Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies.

Transcription

1 MATH 1113 Precalculus FINAL EXAM REVIEW irections: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. Question: 1 QI: ,, ,, , 2, ,, Question: 2 QI: 1535

2 Ship A is 5.28 nautical miles from port. At the port, the angle between ship A and ship is 42. At ship A, the angle between the port and ship is 63. At ship, the angle between the port and ship A is 75. the distance between the port and ship A the distance between the port and ship the distance between ship A and ship the average distance each ship is from port Question: 3 QI: 1601 Which of these ratios defines the cosine function? Question: 4 QI: 1665

3 Given the triangle below, find the missing length and compute the cosecant of angle H. Question: 5 QI: 1753 Which equation could be used to find the height of the lighthouse? Question: 6 QI: 1768 What is the domain of the inverse tangent function? Any real number Question: 7 QI: 1783

4 Use your calculator to evaluate y = tan 1 (4.65). Use degree mode, and give your answer to three decimal places No such number exists Question: 8 QI: 1794 Question: 9 QI: 1809 Question: 10 QI: 1847 Question: 11 QI: 1873

5 A blue boat and a red boat are on the same side of a lake and are 18 miles apart. The blue boat is 30 miles from a lighthouse on the opposite side of the lake. The angle formed by the boats and the lighthouse, and whose vertex is at the blue boat, measures 120. Find the distance from the red boat to the lighthouse miles 42 miles 18.6 miles 38.7 miles Question: 12 QI: 1889 What is the area of a triangle with sides measuring 26 inches, 26 inches, and 17 inches? 35.6 in in in in 2 Question: 13 QI: ,808 I 0 563,135,147 I 0 7,500 I 0 31,622,776 I 0 Question: 14 QI: 2460

6 Question: 15 QI: 2509 Write the equation of a line in slope-intercept form that passes through y = 4x y = 2x + 7 Question: 16 QI: 2544

7

8 Question: 17 QI: Question: 18 QI: Question: 19 QI: 2849

9 Question: 20 QI: Question: 21 QI: 3704

10 The inverse does not exist. Question: 22 QI: 5205 Which of the following functions will have the same graph as w (x) = 3 x+2? a (x) = 9 x b (x) = 9. 3 x c (x) = 3 x + 2 d (x) = 3x + 2 Question: 23 QI: 5214

11 A company has a fixed cost of $2000 when it is producing. Each item that it makes has its own cost of $35. How much will it cost the company to produce 2500 of these items? $2,000 $2,035 $87,500 $89,500 Question: 24 QI: 9279 (x 4) 2 + (y 2) 2 = 3 (x + 4) 2 + (y + 2) 2 = 3 (x + 4) 2 + (y + 2) 2 = 9 (x 2) 2 + (y 4) 2 = 9 Question: 25 QI: 9313 Find the distance between the centers of the two circles whose equations are and. 4 Question: 26 QI: 9327

12 Question: 27 QI: 9340

13 Which of the following points is an x-intercept of the function? (0, 1) (0, 4) (3, 80) (2, 0) Question: 28 QI: 9356 At what values of x, if any, does the following graph pass the vertical line test for functions? Question: 29 QI: 9359 Which of the following statements is true regarding the graph below? The graph is a function because it passes the vertical line test. The graph is not a function because it is undefined at x = 0. The graph is not a function because it fails the vertical line test at x = 0. The graph is not a function because it fails the horizontal line test at y = 0. Question: 30 QI: 9393

14 AC is a right triangle with a hypotenuse of 10 meters and legs of lengths x and y. Express the area of the triangle as a function of x. Question: 31 QI: 9405 Question: 32 QI: 9413

15 Question: 33 QI: 9427 etermine the interval where f (x) = x 2 6x is increasing. Question: 34 QI: 9434 Find the slope of the line through the two points ( 2, 4) and (1, 4). 8 0 Undefined Question: 35 QI: 9463

16 Artificial Technology was studied for the last 12 months and its stock price is plotted on the graph. escribe the slope of the line. Positive Negative Undefined 0 Question: 36 QI: 9477

17 At the gas pump, as the price per gallon increases, the number of customers will decrease. A study at Robbie Robin s gas station revealed the data below. A plot and a fitted line is made to the data. Use the data to identify the equation of the line in slope-intercept form. y = 40x y = 40x y = 40x y = 40x Question: 37 QI: 9490

