FreeExam

Georgia Milestones Assessment System Algebra: Concepts and Connections

Linear, quadratic, and exponential models, with equations, graphs, and data.

These questions are original. This is not an official Georgia Milestones Assessment System test, and FreeExam is not affiliated with the Georgia Department of Education.

  1. 1.A campus path leaves the library door at (1, 2) and reaches the science lab at (7, 14) on a meter grid. What is the slope of that path?

  2. 2.Two bolts on a river gauge are plotted at (3, 5) and (9, 8), and the vertical axis is measured in feet. What is the slope of the segment joining the bolts?

  3. 3.Inside the greenhouse, a watering aisle runs from (0, 4) to (8, 4). How should the slope of this aisle be reported?

  4. 4.A transit line marks a vertical support from (4, 1) up to (4, 9) on the station grid. What is the slope of that support?

  5. 5.After a storm, the grounds crew reroutes a campus path from (-2, 6) down to (4, -3). What is the slope of the rerouted path?

  6. 6.On the campus map, the service lane from the front gate (0, 1) to the field house (5, 16) is straight. Which number is its slope?

  7. 7.A short campus path connects the bike rack at (1, 2) with the oak at (4, 6). What is the straight-line distance, in grid units, between those points?

  8. 8.River-gauge posts stand at (2, 1) and (8, 9) on a coordinate grid measured in meters. How far apart are the posts?

  9. 9.The ends of a greenhouse bench are at (0, 0) and (5, 12), with each unit equal to 1 foot. What distance separates the ends?

  10. 10.Two clips on a transit pole have coordinates (3, 7) and (3, -1). What is the distance from one clip to the other?

  11. 11.A campus maintenance route is drawn as a straight segment from (1, -2) to (8, 22). What is the length of that route?

  12. 12.A greenhouse irrigation span runs from (2, 8) to (10, 23). Which length matches the span?

  13. 13.The endpoints of a footbridge on a coordinate plane are (2, 4) and (10, 12). What is the midpoint of the footbridge?

  14. 14.Lamp posts at the ends of a campus walk sit at (0, 2) and (8, 10). Where is the halfway point of the walk?

  15. 15.A technician places river sensors at (1, 5) and (7, 11) and wants a reader exactly halfway between them. Which point is that location?

  16. 16.Greenhouse corner posts are plotted at (-4, 2) and (6, 8). What is the midpoint of the segment that joins them?

  17. 17.A transit platform runs from a marker at (3, -2) to a marker at (11, 6). Which ordered pair is the center of that platform?

  18. 18.A campus garden is a rectangle with vertices (1, 1), (7, 1), (7, 5), and (1, 5). What is the area of the garden?

  19. 19.The campus plan shows a rectangular practice court with corners (0, 0), (9, 0), (9, 4), and (0, 4). What is the perimeter of the court?

  20. 20.A right triangular planting bed in the greenhouse has vertices (0, 0), (6, 0), and (0, 8). What is the area of the bed?

  21. 21.Warning flags stand at (0, 0), (3, 0), and (0, 4) around a right triangular patch beside a campus path. What is the perimeter of the patch?

  22. 22.A rectangular pad under a river gauge has corners (2, 3), (10, 3), (10, 7), and (2, 7). What is the area of the pad?

  23. 23.A transit storage lot is the rectangle with vertices (1, 2), (13, 2), (13, 7), and (1, 7). What is the perimeter of the lot?

  24. 24.A groundskeeper labels four measurements taken along a campus path. Which of the four numbers is rational?

  25. 25.The river-gauge manual lists 22/7, 3.5, the square root of 36, and pi. Which of those values is irrational?

  26. 26.A greenhouse log records the decimal 0.454545... in which the block 45 repeats forever. What kind of number is that decimal?

  27. 27.Which number below is irrational?

  28. 28.The transit fare table uses -3/5 as an adjustment factor. Why is -3/5 a rational number?

  29. 29.A campus path diagram includes the length given by the square root of 72. Which expression is that length in simplest radical form?

  30. 30.The river gauge model simplifies the square root of 144 before the result is plotted. What is the simplified value?

  31. 31.A greenhouse volume calculation contains the cube root of 27. What is that cube root?

  32. 32.Engineers sizing a transit support use the cube root of 64. Which value is that cube root?

  33. 33.Simplify the square root of 48, the length printed on a campus paving sketch.

  34. 34.A river model includes the cube root of -125. What is the simplified result?

