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MR22 Review for Test3 2013 1. What is the sum of 1) 2) and 3) ? 4) 2. Express in simplest form: 3. A rectangular garden with an area of has a width of . what is the length of the garden? 4. Factor completely: x 4 – 16 5. Express in simplest form: 6. The expression 1) 2) 3) 4) is equivalent to 13. What is the solution set for the equation |3 – 2x| = 5? 1) {–1,4} 3) {–1} 2) {1,–4} 4) {4} 7. For all values of x for which the expression is defined: Express as a single fraction in lowest terms: 8. Perform the indicated operations and simplify completely: 9. Express in simplest form: 10. For all values of for which the expression is defined, solve for : 11. Solve for x: 5 + 12. Solve for x. < – 3 = 9 14. Which represents the solution set for x in the inequality | 2x - l | < 7? 1) 2) 3) 4) {x| x < –3 or x > 4} {x| x < –4 or x > 3} {x| –4 < x < 3} {x| –3 < x < 4} 15. Which graph represents the solution set of |2x + 1| > 7? 1) 2) 3) 4) 16. Express – (2 radical form. – ) in simplest 17. Express the equation below in simplest radical form. 25. The roots of the equation x 2 – 10x + 25 = 0 are 18. The expression below is equivalent to: 1) 2) 3) 1) 2) 3) 4) 4) 19. Solve algebraically for x: 4 – = 1 20. Solve for all values of that satisfy the following equation 21. What is the solution set of 1) {1} 3) {–2,1} = x? 2) {–2} 4) {–1,2} 22. The roots of the equation 2x 2 + 7x – 3 = 0 are 1) 3) 2) 4) 23. Find the solution of the inequality x 2 – 4x > 5, algebraically 24. The discriminant of a quadratic equation is 24. The roots are 1) 2) 3) 4) imaginary real, rational, and equal real, rational, and unequal real, irrational, and unequal imaginary real and irrational real, rational, and equal real, rational, and unequal 26. Determine the sum and the product of the roots of 3x 2 = 11x – 6. 27. Base your answer to the following question on Which equation represents the parabola shown in the accompanying graph? 35. If range? , what are its domain and 1) domain: ; range: 2) domain: ; range: 3) domain: ; range: 4) domain: ; range: 36. The expression below is undefined when x equals 1) f(x) = (x + 1) 2 – 3 2) f(x) = –(x – 3) 2 + 1 3) f(x) = –(x + 3) 2 + 1 4) f(x) = –(x – 3) 2 – 3 1) 0º 3) 45º 4) 60º 37. In the set of real numbers, what is the domain of ? 28. Express in simplest form in terms of i: 29. Express the sum of 4 and 3 simplest radical form, in terms of i. 2) 30º 1) x –5 3) x > –5 in 2) x 4) x –5 0 38. For which value of x is f(x) = 1) 1 30. 2) 0 3) 3 4) –3 39. If The expression above is equivalent to 1) 1 2) – 1 3) i 4) – i 31. Solve for and express the roots in simplest form: 32. When the sum of –4 + 8i and 2 – 9i is graphed, in which quadrant does it lie? 1) I 2) II 3) III 4) IV 33. When represented graphically, in which quadrant does the sum of –4 – i and 3 + 4i lie? , the domain of 34. Given the relation {(8,2), (3,6), (7,5), (k,4)}, which value of k will result in the relation not being a function? 1) 1 2) 2 3) 3 4) 4 1) 2) 3) 4) undefined? 40. Base your answer to the following question on Find if 52. Which expression is equivalent to cos 120°? 41. If f(x) = 2x – 1 and g(x) = 3x + 5, then (f • g)(x) is equal to 53. What is the number of degrees in an angle whose radian measure is ? 1) 5x + 4 3) 6x + 9 42. 1) cos 60° 3) –sin 60° 1) 150 2) 6x + 2 4) 6x 2 + 7x – 5 If f(x) = 3x + 1 and g(x) = x 2 – 43. If f(x) = 2x – 5 and g(x) = 1, find (f • g)(2). 45. What is the inverse of the function 1) 2) 3) 4) ? 1) 2) 58. If 1) 3) 3) III 4) IV 49. Expressed as a function of a positive acute angle, cos (–305º) is equal to 2) cos 55º 4) sin 55º 50. Expressed as a function of a positive acute angle, sin (–230°) is equal to 1) sin 50° 3) cos 50° 3) 4) is 3) 4) , evaluate . 