Method 1).
22)
Provide an appropriate response.
23)
Explain in your own words how to divide rational expressions. (How would you explain
this to a student in this class who was absent from class?).
23)
24)
If (9x –1)(7x –6) is the LCD of two fractions, is (1 –9x)(6–7x) also acceptable as an
LCD? Why or why not?
24)
25)
Explain the difference between adding rational expressions and solving rational equations.
25)
26)
Explain why someone would want to solve A =1
2bh for b.
26)
27)
Consider an equation of inverse variation y =k
x. When x increases, does y increase or
decrease?
27)
28)
What property of real numbers justifies the method of multiplying by the LCD of the
parts? Why?
28)
29)
Consider an equation of direct variation y = kx. When x increases, does y increase or
decrease?
29)
30)
If (3x –5 )2 is the LCD of two fractions, is (5x –3 )2 also acceptable as an LCD? Why or
why not?
30)
31)
Why is 9x – 7
x – 7 not equal to 9?
31)
32)
How can you tell just by looking at a rational expression if it is equal to –1?
32)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Multiply or divide as indicated. Write the answer in lowest terms.
33)
k2+ 11k + 28
k2+ 9k + 14 ·k2+ 8k + 12
k2+ 10k + 24
33)
A)
k + 2
k + 6
B)
k + 4
k + 2
C)
1
D)
1
k + 6
34)
4
5x = ?
25x2
34)
A)
20
25x2
B)
4x2
25x2
C)
4
25x2
D)
20x
25x2
Simplify the complex fraction.
35)
5
3r – 1 –5
5
3r – 1 +5
35)
A)
2 +3 r
3r
B)
2 –3 r
3r
C)
3r
2 –3 r
D)
2 – r
r
Find all values that make the expression undefined.
36)
x2– 4
x2+ 11x + 28
36)
A)
0
B)
7, –4
C)
2, –2
D)
–7, –4
D
Write the rational expression in lowest terms.
37)
a2–49
a2+10a +21
37)
A)
a –7
a +3
B)
a –7
a –3
C)
a +7
a –3
D)
a +7
a +3
A
38)
8+ t
t – 8
38)
A)
1
B)
–1
C)
–t
D)
Already in lowest terms
D
B
Solve the problem.
39)
The numerator of a fraction is 3 times the denominator. If 1 is subtracted from the numerator, and
added to the denominator, the resulting fraction is equal to 14
6. What was the original fraction (not
written in lowest terms)?.
39)
A)
13
7
B)
15
5
C)
7
13
D)
13
5
Rewrite the rational expression with the indicated denominator.
40)
8
7= ?
42
40)
A)
6
42
B)
48
42
C)
7
42
D)
8
42
Simplify the complex fraction.
41)
7m8n2
9m
3m2n9
4n2
41)
A)
28m5
27n6
B)
28m5
27n5
C)
28m6
27n6
D)
28m6
27n9
Solve the equation.
42)
x – 7
8=x + 9
7
42)
A)
– 121
B)
{5}
C)
121
56
D)
7
8
Provide an appropriate response.
43)
Which of the following fractions is equivalent to
1
13 +1
26
1
11 +1
44
?
43)
A)
44
B)
–65
66
C)
–66
65
D)
66
65
Add or subtract. Write the answer in lowest terms.
44)
2
2m2– 7mp – 4p2+7
10m2+ 3mp – p2–2
5m2– 21mp + 4p2
44)
A)
21m – 32p
(2m + p)(m – 4p)(5m – p)
B)
13m – 28p
(2m + p)(m – 4p)(5m – p)
C)
21m – 28p
(2m + p)(m – 4p)(5m – p)
D)
13m – 32p
(2m + p)(m – 4p)(5m – p)
Identify as an equation or an expression.
45)
–3(8 – x) +4x +7
6
45)
A)
Equation
B)
Expression
Solve the equation.
46)
x + 7
8=x + 8
9
46)
A)
{1}
B)
1
72
C)
15
17
D)
5
24
Add or subtract. Write the answer in lowest terms.
47)
6x – z
6x2–36xz +3xz –18z2–x + z
x2–36z2
47)
A)
12x2+ 26xz – 3z2
(x –6z)(x +6z)(6x +3z)
B)
26xz +9z2
(x –6z)(x +6z)(6x +3z)
C)
26xz –9z2
(x –6z)(x +6z)(6x +3z)
D)
26xz –9z2
(x –6z)2(6x +3z)
Simplify the complex fraction.
48)
4+2
x
x
3+1
6
48)
A)
x
12
B)
12
x
C)
12
D)
1
B
Find all values that make the expression undefined.
49)
–3q + 5
q2+9
49)
A)
3, –3
B)
–3
C)
0
D)
Never undefined
D
Multiply or divide as indicated. Write the answer in lowest terms.
50)
3x +9
4x –4·3x –3
6x +18
50)
A)
9x
B)
9(x +3)
24(x – 1)
C)
1
8
D)
3
8
D
C
Rewrite the rational expression with the indicated denominator.
51)
9
8m =?
40m
51)
A)
5
40m
B)
45
40m
C)
8
40m
D)
9
40m
52)
x
5+9
7
52)
A)
x – 9
–2
B)
–7x + 45
–45
C)
x – 9
–35
D)
–7x – 45
–35
53)
1
k +2
3
k2–4
53)
A)
3
k –2
B)
k –2
C)
k –2
3
D)
k +2
3
54)
9– 8x
5x , x = 2
54)
A)
–37
5
B)
5
2
C)
7
10
D)
–7
10
Find the least common denominator for the fractions in the list.
55)
5
x2– 4x – 12 8
x2– 8x + 12
55)
A)
(x – 2)(x + 6)(x – 2)
B)
(x + 2)(x – 6)
C)
(x + 2)(x – 6)(x – 2)
D)
(x – 6)(x – 2)
56)
2x
3– 8 = x
56)
A)
1
24
B)
– 2
C)
3
2
D)
–24
57)
x
x + 2 =?
5x + 10
57)
A)
2x
5x + 10
B)
5x
5x + 10
C)
x
5x + 10
D)
5
5x + 10
Solve the formula for the specified variable.
58)
1
a+1
b=1
c for c
58)
A)
c = a + b
B)
c =ab
a + b
C)
c = ab(a + b)
D)
c =a + b
ab
Identify as an equation or an expression.
59)
2
5x +6=7
8x –9
59)
A)
Expression
B)
Equation
Add or subtract. Write the answer in lowest terms.
60)
4m
m –10 +7+ m
m–1
m2–10m
60)
A)
m2– 3m –71
m2–10m
B)
5m2+7m –71
m2–10m
C)
5m2– 3m –71
m2–10m
D)
5m2– 3m –71
m2– m
Multiply or divide as indicated. Write the answer in lowest terms.
61)
k2+ 6k + 9
k2+ 7k + 12 ·k2+ 4k
k2– 6k – 27
61)
A)
k
k – 9
B)
k2+ 4k
k – 9
C)
k
k2+ 7k + 12
D)
1
k – 9
Solve the problem.
62)
The area of the rectangle is represented by y2+ 11y + 18. What is the width?
y + 2
62)
A)
y + 9
B)
y – 3
C)
y – 9
D)
y + 3
13
Find all values for which at least one denominator is equal to 0. Write answers using the symbol . Do not solve.