  35. 35.On a campus map, the boundary line is y = x + 3. The region on and above that line is shaded. Which inequality describes the shaded region?

  36. 36.A greenhouse chart shows the boundary y = -2x + 4 as a dashed line, with the shading strictly below the line. Which inequality matches the chart?

  37. 37.A transit grid shades every point on or to the right of the vertical line x = 5. Which inequality names that half-plane?

  38. 38.The campus plan shades the open half-plane to the left of the dashed line x = -1. Which inequality fits that shading?

  39. 39.A river gauge shades the region on and above the horizontal line y = 2, where y is the water level in feet. Which inequality describes the shaded side?

  40. 40.A boundary drawn for a greenhouse layout is y = (1/2)x - 1. The line is included, and the shading is the side below the line. Which inequality is shown?

  41. 41.A campus path plan uses the system y is greater than or equal to x, and y is less than or equal to 4. Which point lies in the solution region?

  42. 42.The system for a river work zone is x + y less than or equal to 6, and x greater than or equal to 1. Which point is outside the solution region?

  43. 43.A greenhouse planter must satisfy y greater than or equal to 2x, and x + y less than or equal to 9. Which point is inside both inequalities?

  44. 44.A transit planner shades y less than 2x + 1 together with y greater than x - 3. Does the point (4, 6) belong to the solution region?

  45. 45.Flood planning along the river uses y less than or equal to -x + 8, and y greater than or equal to 1. Which point is in the solution region?

  46. 46.A greenhouse bench is a rectangle with side lengths (x + 3) and (x + 5). Which expression is the area?

  47. 47.A square campus sign has side length 2x + 1. Which polynomial gives the area of the sign?

  48. 48.A transit window is (x + 6) units long and (x - 2) units wide. What is the area expression?

  49. 49.A rectangular greenhouse tray measures 3x by (x + 2). Which expression represents its area?

  50. 50.A campus directory panel has dimensions (x - 4) and (x - 7). What quadratic equals the panel area?

  51. 51.Factor the greenhouse area polynomial x^2 + 8x + 15.

  52. 52.A difference of squares, x^2 - 9, appears in a river cross-section formula. What is its factored form?

  53. 53.Factor x^2 - 5x + 6, the expression for a campus path offset product.

  54. 54.Which factorization is correct for 2x^2 + 7x + 3, a quadratic used in a transit timing model?

  55. 55.Factor x^2 + x - 12 completely over the integers.

  56. 56.The equation x^2 - 5x + 6 = 0 models where a greenhouse border meets the axis. What are the solutions?

  57. 57.Solve x^2 + 7x + 10 = 0 by factoring.

  58. 58.A campus arch calculation reduces to x^2 - 16 = 0. What are the solutions found by factoring?

  59. 59.The river model x^2 - 6x = 0 has a common factor of x. What are the solutions?

  60. 60.Solve x^2 + 2x - 8 = 0 by factoring.

  61. 61.A square greenhouse plot satisfies x^2 = 25, where x is a signed side measure on the grid. What are the solutions?

  62. 62.Solve (x - 3)^2 = 16 by taking square roots.

  63. 63.A transit clearance equation is (x + 2)^2 = 9. Which pair lists both solutions?

  64. 64.The equation 4x^2 = 36 comes from a scaled campus grid. What are the solutions?

  65. 65.Use the quadratic formula to solve x^2 - 4x - 5 = 0. The discriminant is a perfect square. What are the solutions?

  66. 66.Solve 2x^2 + 3x - 2 = 0 with the quadratic formula.

  67. 67.The quadratic formula is used on x^2 + 6x + 5 = 0. Which pair is the solution set?

  68. 68.Solve x^2 - 2x - 3 = 0 with the quadratic formula.

  69. 69.A greenhouse starts with 200 seedlings, and the count grows by 10% each week. How many seedlings are there after 2 weeks?

  70. 70.A plant count in the greenhouse is modeled by 80(1.05)^t, where t is the number of weeks. What percent growth does the model apply each week?

  71. 71.A river sample starts with 125 algae cells and increases by 20% each day. How many cells does the model give after 3 days?

  72. 72.Monthly ridership on a transit line is 1,000 and then grows by 4% each month. Which expression gives the ridership after m months?

  73. 73.A greenhouse culture of 120 cells increases by 50% each hour. What is the count after 2 hours?

