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New York State Regents Examination Algebra II

Exponents, logarithms, polynomials, trigonometry, sequences, and statistics.

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.An Albany planetarium dial is marked with the common logarithm of 1000. What is log base 10 of 1000?

  2. 2.A backup battery in a Syracuse server closet obeys 2^x = 32. What is x?

  3. 3.A Rochester window brace is level when (x - 3)(x + 2) = 0. What are the roots?

  4. 4.A signal worksheet at the Utica rail yard asks for the square of the imaginary unit. What is i^2?

  5. 5.Mile markers on a trail near Lake George follow the arithmetic sequence 4, 7, 10, and so on. What is the 10th term?

  6. 6.A surveyor at Jones Beach reads a 30 degree angle from a baseline. What is the sine of 30 degrees?

  7. 7.A footbridge cable over the Mohawk is modeled by y = (x - 2)^2 + 5. What is the vertex?

  8. 8.A Lockport canal gauge satisfies -3x < 12. Which inequality describes x?

  9. 9.A Buffalo harbor ledger lists 2780000 bolts. Which scientific notation shows that count with a first factor at least 1 and less than 10?

  10. 10.Depth along a Hudson sounding is f(x) = -2x^3 + 5x. Which statement describes the end behavior?

  11. 11.A Rochester recipe card uses (x^2 - 9)/(x^2 + 5x + 6). Which expression is the simplified form after a common factor is canceled?

  12. 12.Morning dock counts are 2, 4, 6 at Lake Placid and 1, 4, 7 at Montauk. Compare the means and the population standard deviations.

  13. 13.Two Geneva sensor readings are the complex numbers 3 + 2i and 4 - 5i. What is their sum?

  14. 14.A Niagara Falls overlook counts 16 viewing sections, and a guide writes log base 2 of 16. What is that value?

  15. 15.Folded maps in a Binghamton archive satisfy 3^x = 81. Solve for x.

  16. 16.A Plattsburgh radio pair multiplies (2 + i)(2 - i). What is the product?

  17. 17.Tickets sold at an Albany concert grow geometrically: 5, 10, 20, and so on. What is the 6th term?

  18. 18.A Cayuga Lake sail diagram uses a 60 degree angle from the dock. What is the cosine of 60 degrees?

  19. 19.Saratoga Springs ticket sales follow y = -3(x + 1)^2 + 4. What is the vertex of this parabola?

  20. 20.A Troy freight limit is written -2x ≤ 10. What is the solution?

  21. 21.The Port of Albany multiplies the counts (3 * 10^4) and (2 * 10^3). Which product is in scientific notation?

  22. 22.A Catskill ridge profile is g(x) = 2x^4 - x + 7. What happens to g(x) at both ends?

  23. 23.Simplify the Beacon ferry ratio (x^2 - 4)/(x - 2) by canceling a common factor.

  24. 24.Study hours are 2, 4, 6 in Poughkeepsie and 10, 10, 13 in Queens. Which comparison of the mean and the population standard deviation is correct?

  25. 25.Add the Canandaigua circuit values 5 - i and -2 + 4i.

  26. 26.A Yonkers scale adds log base 10 of 100 and log base 10 of 10. What is the sum?

  27. 27.A Rome pump schedule uses (2^3)^2. What is that value?

  28. 28.A Oneonta textbook drill asks for i^3. Which value is correct?

  29. 29.The first 10 tolls on an Erie Canal model are the arithmetic series 4 + 7 + 10 + ... with the same difference 3. What is the sum?

  30. 30.A lighthouse angle at Oswego is a right angle. What is the sine of 90 degrees?

  31. 31.Glass shipments in Corning follow y = x^2 - 6x + 5. What is the vertex?

  32. 32.An Elmira storage rule is -5x > 20. Solve for x.

  33. 33.Jamestown divides a grain figure 8.4 * 10^6 by 2 * 10^2. What is the quotient in scientific notation?

  34. 34.A Letchworth gorge model is h(x) = -x^5 + 3x^2. Which end behavior matches the leading term?

  35. 35.Cancel the common factor in the Auburn yield expression (2x^2 + 6x)/(2x).

