Math 101 Practice Questions 32. A = 33. 1. What is the meaning of x3? 2. Evaluate (x − 3)2 + 5 when x = 10. 1 π‘ = 4π , π‘ 1 π for b 1 − π, for m π΄ π 34. r = √ , for A 3 3. Find decimal notations of −11. 35. y = ax2 − bx, for x 4. Find the LCM of 15 and 48. 36. x−6 · x2 37. 5. Find the absolute value: |−7| 38. (2y6)2 Compute and simplify. 6. −6 + 12 + (−4) + 7 8. − 3 8 ÷ 5 2 π¦3 π¦ −4 7. 2.8 − (−12.2) 9. 13 · 6 ÷ 3 · 2 ÷ 13 39. Collect like terms and arrange in descending order: 2x − 3 + 5x3 − 2x3 + 7x3 + x. Compute and simplify. 40. (4x3 + 3x2 − 5) + (3x3 − 5x2 + 4x − 12) 10. Remove parentheses and simplify. 41. (6x2 − 4x + 1) − (−2x2 + 7) 4m + 9 − (6m + 13). 42. −2y2(4y2 − 3y + 1) Solve. 43. (2t − 3)(3t2 − 4t + 2) 11. 3x = −24 12. 3x + 7 = 2x − 5 1 1 13. 3(y − 1) − 2(y + 2) = 0 44. (π‘ − 4) (π‘ + 4) 14. x2 − 8x + 15 = 0 45. (3π − 2)2 15. y − x = 1, y = 3 − x 16. x + y = 17, x − y = 7 17. 4x − 3y = 3, 3x − 2y = 4 18. x2 − x − 6 = 0 19. x2 + 3x = 5 20. 3 − x = √π₯ 2 − 3 21. 5 − 9x ≤ 19 + 5x 23. 0.6x − 1.8 = 1.2x 29. 2π₯ π₯+ 1 = 2 − 30. 2π₯ π₯+ 3 6 π₯ + 48. (3π + 4π 2 )2 4 2π₯−6 22. −8x + 7 = 8x − 3 50. 3π 4 2π 3 ÷ 2 2 π −1 π −2π+1 24. −3x > 24 51. 3 3π₯−1 52. 2 π₯−3 − π₯ 2 −9π₯+20 π₯ 2 −16 7 28. 6π₯ − 2 2π₯ − 1 5 2π₯ + 7 = 47. (π₯ 2 − 0.2π¦)(π₯ 2 + 0.2π¦) 49. 3 25. 23 − 19y − 3y ≥ −12 26. 3y2 = 30 27. (x − 3)2 = 6 46. (15π₯ 2 π¦ 3 + 10π₯π¦ 2 + 5) − (5π₯π¦ 2 − π₯ 2 π¦ 2 − 2) 18 π₯ 2 − 3x 31. √π₯ + 9 = √2π₯ − 3 Solve the formula for the given letter. = 9π₯ 3π₯ +1 · π₯−3 π₯+3 4 + 5π₯ Factor. 53. 8π₯ 2 − 4π₯ 54. 25π₯ 2 − 4 55. 6π¦ 2 − 5π¦ − 6 56. π2 − 8π + 16 57. π₯ 3 − 8π₯ 2 − 5π₯ + 40 58. 3π4 + 6π2 − 72 59. 16π₯ 4 − 1 1 78. π¦ = 3 π₯ − 2 60. 49π2 π 2 − 4 x y 61. 9π₯ 2 + 30π₯π¦ + 25π¦ 2 62. 2ππ − 6ππ − 3ππ + ππ 63. 15π₯ 2 + 14π₯π¦ − 8π¦ 2 79. π¦ = −3 Simplify. 3 1 + π₯ 2π₯ 64. 1 3 − 3π₯ 4π₯ 65. √49 66. −√625 67. √64π₯ 2 x 68. Multiply: √π + π √π − π. y 80. π₯ ≥ −3 69. Multiply and simplify: √32ππ√6π4 π2 . x y Simplify. 71. √243π₯ 3 π¦ 2 70. √150 100 81 64 π₯2 72. √ 73. √ 81. 4π₯ − 3π¦ > 12 74. 4√12 + 2√12 x 75. Divide y √72 and simplify: . √45 76. In a right triangle, where a and b represent the legs and c represents the hypotenuse, a = 9 and c = 41. Find b. 82. Graph π¦ = π₯ 2 + 2π₯ + 1. Label the vertex and the yintercept. Graph. 1 77. π¦ = 3 π₯ − 2 x x y y 83. Solve 9π₯ 2 − 12π₯ − 2 = 0 by completing the square. Show your work. 84. Approximate the solutions of 4π₯ 2 = 4π₯ + 1 to the nearest tenth. Solve. 85. What percent of 52 is 13? 98. Use only the graph below to solve π₯ 2 + π₯ − 6 = 0. 86. 