Name______________________________________________ Date_____________________________________Algebra 2 Common Core

BIG Packet of Cumulative Review Part II

1. For a sequence defined by and

, which of the following is the value

of ?

(1) 53 (3) 108

(2) 76 (4) 126

2. Which of the following formulas properly describes the

sequence

(1) (3)

(2) (4)

3. If a sequence is defined by and then what is the value of the 20th term of this sequence?

(1) 80 (3) 95

(2) 91 (4) 101

4. A concert hall is constructed so that each row has 5 more seats than the row in front of it. If the first row contains 15 seats, how many seats does the 30th row contain?

5. If the first three terms of a geometric sequence are , then what is the value of x?

(1) 5 (3) 8

(2) 7 (4) 11

6. Which of the following is the value of ?

(1) 42 (3) 51

(2) 49 (4) 56

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Sequences and Series

7. For any value of x, the sum is equivalent to

(1) (3)

(2) (4)

8. The series can be represented by

(1) (3)

(2) (4)

9. The sum of the first 100 positive, even integers is

(1) 5,100 (3) 7,500

(2) 10,100 (4) 14,200

10. What is the value of an arithmetic series whose first term is , whose common difference is 8, and which has 30

terms?

(1) (3)

(2) (4)

11. If the following sum represents a geometric series, then which of the following is its value?

(1) (3)

(2) (4)

12. A sequence is given by the recursive definition:

and

State the fourth term of this sequence. Show how you arrived at your answer.

13. Write the following in simplest form in terms of x.

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14. For some value of x the sequence forms the first three terms of an arithmetic sequence.

a) Find the value of x.

b) Determine the numerical value of the 15th term of this sequence.

c) Find the sum of the first 30 terms of this sequence. Show your analysis.

15. In a geometric sequence, the first term is and the eighth term is 17,496. Determine the second term of this sequence. Show how you arrived at your result.

16. If a sequence is defined by the recursive formula:

then what is the value of . Show how you arrived at your answer.

17. The graph of the quadratic function is shown below. Which of the following must be true about the values of a, b, and c?

(1)

(2)

(3)

(4)

18. For the function , over which of the

following intervals is always?

(1) (3)

3

Quadratic Functions

(2) (4)

19. Selected values of a quadratic function are shown below. Which of the following values of x represents an x-intercept of the function?

(1) (3) 6

(2) (4) 10

20. The function is strictly decreasing over which of the following intervals

(1) (3)

(2) (4)

21. The height of an object can be modeled by the equation

. Which of the following is not an equivalent way of expressing this function?

(1) (3)

(2) (4)

22. Which of the following is not a factor of the expression ?

(1) (3)

(2) (4)

23. The trinomial can be written equivalently as

(1) (3)

(2) (4)

24. The expression can be

simplified as the product of and what other binomial?

(1) (3)

(2) (4)

25. The cubic polynomial can be factored as

(1) (3)

4

x 0 2 4

y 9 0

(2) (4)

26. The polynomial can be written as

(1) (3)

(2) (4)

27. The equation has a solution set of

(1) (3)

(2) (4)

28. The quadratic function has one zero at

. At which of the following x-values is its other zero?

(1) (3)

(2) (4)

29. The height of an object in meters above the ground is given by

, where t represents the time, in seconds. For which of the following intervals of t is the object above a height of 350 meters?

(1) (3)

(2) (4)

30. A cable hangs in a parabolic shape above a level surface between two poles such that its height above the surface is

given by the equation , where y is the cable's height above the surface, in feet, and x is the horizontal distance from one of the poles. According to this model, which of the following represents the lowest height the cable is above the surface?

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(1) 8.9 feet (3) 11.3 feet

(2) 10.1 feet (4) 12.2 feet

31. A circle whose center is at and which passes through

the point has a radius equal to

(1) (3)

(2) (4) 8

32. A circle whose equation is has a center at

(1) (3)

(2) (4)

33. A parabola has a focus at and a directrix of the x-axis. Which of the following is the equation of the parabola?

(1) (3)

(2) (4)

34. Write the expression as the product of two linear binomials.

35. Factor the expression below completely.

36. Find the solution set of the equation shown below.

37. Shana believes one of the two binomial factors of is . Is she correct? Explain your answer.

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38. Given , algebraically find all values of x

that solve the equation .