63)
7
10x + 7 +1
x=1
15x – 1
63)
A)
x 0, –7
10 , 1
15
B)
x –7
10 , 1
15 , –7
C)
x –7
10 , 1
15
D)
x 0, –7
10 , 1
15 , 7
64)
In a fraction, what operation does the fraction bar represent?
64)
A)
Subtraction
B)
Division
C)
Addition
D)
Multiplication
65)
x
4–x
6=9
65)
A)
{24}
B)
{54}
C)
108
D)
{36}
Find the LCD for the fractions in the list.
66)
7
x2+ 5x + 6 , 7
2x + 6
66)
A)
2(x – 2)(x – 3)
B)
2(x – 2)(x + 3)
C)
2(x + 2)(x – 3)
D)
2(x + 2)(x + 3)
Identify as an equation or an expression.
67)
6x +3
4=5x
6–6
67)
A)
Expression
B)
Equation
68)
y
y2– 13y +36 +y
y2– 16 =y
y2– 5y – 36
68)
A)
{8, 0}
B)
{1, 0}
C)
{–8, 0}
D)
{–1, 0}
Add or subtract. Write the answer in lowest terms.
69)
4
7– y –3
y –7
69)
A)
–1
7– y
B)
12
7– y
C)
7
7– y
D)
1
7– y
70)
6x2– 9x
–7x , x = 3
70)
A)
27
7
B)
–9
7
C)
9
7
D)
–27
7
71)
5
3r – 1 –5
5
3r – 1 +5
71)
A)
2 –3 r
3r
B)
2 – r
r
C)
3r
2 –3 r
D)
2 +3 r
3r
Multiply or divide as indicated. Write the answer in lowest terms.
72)
z2+ 9z + 18
z2+ 10z + 24 ÷z2+ 3z
z2– 5z – 36
72)
A)
z – 9
z2+ 4z
B)
z – 9
z
C)
z
z2+ 10z + 24
D)
z – 9
73)
3
x–4
y+10
z= 1 for x
73)
A)
z =10xy
xy – 2y + 4x
B)
y =4xz
3xz + 10x – xz
C)
x =3yz
yz + 4z –10y
D)
x =3xyz
yz + 4z –10y
74)
a
a + 5b=?
a2– 25b2
74)
A)
a2– 5ab
a2– 25b2
B)
a2– b2
a2– 25b2
C)
a
a2– 25b2
D)
5ab
a2– 25b2
75)
–1
5m = ?
40m
75)
A)
8
40m
B)
–1
40m
C)
–8
40m
D)
5
40m
Solve the equation.
76)
m +6
m2– 4m – 5 –6
m2– 10m + 25 =m –6
m2– 4m – 5
76)
A)
{66}
B)
{42}
C)
{–11}
D)
{11}
Provide an appropriate response.
77)
True or false? If a fraction with denominator x + 3 must be written as an equivalent fraction with
denominator (x + 3)3, then the original fraction must be multiplied by (x – 3)2 in both the
numerator and the denominator.
77)
A)
True
B)
False
Solve.
78)
2
x=x
3x – 4
78)
A)
{0, 16}
B)
{2, 4}
C)
{0, 4}
D)
Add or subtract. Write the answer in lowest terms.
79)
–6x – 2
x+2x – 9
2x
79)
A)
–10x – 13
2x
B)
–10x – 13
2x2
C)
–10x – 5
2x
D)
–14x – 13
2x
Multiply or divide as indicated. Write the answer in lowest terms.
80)
k2+ 13k + 42
k2+ 14k + 48 ·k2+ 8k
k2+ 11k + 28
80)
A)
k
k2+ 14k + 48
B)
k2+ 8k
k + 4
C)
k
k + 4
D)
1
k + 4
Add or subtract. Write the answer in lowest terms.
81)
–1
y –1–7
1– y
81)
A)
8
y –1
B)
–7
y –1
C)
–8
y –1
D)
6
y –1
Solve the variation problem.
82)
According to Ohm’s law, the electric current, in amperes (A), in a circuit varies directly as the
voltage, in volts (V). When 24 V are applied, the current is 3 A. What is the current when 8 V are
applied?
82)
A)
24.8 A
B)
35 A
C)
8 A
D)
1 A
Multiply or divide as indicated. Write the answer in lowest terms.
83)
y2– 1
5y – 5 ÷y + 1
y + 6
83)
A)
y + 6
B)
1
5
C)
(y + 6)(y + 1)
5(y + 1)
D)
y + 6
5
Rewrite the rational expression with the indicated denominator.
84)
20(x + 1)
x(x – 8)=?
x3– 10x2+ 16x
84)
A)
(x + 1)(x – 2)
x3– 10x2+ 16x
B)
20(x + 1)(x – 2)
x3– 10x2+ 16x
C)
20(x – 2)
x3– 10x2+ 16x
D)
20(x + 1)(x + 2)
x3– 10x2+ 16x
Write the rational expression in lowest terms.
85)
(y + 6)(y – 2)
(y – 2)(y + 3)
85)
A)
2y – 2
2y + 1
B)
y – 6
y – 3
C)
y + 6
y + 3
D)
y + 2
y + 1
Simplify the complex fraction.
86)
x7
9y8
x4
y6
86)
A)
x3
9y14
B)
x3
y2
C)
x3
9y2
D)
x11
9y14
Find the LCD for the fractions in the list.
87)
–4
3a – 15 , 8
a2– 5a
87)
A)
3a – 5
B)
3a(a – 5)
C)
3a2– 5
D)
3a2– 15
Solve the formula for the specified variable.
88)
1
a+1
b= c for a
88)
A)
a=1
c– b
B)
a=b
bc – 1
C)
a=1
bc
D)
a=bc –1
b
Find all values that make the expression undefined.
89)
6y – 9
y2– 9
89)
A)
9
B)
3, –3
C)
3
D)
3
2
Multiply or divide as indicated. Write the answer in lowest terms.
90)
x2–4x –12
6x ·x2–6x
x2–12x +36 ÷x +2
x +6
90)
A)
x +2
x
B)
x +6
6
C)
x –6
x
D)
x +6
2
Write the rational expression in lowest terms.
91)
7k – 21
9– 3k
91)
A)
7
3
B)
1
C)
–1
D)
–7
3
Identify as an equation or an expression.
92)
2
5x +4–2
5x –3
92)
A)
Equation
B)
Expression
Write the rational expression in lowest terms.
93)
x2–y2
y–x
93)
A)
–1
B)
–x+y
C)
–x–y
D)
x+y
94)
a2– 7a
(a + 3)(a – 7)
94)
A)
1
a + 3
B)
a – 7
a + 3
C)
a
a + 3
D)
a2
a + 3
Multiply or divide as indicated. Write the answer in lowest terms.
95)
x2+12x +36
x +6÷x2–36
6x –36
95)
A)
(x +6)2
6
B)
6
C)
1
6
D)
6x –36
x –6
Solve the problem.
96)
A water tank can be filled in 6 min and emptied in 10 min. If the drain is accidentally left open
when the tank is being filled, how long does it take to fill the tank?
