X = 5 Simplify: = -3 – 36



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ALGEBRA II Regents Review

1. Simplify: = 1

2. The expressionis equivalent to which of the following?

a) b) c) d)

3. Solve for x: x = 5


4. Simplify: = -3
5. – 36
6. Simplify:= 34
7. Simplify: =
8. Solve for x:
9. What is the product of the roots of the equation – 2
10. Olive Math is standing on 102nd floor of the Empire State Building, thinking about

mathematics. She realizes that, is she were able to throw a ball from her present position,

the height of the ball in feet, h, at time, t seconds could be modeled by the equation:



  1. How high above the ground is the 102nd floor? 1224

  2. What is the greatest height the ball would reach? 1288

  3. How long would it take to reach that height? 2

  4. How long would it take the ball to hit the ground? 11

11. The roots of the quadratic equationare

a) real, rational, and equal b) real, rational, and unequal

c) real, irrational, and unequal d) imaginary

12. Express the roots of the equationin simplest a + bi form.

13. For which value of k will the roots ofbe real?

a) 1 b) 3 c) 2 d) 4


14. What is the sum of the roots of the equation 1/2
15. Carmela’s parents want her home within 30 minutes of midnight. Which equation represents

her curfew?

a) b) c) d)

16. Express the roots of the equationin simplest a + bi form.

17. Wanda’s Widget Company manufactures widgets. It costs Wanda $1,000 per month for her

fixed costs, plus $10 to produce each widget. If Wanda produces w widgets each month,

what is the average cost per widget?

a) b) c) d)
18. The area of a parallelogram is represented by. If the height of the parallelogram is represented by , find the length of the base of the parallelogram in terms of x.

19. Given:andfind

a) f(g(5)) = 45

b) = 4x2 + 12x + 5

c)=

20. Simplify: = b

21. If x varies inversely as y and x = 6 when y = 8, find x when y = 3. x = 16
22. Findif
23. The center of a circle is (-1,5) and point P(2,3) is on the circle. Write the equation of the circle.

(x + 1)2 + (y – 5)2 = 13

24. What is the center and radius of the circle whose equation is



(x + 1)2 + (y – 2)2 = 4 center: (-1,2) radius = 2

25. If the coordinates of the center of a circle is (2,5) and the radius is 9. Write the equation of

the circle. (x – 2)2 + (y – 5)2 = 81
26. Solve for x: –1/4

27. Expressed without negative exponents, the expression = 2ab13

28. Solve for x:

29. In the set of complex numbers, ifwhat is the value of

a) 24 b) 24 + 6i c) 36 d) 36 + 6i

30. Maria did a study of babysitting tares in her neighborhood over the last three years and

discovered that the function b(t) =represents the change in pricing, where t is the

number of years since 2000. What was the babysitting cost per hour in Maria’ neighborhood

in 2000?

a) $7.50 b) $6.25 c) $5.00 d) $1.20

31. The population of the village of Elfdom in the North Pole suburbs has a steady population

represented by the exponential functionwhere t represents the

number of years since 1985 when the village was incorporated.


  1. In what calendar year will the population be 17,500? 1999

  2. About how many years will it take for the elves to double their 1985 population? 24

32. Solve for x: x = 2


33. Solve for x: x = 6
34. If log a = x and log b = y, thenis equal to

a) b) c) d)

35. If find the value of x. x = 81

36. What is the inverse of

a) b) c) d)
37. An archer shoots an arrow into the air such that its height at any time, t, is given by the

functionIf the maximum height of the arrow occurs at time t = 4, what

is the value of k? k = 128
38. The magnitude (R) of an earthquake is related to its intensity ( I ) by, where T

is the threshold below which the earthquake is not noticed. If the intensity is doubled, its

magnitude can be represented by

a) b) c) d)


39. Jacob is solving a quadratic equation. He executes a program on his graphing calculator and

sees that the roots are real, rational, and unequal. This information indicate to Jacob that the

discriminant is

a) zero b) negative c) a perfect square d) not a perfect square


40. A modulated laser beats a diamond. Its variable temperature, in degree Celsius, is given by

. What is the period of the curve?

a) b) c) d)

41. Melissa and Joe are playing a game with complex numbers. If Melissa has a score of 5 – 4i

and Joe has a score of 3 + 2i, what is their total score?

a) 8 + 6i b) 8 + 2i c) 8 – 6i d) 8 – 2i

42. Find all the roots of x = 2, ±3i


43. Find all the roots of x = ±3, ±1
44. Find all the roots of
45. A store advertises that during its Labor Day sale $15 will be deducted from every purchase

over $100. In addition, after deduction is taken, the store offers an early-bird discount of 20%

to any person who makes a purchase before 10 a.m. If Helen makes a purchase of x dollars,

x >100, at 8 a.m., what, in terms of x, is the cost of Helen’s purchase?

