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New Jersey Student Learning Assessments Algebra I

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

These questions are original. This is not an official New Jersey Student Learning Assessment, and FreeExam is not affiliated with the New Jersey Department of Education.

  1. 1.The brick crew on a campus path uses 4x + 7 = 31, where x is the number of rows still to set. What is x?

  2. 2.A technician calibrates the river gauge with 5(h - 2) = 35, where h is the marked height in feet. What is h?

  3. 3.Two fare-credit formulas on the transit line are set equal: 3f - 8 = 2f + 5. What value of f makes them agree?

  4. 4.A greenhouse mix follows 2(n + 6) = 4n, with n equal to the number of peat scoops. What is n?

  5. 5.Lamp spacing on a campus path satisfies x/3 + 4 = 10. What is x?

  6. 6.An overnight drop at the river gauge is modeled by 12 - 2d = -4. What is d?

  7. 7.Extra cars on the transit line satisfy 7c + 4 = 3c + 24. What is c?

  8. 8.The greenhouse thermostat is set so that (t + 9)/4 = 8. What is t?

  9. 9.Two river-gauge sensors are linked by 6(y + 1) = 2(y + 13). What is y?

  10. 10.A campus path must satisfy 2w - 4 ≥ 8, where w is the width in feet. Which solution is correct?

  11. 11.The river gauge alerts when 3h + 1 > 16. Which inequality describes h?

  12. 12.A transit car stays within its load limit when 5p - 10 ≤ 40. What is the solution for the passenger count p?

  13. 13.Shade cloth goes up in the greenhouse when -2t + 14 < 6, and t is hours of direct sun. Which solution is correct?

  14. 14.The grade of a campus path must satisfy x/2 + 1 ≤ 5. What is the solution?

  15. 15.A safe band on the river gauge is written 4 ≤ 2r - 2. Which values of r satisfy it?

  16. 16.Minutes between trains on the transit line satisfy -3(m - 4) ≥ 9. What is the solution?

  17. 17.Two campus path crews are modeled by y = 2x + 1 and y = -x + 10, with x in hours and y in meters cleared. Which point is the solution?

  18. 18.River-gauge lines are given by x + y = 12 and x - y = 4. What is their intersection?

  19. 19.Two transit routes follow 2x + y = 11 and x + y = 7. Which ordered pair solves both equations?

  20. 20.Greenhouse valves follow 3x - y = 5 and x + y = 7. What point satisfies both?

  21. 21.Campus gate counts fit y = 4x - 2 and 2x + y = 16. Which point is the single solution?

  22. 22.Two transit schedules are y = -2x + 14 and y = x - 1. Where do the graphs meet?

  23. 23.A campus path plan uses y = 3x + 2 and y = 3x - 5. How many solutions does the system have?

  24. 24.River readings are modeled by 2x + y = 6 and 2x + y = 9. How many ordered pairs solve both equations?

  25. 25.A transit planner graphs y = -x + 4 and x + y = 1. What describes the solution set?

  26. 26.Campus equations are y = 2x + 3 and 4x - 2y = -6. How many solutions are there?

  27. 27.The river gauge uses x - y = 4 and 3x - 3y = 12. Which statement is true?

  28. 28.A transit diagram shows 2x + y = 8 together with y = -2x + 8. What is the solution set?

  29. 29.On a meter grid, a campus path leaves the chapel step at (2, 5) and reaches the bell tower at (8, 17). What is the slope?

  30. 30.Staff bolts on the river gauge are plotted at (1, 9) and (5, 1). What is the slope of the line through those bolts?

  31. 31.The edge of a transit platform is drawn from (2, 6) to (11, 6) on the station grid. What is the slope of that edge?

  32. 32.A greenhouse trellis stands vertically from (7, 1) to (7, 12). How should its slope be described?

  33. 33.Elevation along a campus path follows y = -3x + 12, with y in meters and x in blocks from the gate. What is the y-intercept?

  34. 34.A river-gauge trend line is y = (1/2)x - 4. Which ordered pair is the y-intercept?

  35. 35.The transit connector is graphed by y = 5x - 8. Which description matches the equation?

  36. 36.Seedling notes in the greenhouse list the points (0, 3) and (4, 11). Which equation contains both points?

