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Virginia Standards of Learning End-of-Course Algebra II

Polynomials, exponentials, logarithms, rational expressions, and sequences.

These questions are original. This is not an official Virginia Standards of Learning test, and FreeExam is not affiliated with the Virginia Department of Education.

  1. 1.Two flower beds at a Charlottesville community garden are modeled by 4x^2 - 3x + 7 and x^2 + 5x - 2. Which polynomial is their sum?

  2. 2.A Roanoke greenhouse subtracts the model 3x^2 - 6x + 1 from 8x^2 + x - 4. Which polynomial is the difference?

  3. 3.A rectangular banner at the Virginia State Fair in Doswell measures (x + 4) feet by (x - 7) feet. Which polynomial gives its area?

  4. 4.A Winchester orchard labels crate stacks with x^2 - 9x + 20. Which expression is a factorization of that quadratic over the integers?

  5. 5.An Alexandria patio design has area x^2 - 49 square feet. Which identity rewrites that difference of squares?

  6. 6.A Norfolk art class factors the volume expression 8x^3 + 27. Which factorization is correct?

  7. 7.A club poster uses the equation 2^x = 32. The poster hangs in a Richmond club room. What is the solution for x?

  8. 8.A Cape Henry logbook uses 3^x = 81 to count lamp checks. Which value of x makes the equation true?

  9. 9.A bookstore puzzle in Lexington asks for log_5(125). What is that value?

  10. 10.A Harrisonburg choir adds the sound-index values log_2(8) and log_2(4). What is the sum?

  11. 11.A Norfolk weather board subtracts log_10(10) from log_10(1000). What is the result?

  12. 12.A Salem drum line simplifies 2 log_3(9). Which number equals that expression?

  13. 13.A trail counter near Damascus records the equation 5 * 2^x = 40. What is x?

  14. 14.A data file in Fairfax is labeled with log_2(x) = 6. What is x?

  15. 15.Ticket totals at a Williamsburg matinee satisfy x^2 - 5x + 6 = 0. Which pair gives both solutions?

  16. 16.A position, in meters from a Hampton dock, satisfies x^2 + 2x - 15 = 0. Which pair lists the solutions?

  17. 17.A survey equation in Bath County is x^2 - 4x + 13 = 0. Which statement about its solutions is correct?

  18. 18.Students in Blacksburg add the complex numbers 3 + 2i and 4 - 5i. What is the sum?

  19. 19.On a coordinate card at the Science Museum of Virginia in Richmond, a class multiplies 2 + i by 2 - i. What is the product?

  20. 20.A class in Poquoson squares the complex number 1 + i. Which result is correct?

  21. 21.Students in Portsmouth multiply 3 - i by 1 + 2i. Which product is correct?

  22. 22.A Virginia Beach class solves x^2 + 4 = 0 over the complex numbers. Which pair is the solution set?

  23. 23.A recorded temperature in Winchester satisfies |x - 3| = 7. Which values of x solve that equation?

  24. 24.A Hampton ferry will launch when the tide index x satisfies |x - 2| < 5. Which inequality describes the allowed values?

  25. 25.A James River cleanup crew in Richmond has already filled 12 bags and fills 4 more bags each hour. After how many hours is the total 40 bags?

  26. 26.At a Floyd farm stand, 2 bags of apples and 1 basket of pears cost 11 dollars, and 1 bag costs 1 dollar more than 1 basket. What is the price of a bag?

  27. 27.In Leesburg, 4 jars of honey and 1 jar of jam cost 18 dollars. Honey costs 2 dollars more per jar than jam. What does one jar of honey cost?

  28. 28.On a Shenandoah trail map, y = x^2 and y = 2x + 3 meet at two points. Which x-values are those meeting points?

  29. 29.A bridge plan in Lynchburg simplifies (x^2 - 9)/(x - 3). Which description is correct?

