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Name _______________________________________ Date __________________ Class __________________
AZ Merit Review #1
SELECTED RESPONSE
Select the correct answer.
1. Write the radical expression in rational
exponent form.
5
a
3
3. Which values of p give the expression p 2
a real number result when simplified?
p3
p2
a5
p0
1
p0
a5
Select all correct answers.
5a
 1a 
 
5 
4. Which of the following do not have
integer exponents when rewritten in
rational exponent form and simplified?
Assume that s is nonnegative.
2. Write the radical expression in rational
exponent form.
3
s4
k7
7
k3
3
6
s3
4
s6
3
s9
5
s15
8
s2
k7
k4
k10
Match each radical expression with its equivalent rational exponent expression. Assume
that w is nonnegative.
____ 5.
____ 6.
3
5
____ 7.
____ 8.
3
5
w5
A w3
w3
B w5
w5
C w5
w
D w3
3
1
1
2
E w5
2
F w3
5
G w2
3
H w2
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Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date ___________________ Class __________________
CONSTRUCTED RESPONSE
SELECTED RESPONSE
Select the correct answer.
 z  . Assume z is positive.
7
9. Simplify

13. Write c 9d 12
8
3


5
6
using only positive
exponents. Assume c and d are both
positive. Show all work.
56
z3
________________________________________
24
z7
________________________________________
24
z 56
________________________________________
11
________________________________________
z 15
10. Which of the following is equal to
15
j 
3
j
j
2

2
5

1
3
? Assume that j is positive.
________________________________________
________________________________________
14. Write the four expressions in descending
order of resulting exponent when written
in simplified rational exponent form.
Assume t is positive.
5
j2
2
j5
11. Write
________________________________________
6

uv 3

t • t
8
t
5
t7
t
3
2
4
7
1
t

2
5
5
using rational exponents.
________________________________________
Assume u and v are both positive.
5 15
u 2v 2
2 2
u 5v 15
u 5v 15
11 13
u 2v 2
Select all correct answers.
 
5
________________________________________
________________________________________
________________________________________
12. Which of the following are equal to
2
3 5
p
________________________________________
________________________________________
? Assume that p is positive.
________________________________________
p
6
5
1
15
p
1
p30
p
13
1
p5 p
________________________________________
________________________________________
________________________________________
10
p 1
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date ___________________ Class __________________
SELECTED RESPONSE
Select the correct answer.
15. Samantha drove her car for 15 miles at a
certain speed s to get to her first
destination. She then drove 3 miles less
and 10 miles per hour faster to get to her
second destination. Which expression
below models the combined time
Samantha spent driving?
15
12