96)
A)
15 min
B)
1
16 min
C)
33
4 min
D)
1
60 min
Add or subtract. Write the answer in lowest terms.
97)
15
13x–6
13x
97)
A)
9
26x
B)
13x
9
C)
9
D)
9
13x
Solve the problem.
98)
The NCAA Division 4 women’s champion for the 400–m dash in 1998 was Sally Sprintalot of World
State University. Her winning time was 4.89 sec. What was her rate in meters per second?
98)
A)
1956.00 m per sec
B)
79.80 m per sec
C)
81.80 m per sec
D)
83.80 m per sec
Simplify the complex fraction.
99)
4
7
3
5
99)
A)
12
35
B)
20
21
C)
21
20
D)
7
12
Add or subtract. Write the answer in lowest terms.
100)
x
x –5+10
x+5–50
x2–25
100)
A)
x +20
x +5
B)
x –20
x –5
C)
1
D)
x +20
x2–25
Simplify the complex fraction.
101)
6
y
4
y +8
101)
A)
3(y +8 )
2y
B)
24y(y +8 )
C)
y +8
24y
D)
2y
3(y +8 )
Find the LCD for the fractions in the list.
102)
–11
k2+ 14k+ 45, 2
k2+ 6k+ 5, –9
k2+ 2k– 15
102)
A)
(k+ 9)(k + 5)(k + 1)
B)
(k+ 9)(k + 5)(k + 1)(k – 3)
C)
(k+ 9)(k + 1)(k – 3)
D)
(k+ 9)(k+ 5)3(k+ 1)(k – 3)
Simplify the complex fraction.
103)
–9
11
2
9
103)
A)
–81
22
B)
–22
81
C)
–2
11
D)
–7
20
Add or subtract. Write the answer in lowest terms.
104)
9
z2–6
z
104)
A)
3(3z + 2)
z2
B)
3(2z – 3)
z
C)
3(3 + 2z)
z2
D)
3(3 – 2z)
z2
Find the LCD for the fractions in the list.
105)
4
x2+ 6x + 5 , 8
x2+ 11x + 30
105)
A)
(x + 5)(x + 6)
B)
(x – 1)(x – 5)(x + 6)
C)
(x + 1)(x + 5)(x + 6)
D)
(x + 1)(x + 5)
106)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) =900
x + 30, what is the
unit cost for 40 units?
106)
A)
$12.86
B)
$0.75
C)
$22.50
D)
–$7.50
107)
An experienced accountant can prepare a certain complexity of tax return in 9 hr. A novice
accountant can do the job in 16 hr. How long will it take them to do the job working together?
107)
A)
1
25 hr
B)
204
7 hr
C)
519
25 hr
D)
1
144 hr
108)
Martha can rake the leaves in her yard in 6 hr. Her brother can do the job in 2 hr. How long will it
take them to do the job working together?
108)
A)
1
12 hr
B)
3 hr
C)
1
8 hr
D)
11
2 hr
Find the numerical value of the rational expression for the given value of x.
109)
(–4x)3
9x + 6 , x = 3
109)
A)
–576
11
B)
–576
7
C)
576
7
D)
576
11
110)
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 3 foot–candles, find the intensity on a screen
15 ft from the light.
110)
A)
2 foot–candles
B)
75
226 foot–candle
C)
11
3 foot–candles
D)
1
3 foot–candle
111)
Frank can type a report in 6 hr. James can type it in 4 hr . How long will it take the two of them
working together?
111)
A)
22
5 hr
B)
12 hr
C)
1
24 hr
D)
1
10 hr
Divide. Write the answer in lowest terms.
112)
6p – 6
p÷7p – 7
5p2
112)
A)
7
30p
B)
30p3– 30p2
7p2– 7p
C)
42p2+ 84p + 42
5p3
D)
30p
7
Solve the problem.
113)
The speed of a stream is 5 mph. If a boat travels 88 mi downstream in the same time that it takes to
travel 44 mi upstream, what is the speed of the boat in still water?
113)
A)
10 mph
B)
15 mph
C)
18 mph
D)
17 mph
114)
x
x2– 16 –3
x2+ 5x + 4
114)
A)
x2– 2
(x – 4)(x + 4)(x +1)
B)
x2– 2x + 12
(x – 4)(x + 4)
C)
x2+ 2x + 12
(x – 4)(x + 4)(x + 1)
D)
x2– 2x + 12
(x – 4)(x + 4)(x + 1)
Multiply or divide as indicated. Write the answer in lowest terms.
115)
x2+8x +15
x2+5x ·5x
x2+6x +9÷x +5
x +3
115)
A)
x +3
x +5
B)
1
x +5
C)
5
x +5
D)
x
x +5
Find any values for which the rational expression is undefined. Write your answer with the symbol
.
116)
x2– 64
x2– 11x + 24
116)
A)
x 0
B)
x –3, –8
C)
x 8, –8
D)
x 3, 8
Find the numerical value of the rational expression for the given value of r.
117)
r2– r +18
r2+ 6r – 7, r =1
117)
A)
0
B)
18
C)
Undefined
D)
18
37
Write the rational expression in lowest terms.
118)
m2+d2
m–d
118)
A)
m+d
B)
–1
C)
m–d
D)
Already in lowest terms
Find all values for which at least one denominator is equal to 0. Write answers using the symbol . Do not solve.
119)
6x + 1
x + 18 =19x + 15
20x + 3
119)
A)
x –1
6, –15
19
B)
x –18, –3
20 , –1
6, –15
19
C)
x 0, –18, –3
20 , –1
6, –15
19
D)
x –18, –3
20
Rewrite the rational expression with the indicated denominator.
120)
5x – 1
x2+4x +16 = ?
x3–64
120)
A)
(x +4)(5x – 1)
x3–64
B)
(x – 1)(5x – 1)
x3–64
C)
(x –4)(5x – 1)
x3–64
D)
(x –16)(5x – 1)
x3–64
Find all values that make the expression undefined.
121)
r– 6
4
121)
A)
–6
B)
6
C)
Never undefined
D)
0
Find the LCD for the fractions in the list.
122)
1
r2+ 10r + 25, 6
r2+ 5r
122)
A)
r(r + 5)2
B)
(r + 5)2
C)
r(r + 5)
D)
r(r + 1)(r + 5)
A
Multiply or divide as indicated. Write the answer in lowest terms.
123)
20s2+ 9st + t2
3s2– 8st – 3t2·2s2– 7st + 3t2
t2+ 4st – 5s2÷8s2– 2st – t2
3s2+ 4st + t2
123)
A)
1
B)
(t + 4s)
(t + s)(t – s)
C)
t + s
t – s
D)
(t + 4s)2(2s – t)2
(4s + t)2(t2– s2)
C
Add or subtract. Write the answer in lowest terms.
124)
1
m – n2+9
n2– m
124)
A)
9
m – n2
B)
8
m – n2
C)
–8
m – n2
D)
10
m – n2
C
C
Solve the variation problem.
125)
The number of gears a machine can make varies directly as the time it operates. If it can make 1870
gears in 13 hr, how many gears can it make in 8 hr?
125)
A)
1891 gears
B)
143.85 gears
C)
0.0556 gears
D)
1150.77 gears
Add or subtract. Write the answer in lowest terms.
