FreeExam

New Jersey Student Learning Assessments Algebra II

Polynomials, exponentials, logarithms, functions, and sequences.

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.Adding the Atlantic City boardwalk profits 3x^2 - 4x + 1 and 2x^2 + 5x - 6 gives which polynomial?

  2. 2.Subtract the Hoboken ferry model 2x^2 - x + 4 from 5x^2 + 3x - 2. Which polynomial is that difference?

  3. 3.A rectangular banner at the Princeton farmers market has side lengths x + 3 and x - 5 feet. Which polynomial is its area?

  4. 4.Expand the Cape May gift-bundle expression (2x - 1)(x + 4).

  5. 5.A square garden plot in Trenton has side length x + 4 meters. Which expression equals the area (x + 4)^2?

  6. 6.A Jersey City frame uses the lengths x + 6 and x - 6. What is the product of those lengths?

  7. 7.When the Paterson workshop polynomial x^2 + 5x + 3 is divided by x - 2, which remainder is left?

  8. 8.A Princeton notebook divides x^3 - 2x + 1 by x + 1. What remainder appears?

  9. 9.A Morristown tutor divides x^2 + 4x + 1 by x + 3. Which number is the remainder?

  10. 10.A Fort Lee ramp polynomial has (x - 3) as a factor. Which number must be a zero?

  11. 11.A New Brunswick garden bed satisfies x^2 - 5x + 6 = 0. Which pair lists both zeros?

  12. 12.A Bayonne pier brace is modeled by (x - 4)^2 = 0. What is the zero?

  13. 13.A Camden bridge polynomial has a zero at x = -2. Which expression must be a factor?

  14. 14.An orchard count in Freehold satisfies x^2 - 7x + 10 = 0. What is the sum of the two zeros?

  15. 15.Which value is a zero of t^3 - 2t^2 - 5t + 6, the cubic for a Vineland storage rack?

  16. 16.For the Edison robotics polynomial x^2 + x - 6, which expression is a factor?

  17. 17.The stage polynomial (x - 1)(x + 4)(x - 5) is used in Asbury Park. Which number is not a zero?

  18. 18.A Newark sign shop simplifies (x^2 - 9)/(x - 3), with x not equal to 3. What remains after the common factor is canceled?

  19. 19.Summit High reduces (x^2 + 5x + 6)/(x + 2) for x not equal to -2. Which expression is left?

  20. 20.After a Hackensack window formula (x^2 - 16)/(x + 4) loses its common factor, and x is not -4, what quotient remains?

  21. 21.Red Bank printers reduce (x^2 - x - 12)/(x - 4), where x is not 4, by canceling one binomial. What is the reduced form?

  22. 22.Cherry Hill divides (2x^2 - 8x) by (x^2 - 4x), skipping the inputs x = 0 and x = 4. The canceled form equals which number?

  23. 23.Montclair simplifies (x^2 - 4x)/x with x not equal to 0. Cancel the common factor and name the result.

  24. 24.Westfield cancels a common factor in (2x^2 + 6x)/(2x), where x is not 0. Which expression is equivalent?

  25. 25.A Ridgewood trail formula, (x^2 - 2x - 8)/(x - 4) with x not equal to 4, simplifies to which expression?

  26. 26.A Sandy Hook trail marker satisfies sqrt(x + 3) = 5. Which value of x checks in the original equation?

  27. 27.Solve sqrt(2x) = 6 for a Palisades overlook measurement, and keep the solution that checks.

  28. 28.The Barnegat tide note uses sqrt(x - 1) = 3. What is x?

  29. 29.A Long Branch kite height is modeled by sqrt(x + 7) = 2. Which solution checks?

  30. 30.In a Toms River lab, 2*sqrt(x) = 8. What is x?

  31. 31.A Liberty State Park banner length satisfies sqrt(3x + 1) = 4. Which value of x checks?

  32. 32.At High Point, a survey equation is sqrt(4x + 5) = 3. What is the solution?

