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Algebra1Semester2FinalAssignmentIt is very important that you review for the Algebra Final. Here are a few pieces of information you want to know.

� Your Final is worth 15% of your overall grade � The final covers concepts from the entire semester, they are the following

o Unit 6 – Absolute Value Functions o Unit 7 – Using Exponents o Unit 8 Part 1 – Multiplying Polynomials o Unit 8 Part 2 – Factoring Polynomials o Unit 9 Part 1 – Graphing Quadratic Functions o Unit 9 Part 2 – Solving Quadratic Functions o Unit 10 – Exponential Growth and Decay

� The final is 45 multiple choice problems, here are some tips for multiple choice problems o Read the question before you look at the answer o Come o up with the answer in your head before looking at the possible answers, this way the choices

given on the test won't throw you off or trick you o Eliminate answers you know aren't right o Read all the choices before choosing your answer o If there is no guessing penalty, always take an educated guess and select an answer

Finals Schedule This Assignment is due on the day of your final and is worth 500 assignment points. Make sure you show your work for full credit, circling the correct answer is not enough. Date Assignment for that day Monday, June 1 1, 2, 3, 4, 5, 6 Tuesday, June 2 7, 8, 9, 10 Wednesday, June 3 11, 12, 13, 14, 15, 16 Thursday, June 4 20, 21, 22, 23, 24, 25, 26, 27, 28, 33, 34 Friday, June 5 17, 18, 19, 29, 30, 31, 32 Monday, June 8 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45

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1. Which of the following graphs represents � = |�| − 2 ?

A.

C.

B.

D.

2. Reflect the graph of ��� = |�| over the x-axis and translate the function one unit up. Which of the following is the function after the translation?

A. ��� = |�| − 1 C. ��� = |�| + 1

B. ��� = |� + 1| D. ��� = −|�| + 1

3. Which of the following is the solution for x in the equation 2|� + 3| + 6 = 10 ?

A. � = −5 C. � = 1

B. � = −5, � = −1 D. ����������

4. Which of the following is the solution for x in the equation −3|� + 4| = 6 ?

A. � = −6 C. � = −2

B. � = −6 and � = −2 D. ����������

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5. If ��� = 2|� + 3| − 4 and ��� = �� � + 5, use the tables below find the x-value(s) where

��� = ���. ��� = 2|� + 3| − 4

� ���−7 4−6 2−5 0−4 −2−3 −4−2 −2−1 00 21 42 63 84 10

��� = 12 � + 5

� ���−7 1.5−6 2−5 2.5−4 3−3 3.5−2 4−1 4.50 51 5.52 63 6.54 7

A. � = 2, 4, 6 C. � = −6, 2

B. � = 2, 6 D. ����������

6. Which graph below models the solutions to the equation −3|� + 2| + 4 = −2 ?

A.

C.

B.

D.

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7. What is the simplified form of �4� !ℎ# ! ?

A.

−12�$ℎ�� C.

12�%ℎ

B. −64�%ℎ�� D.

�%64ℎ��

8. Let ��� = −3&�/� and ��� = 2&�(/�) *. Find ℎ�� = ��� ∙ ���.

A. ℎ�� = −6&*

)* C. ℎ�� = −5&,

)*

B. ℎ�� = 6)*

&* D. ℎ�� = −6&)

9. What is the simplified form of !$-./01#-0.23./ ? (Assume that 4 ≠ 0, � ≠ 0, and 6 ≠ 0)

A.

9�#6#4! C.

9�*6#4(

B. 9�*4(6# D.

94(�*6#

10. Simplify: 8�*#�

A. √217 C. 3

B. √637 D. √3

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11. A moving company sells boxes for packing items. The large box has a volume of 6�! + 2�� + 3 cubic units. The medium box has a volume of 2�! + 8� − 5 cubic units. A customer purchases two large boxes and one medium box. What is the total volume of the purchased boxes?