18 Question: 38 QI: 9525 Given the graph, find the matching equation. 1 y = x 3 1 y = x 3 y = 3x y = 3x Question: 39 QI: 9549 What is the slope of the line perpendicular to the line y = 2x 5? 2 5 Question: 40 QI: 9556

19

20 Question: 41 QI: 9626 Which relation is represented by the following graph? x = y 2 y = x 3 Question: 42 QI: 9634 Question: 43 QI: 9748

21 Write the equation for the parabola whose graph is shown below. Question: 44 QI: 9774 Identify the y-intercept of the parabola: y = 3x 2 6x 5. y = 0 y = 1 y = 3 y = 5 Question: 45 QI: 9782 What can you conclude about equation of the following parabola? The discriminant is zero. The discriminant is negative. The value of a is 0. The constant is 0. Question: 46 QI: 9797

22 A fence of 200 feet is used to enclose a rectangular garden. Find the maximum area possible for the garden. 50 square feet 2,500 square feet 3,000 square feet 4,000 square feet Question: 47 QI: 9815 Find the vertex of the parabola defined by the function y = 4x 2 + 2x 3 by completing the square. Question: 48 QI: 9948 Given that one zero is x = 2, and another zero is x = 3, find the zeros of f(x) = x 4 3x 3 6x x 24. x = 3, 1 time; x = 2, 3 times x = 3, 1 time; x = 2, 3 times x = 3, 3 times; x = 2, 1 time x = 3, 1 time; x = 2, 3 times Question: 49 QI: or 0, positive; 3 or 1, negative 5, positive; 4, negative 3, positive; 2, negative 3 or 1, positive; 2 or 0, negative Question: 50 QI: 9979

23 Which graph has x = 2 and y = 2 as asymptotes? Question: 51 QI: 10012

24 Graph the following rational function:.

25 Question: 52 QI: Find the vertical asymptote(s), if any, of. No vertical asymptote x = 3 x = 1, x = 1 x = 1 Question: 53 QI: Find the horizontal asymptotes, if any, of the graph of. No horizontal asymptote Question: 54 QI: True or false? is a one-to-one function. true false Question: 55 QI: Find the inverse of the function, f 1 (x), if it exists. Question: 56 QI: 10118

26 Find the inverse of the function, if it exists. The inverse does not exist. Question: 57 QI: Solve Question: 58 QI: Question: 59 QI: A banker can lend money at 9.1% compounded monthly or at 9.3% compounded quarterly. If the length of the loan is 15 years, which type of loan profits the banker more? Question: 60 QI: 10213

27 In 1990 the population of the U.S. was around 250 million and was expected to grow according to the function P (x) = 250,000,000e 0.009x, where x is the number of years after What will the expected U.S. population be in 2004, according to this model? 3.53 billion million 2.6 billion Question: 61 QI: Question: 62 QI: Which of these two functions, oth increase Neither increases or, increases as x increases? Question: 63 QI: Solve.

28 Question: 64 QI: Question: 65 QI: Question: 66 QI: Solve for x Question: 67 QI: Impossible to solve. Solve for x No solution 0.087

29 Question: 68 QI: x = 3 and x = 4. x = 4. x = 5. Question: 69 QI: , Question: 70 QI: % 88% 0.12P P 0 Question: 71 QI: 10475

30 21 minutes 52 minutes 425 minutes The turkey will never reach a temperature of 425 degrees. Question: 72 QI: Quadrant I Quadrant II Quadrant III Quadrant IV Question: 73 QI: Suppose that you are told that two angles measuring 2a + 7 and 3a + 4 degrees are complementary. What are the two angles? 15.8 and and and and 64.6 Question: 74 QI: Question: 75 QI: 11285

31 What is the length of the arc intercepted by an angle of 10 on a circle with a radius of 10 meters? Round the answer to the nearest hundredth meters 0.87 meters 1.75 meters 100 meters Question: 76 QI: Question: 77 QI: Simplify the expression without using a calculator Question: 78 QI: Which of these statements accurately describes the amplitude of a trigonometric function? The amplitude is the number that describes the width of a single repetition of the function. The amplitude is an expression that is used to calculate the period of the function. The amplitude is twice the height of the function from the x-axis to its highest point. The amplitude is a real number value used to help determine the lowest point on the curve and the highest point.

