Download 1) Rationalize the denominator and simplify. 7 175 7 25 7 5 175 5

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
1)
Rationalize the denominator and simplify.
7
175
A)
2)
3)
B)
7
5
175
5
C)
D)
175
25
2)
Identify the pair of like radicals.
3 2
y
A)
-5
C)
4 3
x
and
and
3
2 y2
4 2
x
B)
5t and 3 8t
D)
m m and 5 m
3
3)
Use the multiplication property of radicals to simplify the expression.
38
A)
4)
7
25
3 12
B) 2
C)
19
4 9
D)
38
Simplify the expression using the properties of rational exponents. Assume the variables
represent positive real numbers.
x-4/3
4)
12
y-3/4
A)
5)
6)
x16
y9
B)
y9
C)
x16
D)
y6
y6
x8
5)
Evaluate the square root, if possible.
0.81
A) not a real number
C) -0.9
B) 0.9
D)
0.9 and -0.9
6)
Identify the pair of like radicals.
3
A) 7 and 7
C)
x8
B) -3
D)
- 20 and 8 5
1
32 and 5 48
8 and 16
7)
7)
Solve the equation.
6t = 36t2 + 7t - 20
8)
A)
no solution
C)
t=
B) t =
7
20
D)
20
7
t = 6 and t = -6
Simplify the expression. Assume the variable represents a positive real number.
8)
x24
A) x12
C) x23
B) x
D) x2
9)
How tall is a radio tower if a 100 foot cable anchored to the ground 30 feet from its base
reaches the top of the tower when taut? Round your answer to one decimal place.
A) 104.4 feet
B) 70 feet
C) 95.4 feet
D) 81 feet
9)
10)
The total number of people, P, in one city that have fallen for a telemarketing scam is
approximated by the formula
P = 1,200 + 11,300x
where x is the number of days since a newspaper article exposed the scam. How many
additional people fell for the scam the first day after the article? Round your answer to
the nearest integer.
A) 1,306
B) 241
C) 1,200
D) 106
10)
11)
Use the multiplication property of radicals to simplify the expression.
184
11)
A)
12)
C)
2 92
D)
2 46
Write the expression using rational exponents rather than radical notation. Assume the
variables represent positive real numbers.
3
A)
13)
B) 14
4 46
12)
(-3ab)5
(-3ab)3/5
B) -3ab5/3
C)
-3ab3/5
D)
(-3ab)5/3
Translate the sentence into an equation.
The product of 5 and the difference of 13 and the cube root of a number is 17.
3
A)
5(13 -
C)
5(13 - x)3 = 17
B) 5
x) = 17
D)
2
3
x - 13 = 17
5 3 13 - x = 17
13)
14)
14)
The annual rate of return, r, on an initial investment of P dollars is given by
A 1/t
r=
-1
P
where A is the current value and t is the number of years since the money was invested.
Find the annual rate of return on a $31,000 investment that grew to $41,000 after 10
years. Write your answer as a percent, and round to two decimal places.
A) 3.04%
B) 2.84%
C) 0.03%
D) 2.6%
15)
3
A)
16)
168
8 3 21
B) 2
3
C)
42
2 3 21
D)
8 3 84
16)
Solve the equation.
3
A)
17)
15)
Simplify the cube root.
-2z + 3 -
z=
3
z + 20 = 0
111
4
B) z =
-
17
3
C)
z = -1, z =
2
3
D)
z=-
3
13
17)
Simplify the cube root.
3
3
29
64
24,389
A)
4
B) 3
3
29
64
C)
29
4
D)
29
4
18)
Multiply the expressions. Assume the variable represents a positive real number.
6(2 x + x 15)
A) 2 6x + x 15
B) 2 6x + 3x 10
C) 12 x + 3x 10
D) (2 + x) x + 90
18)
19)
Add the expressions, if possible.
20 10 + 10 10
A) 30 10
B) 30 20
19)
20)
C)
60 10
D)
200 10
Multiply the expressions. Assume the variables represent positive real numbers.
4 6x6 y3 2 10xy6
A)
16x3 y4 15xy
B) 16
15x7 y9
C)
3
32x3 y4 15xy
D)
32xy x5y7
20)
21)
22)
23)
Find the value of n so that the expression is a perfect square trinomial and then factor the
trinomial.
x2 + 10x + n
A)
n = 25; (x + 5)2
B) n
C)
n = 25; (x + 5)(x - 5)
D)
= 100; (x + 10)2
n = 25; (x - 5)2
22)
Choose any method to solve the quadratic equation.