a) 0.20x – 15 b) 0.20x – 3 c) 0.85x – 20 d) 0.80x – 12


46. The inverse of a function is a logarithmic function in the form Which equation

represents the original function?



a) b) c) d)
47. If is an obtuse angle and then it can be concluded that

a) b) c) d)


48. Ifthe numerical value ofis

a)1 b) 0 c) d)


49. Which expression is equivalent to

a) b) c) d)
50. If and what might be the measure of

a) 45° b) 330° c) 135° d) 450°


51. Which of the following is equal in value to

a) b) c) d)

52. The expression has the same value as

a) b) c) d)


53. Ifthen equals which of the following?

a) 1 b) -2 c) 2 d) 0


54. Solve for

θ = 11

55. In circle O, the length of radius OB is 5 inches and the length ofis 5 inches. The measure

of angle is

a) 1 radian b) 60 degrees c) radians d) more than 60°
56. If the coordinates of point A arewhat is the angle measurement formed by OA in the

standard position?



a) b) c) d)

57. As increases fromto, the value of

a) increases only b) increases and then decreases

c) decreases only d) decreases and then increases
58. If andfor what value(s) of x does

a) 0 b) c) d)

59. The motion of spring can be modeled by the equationwhere x is

oscillating and y is the distance, in inches, of the spring from the ceiling. What is the closest

to the ceiling that the spring gets?

a) 1.4 inches b) 1.6 inches c) 3 inches d) 0 inch

60. a) On the same set of axes, sketch the graphs ofandin the

interval Graph


  1. Give the exact value(s) for the intersection(s) of the two graphs. (π,0)

61. If and is in quadrant IV, find

62. Ifand θ is in quadrant III, find sin 2θ.
63. Ifand θ is a negative acute angle, find cos 2θ.
64. The expression 4 + is equivalent to

a) b) c) d)


65. The equationhas which of the following as a possible solution?

a) b) c) d)

66. Ifthen equals

a) b) c) d)

67. In the intervalhow many values of x satisfy the equation



a)1 b) 2 c) 3 d) 0
68. Prove:
69. Prove:
70. Prove:
71. Simplify: =
72. If then y =

a) b) c) d)

73. If x = 4, what is the value of 4
74. The expressionis equivalent to

a) b) c) d)

75. If, then

a) b) c) d)


76. For which of the following functions is

a) b) c) d)


77. Solve for x: x = 1
78. Solve for x: x = 2
79. The number of seconds in the period of a pendulum is the length of time required for the

pendulum to make one complete swing back and forth. The formulagives the

period, T, for a pendulum of length L in feet. If Todd wants to build a grandfather clock with

a pendulum that swings back and forth every 2 seconds, how long, to the nearest tenth of a

foot, should he make the pendulum? 3.2
80. Ifwhat is the value of a?

a) b) 2 c) d)13


81. Evaluate: =
82. What is the product of – 19
83. Expressin simplest a + bi form.
84. Given the quadratic equationin which a, b, c are integers. If the graph

intersects the x-axis in two distinct points whose abscissa are integers, thenmay equal

a) b) 0 c) 8 d) 9

85. Ifand 7 are the roots of the equationthen k must be equal to

a) b) c) 6 d) 8
86. One root of the equation is n. The other root, in terms of n, is

a) n – 3 b) 3 – n c) n/3 d) 3/n


87. If the root ofareand, then

a) p = 2 and q = b)and q = 1 c)and d) and


88. Which of the following is a function?

a) b) c) d)

89. If f(x) = 2x + 1 andfind:

a. = 7 b.= 5


90. The retail price of a new computer is $p. The store is offering an instant rebate, authorized by

the manufacturer, of $250 as well as a store discount of 10% of the sale price.



  1. Write a function f in terms of p that gives the cost of the computer after the instant rebate.

f(p) = p – 250

  1. Write a function g in terms of p that gives the cost of the computer after receiving the store discount. g(p) = .9p

  2. Form the composition functions f(g(p)) and g(f(p)). If the price of the computer is $1200, how much money is saved if the cost is computed using f(g(p)) instead of g(f(p))?

f(g(1200)) = 830 g(f(1200)) = 855 855 – 830 = 25 saved $25
91. Ifandwhat is

a) 2i b) –2i c) 2 + 2i d) 2 – 2i


92. Which statement must be true?



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