  37. 37.A campus path model is y = 4x - 20. Where does the graph cross the x-axis?

  38. 38.When x = 0, a river-gauge model reads 6 feet, and the reading rises 3 feet for each increase of 1 in x. Which equation fits?

  39. 39.A downhill transit link has slope -4 and passes through (1, 9). Which equation matches?

  40. 40.A greenhouse log shows (1, 8), (2, 11), and (3, 14). Which equation fits every row?

  41. 41.Lamp posts along a campus path are numbered 4, 9, 14, 19. What is the common difference of this arithmetic sequence?

  42. 42.Evening marks on the river gauge form the arithmetic sequence 30, 27, 24, 21. What is the 6th term?

  43. 43.Stops on a transit line form an arithmetic sequence with first term 2 and common difference 7. What is the 5th term?

  44. 44.Greenhouse rows are labeled with the arithmetic sequence 11, 16, 21, 26. What is the next label?

  45. 45.Benches on a campus path form an arithmetic sequence. The 3rd bench is at meter 17 and the 7th bench is at meter 37. What is the common difference?

  46. 46.Daily river-gauge checks form an arithmetic sequence with first term 8 and common difference 3. Which expression is the nth term?

  47. 47.A greenhouse starts the week with 200 seedlings, and the count grows by 10% during the week. How many seedlings are there at the end of the week?

  48. 48.A basil tray in the greenhouse starts with 80 plants and increases by 25% in one month. How many plants are there after that month?

  49. 49.Weeds along a campus path start at 40 and increase by 50% each month. How many weeds does the model give after 2 months?

  50. 50.Algae beside the river gauge covers 50 square centimeters and grows by 20% each day. What area does the model give after 2 days?

  51. 51.Ridership on a transit line starts at 2000 people and grows by 5% each year. Which expression gives the ridership after t years?

  52. 52.Each hour, a river model multiplies the previous gauge reading by 1.08. By what percent does the reading grow each hour?

  53. 53.A greenhouse growth note includes the equation 2^x = 16. What is x?

  54. 54.Campus path lights are modeled by 3^x = 81. What is x?

  55. 55.A transit ridership sketch uses 5^x = 125. What is x?

  56. 56.A river model includes 4^x = 64. What is x?

  57. 57.A campus lighting equation is 2^x = 1/8. What is x?

  58. 58.A campus path crew adds the lengths 3x^2 + 2x - 1 and x^2 - 5x + 4, in meters. What is the sum?

  59. 59.Two river-gauge corrections, 5x - 7 and 2x + 9, are added. What is the sum?

  60. 60.Spare-part counts on the transit line are recorded as 6x - 1 and -2x + 8. What is their sum?

  61. 61.A transit schedule subtracts 2x^2 + x - 6 from 5x^2 - 3x + 1. What is the difference?

  62. 62.In the greenhouse, the weight 4x - 3 is subtracted from 9x + 2. What polynomial remains?

  63. 63.A gauge calibration subtracts x^2 + 4x from 3x^2 - x + 2. What is the result?

  64. 64.A rectangular campus sign measures (x + 4) by (x + 2). Which polynomial is its area?

  65. 65.A river-gauge panel measures (2x + 1) by (x + 5). What is the area as a polynomial?

  66. 66.A transit banner is 3x units long and (x^2 - 2x + 4) units wide. Which expression is the area?

  67. 67.A greenhouse frame uses the side factors (x - 3) and (x + 7). What is the expanded product?

  68. 68.A campus area model is the quadratic x^2 + 7x + 12. Which factorization is correct?

  69. 69.A river model uses x^2 - 5x + 6. Which product gives that quadratic?

  70. 70.A transit-area expression is x^2 + x - 12. Which factorization is right?

  71. 71.The greenhouse plan includes x^2 - 9. How does that expression factor?

  72. 72.The length expression 6x^2 + 9x appears on a campus path sketch. Which form has the greatest common factor removed completely?

  73. 73.A gauge formula contains x^2 - 4x - 21. Which factorization is correct?

  74. 74.A campus path model is x^2 - 6x + 8 = 0. What are the solutions?

  75. 75.The river equation x^2 + 3x - 10 = 0 needs to be solved. Which pair works?

