Name Class Date Standardized Test Prep
Multiplying Powers With the Same Base
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. What is the simplified form of (-3x 3y 2)(5xy -1)? C
- 15x3
y2
-15x3y 2
-15x4y
1 4
1 2
2. What is the simplified form of a-9m2n5 b a2m3n5 b ?
5 6
1 8
-18m6n5
-18m6n25
15x4y
G
- 18m5n6
m6n5
- 18mn8
m6n25
3. A rectangular pasture has a fence around the perimeter. The length of the
fence is 16x7 and the width is 48x4 . What is the area of the pasture? C
3x3
128x11
768x11
768x28
4. What is the simplified form of (3.25 * 103)(7.8 * 106) written in scientific
notation? F
2.535 * 1010
2.535 * 1018
2.535 * 1019
25.35 * 109
5. The size of a certain cell is 2.5 * 10-9 m. Another cell is 1.5 * 103 times
larger. How large is the larger cell in scientific notation? D
4 * 10-27 m
4 * 10-12 m
3.75 * 106 m
3.75 * 10-6 m
Extended Response
6. The distance between two astronomical bodies is 6.75 * 106 miles. The
distance from the first body to a third body is 3.56 * 104 times the distance
between the first two bodies.
a. Write an expression that represents the distance between the first and third
bodies. 3.56 × 6.75 × 104 × 106 mi
b. Simplify the distance in part a. 2.403 × 1011 mi
c. Write an expression that represents the distance light would travel from the
first body to the third body and back to the first. 2 × 3.56 × 6.75 × 104 × 106 mi
d. Simplify the distance the light travels in part c. 4.806 × 1011 mi
[4] Correct answers to each part of the question
[3] Mostly correct answers to each part with a few computational errors
[2] Correct answers to 2 or 3 parts with a significant error in understanding or
solving the other parts
[1] Correct answer to 1 part of the problem with significant errors in solving the
remaining parts
[0] No effort made or no parts solved correctly
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Name Class Date Standardized Test Prep
Division Properties of Exponents
Multiple Choice
For Exercises 1–6, choose the correct letter.
1. Which of the following is equivalent to
5
x 6y 2
x 5y 2
1
xy 2
when x ≠ 0 and y ≠ 0? D
3
x 4y
x 4y 2
a 54 b
5-2
5-5
5 a 53 b
63x5
6x5
x 5y
2. Which expression is not equal to 125? F
5°
53
2
5
2
¢
3 -3
5
5
5
3. A fraction reduces to 36. If its numerator is (6x)5 , what is its denominator? B
63x
4. Which is the correct simplification of
4.5 * 107
4.5 * 109
67x5
5.4 * 1012
written in scientific notation? G
1.2 * 103
45 * 106
6.48 * 107
5. Which of the following statements is not true regarding operations with
exponents? B
To divide powers with the same base, subtract the exponents.
To subtract powers with the same base, divide the exponents.
To multiply powers with the same base, add the exponents.
To raise a power to a power, multiply the exponents.
6. Which of the following expressions is written in simplest form?
35x2
(5y)3
a0b
I
x 2y 3z
Short Response
7. A rectangle has an area of 12x 3 y 4 cm2 . It has a width of 3xy cm. What ratio
would you set up to determine the length? What is the length of the rectangle?
12x 3y 4
; 4x 2y 3
3xy
[2] Student uses the correct ratio and finds the correct length.
[1] Student either finds the correct ratio or shows the ability to
find the correct length.
[0] Student’s response shows no effort or does not correctly
find the ratio or the length.
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Name Class Date Standardized Test Prep
Rational Exponents and Radicals
Multiple Choice
For Exercises 1–4, choose the correct letter.
2
1. Which of the following expressions is equivalent to (32b)3 ? B
3
A. 2(32b)3
3
B. 8 22b2
3
C. 32 2b2
D. 2(8b)2
3
2. Which of the following expressions is equivalent to 2 2x5 ? F
5
5
F. 2x 3
3
G. (2x)3
3
H. 2x 5
I. (2x)5
3
3. Which of the following expressions is equivalent to a 2144a3 b - a 227b2 b ? B
3
3
2
A. 9(ab)2
B. 12a2 - 3b 3
C. 12a3 - 3b2
D. (144a)2 - (27b)3
3
2
6
4. A rectangle has an area equivalent to 4 2x7 square units. Which of the
following expressions could be used to find the area of the rectangle? H
2
1
1
F. a8x 3 b ax 2 b
2
2
G. (8x)2 (x)3
Short Response
1
1
H. (8x)3 ax 2 b
1
5. Simplify ax 4 b (20x)2 using the properties of exponents, and then write the
expression in radical form.
1
1
1
1
3
4
ax 4b (20x)2 = x 4(2)(15)x 2 = (2 15)ax 4b = 2 152x 3
[2] Student correctly applies the properties of exponents and
correctly simplifies to find the radical form.
[1] Student incorrectly applies the properties of exponents OR
simplifies incorrectly.
[0] Student’s response shows no effort OR does not correctly
use the properties of exponents and does not simplify
correctly.