s s  10
15
12

s  10 s
15
12

s s  10
s s  10

15
12
16. A traffic engineer is modeling the traffic on
a highway during the morning commute.
The average number of cars on the
highway at both 6 a.m. and
10 a.m. is 4000. However, the number of
cars is greater than 4000 between
6 a.m. and 10 a.m., reaching a peak of
6500 cars at 8 a.m.
a. Choose mathematical variables to
represent the real-world variables in
this situation. Tell which is the
independent variable and which is the
dependent variable.
________________________________________
________________________________________
b. Write a function of the form
f(x)  a(x  h)2  k, where (h, k)
is the vertex of the parabola that
models the number of cars on
the highway at any time between
6 a.m. and 10 a.m. Explain your
reasoning.
________________________________________
________________________________________
17.You want to make an open-top box from the rectangular piece
of cardboard shown. You cut congruent squares from the four
corners of the cardboard and then fold up and tape the
resulting flaps.
a. Suppose you want to know the volume of the box.
Describe the real-world variable on which the volume
depends. Then choose a mathematical variable to
represent the real-world variable and label the diagram
with it.
________________________________________________________________________________________
________________________________________________________________________________________
b. Explain how to find the width, length, and height of the box using the variable
from part a.
________________________________________________________________________________________
c. Write an equation that gives the volume V of the box as a function of the variable
from part a.
________________________________________________________________________________________
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Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date ___________________ Class __________________
18. While researching the heights of tables and chairs for children, you come across the
following table of data. You want to model the data using appropriate functions obtained
through the regression feature on a graphing calculator.
Age of Child
1 year old
2 years old
3 years old
4 years old
5 years old
6 years old
7 years old
8 years old
9 years old
10 years old
11 years old
12 years old
13 years old and up
Chair Seat Height
5 to 7 inches
8 to 10 inches
10 inches
10 to 12 inches
12 inches
12 to 14 inches
13 to 14 inches
14 to 15 inches
14 to 16 inches
16 inches
16 to 17 inches
16 to 18 inches
18 inches
Table Top Height
12 to 14 inches
16 to 18 inches
18 inches
18 to 20 inches
20 inches
20 to 22 inches
21 to 22 inches
22 to 25 inches
22 to 26 inches
24 to 26 inches
24 to 27 inches
24 to 29 inches
26 to 30 inches
a. Identify the three real-world variables given in the table and choose an appropriate
mathematical variable to represent each. Include the unit of measurement for each
defined variable.
b. For each model you want to create, describe which variable is the independent variable
and which is the dependent variable. Explain your reasoning.
SELECTED RESPONSE
Select the correct answer.
19. What does the imaginary number i
represent?
1
1
1
 1
20. Which of the following is equivalent to
121 ?
11
11
11i
121i
Select all correct answers.
21. Find all solutions of the equation
x2  484.
x  22
x  22
x  22i
x  22i
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Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date ___________________ Class __________________
Match each number with its equivalent
form
A 8
____ 22.  8
B 2
____ 23. 82
C 2 2
3
D 20 2
____ 24. 8
E 2i
____ 25. 8
F 8i
____ 26. 800
G 2i 2
H 20i 2
CONSTRUCTED RESPONSE
27. How many real solutions does the equation x4  16  0 have? How many non-real
solutions? State all solution(s) of the equation.
________________________________________
________________________________________
________________________________________
28. Simplify each expression and tell whether it represents a real number or a non-real number.
a.
144  64
________________________________________
________________________________________
b.
144  64
________________________________________
________________________________________
29. How many real solutions and how many non-real solutions does the equation
x2  5  0 have? Describe what implications your answer has for graphing the function y 
x2  5.
________________________________________
________________________________________
________________________________________
30. Why is it imprecise to say that the equation 25x2  27  0 has no solution? Find all solutions
of the equation.
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
Selected Response
Select the correct answer.
31. Let a, b, and c be any real numbers. Find the product ci(a  bi).
ac  bci
bc  aci
bc  aci
bc  aci
32. Which of these expressions is equal to
4  7i?
(6  i)  (2  8i)
(6  i)  (2  8i)
(6  i)  (2  8i)
(6  i)  (2  8i)
Select all correct answers.
33. Which of the following sums, differences, and products can be simplified to 6  3i?
(9  5i)  (3  2i)
(4  2i)  (2  5i)
(9  5i)  (3  2i)
(4  2i)  (2  5i)
3i(1  2i)
3i(1  2i)
Match each sum, difference, or product with its simplified form.
A 12
____ 34. (6  i)  (6  2i)
B 39
____ 35.(6  2i)  (6  2i)
C 40
____ 36.(6  i)  (6  2i)
D i
E 3i
____ 37. (6  2i)  (6  2i)
F 4i
____ 38. (6  i)(6  2i)
G 12  3i
____ 39. (6  2i)(6  2i)
H 34  18i
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
SELECTED RESPONSE
Select the correct answer.
40. Solve x2  3x  4  0 over the set of complex numbers.
x = -3 ± i 7
3
7
x=- ±
i
2 2
3
7
±
2 2
x  1 or x  4
x=-
41. Solve x2  2x  5  0 over the set of complex numbers.
x  1 or x  3
x  1  2i
x  2i
x  2  4i
Select all correct answers.
42. Which of the following are solutions of the equation x2  27  0 over the set of complex
numbers?
3 3
i 3
3i 3
-3 3
-i 3
-3i 3
CONSTRUCTED RESPONSE
43. Describe the solutions of the equation
4x2  6x  3  0 as real or non-real. (Discriminant)
44. Consider the equation
7x2  2x  9  2x2  5x  8.
a. Rewrite the equation in the form ax2  bx  c  0.
________________________________________
b. Find the solution(s) of the equation and describe as real or non-real.
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Algebra 2
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
SELECTED RESPONSE
Select the correct answer.
45. Factor x2  121 over the set of complex numbers.
(x  11)(x  11)
(x  11i)(x  11i)
(x  11i)(x  11i)
(x  11i)(x  11i)
46. Factor x2  4x  5 over the set of complex numbers.
(x  1)(x  5)
(x 2  i))(x  2  i))
(x 2  i))(x  2  i))
(x 2  i))(x  2  i))
SELECTED RESPONSE
Select the correct answer.
47. How many roots does the polynomial
x3  6x2  12x  8 have in the set of complex numbers?
0
1
2
3
Select the correct answer for each
lettered part.
48. Use the corollary of the fundamental theorem of algebra to find the number of complex
roots for each polynomial.
a. x2  4x  4
1
2
3
4
b. 12x2  4x3  2x  1
1
2
3
4
c. x  2x  2x
1
2
3
4
d. x  81
1
2
3
4
4
3
2
49. Sheila says that x2  18x  81 has one real root, 9. She uses the corollary of the
fundamental theorem of algebra to conclude that the polynomial must have one non-real
root. Is Sheila correct? Explain. Then state all complex roots of the polynomial.
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Algebra 2
3
Common Core Assessment Readiness