32 Question: 79 QI: Question: 80 QI: hours 10 hours 7000 hours Question: 81 QI: Question: 82 QI: 11359

33 What is the amplitude of the function y = 3 sin x + 2? π 0 Question: 83 QI: The temperature of a particular patient in a hospital is modelled by the following function where t is the time in hours: 3.5 hours 14 hours 7 hours How long will it take for the patient s temperature to reach its first maximum? Question: 84 QI: In which quadrant is cos θ > 0 and tan θ < 0? Quadrant I Quadrant II Quadrant III Quadrant IV Question: 85 QI: 11375

34 Which of the following is a graph of one period of y = cot 2x? Question: 86 QI: 11379

35 etermine an equation for the graph below. The graph shows one complete period. y = sec x y = sec x y = csc x y = csc x Question: 87 QI: etermine the exact value of Question: 88 QI: Solve the following equation for x: Question: 89 QI: 11400

36 5.3 mi 8.8 mi 7.5 mi 3.9 mi Question: 90 QI: Question: 91 QI: Question: 92 QI: 11440

37 Question: 93 QI: Question: 94 QI: Question: 95 QI: Question: 96 QI: 11495

38 A is a line 652 feet long on one bank of a stream. C is a point on the opposite bank. AC = 50 and AC = 48. Find the width of the stream from C to A Question: 97 QI: Question: 98 QI: Question: 99 QI: No solution impossible Question: 100 QI: 13854

39 etermine the domain for the function: The answer is not shown. Question: 101 QI: eginning with the function y = (x 1) 2 + 2, what function would represent the same curve 4 times wider? y = 4 (x 1) Question: 102 QI: y = 4 (x 1) etermine the distance between the two points ( 3, 11) and (4, 15). Round your answer to the nearest hundredth, if needed Question: 103 QI: For two angles to be described as coterminal, which of the following must be the difference in their measures? A multiple of 360 A multiple of 720 Question: 104 QI: , 2.791, 5.064, and radians and radians and radians and radians.

40 Question: 105 QI: x y 2x 2y Write an expression for the horizontal leg of the triangle. Question: 106 QI: Question: 107 QI: 16472

41 Question: 108 QI: The distance between two points can be found. Using an averaging formula Using a formula derived from the Pythagorean Theorem. y finding the length of a parallel line. y dividing by the negative inverse of the length of a perpendicular line. Question: 109 QI: Any point (x, y) that is the square root of the distance away from the point (h, k) is on the circle whose radius is r. true false Question: 110 QI: Identify the center and radius of the circle. (x 2 4x + 4) + ( y 2 + 6y + 9) = 16 ( 3, 4), 4 (2, 3), 4 (3, 1), 16 ( 2, 3), 8 Question: 111 QI: 18459

42 Graph. (x + 3) 2 + ( y + 4) 2 = 36 Question: 112 QI: The Law of Sines states that for any triangle AC with sides a, b, and c and opposite angles A,, and C, true false a sin A = b sin = c sin C. Question: 113 QI: 20309

43 Question: 114 QI: m m m m

44 Sketch the graph of the function without recourse to a graphic calculator. g(x) = 3 x Graph A Graph Graph C Graph

45 Question: 115 QI: For which x values does the graph of y = 4 x cross the x-axis? None Negative values of x x values less than 1 Positive values of x Question: 116 QI: The formula relating arc length, radius and a central angle is θ = sr. true false Question: 117 QI: true false Question: 118 QI: What is the equation for this graph? y = sin x y = cos x y = 2 sin x y = 2 cos x Question: 119 QI: true false

46 Question: 120 QI: The function y = sec 2x has zeros at x = π / 4 and x = 3π / 4. true false Question: 121 QI: Which of the following is equal to tan 340? cot 40 tan 20 tan 70 tan 20 Question: 122 QI: true false Question: 123 QI: sin 2 x tan 2 x sin 2 x + 1 Question: 124 QI: The distance r to a star is measured in parsecs, but astronomers like to use the istance Modulus M given by the formula M = 5 log r 5. If a star is 52 parsecs away, what is its distance modulus? Round your answer to the nearest hundredth.