12 is 20% of what? 87. In checking records, a contractor finds that crew A can resurface a tennis court in 8 hrs. Crew B can do the same job in 10 hrs. How long would they take if they worked together? 88. The area of a rectangular movie screen is 96ft2. The length is 4ft longer than the width. Find the length and the width of the movie screen. 89. The speed of a boat in still water is 8km/h. It travels 60km upstream and 60km downstream in a total time of 16 hours. What is the speed of the stream? 99. Find the x-intercepts of π¦ = π₯ 2 + 4π₯ + 1. 100. Find the slope and the y-intercept: −6π₯ + 3π¦ = −24 90. The length of a rectangular garage floor is 7m more than the width. The length of a diagonal is 13m. Find the length of the garage floor. 101. Determine whether the graphs of the following equations are parallel, perpendicular, or neither. 91. The sum of the squares of two consecutive odd integers is 74. Find the integers. 102. Find the slope of the line containing the points (−5, −6) and (−4,9). 92. Solution A is 75% alcohol and solution B is 50% alcohol. How much of each is needed in order to make 103. Find an equation of variation in which y varies directly as x and π¦ = 100 when π₯ = 10. Then find the value of y when π₯ = 64. 2 60L of a solution that is 663% alcohol? 93. The Eiffel Tower in Paris is 984ft tall. How long would it take an object to fall to the ground from the top? (See the formula in Example 11 of Section 9.2.) 94. A student’s paycheck varies directly as the number of hours worked. The pay was $242.52 for 43 hrs of work. What would be the pay for 80 hrs of work? Explain the meaning of the variation constant. 95. Three-fifths of the automobiles entering the city each morning will be parked in the city parking lots. There are 3654 such parking spaces filled each morning. How many cars enter the city each morning? 96. A candy shop wants to mix nuts worth $3.30 per pound with another variety worth $2.40 per pound in order to make 42 lbs of a mixture worth $2.70 per pound. How many pounds of each kind of nuts should be used? 97. An airplane flew for 3 hrs with a 20-mph tail wind. The return flight against the same wind took 4 hrs. Find the speed of the plane in the air. 104. Find an equation of variation in which y varies inversely as x and π¦ = 100 when π₯ = 10. Then find the value of y when π₯ = 125. Determine whether each of the following is the graph of a function. 105. 106. A. Graph the function. 107. π(π₯) = π₯ 2 + π₯ − 2 B. 108. π(π₯) = |π₯ + 2| 109. For the function π described by π(π₯) = 2π₯ 2 + 1 7π₯ − 4, find π(0), π(−4), andπ (2). 