126)
6
2r2– 9rs – 5s2–8
6r2– 31rs + 5s2+9
12r2 + 4rs – s2
126)
A)
29r – 43s
(2r + s)(r – 5s)(6r – s)
B)
61r – 59s
(2r + s)(r – 5s)(6r – s)
C)
61r – 43s
(2r + s)(r – 5s)(6r – s)
D)
29r – 59s
(2r + s)(r – 5s)(6r – s)
127)
4
2x –3–6
3–2 x
127)
A)
–10
2x –3
B)
10
2x –3
C)
2
2x –3
D)
–2
2x –3
128)
If x varies inversely as v, and x =12 when v =8, find x when v =16.
128)
A)
x =48
B)
x =6
C)
x =64
D)
x =2
Divide. Write the answer in lowest terms.
129)
3x2
5÷x3
35
129)
A)
21
x
B)
x
21
C)
x5
58
D)
21x2
x3
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
Divide. Write the answer in lowest terms.
131)
x2–81
x÷2x +18
x –9
131)
A)
2(x +9)2
x
B)
2x
(x –9)2
C)
(x –9)2
2x
D)
(x –9)2
x
132)
2
r+5
r – 9
132)
A)
18r – 7
r(9– r)
B)
7r – 18
r(r – 9)
C)
7r – 18
r(9– r)
D)
18r – 7
r(r – 9)
Write the rational expression in lowest terms.
133)
y2– 3y – 28
y2– 4y – 32
133)
A)
–3y – 7
–4y – 8
B)
–3y – 28
–4y – 32
C)
–y2– 3y – 28
y2– 4y – 32
D)
y – 7
y – 8
134)
2t2– 5t –12
3t2– 4t –7·3t2+ 11t –42
t2+ 2t –24
134)
A)
2t + 3
t + 1
B)
(2t + 3)(t +4)
(t + 6)(3t –7)
C)
2t + 3
t – 1
D)
(2t + 3)(t + 6)
(t + 1)(t – 6)
135)
8
r2+4r, –5
8r +32, 1
r2+8r +16
135)
A)
8(r +4)
B)
r(r +4)2
C)
8r(r +4)2
D)
8(r +4)2
136)
13
x – 16 +2
x – 8 = 0
136)
A)
x –16, –8
B)
x 16, 8, 13, 2
C)
x 16, 8
D)
x –16, –8, –13, –2
Add or subtract. Write the answer in lowest terms.
137)
6
8x –2–9
2–8 x
137)
A)
–3
8x –2
B)
3
8x –2
C)
–15
8x –2
D)
15
8x –2
138)
S =a
1 – r for r
138)
A)
r =a
S
B)
r =a
S– 1
C)
r =S – a
S
D)
r = S – a
139)
1
m – 2 –8
m + 2 =11
m2– 4
139)
A)
{–1}
B)
{1, –1}
C)
{1}
D)
140)
2x2
4·24
x3
140)
A)
12x2
x3
B)
12
x
C)
x
12
D)
48x2
4x3
Solve the variation problem.
141)
The gravitational attraction between two masses varies inversely as the square of the distance
between them. If the force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction
when the masses are 6 ft apart?
141)
A)
2 lb
B)
4 lb
C)
1 lb
D)
3 lb
142)
21
q – 4 –5
q – 4
142)
A)
21(q – 4)
5(q – 4)
B)
16
q
C)
26
q – 4
D)
16
q – 4
143)
x
x2– 16 –8
x2+ 5x + 4
143)
A)
x2– 7x + 32
(x – 4)(x + 4)
B)
x2– 7
(x – 4)(x + 4)(x +1)
C)
x2– 7x + 32
(x – 4)(x + 4)(x + 1)
D)
x2+ 7x + 32
(x – 4)(x + 4)(x + 1)
144)
–1
10 –3
6x
144)
A)
–6
30 –6x
B)
3x –15
30x
C)
–3x +15
30x
D)
–3x –15
30x
145)
7
x +6+1
x
145)
A)
7x +6
x(x +6)
B)
8x +6
(x +6)
C)
8x +6
x
D)
8x +6
x(x +6)
146)
Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 162 mi in the same time
that Dana travels 147 mi. If Chuck’s rate of travel is 5 mph more than Dana’s, and they travel the
same length of time, at what speed does Chuck travel?
146)
A)
56 mph
B)
49 mph
C)
52 mph
D)
54 mph
Write the rational expression in lowest terms.
147)
2x – 2y – bx + by
2x – 2y + bx – by
147)
A)
–1
B)
1
C)
2+ b
2– b
D)
2– b
2+ b
Rewrite the rational expression with the indicated denominator.
148)
–6
x2+ 2x= ?
x(x + 2)(x + 3)
148)
A)
–6(x + 3)
x(x + 2)(x + 3)
B)
–6(x – 3)
x(x + 2)(x + 3)
C)
–6
x(x + 2)(x + 3)
D)
–6(x + 2)
x(x + 2)(x + 3)
Find the numerical value of the rational expression for the given value of x.
149)
7– 5x
6x2+ 4x – 1 , x = –3
149)
A)
22
41
B)
22
65
C)
–8
41
D)
–8
65
Solve.
150)
–5 x
2x +2=7x
4x +4+6x –1
x +1
150)
A)
{4}
B)
–4
41
C)
4
41
D)
1
41
Find the LCD for the fractions in the list.
151)
–7
9y , 11
12y
151)
A)
77y
B)
36y
C)
–77y
D)
9y
Find the numerical value of the rational expression for the given value of x.
152)
5x – 1
9x , x = 3
152)
A)
14
27
B)
16
27
C)
52
93
D)
2
27
Add or subtract. Write the answer in lowest terms.
153)
9
3x –7+5
7–3 x
153)
A)
14
3x –7
B)
–14
3x –7
C)
–4
3x –7
D)
4
3x –7
Identify as an equation or an expression.
154)
–3x +2=8x +4
9
154)
A)
Expression
B)
Equation
B
Find all values that make the expression undefined.
155)
z– 2
4– z
155)
A)
4
B)
Never undefined
C)
–4
D)
4, 2
A
Multiply or divide. Write the answer in lowest terms.
156)
5(p – 1)
p÷6(p – 1)
2p2
156)
A)
30p2+ 60p + 30
2p3
B)
5p
3
C)
10p3– 10p2
6p2– 6p
D)
3
5p
B
D
Add or subtract. Write the answer in lowest terms.
157)
x +7y
x2+ 2xy +y2+x – y
x2+8xy +7y2
157)
A)
2x2+14xy +48y2
(x +7y)2(x + y)
B)
2x2+14xy +48y2
(x + y)2(x +7y)
C)
2x2+14xy +48y2
(x + y)(x +7y)
D)
2x2+14xy +48y2
(x + y)3
158)
xy –5x +3y –15
xy +4x +3y +12
158)
A)
y –5
y +4
B)
xy –5x +3y –15
xy +4x +3y +12
C)
y –4
y +5
D)
y +5
y –4
159)
y2– 3y – 10
y2+ 4y – 45
159)
A)
–3y – 10
4y – 45
B)
y + 2
y + 9
C)
–y2– 3y – 10
y2+ 4y – 45
D)
–3y – 2
4y – 9
Solve the problem.