A. 14�$ + 12�! + 1 cubic units C. 14�! + 2�� + 8� − 2 cubic units

B. 14�$ + 4�� + 8� + 1 cubic units D. 14�! + 4�� + 8� + 1 cubic units

12. What is the product of the binomials: �: − 8�: + 5 ?

A. :� − 40 C. : − 3

B. :� + 13: − 40 D. :� − 3: − 40

13. What is the simplified form of �; + 7� ?

A. ;� + 14; + 49 C. ;� + 49; + 49

B. ;� + 49 D. ; + 49

14. The polynomial �� + 11� + 30 is factorable. One factor is �� + 6, what is the other factor?

A. �� + 1 C. �� − 5 B. �� + 3 D. �� + 5

15. Which of the following is a factor of 3�� − 12 ?

A. �� + 12 C. �� − 2 B. �� − 4 D. �� + 4

16. Which of the following is a factor of 2�� + 7� − 30 ?

A. �� − 5 C. �� − 12 B. �� + 6 D. �� − 6

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17. What is the solution to �� + 8� = 84 ?

A. � = −12, � = 7 C. � = −14, � = 6

B. � = 14, � = −6 D. � = −12, � = 4

18. Solve for x in 16�� − 49 = 0 .

A. � = ±4916 C. � = 1649

B. � = ±74 D. � = 74

19. The height �ℎ, in feet, of a person jumping off a diving platform can be modeled by the equation ℎ = −16�� + 4� + 6 where � represents the time in seconds the person is in the air. After how many seconds does the person jumping off the platform enter the water?

A. −12 �=&��) C.

43 �=&��)�

B. 34 �=&��) D. 2�=&��)�

20. Given the equation and graph of � = −�� − 1, what is the domain and range?

A. Domain: >��:=>���4;=:� Range: � ≥ 1

B. Domain: >��:=>���4;=:� Range: � ≤ 1

C. Domain: >��:=>���4;=:� Range: � ≤ −1

D. Domain: −1 ≤ � ≤ 1 Range: � ≤ −1

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21. Which of the following quadratic functions represents the function graphed below?

A. � = 12 �� − 5

B. � = 2�� − 5

C. � = 12 �� + 5�

D. � = 2�� − 5�

22. Which of the following graphs represents ��� = �� − 4�?

A.

C.

B.

D.

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23. Translate the graph of ��� = �� four units to the left, three units up and stretch the graph by a factor of 2. Which of the following is the function after the transformations?

A. ��� = 12 �� + 4� + 3 C. ��� = 2�� + 4� + 3

B. ��� = 12 �� − 4� + 3 D. ��� = 2�� − 4� + 3

24. Which of the following quadratic functions represents the function graphed?

A. � = −�� − 3� − 1

B. � = −�� + 3� − 1

C. � = −�� + 1� − 3

D. � = −�� − 1� − 3

25. Which of the following is the vertex for ��� = −4�� − 5� + 2 ?

A. �25, 2 C. �−5, 2 B. �−20, 2 D. �5, 2

26. What is the y-intercept of the graph of � = 2�� − 1� + 3 ?

A. �1, 3 C. �0, 3 B. �0, 5 D. �0, 1

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27. Given the graph of � = ��, what is the solution for x after the transformation down four units and left three units?

A. � = −2, � = 2

B. � = 3

C. � = −5, � = −1

D. � = −4, � = 3

28. Which of the following are the x-intercepts for � = �� + 2� − 16

A. �−6, 0, �2, 0 C. �−6, 0, �−2, 0 B. �−2, 0, �16, 0 D. �2, 0, �−16, 0

29. What is the solution to ℎ� + 9ℎ − 4 = 0 ?

A. ℎ = −9 − √652 , ℎ = −9 + √652 C. ℎ = 9 − √972 , ℎ = 9 + √972

B. ℎ = 9 − √652 , ℎ = 9 + √652 D. ℎ = −9 − √972 , ℎ = −9 + √972

30. Which of the following is a solution to 2�� + 14� = 18 ?

A. � = 7 ± √852 C. � = −7 ± √852

B. � = −7 ± √132 D. � = 14 ± √3404

31. Which of the following is the vertex form for ��� = �� + 4� + 7 ?

A. ��� = �� + 2� + 3 C. ��� = �� + 2� + 7

B. ��� = �� − 2� + 4 D. ��� = �� − 2� + 3

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32. What is the y-intercept of the graph of � = �� + 9� + 15 ?