110. An airplane flies 408 mi against the wind and 492 mi with the wind in a total time of 3 hrs. The speed of the airplane in still air is 300 mph. If we assume there is some wind, the wind is between: A. 8 and 15 mph. B. 15 and 22 mph. C. 22 and 29 mph. D. 29 and 26 mph. C. 111. Solve: 2π₯ 2 + 6π₯ + 5 = 4. A. −3 ± √7 B. −3 ± 2√7 C. No real solutions 112. Solve for b: π = D. −3±√7 2 π+π . 3π A. π = 3ππ − π B. π = π+π 3π C. π = π(3π − 1) D. π = π 3π−1 113. Which of the following is the graph of 3π₯ − 4π¦ = 12? D. 114. Solve: |π₯| = 12. 115. Simplify: √√√81 116. Find b such that the trinomial π₯ 2 − ππ₯ + 225 is a square 117. Find x. Determine whether each pair of expressions is equivalent. 118. π₯ 2 − 9, 119. (π₯ − 3)(π₯ + 3) 120. (π₯ + 5)2 , π₯ 2 + 25 122. √π₯ 2 , |π₯| π₯+3 , 3 π₯ 121. √π₯ 2 + 16, π₯+4 Answer Key 1. π₯ · π₯ · π₯ 28. 2. 54 2 9 29. −5 3. −0. 27 30. No solution 4. 240 31. 12 5. 7 32. π = 6. 9 33. 7. 15 8. π΄π‘ 4 π‘π π‘+π 34. π΄ = ππ 2 3 − 20 35. π₯ = 9. 4 π+√π2 +4ππ¦ 2π 1 π₯4 10. −2π − 4 36. 11. −8 37. π¦ 7 12. −12 38. 4π¦12 13. 7 39. 10π₯ 3 + 3π₯ − 3 14. 3, 5 40. 7π₯ 3 − 2π₯ 2 + 4π₯ − 17 15. (1, 2) 41. 8π₯ 2 − 4π₯ − 6 16. (12, 5) 42. −8π¦ 4 + 6π¦ 3 − 2π¦ 2 17. (6, 7) 43. 6π‘ 3 − 17π‘ 2 + 16π‘ − 6 18. −2, 3 44. π‘ 2 − 16 19. 1 −3±√29 2 45. 9π2 − 12π + 4 20. 2 46. 15π₯ 2 π¦ 3 + π₯ 2 π¦ 2 + 5π₯π¦ 2 + 7 21. {π₯|π₯ ≥ −1} 47. π₯ 2 − 0.04π¦ 2 22. 8 48. 9π2 + 24ππ 2 + 16π 4 23. −3 49. 2 π₯+3 50. 3π(π−1) 2(π+1) 51. 27π₯−4 5π₯(3π₯−1) 52. −(π₯−2)(π₯+1) (π₯+4)(π₯−4)(π₯−5) 24. {π₯|π₯ < 8} 35 25. {π¦|π¦ ≤ 22} 26. −√10, √10 27. 3 ± √6 53. 4π₯(2π₯ − 1) 77. 54. (5π₯ − 2)(5π₯ + 2) 55. (3π¦ + 2)(2π¦ − 3) 56. (π − 4)2 57. (π₯ − 8)(π₯ 2 − 5) 58. 3(π2 + 6)(π + 2)(π − 2) 59. (4π₯ 2 + 1)(2π₯ + 1)(2π₯ − 1) 60. (7ππ + 2)(7ππ − 2) 78. 61. (3π₯ + 5π¦)2 62. (π − 3π)(2π + π) 63. (5π₯ − 2π¦)(3π₯ + 4π¦) 64. − 42 5 65. 7 66. −25 67. 8π₯ 79. 68. √π2 − π 2 69. 8π2 π√3ππ 70. 5√6 71. 9π₯π¦√3π₯ 72. 10 9 73. 8 π₯ 74. 12√3 75. 2√10 5 76. 40 80. 81. 96. $3.30 per pound: 14 lb; $2.40 per pound 28 lb 97. 140 mph 98. −3, 2 99. (−2 − √3, 0), (−2 + √3, 0) 100. Slope: 2; π¦-intercept: (0, −8) 101. Neither 102. 15 103. π¦ = 10π₯; 640 82. 104. π¦ = 1000 ;8 π₯ 105. Yes 106. No 107. 83. 2±√6 3 84. −0.2, 1.2 85. 25% 86. 60 4 87. 4 9 hr 108. 88. Length: 12 ft; width 8 ft 89. 2km/h 90. 12 m 91. 5 and 7; −7 and −5 92. 40 L of A; 20 L of B 93. About 7.8 sec 94. $541.20; the variation constant is the amount earned per hour 109. −4; 0; 0 95. 6090 cars 111. D 110. C 112. D 113. C 114. −12, 12 115. √3 116. −30, 30 117. √6 3 118. Yes 119. No 120. No 121. No 122. Yes