160)
The difference of the reciprocals of two consecutive integers is 1
20. Find the integers.
160)
A)
4 and 5 or –4 and –5
B)
3 and 4 or –3 and –4
C)
5 and 6 or –5 and –6
D)
10 and 11 or –10 and –11
Multiply. Write the answer in lowest terms.
161)
2r –6
18r2+36r·9r +18
12 –4r
161)
A)
–2
4(3 – r)
B)
r – 3
4r(3 – r)
C)
–1
4r
D)
1
4
Write the rational expression in lowest terms.
162)
20k3
5k
162)
A)
15
B)
4k2
C)
4k
D)
15k2
Solve the problem.
163)
A plane flies 500 mi with the wind and 300 mi against the wind in the same length of time. If the
speed of the wind is 23 mph, what is the speed of the plane in still air?
163)
A)
117 mph
B)
97 mph
C)
92 mph
D)
82 mph
Find all values that make the expression undefined.
164)
b –6
6b –18
164)
A)
3
B)
0
C)
18
D)
–6
Solve the variation problem.
165)
The weight of an object on the moon varies directly as its weight on earth. A person who weighs
153 lb on earth weighs 30.6 lb on the moon. How much would a 167–lb person weigh on the moon?
165)
A)
33.4 lb
B)
0.2 lb
C)
350.6 lb
D)
835 lb
Solve the problem.
166)
If m varies directly as p, and m =48 when p =6, find m when p is 3 .
166)
A)
m =9
B)
m =24
C)
m =64
D)
m =36
167)
The area of the rectangle is represented by y2– 7y – 18. What is the length?
y + 2
167)
A)
y + 9
B)
y + 2
C)
y – 2
D)
y – 9
Solve the equation.
168)
–2x
2x +12 =7x
4x +24 +6x –1
x +6
168)
A)
–4
35
B)
1
35
C)
{4}
D)
4
35
Find the LCD for the fractions in the list.
169)
8
p – q , 3
q – p
169)
A)
p – q
B)
p2+q2
C)
p2–q2
D)
q + p
170)
9
20 , –5
6 , 4
30
170)
A)
12
B)
60
C)
20
D)
30
171)
The sum of the reciprocals of two consecutive integers is 19
90. Find the integers.
171)
A)
8 and 9
B)
19 and 20
C)
10 and 11
D)
9 and 10
Provide an appropriate response.
172)
True or false? If a fraction with denominator x + 3 must be written as an equivalent fraction with
denominator (x + 3)2, then the original fraction must be multiplied by x + 3 in both the numerator
and the denominator.
172)
A)
True
B)
False
Solve the formula for the specified variable.
173)
I =kE
R for R
173)
A)
R =I
kE
B)
R =kE
I
C)
R = kE – I
D)
R = kEI
Provide an appropriate response.
174)
True or false? The LCD of the two fractions 1
a and 1
c is ac if the greatest common factor of a and
c is not 1.
174)
A)
True
B)
False
Write the rational expression in lowest terms.
175)
z3+64
z3–4z2+16z
175)
A)
z +16
z
B)
z –4
z
C)
z –4
4
D)
z +4
z
176)
a2–b2–4a +4b
3a +3b –12
176)
A)
a +b
12
B)
b –a
3
C)
a2–b2
12
D)
a –b
3
177)
True or false? If xa and xb are denominators of two fractions and a>b, then xa is the LCD.
177)
A)
True
B)
False
178)
A boat goes 720 mi downstream in the same time it can go 640 mi upstream. The speed of the
current is 9 mph. Find the speed of the boat in still water.
178)
A)
136 mph
B)
144 mph
C)
162 mph
D)
153 mph
179)
PV
T=pv
t for P
179)
A)
P =pvV
tT
B)
P =tvT
pV
C)
P =pvT
tV
D)
P =pv
tTV
Find the LCD for the fractions in the list.
180)
3
30, 7
18
180)
A)
18
B)
45
C)
30
D)
90
Multiply or divide as indicated. Write the answer in lowest terms.
181)
5r –15
16r2+32r·8r +16
30 –10r
181)
A)
–5
4(3 – r)
B)
r – 3
4r(3 – r)
C)
1
4
D)
–1
4r
Solve the equation.
182)
7x
2+ x =8
182)
A)
16
7
B)
28
C)
16
9
D)
56
9
183)
x
x + 3 =?
5x + 15
183)
A)
5
5x + 15
B)
3x
5x + 15
C)
x
5x + 15
D)
5x
5x + 15
Find the numerical value of the rational expression for the given value of r.
184)
8r + 5
5r2+ 3r + 1 , r = –4
184)
A)
37
69
B)
–37
69
C)
–27
91
D)
–9
23
Solve the equation.
185)
x – 2
x –9=10
9– x
185)
A)
{–12}
B)
{12}
C)
{–8}
D)
{8}
186)
The time necessary to make an enlargement of a photo negative varies directly as the area of the
enlargement. If 120 sec are required to make a 3×5 enlargement, find the time required for a 4×6
enlargement.
186)
A)
192 sec
B)
240 sec
C)
216 sec
D)
168 sec
187)
The weight of a liquid varies directly as its volume. If the weight of the liquid in a cubical container
3 cm on a side is 81 g, find the weight of the liquid in a cubical container 5 cm on a side.
187)
A)
375 g
B)
15 g
C)
110 g
D)
125 g
Add or subtract. Write the answer in lowest terms.
188)
2
r+5
r – 9
188)
A)
18r – 7
r(r – 9)
B)
7r – 18
r(r – 9)
C)
7r – 18
r(9– r)
D)
18r – 7
r(9– r)
Find all values that make the expression undefined.
189)
x2– 81
x2– 7x + 12
189)
A)
0
B)
9, –9
C)
–4, –3
D)
4, 3
Find the LCD for the fractions in the list.
190)
–2
n –8 , 5
8– n
190)
A)
n2+ 64
B)
8– n
C)
n + 8
D)
n2– 64
Add or subtract. Write the answer in lowest terms.
191)
8
4– m +5
m –4
191)
A)
13
4– m
B)
3
4– m
C)
40
4– m
D)
–3
4– m
Write the rational expression in lowest terms.
192)
y2+ 9y + 14
y2+ 13y + 42
192)
A)
–y2+ 9y + 14
y2+ 13y + 42
B)
y + 2
y + 6
C)
9y + 14
13y + 42
D)
9y + 1
13y + 3
Solve the problem.
193)
One maid can clean the house in 8 hr. Another maid can do the job in 4 hr. How long will it take
them to do the job working together?
193)
A)
8 hr
B)
1
12 hr
C)
22
3 hr
D)
1
32 hr
C
Find all values that make the expression undefined.
194)
7
a+ 9
194)
A)
Never undefined
B)
–9
C)
0
D)
9
B
Multiply or divide as indicated. Write the answer in lowest terms.
195)
3(k –8)2
15(k +8) ·5(k +8)2
9(k –8)
195)
A)
5(k –8)
(k +8)
B)
(k +8)2
9
C)
(k +8)(k –8)
9
D)
15(k +8)
(k –8)
C
B
Determine whether the situation or equation represents direct or inverse variation.