A. �0, 9 C. �0, 15 B. �9, 15 D. �0, −15

33. What is the vertex of the function ��� = −2�� + 8� − 9 ?

A. �−4,−73 C. �−2,−33 B. �4, −9 D. �2, −1

34. Before a truck can drive through a tunnel, it must be determined if the load can fit safely

through the tunnel. The parabola ��� = − �# �� − 8� + 16 models the curve of the tunnel.

If a truckload is 12�==� high what is the maximum width it could be?

A. 4�==�

B. 8�==� C. 12�==� D. 16�==�

35. Which of the following best describes the data in the table?

� 1 2 3 4� 3 9 27 81

A. Exponential with a growth rate of 3

B. Linear with a rate of change of 6

C. Quadratic with a second difference of 12

D. none of the above

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36. Since the year 2001 the population of community A grows exponentially as illustrated in the table. The exponential rate of growth is 1.3. What are the units for the rate of growth in the table?

�=>: 2001 2002 2003 2004 2005 20066=�6�= 1200 1560 2028 2636.4 3427.32 4455.52

A. people per year

B. years per people

C. years

D. people

37. Determine which of the following equations represent exponential growth or decay.

Equation 1 Equation 2 Equation 3 Equation 4

� = 1.5 A

� = 0.8A

� = 0.5 A

� = 2.7A

A. Equation 1: Growth Equation 2: Growth Equation 3: Decay Equation 4: Decay

C. Equation 1: Decay Equation 2: Growth Equation 3: Growth Equation 4: Decay

B. Equation 1: Decay Equation 2: Decay Equation 3: Growth Equation 4: Growth

D. Equation 1: Growth Equation 2: Decay Equation 3: Decay Equation 4: Growth

38. If ��� = 3 ∙ 4A and ��� = 3 ∙ 2A, compare the functions and determine which of the following statements is correct.

A. The x-intercept of ��� is greater than the x-intercept of ���. B. The y-intercept of ��� is greater than the y-intercept of ���.

C. The functions increase at the same rate.

D. The functions have the same y-intercept.

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39. What is the solution for x in 4A = 64 ?

A. � = 16 C. � = 3

B. � = 4 D. � = 2

40. What is the solution for x in 5�A % = 125 ?

A. � = 6 C. � = 5

B. � = 4 D. � = 3

41. What is the solution to the system graphed?

A. �2, 4 B. �4, 2 C. �1, 2 D. ����������

42.

What is the solution for x in the system?

B � = 8� = 2A

A. � = 13 C. � = 1

B. � = 12 D. � = 3

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43. Which of the following represents the function ��� = 3 ∙ 2A − 5 ?

A.

C.

B.

D.

44. Use the table below to help determine which function has the greatest value as x gets larger and larger.

� ��� = � + 3 ��� = 3� ℎ�� = �! ��� = 3A

3

4

5

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A. ��� has the greatest value as x gets larger and larger.

B. ��� has the greatest value as x gets larger and larger.

C. ℎ�� has the greatest value as x gets larger and larger.

D. ��� has the greatest value as x gets larger and larger.

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45. The maximum height reached by a bouncing ball is given by ℎ�� = 10�0.75A where h is measured in feet and x is the bounce number. Describe the domain of this function and what it means when � = 0.

A. The domain is all real numbers. When the bounce number � = 0, the height h of the ball is 10�==�, which represents its original height of the ball before it is dropped and bounces.

B. The domain is all real numbers. When the bounce number � = 0, the height h of the ball is 7.5�==�, which represents its original height of the ball before it is dropped and bounces.

C. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the bounce number x and does not have units. When � = 0 the height h of the ball is 10�==�, which represents its original height of the ball before it is dropped and bounces.

D. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the bounce number x and does not have units. When � = 0 the height h of the ball is 7.5�==�, which represents its original height of the ball before it is dropped and bounces.