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Name
Class
6-2
Date
Standardized Test Prep
Multiplying and Dividing Radical Expressions
Multiple Choice
For Exercises 1−5, choose the correct letter. Assume that all variables are
positive.
3
3
1. What is the simplest form of !
249x ? "
7x2 ?
7x !7x
27x
7x
3 2
27"
x
4"5x7y6
4x3y3 !5x
3
15xy!
y
5xy !15x
5x !x
2y
5x2y
2
2. What is the simplest form of "80x7y6 ?
2x3y3 !20x
4x6y6"5x3
3
3
3. What is the simplest form of " 25xy2 ? " 15x2 ?
3
5x"
3y2
3
5x !
3y
4. What is the simplest form of
5"3x4
2"3y2
"75x5
?
"12xy2
5x2
2y
3
2"x2y
5. What is the simplest form of 3
?
"4xy2
3
"x2y
2y
3
3
"2xy2
y
x !2y
y
3
!2y
xy
Short Response
6. The volume V of a wooden beam is V 5 ls2, where l is the length of the beam
and s is the length of one side of its square cross section. If the volume of the
beam is 1200 in.3 and its length is 96 in., what is the side length? Show your
work.
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17
Name
Class
6-3
Date
Standardized Test Prep
Binomial Radical Expressions
Multiple Choice
For Exercises 1−5, choose the correct letter.
1. What is the simplest form of 2!72 2 3 !32?
2 !72 2 3 !32
24 !2
22 !2
0
2. What is the simplest form of A2 2 !7B A1 1 2 !7B?
212 1 3 !7
16 1 5 !7
212 2 3 !7
3 1 !7
3. What is the simplest form of A !2 1 !7B A !2 2 !7B?
9 1 2 !14
9 2 2 !14
4. What is the simplest form of
214 1 7 !5
25
7
?
2 1 !5
9
214 2 7 !5
14 1 7 !5
14 2 7 !5
3
3
3
5. What is the simplest form of 8!5 2 !40 2 2 !135?
3
16 !
5
3
12 !
5
3
4!
5
0
Short Response
6. A hiker drops a rock from the rim of the Grand Canyon. The distance it falls d
in feet after t seconds is given by the function d 5 16t2 . How far has the rock
fallen after (3 1 !2) seconds? Show your work.
Prentice Hall Algebra 2 • Teaching Resources
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27
Name
Class
Date
Standardized Test Prep
6-4
Rational Exponents
Multiple Choice
For Exercises 1−5, choose the correct letter.
1
1
1
1. What is 123 ? 453 ? 503 in simplest form?
!27,000
1
1
30
1073
27,000
3
"
(xy)2
3 2
"
xy
2
2. What is x3 ? y3 in simplest form?
x3"y3
1
"xy3
1
1
3. What is x3 ? x2 ? x4 in simplest form?
13
1
x 12
2 1
4. What is £
1
x 24
5
x9
x 24
1
x
5
xy 2
y2
6
x3y3
1 3≥
in simplest form?
x2y4
5
5
x 7y 2
xy 2
5
1
5. What is (232x10 y35)25 in simplest form?
2x2y7
2
2 2 7
x y
2
1
2x2 y7
2
x2 y7
Short Response
6. The surface area S, in square units, of a sphere with volume V, in cubic units,
1
2
is given by the formula S 5 p 3(6V )3 . What is the surface area of a sphere with
1
volume 43 mi3? Write your answer in terms of p 3 . Show your work.
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37
Name
Class
6-6
Date
Standardized Test Prep
Function Operations
Multiple Choice
For Exercises 125, choose the correct letter.
1. Let f (x) 5 22x 1 5 and g(x) 5 x3. What is (g 2 f )(x)?
x3 2 2x 1 5
2x3 2 2x 1 5
x3 1 2x 2 5
2x3 1 2x 2 5
2. Let f (x) 5 3x and g(x) 5 x2 1 1. What is ( f · g)(x)?
9x2 1 3x
9x2 1 1
3x3 1 3x
3x3 1 1
f
3. Let f (x) 5 x2 2 2x 2 15 and g(x) 5 x 1 3. What is the domain of g (x)?
all real numbers
x 2 23
x 2 5, 23
x.0
4. Let f (x) 5 !x 1 1 and g(x) 5 2x 1 1. What is (g + f )(x)?
2 !x 1 3
!2x 1 1 1 1
2x !x 1 2x 1 !x 1 1
2x 1 !x 1 2
1
5. Let f (x) 5 x and g(x) 5 x2 2 2. What is ( f + g)(23)?
17
9
17
1
7
29
7
23
Short Response
6. Suppose the function f (x) 5 0.035x represents the number of U.S. dollars
equivalent to x Russian rubles and the function g(x) 5 90x represents the
number of Japanese yen equivalent to x U.S. dollars. Write a composite
function that represents the number of Japanese yen equivalent to x Russian
rubles. Show your work.
Prentice Hall Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
57