  33. 33.A Secaucus loading dock uses sqrt(x + 8) = 6. Which number solves the equation and checks?

  34. 34.A Newark power reading is written as 16^(1/2). What is that value?

  35. 35.Hoboken freight tags use the power 8^(2/3). Which number equals it?

  36. 36.Evaluate 27^(1/3) for a Trenton volume label.

  37. 37.A Paterson dye formula contains 32^(2/5). What is its value?

  38. 38.An Edison lab note asks for 81^(3/4). Which result is correct?

  39. 39.A Camden blueprint uses 9^(3/2). What number is that?

  40. 40.Union City writes a scale factor as 4^(-1/2). Which value matches?

  41. 41.Elizabeth's packing model includes 125^(2/3). What is that value?

  42. 42.The member count for a club in Hoboken satisfies the equation 2^x = 32. What is x?

  43. 43.Which exponent x satisfies 3^x = 81 on an NJ Transit passenger counter?

  44. 44.Cape May counts lighthouse flashes with 5^x = 125. The exponent x equals what?

  45. 45.A Meadowlands display shows the equation 2^x = 8. Which value of x makes it true?

  46. 46.Newark's archive uses powers of ten in the equation 10^x = 1000. Find x.

  47. 47.Atlantic City strings boardwalk lights so that 4^x = 64. What is x?

  48. 48.A New Brunswick book club waiting list obeys 2^x = 128. Solve for x.

  49. 49.A Millville kiln record contains the equation 6^x = 36. What is x?

  50. 50.What is log base 2 of 32, the inverse question for the exponential equation 2^x = 32?

  51. 51.A Trenton filing code stores log base 10 of 1000. What is the value?

  52. 52.Evaluate log base 3 of 81 for a Princeton Junction timetable.

  53. 53.A Paramus inventory tag stores log base 5 of 25. Which number is it?

  54. 54.What is log base 2 of 8 on a Bayonne signal chart?

  55. 55.A Fort Lee engineer knows that log base 2 of 16 equals 4. Which exponential equation states the same fact?

  56. 56.Find log base 4 of 64 for a Camden stage timer.

  57. 57.A Woodbridge meter reads log base 10 of 100. What is the reading?

  58. 58.Adding 3 to every output of a Cape May temperature function moves the graph in which way?

  59. 59.Replacing the input x with x - 2 on a Hoboken ferry graph moves the graph which way?

  60. 60.If a Garden State Parkway model uses f(x + 4) in place of f(x), the graph is shifted in which direction?

  61. 61.Multiplying a shore-depth function at Island Beach by -1 reflects its graph across which axis?

  62. 62.Using f(-x) instead of f(x) for a Palisades skyline graph reflects the graph across which axis?

  63. 63.Doubling every y-value of a Meadowlands attendance graph, while keeping each x-value fixed, is which change?

  64. 64.Subtracting 5 from each output of a Brick Township rainfall function moves the graph which way?

  65. 65.Halving every output of a Vineland greenhouse function, without moving the inputs, is which change?

  66. 66.A Newark fare is f(x) = 2x + 6. Which function is the inverse of f?

  67. 67.A Lambertville mile marker uses f(x) = x - 4. What is the inverse function?

  68. 68.A Jersey City scale is f(x) = 3x. Which rule is the inverse?

  69. 69.A Morristown thermostat uses f(x) = (1/2)x + 1. What is the inverse?

  70. 70.A Passaic River gauge uses f(x) = 4x - 8. Which expression is the inverse?

  71. 71.A Somerville bus rule is f(x) = x/5 + 2. Find the inverse.

  72. 72.A path near the Delaware Water Gap uses f(x) = -2x + 4. What is the inverse?

  73. 73.A Cherry Hill ticket price is f(x) = 5x + 10. Which function undoes f?

  74. 74.Atlantic City parade banners are numbered 4, 7, 10, 13. If the same difference continues, what is the next number?

  75. 75.Weekend ferry counts in Weehawken form 3, 6, 12, 24. If the same multiplier continues, what is the next term?