  76. 76.A transit model is x^2 - 9 = 0. What are the solutions?

  77. 77.A greenhouse equation is x^2 + 8x + 12 = 0. Which values of x satisfy it?

  78. 78.A campus model simplifies to x^2 + 5x = 0. What are the solutions?

  79. 79.A transit support model is x^2 = 49. What are the solutions?

  80. 80.In the greenhouse, (x - 1)^2 = 25. What are the solutions?

  81. 81.A campus paving equation is 3x^2 = 48. What are the solutions?

  82. 82.A river-gauge equation is (x + 2)^2 = 9. Which values of x work?

  83. 83.Use the quadratic formula on the campus model x^2 - 2x - 15 = 0. The discriminant is a perfect square. What are the solutions?

  84. 84.Use the quadratic formula to solve 2x^2 + 3x - 2 = 0 for the river gauge. The discriminant is a perfect square. Which pair is the solution?

  85. 85.A transit equation is x^2 + 6x + 5 = 0. Use the quadratic formula. What are the solutions?

  86. 86.A greenhouse equation is x^2 - 8x + 12 = 0. Use the quadratic formula. The discriminant is a perfect square. What are the solutions?

  87. 87.A campus path height is modeled by y = (x - 2)^2 + 5. What is the vertex, and which way does the parabola open?

  88. 88.A river-gauge curve is y = -x^2 - 3. Which description is correct?

  89. 89.The transit canopy model is y = 2(x - 3)^2 + 1. What is the equation of the axis of symmetry?

  90. 90.Greenhouse temperature deviation follows y = -2(x - 1)^2 + 9. What is the maximum value of y?

  91. 91.A campus model is y = x^2 - 8x + 15. What is the vertex, and which way does the graph open?

  92. 92.A quadratic river model has this short table: when x = -2, y = 3; when x = -1, y = 1; when x = 0, y = 3. Which statement fits?

  93. 93.A transit cost model is y = (x + 4)^2 + 2. What is the minimum value of y?

  94. 94.The greenhouse model y = -3x^2 + 6x + 1 has a highest point and then decreases. Which way does the parabola open?

  95. 95.A campus path fund starts at 100 dollars. Plan L adds 20 dollars each month. Plan E multiplies by 1.2 each month. Which statement is true for a large number of months?

  96. 96.River-gauge forecast A increases by 2 feet each day. Forecast B increases by 15% each day. How do the two rules differ?

  97. 97.A transit line compares y = 50x + 80 with y = 80(2)^x, using the same nonnegative input x. Which model shows repeated doubling?

  98. 98.Greenhouse trial L uses y = 10 + 4x. Trial E uses y = 10(1.5)^x. Both equal 10 at x = 0. Which trial is larger at x = 2?

  99. 99.During a flood watch, a linear river-gauge model predicts 3t + 6 feet, and an exponential model predicts 4(1.5)^t feet. At t = 2 hours, which prediction is higher?

  100. 100.A scatter plot of campus path length and minutes walked shows points rising from lower left to upper right, close to a straight line. Which description fits a line of fit?

  101. 101.Hours since dawn and river-gauge height, in feet, are plotted as a scatter. A line of fit goes through (0, 4) and (6, 7). What height does that line predict at 2 hours?

  102. 102.On a transit scatter plot, x is the number of stops and y is the ride time in minutes. A line of fit predicts 28 minutes for 6 stops, but the plotted point at 6 stops is 31 minutes. What does the residual say?

  103. 103.A greenhouse scatter plot compares hours of shade with tomato yield. The cloud of points falls from upper left to lower right. What should a line of fit show?

  104. 104.Depths recorded at the river gauge, in feet, are 4, 7, 6, and 7. What is the mean?

  105. 105.A campus path crew records the minutes spent on four repairs: 10, 14, 9, and 15. What is the mean time?

  106. 106.Five greenhouse trays hold 6, 8, 11, 7, and 8 seedlings. What is the mean number of seedlings?

  107. 107.A transit line lists weekday riders, in hundreds, as 20, 24, 28, and 28. What is the mean?

  108. 108.The endpoints of a campus path are (1, 3) and (7, 11). What is the midpoint?