47 Question: 125 QI: Question: 126 QI: eginning with the function y = x 2, which of the following shows the changes you would make so that the vertex lies at (2, 4) and the parabola opens in a positive direction? y = (x + 2) 2 4 y = (x 2) 2 4 y = (x + 4) 2 2 y = (x 4) Question: 127 QI: The function y = 2x 2 + x + 3 has a maximum value. true false Question: 128 QI: f (x) = 3x 3 5x 2 + 6x 4 has 3 or 1 negative real zeros. true false Question: 129 QI: Find a polynomial of degree 3 with zeros x = 1, 8, 8, and f (1) = 126 x 3 x 2 64x 64 x 3 + x 2 64x 64 x 3 + x x + 64 x 3 + x x + 64

48 Question: 130 QI: Find all real zeros and their multiplicities. f (x) = (x 4) (x + 5) (x 2 9) Question: 131 QI: Write this full statement (equation) in mathematical shorthand: "The power to which 6 must be raised in order to get 36 is 2." log 2 36 = 6 log 6 2 = 36 log 6 36 = 2 log 2 6 = 36 Question: 132 QI: Question: 133 QI: 25578

49 Question: 134 QI: True or false? log is an expression that cannot be evaluated. true false Question: 135 QI: Use the change of base formula to approximate the value of log Question: 136 QI: 25832

50 Sketch the graph of.

51 Question: 137 QI: Question: 138 QI: 26479

52 Question: 139 QI: Using the compound interest formula, approximately how many years would it take for an investment of $10,000 at 6% interest, compounded quarterly, to have a value of $20,000? 9 years, 1 month 10 years, 6 months 11 years, 11 months 11 years, 8 months Question: 140 QI: 26797

53 Which transformation occurs when y = x 2 becomes y = x 1/2? Question: 141 QI: If you want to invest $6,000 and have it increase to $7,500 in 3 years, what rate of interest rounded to the nearest tenth of a percent is necessary if your investment is compounded continuously? 5.5% 6.8% 7.4% 8.7%

54 Question: 142 QI: y = mx + b is the form of a line. Question: 143 QI: Is the following function odd, even, both or neither? f (x) = x odd even both odd and even neither odd nor even Question: 144 QI: True or false? true false Question: 145 QI: Given r (x) = 7x 22 and t (x) = x 2 + 3, express the sum (r + t) (x). x 2 + 7x 19 x 2 + 7x x 19 7x 2 25 Question: 146 QI: 39523

55 Set up the composite when Simplify. and. Question: 147 QI: Given f (x) = 2x + 8, find the value of f (7) + f ( 5) Question: 148 QI: 40556

56 Graph: (x) =

57 Question: 149 QI: Question: 150 QI: Use a calculator to evaluate the expression Question: 151 QI: 40724

58

59 Question: 152 QI: Find a point-slope form of an equation of the line that passes through the point and has the slope Question: 153 QI: 46254

60 Find the graph of the function.

61 Question: 154 QI: units to the right and 7 units down 5 units to the left and 7 units up 5 units to the left and 7 units down 5 units to the right and 7 units up Question: 155 QI: eginning with the graph of the function which of the following shows the changes you would make to the function so that the vertex lies at and the parabola becomes 4 times more compressed and it opens in a positive direction? Question: 156 QI: Given that a function is reflected across the x-axis and we know the points and are on the curve, what points must lie on the reflection? Question: 157 QI: A parabola reflected over the x-axis would have the equation:

62 Question: 158 QI: Find all the real zeros of: Question: 159 QI: 49696

63 Identify the graph that is represented by a polynomial function that has one negative real root with even multiplicity.

64 Question: 160 QI: What are the coordinates of point A? Question: 161 QI: If f ( 6) = 19, then f 1 (19) =? 6 19 Question: 162 QI: Are the following functions inverses of each other? yes no

65 Question: 163 QI: Which of the following is not an exponential function? All of the above are exponential functions. Question: 164 QI: Solve for a. log (log a) = No Solution Question: 165 QI: Choose the function that best corresponds with the graph. Question: 166 QI: 79136

66 Choose the asymptotes for the function. x = 3 y = x x = 3 y = x x = 3 y = x + 6 x = 3 y = x + 6 Question: 167 QI: escribe the end behavior of the graph of the following function. The graph points up on both ends. The graph points down on both ends. The graph points down on the left end and up on the right end. The graph points up on the left end and down on the right end. Question: 168 QI: Question: 169 QI: Suppose f (x) is a polynomial function with real coefficients and zeros. Find three additional zeros of f (x).

