1. Final Exam Review Questions 3 Days
Precalculus
Final Exam Review Questions
3 Days

2. DAY 1

3. 1.) Find the values of θ for which this equation is true: sin θ = 0
a °k
b. 90° + 180°k
c. 0° + 360°k
d. 90° + 270°k

4. 2.) Find the values of θ for which this equation is true: cot θ = 0
a °k
b. 90° + 180°k
c. 0° + 360°k
d. 90° + 270°k

5. 3.) Which cosine equation has an amplitude of 2, period of 180°, and the phase shift of 0°.
a. y = 4cos 2θ
b. y = 2cos 4θ
c. y = 4cos 4θ
d. y = 2cos 2θ

6. 4.) Which sine equation has an amplitude of 3, period of 360°, and the phase shift of 90°.
a. y = cos (3θ – 180°)
b. y = 3cos (θ – 30°)
c. y = 3cos (θ – 90°)
d. y = 3cos (θ – 360°)

7. 5.) Which graph represents this equationb. c. d.

8. 6.) Which graph represents this equationb. c. d.

9. 7.) Find the values of x if
0° ≤ x ≤ 360°, and satisfy this equation: x = arcsin ½
a. 30°, 150°
b. 0°, 90°
c. 30°, 210°
d. 0°, 30°, 90°

10. 8.) Find the values of x if
0° ≤ x ≤ 360°, and satisfy this equation:
a. 30°, 150°
b. 0°, 90°
c. 30°, 210°
d. 0°, 30°, 90°

11. 9.) Evaluate sec (cos-1 ½). Assume all angles are in Quadrant I (for cos, sin, tan)
b. 2
c. 1/2
d. 4/5

12. 10.) Evaluate cos (cot-1 4/3). Assume all angles are in Quadrant I (for cos, sin, tan)5 3
b. 2 4
c. 1/2
d. 4/5

13. 11.) Evaluate . Assume all angles are in Quadrant I (for cos, sin, tan)
b. 2 c.
d. 0

14. 12.) Evaluate . Assume all angles are in Quadrant I (for cos, sin, tan)
b. 2 c.
d. 0

15. 13.) State the domain of y = Cos-1 x
a. All real numbers
b. -1 ≤ x ≤ 1
c. 0° < x < 180°
d. -90° < x < 90°

16. 14.) State the domain of y = sin-1 x
a. All real numbers
b. -1 ≤ x ≤ 1
c. 0° < x < 180°
d. -90° < x < 90°

17. 15.) State the domain of
y = Cos-1 x + 1
a. All real numbers
b. -1 ≤ x ≤ 1
c. 0° < x < 180°
d. -90° < x < 90°

18. 16.) Determine a counterexample for the following statement:
Arccos (x) = Arccos (-x) for -1 ≤ x ≤ 1
a. x = 2
b. x = -1
c. x = 0
d. x = 1

19. 17.) Determine a counterexample for the following statement:
Sin-1 (x) = -Sin-1 (-x) for -1 ≤ x ≤ 1
a. x = 2
IT’s a TRUE STATEMENT
There is no counter example
b. x = -1
c. x = 0
d. x = 1

20. 18.) Find the inverse of the function:
y = 2x + 7 a. b. c. d.

21. 19.) Write a cosine equation with a phase shift 0 to represent a simple harmonic motion with initial
position = -7, amplitude = 7, and period = 4 a. b. c. d.

22. 20.) Write a sine equation with a phase shift 0 to represent a simple harmonic motion with initial
position = 0, amplitude = 22, and period = 12 a. b. c. d.

23. 21.) Solve for 0° ≤ θ ≤ 90°: If cot θ = 2, find tan θ
b. 2/3
c. 1
d. 0

24. 22.) Solve for 0° ≤ θ ≤ 90°: If tan θ = 1, find cot θ
b. 2/3
c. 1
d. 0

25. 23.) Solve for 0° ≤ θ ≤ 90°: If sin θ = 40/41,
find tan θ
a. 1/2
b. 0
c. 9/40
d. 40/9

26. 24.) SIMPLIFY a. b. c. d.

27. 25.) SIMPLIFY a. b. c. d.

28. 26.) Find a numerical value of one trig function.b. c. d.

29. 27.) Find a numerical value of one trig function.b. c. d.

30. a. b. c. d. 28.) Use the sum or difference identity to find the
exact value of cos 255° a. b. c. d.

31. a. b. c. d. 29.) Use the sum or difference identity to find the
exact value of sin 195° a. b. c. d.