  76. 76.A Red Bank choir starts at 5 singers and adds 2 singers at each rehearsal, giving 5, 7, 9, and so on. How many singers are at the 6th count?

  77. 77.A Pine Barrens marker sequence starts at 2 and multiplies by 3 each time. What is the 5th term?

  78. 78.Four donation totals at a Montclair bake sale are 2, 5, 8, and 11 dollars. What is the sum of these four terms?

  79. 79.Library visits in Princeton Junction are listed as 5, 10, 20, 40. What is the common ratio?

  80. 80.The Red Bank robotics team starts with 7 members and adds 4 members after each of 5 meetings. How many members are there after those 5 additions?

  81. 81.A Sandy Hook buoy battery reads 64, 32, 16, 8 on four checks. If the same halving continues, what is the next reading?

  82. 82.A ramp at a Newark museum rises at 30 degrees. What is the sine of 30 degrees?

  83. 83.A roof beam in Hopewell meets the horizontal at 60 degrees. What is the cosine of 60 degrees?

  84. 84.A flagpole in Trenton stands at 90 degrees from the ground. What is sin(90 degrees)?

  85. 85.A boardwalk in Ocean City runs flat, at 0 degrees from the horizontal. What is cos(0 degrees)?

  86. 86.A driveway in Summit climbs at 45 degrees. What is tan(45 degrees)?

  87. 87.A canal lock in Lambertville is level with the water, an angle of 0 degrees. What is sin(0 degrees)?

  88. 88.A right triangle on a Hoboken gym floor has legs 3 and 4 and hypotenuse 5. For the acute angle opposite the side of length 3, what is the sine?

  89. 89.A right triangle on a Camden field has sides 5, 12, and 13, with 13 the hypotenuse. What is the cosine of the acute angle next to the side of length 12?

  90. 90.On the unit circle, which coordinates match the angle 0 degrees?

  91. 91.A navigation drill at Sandy Hook marks 90 degrees on the unit circle. Which point is that?

  92. 92.Which point on the unit circle corresponds to 180 degrees?

  93. 93.At 270 degrees, what are the unit-circle coordinates?

  94. 94.Which ordered pair is the unit-circle point at 45 degrees?

  95. 95.A unit-circle diagram in a Princeton classroom marks 30 degrees. Which point is correct?

  96. 96.Four quiz scores from a class in Elizabeth are 4, 6, 8, and 10. What is the mean?

  97. 97.Three ferry wait times in Jersey City, in minutes, are 2, 5, and 8. What is the mean wait?

  98. 98.Two Newark attendance lists have the same mean. List A is 10, 10, 10, 10. List B is 0, 10, 10, 20. Which statement is true?

  99. 99.Two temperature lists from a Vineland greenhouse both have mean 5. List C is 5, 5, 5. List D is 1, 5, 9. How do the standard deviations compare?

  100. 100.Scores are described by a normal curve with mean 70. A student scores 70. Where does that score sit on the curve?

  101. 101.Heights of a club in Montclair follow a normal curve. One height is many standard deviations above the mean. Where is it on the curve?

  102. 102.Commute times in Edison are modeled with a normal curve. About what portion of the times are within one standard deviation of the mean?

  103. 103.Two lists of lap times, in seconds, from a track in Toms River have the same mean. List P is 8, 9, 10. List Q is 1, 9, 17. Which list has the larger standard deviation?

  104. 104.A jar at a Newark street fair holds 3 red tickets and 2 blue tickets. One ticket is drawn at random. What is the probability it is red?

  105. 105.A student in Hoboken flips a fair coin twice. What is the probability of two heads?

  106. 106.A fair six-sided die is rolled at a game booth in Point Pleasant. What is the probability of an even number?

  107. 107.A simple weather model for Cape May says the probability of rain on Saturday is 1/5. What is the probability that it does not rain?

  108. 108.A spinner at an Asbury Park arcade has 4 equal sections, and one section is labeled star. If the spinner is fair, what is the probability it lands on star?