196)
The cross–sectional area of a tree and its age
196)
A)
Direct
B)
Inverse
197)
y =5
x3
197)
A)
Direct
B)
Inverse
Solve the problem involving direct or inverse variation.
198)
If x varies inversely as y2, and x =2 when y =8, find x when y =2.
198)
A)
x =8
B)
x =16
C)
x =32
D)
x =4
Solve the equation.
199)
2
t=t
–3t – 4
199)
A)
{0, 4}
B)
{–2, –4}
C)
{0, 16}
D)
Add or subtract. Write the answer in lowest terms.
200)
3–4y
40 –8–4y
72
200)
A)
–56y – 13
360
B)
–16y – 13
360
C)
–56y + 67
360
D)
–16y + 67
360
Multiply. Write the answer in lowest terms.
201)
2z3
3·12
z2
201)
A)
8z2
z3
B)
8
z
C)
z
8
D)
8z
Provide an appropriate response.
202)
Which of the following complex fractions is equivalent to
3–1
5
8–3
5
?
202)
A)
–3–1
5
–8–3
5
B)
–3+1
5
8–3
5
C)
–3+1
5
–8+3
5
D)
3+1
5
8+3
5
Multiply or divide as indicated. Write the answer in lowest terms.
203)
y3– 2y
y2– 4 ÷y2+ 6y – 27
y2+ 11y + 18
203)
A)
y
y – 3
B)
(y + 2)(y + 3)
y(y2– 2)
C)
y(y2– 2)
(y – 2)(y – 3)
D)
(y – 2)(y – 3)
y(y2– 2)
Solve the problem.
204)
Mara can type 2205 words in 3
4 hr (45 minutes). How many words per minute can she type?
204)
A)
1654 words per min
B)
65 words per min
C)
37 words per min
D)
49 words per min
Solve the equation.
205)
15
x=8–1
x
205)
A)
{1}
B)
{2}
C)
4
7
D)
15
8
Write the rational expression in lowest terms.
206)
8x +10
12x +15
206)
A)
2
3
B)
2
C)
3
2
D)
1
Find the numerical value of the rational expression for the given value of x.
207)
4x + 2
3x2– 2x – 4 , x = –4
207)
A)
9
26
B)
–7
22
C)
–7
26
D)
–9
26
Find the LCD for the fractions in the list.
208)
2
15r9s , 9
10r3s4
208)
A)
30r9s
B)
30r12s5
C)
30r3s4
D)
30r9s4
Determine whether the situation or equation represents direct or inverse variation.
209)
The ability of a truck to climb hills and the weight of its cargo
209)
A)
Direct
B)
Inverse
Solve the problem.
210)
The speed of a stream is 4 mph. If a boat travels 64 mi downstream in the same time that it takes to
travel 32 mi upstream, what is the speed of the boat in still water?
210)
A)
14 mph
B)
12 mph
C)
8 mph
D)
15 mph
211)
A boat can go 102 mph in still water. It takes as long to go 560 mi upstream as it does to go
downstream 630 mi. How fast is the current?
211)
A)
1 mph
B)
5 mph
C)
6 mph
D)
7 mph
212)
A man rode a bicycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5
hr. If his biking rate was 10 mph faster than his hiking rate, what was each rate?
212)
A)
Biking: 13 mph; hiking: 3 mph
B)
Biking: 14. mph; hiking: 4.5 mph
C)
Biking: 12 mph; hiking: 2 mph
D)
Biking: 11.5 mph; hiking: 1.5 mph
213)
One maid can clean the house in 2 hr. Another maid can do the job in 8 hr. How long will it take
them to do the job working together?
213)
A)
1
10 hr
B)
13
5 hr
C)
22
3 hr
D)
1
16 hr
Solve the equation.
214)
4
x –1+4
2x –2=6
214)
A)
{2}
B)
{1}
C)
{0}
D)
{24}
Solve the problem.
215)
One printer can do a printing job in 4 hr. Another printer can do the same job in 14 hr. How long
does it take the two printers to do the job working together?
215)
A)
53
5 hr
B)
1
18 hr
C)
31
9 hr
D)
218
19 hr
Find the LCD for the fractions in the list.
216)
4
m2– 5m , 9
m2– 8m + 15
216)
A)
m(m – 5)(m – 3)
B)
(m – 2)2
C)
m(m – 2)2
D)
m(m – 2)(m – 3)
Solve the problem.
217)
In a certain fraction, the numerator is 4 less than the denominator. If 4 is added to both the
numerator and the denominator, the resulting fraction is equal to 8
12. What was the original
fraction (not necessarily written in lowest terms)?.
217)
A)
8
12
B)
4
8
C)
8
4
D)
12
8
Determine whether the situation or equation represents direct or inverse variation.
218)
y =6x2
218)
A)
Direct
B)
Inverse
Multiply or divide. Write the answer in lowest terms.
219)
2t2– 3t –9
3t2– 3t –6·3t2+ 12t –36
t2+ 3t –18
219)
A)
2t + 3
t – 1
B)
(2t + 3)(t +3)
(t + 6)(3t –6)
C)
(2t + 3)(t + 6)
(t + 1)(t – 6)
D)
2t + 3
t + 1
Solve the problem.
220)
The sum of an integer and its reciprocal is 65
8. Find the integer.
220)
A)
9
B)
8
C)
65
D)
7
Provide an appropriate response.
221)
If the rational expression 9x9y6
7p9q represents the area of a rectangle and 7x8y4
p8 represents the
length of the rectangle, what rational expression represents the width?
221)
A)
9x9y6
p13q
B)
9xy2
14pq
C)
9x9y6
49p13q
D)
9xy2
49pq
Solve the variation problem.
222)
The weight of a body above the surface of the earth is inversely proportional to the square of its
distance from the water of the earth. What is the effect on the weight when the distance is
multiplied by 2?
222)
A)
The weight is multiplied by 4.
B)
The weight is divided by 4.
C)
The weight is divided by 2.
D)
The weight is multiplied by 2.
Add or subtract. Write the answer in lowest terms.
223)
5x
x +5+1
x –5
223)
A)
5x +1
(x +5)(x –5)
B)
5x2– 24x +5
x2+10x +25
C)
5x2– 24x +5
x2–25
D)
5x2– 24x +5
x2–10x +25
224)
8a + 6b
2 –8a – 6b
2
224)
A)
36b
B)
0
C)
6b
D)
8a
Multiply. Write the answer in lowest terms.
225)
4p – 4
p·4p2
5p – 5
225)
A)
16p3– 16p2
5p2– 5p
B)
16p
5
C)
20p2+ 40p + 20
4p3
D)
5
16p
Solve the problem.
226)
The amount of time it takes a swimmer to swim a race varies inversely as the average speed of the
swimmer. A swimmer finishes a race in 50 seconds with an average speed of 3 feet per second. Find
the average speed of the swimmer if it takes 25 seconds to finish the race.
226)
A)
7 ft/sec
B)
8 ft/sec
C)
5 ft/sec
D)
6 ft/sec
Simplify the complex fraction.