32. a. b. c. d. 30.) Use the sum or difference identity to find the
exact value of tan (-105°) a. b. c. d.

33. a. b. c. d. 31.) If tan x = 4/3 and cot y = 5/12, find sin (x – y) 5 x13 12 a. 3 y 5 b. c. d.

34. a. b. c. d. 32.) If sin x = 8/17 and tan y = 7/24, find cos (x – y) 1725 7 a. 15 y 24 b. c. d.

35. 33.) If tan θ = 5/12 and θ is in Quadrant III, find the exact value of cos 2θ13 b. c. d.

36. 34.) If tan θ = 5/12 and θ is in Quadrant III, find the exact value of sin 2θb. c. d.

37. 35.) Use a half-angle identity to find the value of sinb. c. d.

38. 36.) Use a half-angle identity to find the value of cosb. c. d.

39. 37.) Solve for 0° ≤ x ≤ 180°:
a. 0°, 90°
b. 30°, 150°
c. 0°, 180°
d. 120°

40. 38.) Solve for 0° ≤ x ≤ 180°:
a. 0°, 90°
b. 30°, 150°
c. 0°, 180°
d. 120°

41. DAY 2

42. 39.) Solve for 0° ≤ x ≤ 180°:
a. 0°, 90°
b. 30°, 150°
c. 0°, 180°
d. 120°

43. 40.) Write the equation 5x – y + 3 = 0 in normal form.b. c. d.

44. 41.) Write the equation 5x + y = 7 in normal form.b. c. d.

45. 42.) Write the standard form of the equation of a line for which the length of the normal is 3 and the
normal makes a 60° angle with the positive x-axis. a. b. c. d.

46. 43.) Write the standard form of the equation of a line for which the length of the normal is 2 and the
normal makes a 150° angle with the positive x-axis. a. b. c. d.

47. 44.) Write the standard form of the equation of a line for which the length of the normal is 32 and the
normal makes a 120° angle with the positive x-axis. a. b. c. d.

48. a. b. c. d. 45.) Find the distance in units between P(-3, 5) and
12x + 5y – 3 = 0 a. b. c. d.

49. a. b. c. d. 46.) Find the distance in units between P(-5, 0) and
x – 3y + 11 = 0 a. b. c. d.

50. 47. ) has a magnitude of 1. 5 cm and a amplitude of 135°
47.) has a magnitude of 1.5 cm and a amplitude of 135°. Find the magnitude of its vertical and horizontal
components. a. b. c. d.

51. 48. ) has a magnitude of 4. 3 cm and a amplitude of 330°
48.) has a magnitude of 4.3 cm and a amplitude of 330°. Find the magnitude of its vertical and horizontal
components. a. b. c. d.

52. 49.) has a magnitude of 4.2 m. If , what is the magnitude of ?b. c. d.

53. 50.) has a magnitude of 4.2 m. If , what is the magnitude of ?b. c. d.

54. 51.) Find the ordered pair that represents the vector
from A(-2, 5) to B(1, 3). ?
a. (3, -2)
b. (7, 5)
c. (5, -5)
d. (2, 6)

55. 52.) Find the ordered pair that represents the vector
from A(-9, 2) to B(-4, -3). ?
a. (3, -2)
b. (7, 5)
c. (5, -5)
d. (2, 6)

56. 53.) If is a vector from A(12, -4) to B(19, 1), find the magnitude of

57. 54.) If is a vector from A(-9, 2) to B(-4, -3), find the magnitude of

58. a. b. c. d. 55.) Write the as the sum of unit vectors for points
C(-1, 2) and D(3, 5). a. b. c. d.

59. 56.) Find an ordered pair to represent in each equation if = (1, -3, -8) and = (3, 9, -1)b. c. d.

60. 57.) Find an ordered pair to represent in each equation if = (1, -3, -8) and = (3, 9, -1)b. c. d.

61. 58.) Find the ordered triple that represents the vector
from A(8, 1, 1) to B(4, 0, 1). ?
a. (3, -2, 10)
b. (7, 5, -3)
c. (5, -5, 2)
d. (-4, -1, 0)

62. 59.) Find the inner product of: (3, 5)  (4, -2)a. b. c. d.

63. 60.) Find the inner product of: (4, 2)  (-3, 6)a. b. c. d.

64. 61.) Find the inner product of: (7, -2, 4)  (3, 8, 1)a. b. c. d.

65. 62.) Find the cross product: (7, 2, 1) x (2, 5, 3)a. b. c. d.

66. 63.) Find the cross product: (-1, 0, 4) x (5, 2, -1)a. b. c. d.