  74. 74.Membership on a campus project doubles every week and satisfies 2^x = 16. What is the value of x?

  75. 75.A greenhouse growth check reduces to the equation 3^x = 81. What is x?

  76. 76.Solve 9^x = 27.

  77. 77.A transit headway equation is 5^(x - 1) = 25. What is x?

  78. 78.Campus path lamps form an arithmetic sequence with first term 4 and common difference 3. Which explicit rule gives term number n?

  79. 79.Daily river-gauge readings form the arithmetic sequence 12, 15, 18, and so on. What is the 10th reading?

  80. 80.Afternoon water levels on a river gauge are 20, 17, 14, and 11. What is the common difference of this arithmetic sequence?

  81. 81.An arithmetic sequence used for greenhouse tray counts has the explicit rule a(n) = 7 + (n - 1) times 2. What is a(6)?

  82. 82.The first term of an arithmetic sequence of transit mile markers is 5, and the fourth term is 14. What is the common difference?

  83. 83.Distances to successive stops on a transit line form the arithmetic sequence 2, 6, 10, 14. Which explicit rule matches the sequence?

  84. 84.A transit ride costs $2.00 plus $0.50 for each mile. What is the cost of an 8-mile ride?

  85. 85.River height in feet is modeled by h = 0.4t + 3, where t is hours after noon. What does the 3 represent?

  86. 86.A campus shuttle distance in miles is d = 12t, and the model is used only for times from 0 hours through 6 hours. What is the domain of this function in context?

  87. 87.Greenhouse air temperature follows T = -2h + 78, where h is hours after sunset and T is in degrees. What is the slope, and what does it mean?

  88. 88.Distance remaining on a campus path is r = -5t + 40, with r in meters and t in minutes. What is the starting distance?

  89. 89.Elevation along a transit line is e = 3s + 10, where s is the number of stations after the depot and e is in meters. What is the elevation at s = 4?

  90. 90.A greenhouse cable hangs in the graph of y = (x - 2)^2 + 5. What is the vertex?

  91. 91.The graph of y = 3(x + 4)^2 - 1 models a river-channel cross section. What is the axis of symmetry?

  92. 92.A transit arch is modeled by y = -2(x - 1)^2 + 6. In which direction does the parabola open?

  93. 93.A campus path survey records these points on a parabola: (0, 6), (1, 3), (2, 2), (3, 3), and (4, 6). What is the vertex?

  94. 94.The equation y = x^2 - 6x + 5 describes a greenhouse sprinkler pattern. What is the axis of symmetry?

  95. 95.A greenhouse count is recorded as 5, 10, 20, 40 over four equal time steps. Which kind of model fits this pattern?

  96. 96.River readings taken one hour apart are 4, 7, 10, and 13. Which description fits the pattern?

  97. 97.For inputs x = 0, 1, 2, and 3, a campus model outputs 0, 1, 4, and 9. Which type of function matches the outputs?

  98. 98.A transit planner compares y = 4x + 10 and y = 2^x for large positive x. Which statement is true?

  99. 99.Three models for a river count are y = 3x + 2, y = x^2, and y = 3^x. Which model has the greatest increase from x = 2 to x = 3?

  100. 100.A scatter plot compares hours spent on a campus path study walk with quiz scores. The cloud of points rises as the hours increase, and a line of fit slopes upward. What association does the plot show?

  101. 101.A line of fit for a river gauge is y = 2x + 4, where x is the day number and y is the reading in centimeters. What reading does the line predict when x = 5?

  102. 102.In a greenhouse experiment, a scatter plot shows tomato count against shade percent. The line of fit falls as the shade percent increases. What is true about the slope of that line of fit?

  103. 103.A line of fit for transit delays is y = x + 3. One point on the scatter plot is (4, 9). What is the residual for that point if residual means actual y minus predicted y?

  104. 104.Five river-gauge readings, in feet, are 4, 6, 8, 10, and 12. What is the mean of the readings?

  105. 105.Times, in minutes, for five walks on a campus path are 12, 15, 18, 21, and 9. What is the range of the times?

  106. 106.Four seedlings in a greenhouse have heights 7 cm, 9 cm, 11 cm, and 13 cm. What is the mean height?

  107. 107.Four recorded delays on a transit line, in minutes, are 2, 2, 2, and 2. What is the range of this data set?

  108. 108.The data set 5, 8, 11 has mean 8. Each value is increased by 2. What is the mean of the new data set?