FreeExam

New York State Regents Examination Algebra I

One hundred eight questions on equations, inequalities, functions, systems, and exponents.

These questions are original. This is not an official New York State Regents Examination, and FreeExam is not affiliated with the New York State Education Department.

  1. 1.A harbor crane balance reads 5x - 7 = 23 when x counts extra crates on the hook, so how many extra crates is that?

  2. 2.After nine riders step into a subway elevator, the sensor equation x + 9 = 26 records the new total, so how many riders were already inside?

  3. 3.The print shop packs banners with the rule 3(x + 4) = 27, where x is the count beyond a starter set of four, so what is x?

  4. 4.Elevator parts arrive as 3x + 2x = 40 matching bolts in two bins, so what is x?

  5. 5.An elevator holds fewer riders than the limit x + 4 < 15, so which solution describes x?

  6. 6.On a subway elevator graph, a car moves from (0, -2) to (3, 7), so what is the slope between those points?

  7. 7.An elevator line is written y = 4x + 1 on the repair chart, so what is the slope of that line?

  8. 8.For the auditorium seating rule f(x) = 2x + 5, what is f(4)?

  9. 9.Elevator equations y = x + 2 and y = 2x meet at one point, so which point is the intersection?

  10. 10.Subway display bulbs are counted by 10 to the second power, so what number of bulbs is that?

  11. 11.Subway elevators stop at floors 4, 7, 10, and 13 in an arithmetic sequence, so what is the common difference?

  12. 12.An elevator checklist evaluates 8 + 4 × 2, so what is the value?

  13. 13.An elevator repair log shows 4x + 3 = 31 spare brackets, so how many brackets does one group of x contain?

  14. 14.Before the noon ferry leaves, the headway equation x - 12 = 5 gives minutes past the hour, so what is x?

  15. 15.Crews clear a subway elevator using 2(x - 5) = 18, where x is the original passenger count, so what is x?

  16. 16.Ferry fuel notes simplify to 7x - 2x + 4 = 19 barrels, so what is x?

  17. 17.A library fine rule is written -2x < 10 for the late days still allowed, so which solution is correct?

  18. 18.A subway car graph passes through (1, 2) and (4, 11), so what is the slope?

  19. 19.Headway is graphed as y = -2x + 9 for the afternoon ferry, so what is the y-intercept?

  20. 20.Elevator load is f(x) = x + 12, so what is f(5) when five extra carts are waiting?

  21. 21.A ferry schedule uses y = x + 6 while a harbor crane log uses y = 3x, so at which point do the graphs meet?

  22. 22.Ferry mileage tags show 10 to the fourth power, so what number is printed on the tag?

  23. 23.Ferry departures run 8, 13, 18, 23 in an arithmetic sequence, so what is the next departure number?

  24. 24.Ferry timing uses 20 - 6 ÷ 2 minutes on the dispatch card, so what is the value?

  25. 25.Ferry dispatch solves 3x - 5 = 16 for boats held in reserve, so how many boats is x?

  26. 26.During a membership drive, guest cards are bundled by 6x = 42, so how many cards are in one bundle x?

  27. 27.The Saturday ferry uses 4(x + 2) = 36 for the ramp crew count, so what is x?

  28. 28.A membership form shows 4x + 3 + x = 23 guest stickers, so what is x?

  29. 29.Ferry headway must satisfy x - 6 > 10 minutes between boats, so which solution is correct?

  30. 30.Ferry positions are (2, 5) and (6, 13) on the headway chart, so what is the slope?

  31. 31.A membership line has slope 3 and y-intercept -4, so which equation matches the price graph?

  32. 32.A ferry rule is g(x) = 3x - 1, so what is g(6) for a six-stop headway?

  33. 33.A print-shop system is x + y = 8 and 2x + 2y = 16 for two copies of one paper order, so how many solutions are there?

  34. 34.A museum model multiplies 10^2 by 10^3 for two tile counts, so which power of 10 equals the product?

  35. 35.Museum visits form the arithmetic sequence 20, 17, 14, 11, so what is the common difference?

  36. 36.A museum count is 3 × (5 + 2) visitors in equal groups, so what is the value?

  37. 37.Museum pricing uses 2x + 11 = 27 for a family add-on, so what is x?

  38. 38.Gardeners divide a rooftop bed by the equation x/4 = 9 equal rows, so how many plants is x?

  39. 39.A museum workshop sets 5(x - 1) = 20 chairs around the tables, so what is x?

  40. 40.Garden edging uses 8x - 3x - 2 = 18 meters on the roof plan, so what is x?

  41. 41.Museum capacity is limited by 3x ≤ 18 tour seats, so what is the solution?

  42. 42.Membership sales move from (1, 9) to (3, 3) on the weekly graph, so what is the slope?

  43. 43.The roof plan uses y = -x + 6 for the length of one path, so what is the slope?

  44. 44.Membership value is h(x) = 10 - x, so what is h(4) after four guest passes are used?

  45. 45.Ferry lines are x + y = 10 and x - y = 4, so which ordered pair solves the system?

  46. 46.Museum staff label a display with 10 to the third power tiny tiles, so what number of tiles is that?

  47. 47.Rooftop boxes increase by 6 from a start of 5 in an arithmetic sequence, so what is the fourth term?

  48. 48.Garden measurements give 18 ÷ 3 + 4 × 2 for the roof plan, so what is the value?

  49. 49.Planters on the roof satisfy 5x - 4 = 21 herb pots, so what is x?

  50. 50.Ticket sellers at the school auditorium solve x + 18 = 53 reserved seats, so how many seats were sold before the last 18?

  51. 51.Raised beds follow 2(x + 8) = 30 on the roof plan, so what is x?