  36. 36.Noon temperatures are 6, 8, 10, 12 in Binghamton and 9, 9, 9, 9 in Oneonta. Compare the means and population standard deviations.

  37. 37.Subtract 1 - 3i from 6 + 2i for a Watkins Glen filter. What is the difference?

  38. 38.A Seneca Lake dilution is 1/8 of a full tank, and a tech writes log base 2 of 1/8. What is that logarithm?

  39. 39.Kingston floodgates satisfy 5^(x - 1) = 125. What is x?

  40. 40.A Newburgh impedance is the complex number 3 + 4i. What is its modulus?

  41. 41.A Glens Falls donation drive adds the geometric series 2 + 6 + 18 + 54. What is the sum?

  42. 42.A Fort Ticonderoga wheel turns through a straight angle of 180 degrees. What is that angle in radians?

  43. 43.A Whiteface wind graph is y = 4 sin(x) + 1. What is the amplitude?

  44. 44.A New Paltz tolerance is |x - 2| < 5. Which solution set is correct?

  45. 45.A Montauk plankton count is 0.00045. Write it in scientific notation.

  46. 46.Factor the Kingston garden polynomial x^2 - 5x + 6.

  47. 47.For a Hyde Park path model p(x) = x^3 - 2x + 4, what is the remainder when p(x) is divided by x - 1?

  48. 48.Solve (x + 1)/(x - 1) = 2 for a Peekskill ramp, excluding any value that makes a denominator 0.

  49. 49.A dispatcher at Grand Central chooses 2 of 5 Metro-North cars for inspection. Order does not matter. How many choices are there?

  50. 50.A Battery Park sight line makes a 45 degree angle with the walkway. What is the tangent of 45 degrees?

  51. 51.A High Line light pattern follows y = sin(2x), with x in radians. What is the period?

  52. 52.A Flushing fare rule is f(x) = 3x + 6. What is the inverse function?

  53. 53.In Astoria, f(x) = x^2 and g(x) = x + 1. What is f(g(2))?

  54. 54.A Woodstock sound model uses y = log(x - 4), with log base 10. Which describes the domain?

  55. 55.An Adirondack sapling count starts at 200 and grows by 5 percent each year. What is the count after 2 years?

  56. 56.A Brookhaven sample starts at 80 mg and has a half-life of 3 hours. How many milligrams remain after 9 hours?

  57. 57.Expand the Hempstead banner polynomial (x + 4)(x - 1).

  58. 58.Factor x^3 - 8 for a Skaneateles cistern volume.

  59. 59.Solve x^2 - 4x - 5 = 0 for the Cayuga inlet gates.

  60. 60.For the Chautauqua model x^2 + 2x + 5 = 0, what is the discriminant, and what does it say about real solutions?

  61. 61.On a Bear Mountain graph, y = x^2 meets y = x + 2. Which points are the intersections?

  62. 62.Along the Massena river road, f(x) = x^2. What is the average rate of change from x = 1 to x = 4?

  63. 63.A river gauge at Ogdensburg satisfies log base 2 of x = 5. What is x?

  64. 64.A Hamilton lab notebook shows ln(e^4). What is that value?

  65. 65.At Cape Vincent, a decay base is raised to the power 0. What is e^0?

  66. 66.Solve sqrt(x + 5) = 4 for a footbridge at Ausable Chasm.

  67. 67.Simplify sqrt(50) for a Howe Caverns rope length.

  68. 68.A Fire Island dune model uses 8^(2/3). What is that value?

  69. 69.Lock numbers on a short Erie Canal tour start at 3 and then follow a_n = a_(n - 1) + 5. What is the 4th term?

  70. 70.A Mohawk crew labels four docks 1 through 4 and adds those labels. What is the sum from k = 1 to 4 of k?

  71. 71.A Hudson crossing has angle A = 30 degrees opposite a side of 4 meters, and angle B = 90 degrees. How long is the side opposite angle B?

  72. 72.A Jones Beach wheel is turned by pi/3 radians. What is the cosine of pi/3?