67. 64.) Name the polar curve of: r = 5 + 2cos θb. c. d.

68. 65.) Name the polar curve of: r = 3 + 3sin θb. c. d.

69. 66.) Name the polar curve of: r = 2θb. c. d.

70. 67.) Convert into polar coordinates.b. c. d.

71. 68.) Convert into polar coordinates.b. c. d.

72. 69.) Convert into rectangular coordinates.b. c. d.

73. 70.) Convert into rectangular coordinates.b. c. d.

74. 71.) Change this polar equation into a rectangular equation.b. c. d.

75. 72.) Change this polar equation into a rectangular equation.b. c. d.

76. 73.) Change this rectangular equation into a polar equation.b. c. d.

77. 74.) Change this rectangular equation into a polar equation.b. c. d.

78. 75.) Identify the conic section:a. b. c. d.

79. 76.) Identify the conic section:a. b. c. d.

80. 77.) Identify the conic section:a. b. c. d.

81. 78.) Identify the conic section:a. b. c. d.

82. 79.) What is the correct vertex of this conic section :b. c. d.

83. 80.) What is the correct vertex of this conic section :b. c. d.

84. 81.) Which conic section has a directrix of y = 0b. c. d.

85. 82.) Which conic section has a directrix of x = 1/2b. c. d.

86. 83.) Which conic section has focal pointb. c. d.

87. DAY 3

88. a. b. c. d. 84.) Which conic section has focal point Center is (1, 2)
Just match
up the centers
Center is (4, -2) c.
Center is (1, 2) d.
Center is (½, -4/5)

89. a. b. c. d. 85.) What is the eccentricity of this conic section: 9 81 c.
Eccentricity = c/a d.

90. 86.) What is the eccentricity of this conic section:b. c. d.

91. 87.) Which standard form equation of an hyperpola has slant asymptotes:b. c. d.

92. 88.) Which standard form equation of an hyperpola has slant asymptotes:b. c. d.

93. 89.) Express using radicals:b. c. d.

94. 90.) Express using radicals:b. c. d.

95. 91.) Express using rational exponents:b. c. d.

96. 92.) Write this in logarithmic form:b. c. d.

97. 93.) Write this in logarithmic form:b. c. d.

98. 94.) Evaluate each expression:b. c. d.

99. 95.) Evaluate each expression:b. c. d.

100. 96.) Solve: a. b. c. d.

101. 97.) Solve: a. b. c. d.

102. 98.) Solve: a. b. c. d.

103. 99.) Solve: a. b. c. d.

104. 100.) Solve: a. b. c. d.

105. 101.) Which sequence below is arithmetic. :
d. 2, 4, 8, …

106. 102.) Which sequence below is geometric. :
a. 4, 8, 12, …
b. 9, 3, 1, ..
c. 1.5, 3, 4.5, …
d. -5, -3, -1, …

107. a. 9 b. -5 c. -25 d. 10 103.) Find 16th term in the sequence:
1.5, 2, 2.5, …
a. 9
b. -5
c. -25
d. 10

108. a. 9 b. -5 c. -25 d. 10 104.) Find 19th term in the sequence:
11, 9, 7, …
a. 9
b. -5
c. -25
d. 10

109. 105.) Find 9th term in the sequence:a. b. c.
d. 10

110. 106.) What is the sum of the first 11 terms of the arithmetic sequence: :
-3 – … a. b. c.
d. 59

111. 107.) What is the sum of the first 9 terms of the geometric sequence: :… a. b. c. d

112. 108.) Evaluate the limit of a. b. c. d.

113. 109.) Evaluate the limit of a. b. c. d.

114. 110.) Find the sum of this infinite geometric series:a. b. c. d.

115. 111.) Find the sum of this infinite geometric series:a. b. c. d.

116. 112.) Evaluate the limit of a. b. c. d.

117. 113.) Evaluate the limit of a. b. c. d.

118. a. b. c. d. 114.) Evaluate the limit of as x approaches 1 for
f(x) = 2x + 1 and g(x) = x – 3 a. b. c. d.

119. a. b. c. d. 115.) Evaluate the limit of as x approaches 1 for
f(x) = 3x – 4 and g(x) = 2x + 5 a. b. c. d.

120. 116.) Find the derivative of:b. c. d.

121. 117.) Find the derivative of:b. c. d.

122. 118.) Find the derivative of:b. c. d.

123. 119.) Find the integral of: a. b. c. d.

124. 120.) Find the integral of: a. b. c. d.

125. 121.) Find the integral of: a. b. c. d.