6y + 3 = -4y2
A)
2 + 3, 2 - 3
C)
-
B) -
9 1
,
2 3
D)
105 1
105
1
+
,- 4
12
4
12
There are no real-valued solutions.
23)
Solve the equation by using the quadratic formula.
17y - 6 + 39y2 = 0
3 13
1 2
A) ,
B) ,
2 3
3 5
C)
D)
There are no real-valued solutions.
21)
-
2 3
,
3 13
24)
Determine the domain and range of the relation.
{(2, 1), (9, 6), (3, 7), (-8, 4), (9, 9), (3, 4)}
A) Domain {2, 9, 3, -8); range {1, 6, 7, 4, 9, 4}
B) Domain {2, 9, 3, -8}; range {1, 6, 7, 4, 9}
C) Domain {2, 9, 3, -8, 9, 3}; range {1, 6, 7, 4, 9, 4}
D) None of the above
24)
25)
Solve the equation by using the quadratic formula.
x2 + 7x + 2 = 0
-7 ± 41
-7 ± 47
A)
B)
C) -7 ± 47
2
2
25)
26)
D)
-7 ± 41
Find the value of n so that the expression is a perfect square trinomial and then factor the
trinomial.
j2 - 6j + n
A)
n = 9; (j - 3)2
B) n
C)
= 9; (j - 3)
4
n = 3; (j - 3)2
D)
n = 3; (j + 3)2
26)
27)
A)
28)
27)
Solve the equation by using the square root property.
22 1
a=
5
25
3
5
B)
1
5
C)
1 1
,5 5
D)
1 3
,
5 5
A model rocket is launched from a raised platform at a speed of 128 feet per second. Its
height in feet is given by
y = -16t2 + 128t + 20 (t = seconds after launch).
28)
a. After how many seconds does the object reach its maximum height?
b. What is the maximum height reached by the rocket?
A) a. 6 seconds;
B) a. 8 seconds;
C) a. 2 ;
D) a. 4 seconds;
b. 212 ft
b. 20 ft
b. 212 ft
b. 276 ft
29)
Solve the equation by using the square root property.
t2 = -144
A) ±12
B) 13
C) There are no real-valued solutions.
D) 12
29)
30)
Solve the equation by using the square root property.
(x + 3)2 = 3
30)
A)
31)
32)
3± 3
D)
± 6
31)
B) -12
D)
not a real number
Convert the expression to radical notation. Assume the variable represents a positive real
number.
18z2/3
3
18 z2
B)
3
18z2
C)
2
18 z3
D)
3
5 - x2
B)
5 + x2
C)
5 + x2
D)
-3 10
B) 7
33)
5 - x2
34)
Subtract the expressions, if possible.
2 10 - 5 10
A)
32)
(18z)2
Multiply the radical expressions. Assume the variable represents a positive real number.
( 5 + x)( 5 - x)
A)
34)
C)
± 3
What is the principal square root of 144?
A) 12
C) -12 and 12
A)
33)
B) -3
±6
C)
10
5
-6 10
D)
2 10 - 5 10
35)
Simplify the expression. Assume the variable represents a positive real number.
16y32
-4
81
A)
36)
37)
38)
-
4y28
9
B)
2y8
3
C)
4y28
9
D)
-
35)
2y8
3
36)
Solve the equation by using the quadratic formula.
4 1
- = x - 5x2
3 6
A)
161
1
±
10
10
B) -
C)
There are no real-valued solutions.
D)
1 8
,
2 15
-8,
9
30
37)
Find the vertex of the parabola.
y = -2x2 + 16x - 3
A) (16, -3)
B) (4, 29)
C)
(0, -3)
D)
(-2, 13)
38)
Evaluate the root, if possible.
4
256
A) not a real number
C) -4
39)
40)
B) 4
D)
4 and -4
39)
Find the vertex of the parabola.
y = 5x2 + 10
A) (0, 10)
B) (10, 0)
C)
(5, 10)
D)
(-10, 0)
Use the division property of radicals, if necessary, to simplify the expression. Assume the 40)
variable represents a positive real number.
4t
t5
A)
2
t2
B)
2
C)
t2
6
2
t4
D)
2
t4
Answer Key
Testname: TEST4PRACTICE
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
B
A
D
B
B
C
B
A
C
D
D
D
A
B
C
B
C
B
A
A
A
D
D
B
A
A
D
D
C
B
A
A
A
A
D
B
B
B
A
B
7