67 MATH 1113 Precalculus FINAL EXAM REVIEW ANSWERS Question: 1. I: 758 Question: 2. I: 1535 C Question: 3. I: 1601 C Question: 4. I: 1665 C Question: 5. I: 1753 C Question: 6. I: 1768 A Question: 7. I: 1783 Question: 8. I: 1794 A Question: 9. I: 1809 A Question: 10. I: 1847 Question: 11. I: 1873 Question: 12. I: 1889 Question: 13. I: 2453 Question: 14. I: 2460

68 Question: 15. I: 2509 Question: 16. I: 2544 C Question: 17. I: 2610 C Question: 18. I: 2755 A Question: 19. I: 2849 Question: 20. I: 2950 Question: 21. I: 3704 Question: 22. I: 5205 Question: 23. I: 5214 Question: 24. I: 9279 E Question: 25. I: 9313 Question: 26. I: 9327 Question: 27. I: 9340 Question: 28. I: 9356 Question: 29. I: 9359 A Question: 30. I: 9393 A

69 Question: 31. I: 9405 Question: 32. I: 9413 Question: 33. I: 9427 Question: 34. I: 9434 C Question: 35. I: 9463 A Question: 36. I: 9477 Question: 37. I: 9490 A Question: 38. I: 9525 Question: 39. I: 9549 Question: 40. I: 9556 Question: 41. I: 9626 Question: 42. I: 9634 Question: 43. I: 9748 Question: 44. I: 9774 Question: 45. I: 9782 Question: 46. I: 9797

70 Question: 47. I: 9815 Question: 48. I: 9948 Question: 49. I: 9953 Question: 50. I: 9979 Question: 51. I: Question: 52. I: Question: 53. I: A Question: 54. I: Question: 55. I: A Question: 56. I: A Question: 57. I: Question: 58. I: C Question: 59. I: Question: 60. I: C Question: 61. I: C Question: 62. I: 10235

71 Question: 63. I: Question: 64. I: Question: 65. I: Question: 66. I: A Question: 67. I: C Question: 68. I: Question: 69. I: A Question: 70. I: Question: 71. I: Question: 72. I: Question: 73. I: C Question: 74. I: Question: 75. I: C Question: 76. I: Question: 77. I: Question: 78. I: 11333

72 Question: 79. I: Question: 80. I: A Question: 81. I: A Question: 82. I: A Question: 83. I: A Question: 84. I: Question: 85. I: Question: 86. I: Question: 87. I: A Question: 88. I: A Question: 89. I: A Question: 90. I: A Question: 91. I: Question: 92. I: C Question: 93. I: C Question: 94. I: 11446

73 Question: 95. I: A Question: 96. I: A Question: 97. I: C Question: 98. I: Question: 99. I: C Question: 100. I: C Question: 101. I: C Question: 102. I: C Question: 103. I: C Question: 104. I: A Question: 105. I: C Question: 106. I: Question: 107. I: C Question: 108. I: Question: 109. I: Question: 110. I: 18453

74 Question: 111. I: A Question: 112. I: Question: 113. I: Question: 114. I: Question: 115. I: A Question: 116. I: Question: 117. I: Question: 118. I: A Question: 119. I: A Question: 120. I: Question: 121. I: Question: 122. I: Question: 123. I: Question: 124. I: Question: 125. I: A Question: 126. I: 25057

75 Question: 127. I: Question: 128. I: Question: 129. I: Question: 130. I: Question: 131. I: C Question: 132. I: Question: 133. I: Question: 134. I: A Question: 135. I: C Question: 136. I: A Question: 137. I: Question: 138. I: Question: 139. I: Question: 140. I: Question: 141. I: C Question: 142. I: slope-intercept,slope intercept

76 slope-intercept,slope intercept Question: 143. I: Question: 144. I: Question: 145. I: A Question: 146. I: Question: 147. I: Question: 148. I: C Question: 149. I: Question: 150. I: E Question: 151. I: C Question: 152. I: C Question: 153. I: Question: 154. I: Question: 155. I: Question: 156. I: C Question: 157. I: C Question: 158. I: 49427

77 A Question: 159. I: A Question: 160. I: C Question: 161. I: A Question: 162. I: A Question: 163. I: Question: 164. I: Question: 165. I: A Question: 166. I: C Question: 167. I: Question: 168. I: A Question: 169. I: E