  52. 52.Print totals read 2x + 6x - 5 = 27 poster packs, so what is x?

  53. 53.Rooftop water use follows 2x + 1 > 13 liters, so which inequality gives x?

  54. 54.Garden plots are marked (0, 4) and (5, 4) on the roof drawing, so what is the slope?

  55. 55.Poster counts follow y = 5x - 2 at the print shop, so what is y when x = 3?

  56. 56.Garden yield is p(t) = 4t + 2, so what is p(3) after three weeks on the roof?

  57. 57.Bed counts on the roof plan are y = 2x + 1 and y = 2x + 5, so how many solutions does the system have?

  58. 58.Garden lights simplify 10^6 ÷ 10^2 on the roof plan, so which power of 10 equals the quotient?

  59. 59.Print jobs number 12, 19, 26, 33 in an arithmetic sequence, so what is the common difference?

  60. 60.A print quote is 5 + 3^2 × 2 dollars for one rush order, so what is the value?

  61. 61.A poster order follows 6x + 8 = 44 sheets in the print shop, so what is x?

  62. 62.Cable paid out by the harbor crane fits x - 20 = 15 meters, so what is x?

  63. 63.Binding a booklet gives 3(x - 6) = 12 pages in the print shop, so what is x?

  64. 64.Auditorium cables satisfy x + 5x + 8 = 32 connectors, so what is x?

  65. 65.A print quota is -4x ≤ 20 leftover sheets, so what is the solution?

  66. 66.A print graph goes through (3, 1) and (3, 8), so what is the slope of that vertical order line?

  67. 67.Seating is modeled by y = 2x + 7 in the school auditorium, so what is x when y = 19?

  68. 68.Print-shop page cost is c(n) = 2n + 9, so what is c(0) when no extra pages are added?

  69. 69.Print order sheets are x + y = 6 and 3x + 3y = 18, so how many solutions exist?

  70. 70.Print labels use (10^2)^3 for a stack of sticker sheets, so which power of 10 matches?

  71. 71.Auditorium rows are numbered 30, 27, 24 in an arithmetic sequence, so what is the next row number?

  72. 72.Auditorium setup evaluates (12 - 4) ÷ 2 + 5 spare chairs, so what is the value?

  73. 73.Rows in the school auditorium fit 4x - 9 = 19 marked seats, so what is x?

  74. 74.Librarians group returned books by 9x = 81, so how many books are in one group x?

  75. 75.Ushers rope a section with 6(x + 1) = 42 seats in the school auditorium, so what is x?

  76. 76.Crane counterweights follow 9x - 4x + 1 = 21 tons, so what is x?

  77. 77.Auditorium aisles obey -3x > 12 open feet, so what is the solution?

  78. 78.Auditorium steps connect (2, -1) and (6, 7), so what is the slope?

  79. 79.A crane chart is y = -3x + 12, so what is y when x = 2?

  80. 80.Seat function k(x) = 5x - 4 gives a row total in the school auditorium, so what is k(2)?

  81. 81.Stage marks in the school auditorium satisfy y = -x + 8 and y = x, so where do they meet?

  82. 82.Auditorium speakers compare powers when finding 2^3 × 2^4, so what is that product?

  83. 83.Crane loads 9, 14, 19, 24, 29 form an arithmetic sequence, so what is the tenth term?

  84. 84.Crane math uses 2 × 6 + 4 × 3 for a hook diagram, so what is the value?

  85. 85.The harbor crane gauge reads 7x + 2 = 30, so what is x?

  86. 86.Each print-shop tray holds an equal share in x/6 = 8, so how many sheets is x?

  87. 87.A crane sling satisfies 4(x - 3) = 28, so what is x?

  88. 88.Library shelves are tagged by 3x + x - 7 = 9, so what is x?

  89. 89.The crane manual requires -5x ≥ 15, so what is the solution?

  90. 90.Crane height changes from (-2, 3) to (2, 11), so what is the slope?

  91. 91.Late fees follow y = 4x + 3 at the library desk, so which pair names the slope and the y-intercept?

  92. 92.Hook load is m(x) = 8 - 2x for the harbor crane, so what is m(3)?

  93. 93.Crane settings are 2x + y = 7 and 2x + y = 3, so how many solutions are there?

  94. 94.Crane sensors store the product 10^5 × 10^0, so what is that product?

  95. 95.Library fines in cents are 15, 25, 35, 45 in an arithmetic sequence, so what is the fifth term?

  96. 96.A library expression is 16 - 2 × (3 + 1) for a fine table, so what is the value?

  97. 97.Overdue books follow 3x - 6 = 15 at the library desk, so what is x?

  98. 98.Midday elevator checks use 8x + 5 = 45 inspection points, so what is x?

  99. 99.A spare ferry is held when 2x - 14 = 8 minutes of headway remain, so what is x?

  100. 100.Gift memberships satisfy 9x + 4 = 49 bonus passes, so what is x?

  101. 101.Tomato boxes on the roof obey 4x - 7 = 17, so what is x?

  102. 102.Late slips are bundled by 5(x + 3) = 40 at the library, so what is x?

  103. 103.Library quiet hours use -x < 8, so what is the solution for the fine chart?

  104. 104.Museum visitor caps use -2x ≤ -8, so what is the solution for the membership desk?

  105. 105.Fines grow under -6x > -18 at the library desk, so what is the solution?

  106. 106.Fine totals plot from (4, 10) to (8, 2) on the library graph, so what is the slope?

  107. 107.Overdue cost is d(x) = 3x + 1 at the library, so what is x when d(x) = 16?

  108. 108.Library archive codes use 10^4 ÷ 10^4, so what is the quotient?