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1
2
I. a8x 2 b ax 3 b
Name Class Date Standardized Test Prep
Adding and Subtracting Polynomials
Multiple Choice
For Exercises 1–6, choose the correct letter.
1. What is the degree of the monomial 3x 2y 3 ? C
A. 2
B. 3
C. 5
D. 6
2. What is the simplified form of 8b3c2 + 4b3c2 ? G
G. 12b3c2
F. 12bc
H. 12b6c4
I. 12b9c4
3. How is 6d - 8 + 4d 2 written in standard form? A
A. 4d 2 + 6d - 8
B. 4d 2 + 6d + 8
C. 4d 2 - 6d - 8
D. 4d 2 - 6d + 8
4. What is the simplified form of (4j 2 + 6) + (2j 2 - 3)? G
F. 6j 2 - 3
G. 6j 2 + 3
H. 6j 2 + 9
I. 4j 4 + 3
5. What is the difference of the following polynomials? D
6x3 - 2x2 + 4
- (2x3 + 4x2 - 5)
A. 4x 3 - 2x2 - 1
B. 8x 3 + 6x2 - 1
C. 4x 3 - 2x2 + 1
D. 4x 3 - 6x2 + 9
6. What is the simplified form of (3x 2 - 4x + 6x) + (5x 3 + 2x 2 - 3x) in
standard form? I
F. 5x 3 + 10x 2 - x
G. 8x 3 - 2x2 + 3x
H. 5x 3 + 10x 2 - 5x
I. 5x 3 + 5x2 - x
Short Response
7. Suppose you have been given this polynomial.
5b + 4b2 - 3b4 + 3
a. How can you write this polynomial in standard form?
−3b4 + 4b2 + 5b + 3
b. What is the degree of this polynomial? Explain.
4; b4 is the term with the greatest degree
[2] Both parts answered correctly with full explanations
[1] One part answered correctly or both parts answered correctly with incomplete
explanations
[0] Neither part answered correctly
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Name Class Date Standardized Test Prep
Multiplying Binomials
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. What is the simplified form of (x - 2)(2x + 3)? Use the Distributive Property. A
A. 2x 2 - x - 6
B. 2x 2 - 6
C. 2x 2 - 7x - 6
D. 2x 2 + x - 6
2. What is the simplified form of (3x + 2)(4x - 3)? Use a table. I
F. 12x 2 + 18x + 6
G. 12x 2 + x - 6
H. 12x 2 + 18x - 6
3. What is the simplified form of (4p - 2)(p - 4)? B
A. 4p2 + 6p - 16
B. 4p2 - 18p + 8
C. 4p2 - 14p - 6
I. 12x 2 - x - 6
D. 4p2 - 6p + 16
4. The radius of a cylinder is 3x - 2 cm. The height of the cylinder is x + 3 cm.
What is the surface area of the cylinder? I
F. 2p(3x2 + 10x - 8)
G. 2p(12x2 + 7x - 2)
H. 2p(12x2 - 2x + 13)
I. 2p(12x2 - 5x - 2)
5. What is the simplified form of (2x 2 + 4x - 3)(3x + 1)? C
A. 6x 3 + 10x 2 - 5x + 3
B. 6x 3 + 14x 2 + 5x - 3
C. 6x 3 + 14x 2 - 5x - 3
D. 6x 3 - 10x 2 - 5x - 3
Short Response
6. A soup can that is a cylinder has a radius of 2x - 1 and a height of 3x. What is
the surface area of the soup can? Show your work. 20Px 2 − 14Px + 2P
[2] Correct polynomial written with all work shown
[1] Polynomial written with minor calculation error or inadequate work shown
[0] No correct work shown
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Name Class Date Standardized Test Prep
Complex Numbers
Multiple Choice
For Exercises 1−8, choose the correct letter.
1. What is the simplified form of (-8 + 5i) + (3 - 2i)? B
-14 + 31i
-5 + 3i
-11 + 7i
5 - 3i
2. What is the simplified form of (11 - 6i) - (-4 + 12i)? I
7 + 6i
7 - 18i
15 + 6i
3. What is the simplified form of (5 + 1-36) - (-4 - 1-49)? D
9 - 13i
9 + 85i
15 - 18i
1-i
9 + 13i
15
15i
4. What is the simplified form of (-5i)(-3i)? G
-15i
-15
5. What is the simplified form of (-3 + 2i)(1 - 4i)? C
-2 - 2i
-11 - 10i
5 + 14i
-3 - 8i
55 - 48i
55 + 48i
5 3
4 - 2i
7
11
10 - 10i
6. What is the simplified form of (8 - 3i)2 ? H
16 - 6i
73
5 + 3i
7. What is 4 - 2i written as a complex number? A
13
7
1
11
10 + 10i
10 + 10i
8. What is the factored form of the expression4x 2 + 36? G
4(x + 3i)2
4(x + 6i)2
4(x + 3i)(x - 3i)
4(x + 6i)(x - 6i)
Short Response
9. What are the solutions of 2x 2 + 3x + 6 = 0? Show your work.
t 139
[2] − 3
4
4 i;
[1] quadratic formula properly used, but some computational
errors OR correct solutions without work shown
[0] incorrect answers and no work shown OR no answers given
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