39. Find the x coordinates where the line intersects the

circle . Only an algebraic solution is acceptable.

40. Find all zeroes of the piecewise function

. Justify your answer algebraically.

41. Solve the following equation for all values of x algebraically.

42. Algebraically determine the solution to the inequality below. Plot its solution on the number line provided.

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43. Place the following quadratic function in . Identify the coordinates of its turning point.

44. The per unit cost, in dollars, of producing n items is given by:

Algebraically, determine the minimum per unit cost and the number of items that should be produced to obtain this minimum.

45. A parabola has a focus at and a directrix of .

a) Create a rough sketch of the parabola on the axes below. Label the focus and directrix

b) What are the coordinates of the vertex of the parabola? Show how you found your answer.

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c) Determine the equation of the parabola using the locus definition of a parabola.

46. Given that both and are positive numbers, which of the following equations would describe the graph shown below

given that it is a transformation of the graph of .

(1)

(2)

(3)

(4)

47. Which of the following represents the domain of the function

?

(1) (3)

(2) (4)

48. If the function is defined only on the domain , then which of the following represent its range?

(1) (3)

(2) (4)

49. Which of the following is the solution set to: ?

(1) (3)

(2) (4)

50. If then for which value of x is ?

(1) (3)

(2) (4)

51. The expression can be written at , where k is some integer. Which of the following represents the value of k?

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Radicals and The Quadratic Formula

(1) (3)

(2) (4) 4

52. The expression can be written equivalently as

(1) (3)

(2) (4)

53. The radical expression can be simplified to

(1) (3)

(2) (4)

54. The expression is the same as

(1) (3)

(2) (4)

55. The expression can be written, for , as

(1) (3)

(2) (4)

56. Which of the following is the simplified version of ?

(1) (3)

(2) (4)

57. Which of the following represents the solution set to:

?

(1) (3)

(2) (4)

58. Which of the following represent the roots of the equation ?

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(1) (3)

(2) (4)

59. What are the zeroes of ?

(1) (3)

(2) (4)

60. The larger root of the equation is closest to

(1) 1.43 (3) 2.57

(2) 1.87 (4) 3.19

61. Given the function answer the following:

a) Graph the function on the grid shown.

b) Explain how the graph of has been transformed into

the graph of .

c) What are the domain and range of ?

Domain: Range:

62. Write in simplest radical form. Show how you arrived at your answer.

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63. A projectile is fired vertically from an initial height of 8 feet with an initial velocity of 340 feet per second. Its height above the ground in feet can be modeled as a function of time by the

equation , where t represents the seconds since fired

a) Determine, algebraically, when the projectile hits the ground to the nearest tenth of a second.

b) Write an inequality and solve it algebraically to determine all times at which the projectile is at or above 1,000 feet. Round all times to the nearest tenth of a second.

64. Solve the following system of equations algebraically.

65. Which of the following is the solution to ?

(1) (3)

(2) (4)

12Complex Numbers

66. Which of the following is the correct simplification of ?

(1) (3)

(2) (4)

67. Which of the following is equivalent to , where

a, b, and c are real numbers and ?

(1) (3)

(2) (4)

68. Which of the following is the sum of and ?

(1) (3)

(2) (4)

69. If and then which of the following is equivalent to the expression ?

(1) (3)

(2) (4)

70. The product of and which of the following will result in a purely imaginary number?

(1) (3)

(2) (4)

71. If the product of and is found, where a and b are real numbers, then the real component of the result is given by

(1) (3)

(2) (4)

72. For which of the following values of b will the equation have real solutions?

(1) (3)

(2) (4)

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73. Explain why the product of and produces a purely real number as a result.

74. Find the solutions to in simplest form.

75. Evaluate the following complex arithmetic problem. Show all steps and express your final answer in simplest form.

76. If n is a positive integer, then the expression is always equivalent to . Explain why.

77. Given the quadratic equation , determine all values of a that will result in this equation having non-real solutions. Show the work that leads to your answer.

78. Explain why there is no real number value of b that can cause

to be tangent to the x-axis.

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