227)
4
k +6–1
k –8
3
k –8+2
k +5
227)
A)
(3k –38)(k +5)
(k +6)(5k – 1)
B)
(3k –38)
(k +6)(5k – 1)
C)
(3k –38)(k –5)
(k –6)(5k – 1)
D)
(3k –38)(k +5)
(k +6)(5k + 1)
Multiply or divide as indicated. Write the answer in lowest terms.
228)
z2+ 12z + 32
z2+ 13z + 40 ÷z2+ 4z
z2+ 12z + 35
228)
A)
z + 7
B)
z
z2+ 13z + 40
C)
z + 7
z2+ 5z
D)
z + 7
z
Solve the problem.
229)
Tom Quig traveled 250 mi east of St. Louis. For most of the trip he averaged 70 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 7 hr,
how many miles did he drive at the reduced speed?
229)
A)
50 mi
B)
60 mi
C)
40 mi
D)
35 mi
Write the rational expression in lowest terms.
230)
8– m
m – 8
230)
A)
–1
B)
–m
C)
1
D)
Already in lowest terms
Rewrite the rational expression with the indicated denominator.
231)
5
2x = ?
6x2
231)
A)
5x2
6x2
B)
15
6x2
C)
5
6x2
D)
15x
6x2
D
Provide an appropriate response.
232)
In the given problem 25(y + 6)
5(y – 8)÷?
(y – 8)(y + 1)=5(y + 1)
(y – 6), what must be the factors that are
represented by the question mark?
232)
A)
(y + 1)2(y – 8)2
(y – 6)(y + 6)
B)
(y – 6)2
C)
25(y + 6)
(y – 6)(y – 8)2
D)
(y + 6)(y – 6)
D
Add or subtract. Write the answer in lowest terms.
233)
4x
x +4+1
x –4
233)
A)
4x2– 15x +4
x2+8x +16
B)
4x2– 15x +4
x2–8x +16
C)
4x +1
(x +4)(x –4)
D)
4x2– 15x +4
x2–16
D
A
Solve the formula for the specified variable.
234)
2x +9
z=3
y for z
234)
A)
z =9y
3– 2x
B)
z =–9y
2x – 3
C)
z =3– 2xy
9y
D)
z =–9y
2xy – 3
Add or subtract. Write the answer in lowest terms.
235)
3y2
y – 1 +–3y
y – 1
235)
A)
3y
B)
0
C)
3y
y – 1
D)
3y(y + 1)
y – 1
236)
4
y2– 3y + 2 +6
y2– 1
236)
A)
48y – 8
(y – 1)(y + 1)(y – 2)
B)
10y – 8
(y – 1)(y – 2)
C)
8y – 10
(y – 1)(y + 1)(y – 2)
D)
10y – 8
(y – 1)(y + 1)(y – 2)
Rewrite the rational expression with the indicated denominator.
237)
4(x +3)
x(x –6) =?
x3–11x2+30x
237)
A)
(x +3)(x –5)
x3–11x2+30x
B)
4(x +3)(x +5)
x3–11x2+30x
C)
4(x +3)(x –5)
x3–11x2+30x
D)
4(x +3)(x –4)
x3–11x2+30x
Multiply or divide. Write the answer in lowest terms.
238)
x2+ 4x + 4
x2– 9 ·x – 3
x + 2
238)
A)
x + 2
x + 3
B)
x + 2
(x + 3)2
C)
x – 2
x + 3
D)
x + 2
x – 3
Solve the problem involving direct or inverse variation.
239)
If m varies directly as p, and m =36 when p =9, find m when p is 8 .
239)
A)
m =81
B)
m =32
C)
m =64
D)
m =16
Write the rational expression in lowest terms.
240)
tx + t +2x +2
6x +6
240)
A)
t +2
6
B)
t –2
6
C)
t –6
2
D)
t +6
6
Find the LCD for the fractions in the list.
241)
5
t , 4
t – 3
241)
A)
t
B)
t – 3
C)
t(t – 3)
D)
20
Add or subtract. Write the answer in lowest terms.
242)
3
x –9+6
9– x
242)
A)
–3
x –9
B)
18
x –9
C)
3
x –9
D)
9
x –9
Solve the equation.
243)
x
x –5–5=5
x –5
243)
A)
{–5}
B)
{5}
C)
–5
4
D)
Find the least common denominator for the fractions in the list.
244)
–1
10x5, 1
18x4, –3
45x2
244)
A)
90x5
B)
45x20
C)
18x2
D)
30x5
245)
The number of errors that a rookie makes as a fielder and the probability that he will remain a
starting player
245)
A)
Direct
B)
Inverse
Solve the equation.
246)
6
m +3–5
m –3=–36
m2–9
246)
A)
{–3}
B)
{6}
C)
{3}
D)
Solve the formula for the specified variable.
247)
P =A
1 + rt for r
247)
A)
r = P – tA
B)
r =A – P
Pt
C)
r =P – 1
At
D)
r =P – A
1 + t
Solve the problem.
248)
The winner of the 1998 Peoria 500 (mile) race was Serge Bologna, with an average rate of 185.299
mi per hr. What was his time (to the nearest thousandth of an hour)?
248)
A)
2.919 hr
B)
0.299 hr
C)
12.698 hr
D)
2.698 hr
Add or subtract. Write the answer in lowest terms.
249)
m2– 11m
m – 6 +30
m – 6
249)
A)
m2– 11m + 30
m – 6
B)
m – 6
C)
m + 5
D)
m – 5
Find the LCD for the fractions in the list.
250)
13
16y5 , 19
20y2
250)
A)
80y7
B)
16y5
C)
19y7
D)
80y5
Solve the problem.
251)
Find an expression that represents the perimeter of the rectangle. Give the simplified form.
15k + 21
4
3
5k + 7
251)
A)
9
4
B)
75k2+ 210k + 159
2(5k + 7)
C)
75k2+ 210k + 159
4(5k + 7)
D)
75k2+ 210k + 147
2(5k + 7)
Solve the equation.
252)
6
y + 5 –8
y – 5 =2
y2– 25
252)
A)
{–36}
B)
{72}
C)
{36}
D)
253)
The frequency that you brush your teeth and the length of time that you retain all your teeth
253)
A)
Inverse
B)
Direct
254)
If one form of the correct answer of a difference of two rational expressions is 11
k –4, what would
be an alternate form of the answer if the denominator is 4– k?
254)
A)
–11
k +4
B)
11
k –4
C)
–11
4– k
D)
11
k +4
Solve the problem.
255)
A machine can fill 3580 boxes of cereal in 0.4 hour. How many boxes of cereal can it fill per hour?
255)
A)
8950 boxes per hr
B)
1432 boxes per hr
C)
3580 boxes per hr
D)
7160 boxes per hr
Solve the equation.
256)
7x
5+ 2 =1
5
256)
A)
12
5
B)
–9
7
C)
5
7
D)
–7
5
Write the rational expression in lowest terms.
257)
–20x3y5
5xy2
257)
A)
–4x2y3
B)
–4xy3
C)
–15x2y2
D)
–4x2y2
Simplify the complex fraction.
258)
x7
5y8
x3
y4
258)
A)
x4
y4
B)
x4
5y12
C)
x4
5y4
D)
x10
5y12
Multiply or divide as indicated. Write the answer in lowest terms.
