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Name_______________________________________ Date_________________ Class________________ Block 8 TN Ready Common Core Assessment SELECTED RESPONSE Select the correct answer. 1. Write the radical expression in rational exponent form. 2. Write the radical expression in rational exponent form. k 4 k 10 3. Which values of p give the expression a real number result when simplified? p 3 p 2 p 0 p 0 Select all correct answers. 4. Which of the following do not have integer exponents when rewritten in rational exponent form and simplified? Assume that s is nonnegative. Match each radical expression with its equivalent rational exponent expression. Assume that w is nonnegative. _____5. _____6. _____7. _____8. A B C D 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
Transcript of Ch · Web viewName Date Class Name Date Class Name Date Class Name Date Class Name Date Class Name...
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Block 8 TN Ready Common Core AssessmentSELECTED RESPONSE
Select the correct answer.
1. Write the radical expression in rational exponent form.
2. Write the radical expression in rational exponent form.
k4
k10
3. Which values of p give the expression a real number result when simplified?
p 3
p 2
p 0
p 0
Select all correct answers.
4. Which of the following do not have integer exponents when rewritten in rational exponent form and simplified? Assume that s is nonnegative.
Match each radical expression with its equivalent rational exponent expression. Assume that w is nonnegative.
_____ 5.
_____ 6.
_____ 7.
_____ 8.
A
B
C
D
E
F
G
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Algebra 2 Common Core Assessment Readiness
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H
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.
9. Simplify Assume z is positive.
10. Which of the following is equal to
Assume that j is positive.
11. Write using rational exponents. Assume u and v are both positive.
Select all correct answers.
12. Which of the following are equal to
Assume that p is positive.
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Algebra 2 Common Core Assessment Readiness
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CONSTRUCTED RESPONSE
13. Write using only positive exponents. Assume c and d are both positive. Show all work.
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14. Write the four expressions in descending order of resulting exponent when written in simplified rational exponent form. Assume t is positive.
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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
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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?
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.
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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.
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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.
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b. Explain how to find the width, length, and height of the box using the variable from part a.
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Algebra 2 Common Core Assessment Readiness
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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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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 Chair Seat Height Table Top Height
1 year old 5 to 7 inches 12 to 14 inches
2 years old 8 to 10 inches 16 to 18 inches
3 years old 10 inches 18 inches
4 years old 10 to 12 inches 18 to 20 inches
5 years old 12 inches 20 inches
6 years old 12 to 14 inches 20 to 22 inches
7 years old 13 to 14 inches 21 to 22 inches
8 years old 14 to 15 inches 22 to 25 inches
9 years old 14 to 16 inches 22 to 26 inches
10 years old 16 inches 24 to 26 inches
11 years old 16 to 17 inches 24 to 27 inches
12 years old 16 to 18 inches 24 to 29 inches
13 years old and up 18 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?
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Algebra 2 Common Core Assessment Readiness
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20. Which of the following is equivalent to
?
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
Match each number with its equivalent form
_____22.
_____23.
_____24.
_____25.
_____26.
A 8B 2
CDE 2iF 8i
GH
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.
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28. Simplify each expression and tell whether it represents a real number or a non-real number.
a.
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b.
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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.
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30. Why is it imprecise to say that the equation 25x2 27 0 has no solution? Find all solutions of the equation.
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Algebra 2 Common Core Assessment Readiness
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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.
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Algebra 2 Common Core Assessment Readiness
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_____34. (6 i) (6 2i)
_____ 35.(6 2i) (6 2i)
_____36.(6 i) (6 2i)
_____37. (6 2i) (6 2i)
_____38. (6 i)(6 2i)
_____39. (6 2i)(6 2i)
A 12B 39C 40D iE 3iF 4iG 12 3iH 34 18i
SELECTED RESPONSE
Select the correct answer.
40. Solve x2 3x 4 0 over the set of complex numbers.
x 1 or x 4
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?
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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.
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b. Find the solution(s) of the equation and describe as real or non-real.
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Algebra 2 Common Core Assessment Readiness
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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. x4 2x2 2x 1 2 3 4
d. x3 81 1 2 3 4
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Algebra 2 12 Common Core Assessment Readiness
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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 13 Common Core Assessment Readiness