59. In which interval of f(x) = cos(x)is the inverse also a function? 48. If sin is less than 0 and sec is greater than 0, in which quadrant does the terminal side of lie? 1) –cos 55º 3) –sin 55º 2) 57. The value of sine and cosine sine and secant sine and tangent sine and cosecant 2) II 56. Base your answer to the following question on If and , what is ? 1) 47. Which functions are positive for angles terminating in Quadrant II? 1) I 4) 518 1) 2) 3) 4) 46. If x varies inversely as y, and x = –34 when y = –2, find x when y = 4. 1) 2) 3) 4) 3) 330 55. What is the solution set of the equation when ? evaluate 2) y = 4) y = 3) y = 2) 165 54. Express 450º in radian measure. 44. What is the inverse of the function y = 3x – 2? 1) y = 3x + 2 2) cos 30° 4) –sin 30° 2) –sin 50° 4) –cos 50° 51. Express sin 150° as a function of a positive acute angle. 60. If 1) sin A = 3) cos A = 2) 4) = A then 2) sin A = 4) cos A = 61. What is the principal value of 1) 3) 2) 4) 62. Express the value of sin (Arc tan radical form. ) in simplest 63. Which equation is graphed in the diagram below? 69. Which equation is represented by the graph below? 1) 2) 1) 3) 3) 4) 64. What is the period of the function f( ) = –2cos 3 ? 1) 2) 3) 4) 2 65. What is the period of the function y = sin( – )? 1) 2) 3) 4) 6 66. A mass on a spring oscillates according to the equation x(t) = 3 + 7 cos(4t + 3). What is the amplitude of its motion? 1) 3 2) 4 3) 7 4) 10 67. What is the maximum value of y for the equation y = 1 + 3 sin x? 1) 1 2) 2 3) 3 4) 4 68. The graph of which equation has amplitude 2 and period ? 1) y = 2 cos 2x 3) y = 2 sin x 2) y = sin 2x 4) y = 2 cos x 2) 4) 70. Write an equation for the graph of the trigonometric function shown below. 71. A radio transmitter sends a radio wave from the top of a 50-foot tower. The wave is represented by the accompanying graph. What is the equation of this radio wave? 1) y = sin x 3) y = sin 1.5x 2) y = 1.5 sin x 4) y = 2 sin x 72. Which equation is represented in the graph below? 1) y = 2 sin x 3) y = 2 cos x 2) y = sin 2x 4) y = cos 2x 73. What is the solution set for the interval 1) {30°, 150°} 3) {30°, 330°} in 2) {60°, 120°} 4) {60°, 300°} 74. Solve the equation 2 tan C – 3 = 3 tan C – 4 algebraically for all values of C in the interval 0° C< 360°. 75. Find all values of in the interval 0° 360° that satisfy the equation sin 2 = sin . 76. Base your answer to the following question on Solve the following equation algebraically for all values of in the interval 0° 180°. 2 sin – 1 = 0 2) is equivalent to 1) 77. The expression cot • sec is equivalent to 1) 79. The expression 3) csc 4) sin 78. The expression 1 – sec x is equivalent to 1) –tan x 2) 3) 4) 2) 3) 4) 80. If sec (a + 15)° = csc (2a)°, find the smallest positive value of a, in degrees. 81. If tan (x + 20) = cot x, a value of x is 1) 35 2) 45 3) 55 4) 75 82. If sin (2x + 20)° = cos 40°, find x. Answer Key MR22 Reveiw for Test3 in 2nd marking period 2013 1. 2. 2 – or 3. 4. (x 2+4)(x+2)(x–2) 5. 6. 35. 1 71. 2 36. 3 72. 3 37. 1 73. 4 38. 3 74. 45 and 225 39. 4 75. 0, 60, 180, 300 76. 30 and 150 40. 2 41. 3 77. 3 42. 10 78. 2 8. 43. 7 79. 1 9. 44. 2 80. 25 10. 45. 4 81. 1 82. 15 7. 11. 6 46. 17 12. 0 < x < 2 47. 4 13. 1 48. 4 14. 4 49. 2 15. 1 50. 1 16. 51. 17. 52. 4 53. 2 18. 19. 1 sin 30º or cos 60º 54. 7 20. and 55. 3 21. 1 56. 4 22. 3 57. 4 23. x < –1 or x > 5 58. 24. 4 59. 3 25. 3 60. 1 3 27. Sum = and product 61. = 2 62. 3 63. 28. 64. 2 26. 4 29. 17i 65. 4 30. 3 66. 3 67. 4 68. 1 69. 1 31. 32. 33. 34. 3 II 3 70. y = –3 sin 2x