  73. 73.A Coney Island boom is set at 150 degrees from the walkway. What is the sine of 150 degrees?

  74. 74.A Liberty Island beacon rotates 400 degrees from its start. Which coterminal angle between 0 and 360 degrees matches it?

  75. 75.At West Point, arcsin(1/2) is needed in degrees, using the principal value. What is that angle?

  76. 76.An Inwood hill profile uses f(x) = x^3. Which symmetry statement is correct?

  77. 77.The Newburgh traffic ratio (2x + 1)/(x - 3) has which horizontal asymptote?

  78. 78.The Hudson town model y = 1/(x - 5) has a vertical asymptote at which line?

  79. 79.The Rhinebeck ratio (x^2 - 1)/(x - 1) is undefined at x = 1 but simplifies elsewhere. Where is the hole?

  80. 80.At a Riverhead farm stand, packing time varies inversely with the number of workers. Four workers take 6 hours. How long do 8 workers take?

  81. 81.A Cooperstown drawer has 5 red sleeves and 3 blue sleeves. One sleeve is drawn at random. What is the probability it is red?

  82. 82.At a Rockaway booth, a fair six-sided die is rolled and a spinner with 3 equal sectors A, B, and C is spun. What is the probability of an even number and sector A?

  83. 83.A Brooklyn reading list has mean 100 and population standard deviation 15. How many standard deviations above the mean is a score of 130?

  84. 84.An Albany score of 88 comes from a class with mean 80 and population standard deviation 4. A Troy score of 85 comes from a class with mean 75 and population standard deviation 10. Which score is higher relative to its class?

  85. 85.A Watertown snowfall model is y = 2x + 3, with x in days after December 1 and y in inches. What does it predict when x = 5?

  86. 86.At Dunkirk, a line of fit is y = 2x + 1. When x = 3, the observed y is 10. What is the residual, observed minus predicted?

  87. 87.Complete the square for the Penn Yan greenhouse model x^2 + 8x + 3.

  88. 88.Factor 2x^2 + 7x + 3 for a Bath orchard count.

  89. 89.Divide x^2 + 5x + 6 by x + 2 for a Cortland plot. What is the quotient?

  90. 90.Solve sqrt(x + 2) = x for a Warrensburg trail marker, and reject any extraneous result.

  91. 91.Solve (x - 1)/(x + 2) > 0 for a Nyack dock schedule.

  92. 92.Solve |2x - 1| = 7 for a Suffern gate setting.

  93. 93.At Long Beach, log base 10 of x equals 2. What is log base 10 of x^3?

  94. 94.A Greenport crate count is modeled by 27^(2/3). What is that number?

  95. 95.Multiply (1 + sqrt(2))(1 - sqrt(2)) for an Orient Point piling length.

  96. 96.Divide 4 + 2i by 1 - i for a Snug Harbor phase shift. What is the quotient?

  97. 97.Ice huts on Saranac Lake follow a_n = 3 * 4^(n - 1). What is the third term?

  98. 98.On Lake George, sin(theta) = 3/5 and theta is in quadrant I. What is cos(theta)?

  99. 99.A Keuka Lake angle theta measures 30 degrees. What is sin(2 * theta)?

  100. 100.A Piermont pier sketch uses a 45 degree angle. What is that measure in radians?

  101. 101.The Cold Spring graph of y = x^2 is changed to y = (x - 3)^2. Which transformation is that?

  102. 102.Sleepy Hollow replaces a graph y = f(x) with y = -f(x). What does that do to the graph?

  103. 103.A Monticello growth curve is y = 2^x. Which set is the range?

  104. 104.If f(x) = 10^x for a Potsdam lab scale, what is the inverse function?

  105. 105.A Oneida Lake depth fit is 7x^3 - x + 2. What is the degree of this polynomial?

  106. 106.The Fulton gate equation x^2 - 7x + 10 = 0 has two roots. What is their sum?

  107. 107.Expand (x + 1)^3 for a Schenectady bin count.

  108. 108.The Saratoga trails club has 6 members and must send 2 delegates. Order does not matter. How many different pairs are possible?