259)
t – 7
t2– 5t –14 ·t + 2
t2–14t +49
259)
A)
(t – 7)
(t –7)(t –7)(t + 7)
B)
1
(t –7)(t –7)
C)
–1
7(t +7)
D)
t
(t +7)(t +7)
Multiply or divide. Write the answer in lowest terms.
260)
z2+ 7z + 10
z2+ 10z + 16 ÷z2+ 5z
z2+ 3z – 40
260)
A)
z – 5
z
B)
z – 5
z2+ 8z
C)
z – 5
D)
z
z2+ 10z + 16
Write the rational expression in lowest terms.
261)
x3–64
x2+4x +16
261)
A)
x +16
B)
x –16
C)
x –4
D)
x +4
262)
pq –2p +3q –6
qr +5q –2r –10
262)
A)
p +3
r +5
B)
pq –2p +3q –6
qr +5q –2r –10
C)
p +3
q –5
D)
p –3
r +5
Find all values for which at least one denominator is equal to 0. Write answers using the symbol . Do not solve.
263)
15
16x–2
11x=x
6
263)
A)
x 16, 11
B)
x 0
C)
x 16, 11, 6
D)
x 0, 16, 11
264)
1
a+ 1
1
a– 1
264)
A)
a
1 – a2
B)
1 – a2
C)
1 + a
1 – a
D)
1
C
265)
5
4z
265)
A)
0.25
B)
4
C)
0
D)
Never undefined
C
266)
x
10 +9
5=x – 5
5
266)
A)
{14 }
B)
{28 }
C)
{23 }
D)
{19 }
B
B
Solve the formula for the specified variable.
267)
1
x–1
y+1
z= 5 for x
267)
A)
y =xz
5yz + z –x
B)
z =xy
5xy + y –x
C)
x =5yz
yz + z –y
D)
x =yz
5yz + z –y
268)
1
45x2 , 9
5x3
268)
A)
5x3
B)
45x2
C)
45x5
D)
45x3
269)
The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If
an object with a mass of 4 kg stretches a spring 25 cm, find the stretch when the object has a mass of
15 kg.
269)
A)
44 cm
B)
4.15 cm
C)
2.4 cm
D)
93.75 cm
270)
7
n , –5
2+ n , 4
2– n
270)
A)
n(2+ n)(2– n)
B)
n + 2
C)
n2+ 4
D)
4n2
271)
8x –2
x +9–x
8+9
271)
A)
Expression
B)
Equation
272)
If s varies directly as t2, and s =567 when t =9, find s when t is 8 .
272)
A)
s =72
B)
s =63
C)
s =504
D)
s =448
273)
2x + 3
10x2+ 19x + 6
273)
A)
2x + 3
10x2+ 19x + 6
B)
1
5x + 2
C)
2x
5x + 2
D)
2x + 5
5x + 19
274)
P =A
1 + rt for t
274)
A)
t= P –rA
B)
t=P – A
1 +r
C)
t=P – 1
Ar
D)
t=A – P
Pr
275)
m2– 11m
m – 6 +30
m – 6
275)
A)
m2– 11m + 30
m – 6
B)
m – 5
C)
m + 5
D)
m – 6
Solve the problem.
276)
Find an expression that represents the area of the rectangle. Give the simplified form.
10p – 6
5
3
5p – 3
276)
A)
5
6
B)
3
5
C)
6
5
D)
2
5
Multiply or divide as indicated. Write the answer in lowest terms.
277)
b3–8a3
4a3+4a2b+ ab2÷4a2+2ab +b2
–a3– ab3
277)
A)
b3–a2
2a + b
B)
–(b–2a)
(2a + b)2(a2+b3)
C)
–a2–b3
2a + b
D)
–(b –2a)(a2+b3)
(2a + b)2
278)
5a –5b –a2+b2
9a2–6ab +b2·9a2–b2
3a2– 2ab –b2
278)
A)
5– a – b
B)
3a – b
5– a – b
C)
5+ a + b
3a – b
D)
5– a – b
3a – b
Add or subtract. Write the answer in lowest terms.
279)
5
15x+3
15x
279)
A)
8
15x
B)
1
C)
8
30x
D)
15x
8
Find the LCD for the fractions in the list.
280)
7
x2 , 9
x7
280)
A)
2x2
B)
x2
C)
9x7
D)
x7
Multiply or divide as indicated. Write the answer in lowest terms.
281)
4x2– 7xy – 2y2
y2+ 4xy – 5x2·y2+ 2xy – 3x2
8x2+ 6xy + y2÷3x2– 5xy – 2y2
10x2+ 3xy – y2
281)
A)
(y + 3x)2
2x – y
B)
1
C)
5x – y
5x + y
D)
x – 2y
y + 5x
282)
A quantity, 2
3 of it, 1
2 of it, and 1
7 of it, added together, equals 37. What is the quantity?
282)
A)
1554
97
B)
42
97
C)
3589
42
D)
97
42
Multiply or divide as indicated. Write the answer in lowest terms.
283)
25x2–9
x2–1÷5x + 3
x – 1
283)
A)
x + 1
5x – 3
B)
5x – 3
x + 1
C)
5x + 3
x – 1
D)
(5x + 3)(25x2–9)
(x2– 1)(x – 1)
Solve the problem.
284)
A jet plane traveling at a constant speed goes 1200 mi with the wind, then turns around and travels
for 1000 mi against the wind. If the speed of the wind is 50 mph and the total flight took 4 hr, find
the speed of the plane.
284)
A)
550 mph
B)
435 mph
C)
605 mph
D)
525 mph
Solve the equation.
285)
6
m + 5 = 1 –1
m – 5
285)
A)
{1, 5}
B)
{0, 7}
C)
{0, –5}
D)
Write the rational expression in lowest terms.
286)
m2– 9m
9– m
286)
A)
–(m + 3)
B)
m + 3
C)
–m
D)
m
287)
y2+ 4y – 21
y2+ 3y – 28
287)
A)
–y2+ 4y – 21
y2+ 3y – 28
B)
4y – 3
3y – 4
C)
y – 3
y – 4
D)
4y – 21
3y – 28
Divide. Write the answer in lowest terms.
288)
3r –9s
8r –16s÷12s –4r
2r – 4s
288)
A)
16
3
B)
–16
3
C)
–1
16
D)
–3
16
Find the LCD for the fractions in the list.
289)
8
8a + 64 , 9
a2+ 8a
289)
A)
8a2+ 8
B)
8a(a + 8)
C)
8a + 8
D)
8a2+ 64
Add or subtract. Write the answer in lowest terms.
290)
5m
m – 6 +–30
m – 6
290)
A)
0
B)
5
m – 6
C)
5(m + 6)
m – 6
D)
5
Provide an appropriate response.
291)
True or false? If e is a multiple of d, then the LCD for 1
e and 1
d is ed.
291)
A)
True
B)
False
292)
b
b2– 25 +5
b + 5 –6
b
292)
A)
6b2– 25b + 150
b(b + 5)(b – 5)
B)
25(b – 6)
(b + 5)(b – 5)
C)
25(b + 6)
b(b + 5)(b – 5)
D)
–25(b – 6)
b(b + 5)(b – 5)
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7