  30. 30.A scale calculation at the Mariners' Museum in Newport News multiplies x/(x + 2) by (x + 2)/(x - 5). Where that product is defined, which expression equals it?

  31. 31.A painter in Staunton combines 1/2 of a can with 3/x of a can, where x is a positive number of helpers. Which expression is that total?

  32. 32.A canoe club on the New River near Radford solves x/(x - 2) = 3. Which value of x is the solution?

  33. 33.A mill ratio in Augusta County is written (x + 3)/(x - 2) = 5/(x - 2). Which statement describes the solution set?

  34. 34.Tide ratios at Yorktown are modeled by f(x) = (x + 1)/(x^2 - 4). Which set is the domain?

  35. 35.A graph posted in a Virginia Beach classroom shows g(x) = (3x + 1)/(x - 6). Which line is the vertical asymptote?

  36. 36.An Arlington class graphs h(x) = (2x^2 + 5)/(x^2 - 1). Which line is the horizontal asymptote?

  37. 37.A Blue Ridge elevation model is p(x) = -2x^3 + x. What happens to p(x) as x grows without bound?

  38. 38.A footbridge offset in Albemarle County is f(x) = (x + 1)(x - 2)(x - 4). What is the y-intercept?

  39. 39.In a Culpeper class, p(x) = x^3 - 2x^2 + x - 4. What remainder results when p(x) is divided by x - 2?

  40. 40.Which expression is a factor of x^3 - 6x^2 + 11x - 6, the polynomial on a workshop sheet in Bristol?

  41. 41.A crate model in South Boston is x^3 - 7x^2 + 14x - 8. What is the sum of its three zeros?

  42. 42.A brace in a Buena Vista barn has length sqrt(72) feet. Which expression is that length in simplest radical form?

  43. 43.Two trail segments near Crabtree Falls measure 3 sqrt(8) miles and sqrt(18) miles. What is their combined length in simplest form?

  44. 44.A map scale for the Great Dismal Swamp is written 4/sqrt(2). Which equivalent expression has a rational denominator?

  45. 45.A depth, in feet, inside Luray Caverns satisfies sqrt(x + 5) = 4. What is x?

  46. 46.A kite height over First Landing State Park satisfies sqrt(x + 2) = x. Which value solves the original equation?

  47. 47.A storage cube at a Suffolk warehouse satisfies the cube root of (x - 1) equals 2. What is x?

  48. 48.A Loudoun vineyard index equals 16 raised to the power 3/4. What is that value?

  49. 49.A drawing of Monticello uses the scale factor 4^{-2}. What is the value of that factor?

  50. 50.Ospreys near the Chesapeake Bay are modeled by P = 40 * 2^{t/5}, with t in years. What is P when t = 10?

  51. 51.In a Fredericksburg art class, watercolor strength follows A = 200 * (1/2)^{t/3}, with t in hours. What is A when t = 6?

  52. 52.A puzzle at the Virginia Museum of Fine Arts states that log_6(x) = 2. What is x?

  53. 53.A computer club at George Mason University in Fairfax evaluates log_2(2^7). What is the value?

  54. 54.A cabin lockbox near Smith Mountain Lake opens when log_3(x - 1) = 2. What is x?

  55. 55.For a positive number x, which expression equals log_2(8x) on a Richmond algebra card?

  56. 56.A Waynesboro formula card shows 2 log_5(x) - log_5(y), with x and y positive. Which single logarithm matches it?

  57. 57.Two plantings at Maymont in Richmond are compared by the equation 9^x = 27. What is x?

  58. 58.A peanut sorter in Suffolk applies g(x) = x^2 and then f(x) = 2x + 1. What is f(g(3))?

  59. 59.A bakery price in Covington is f(x) = 3x - 6. Which function is the inverse of f?

  60. 60.A Bridgewater class studies f(x) = 5^x. Which function is the inverse of f?

  61. 61.A mile-marker function along Skyline Drive is y = log_2(x - 4). Which inequality gives its domain?

  62. 62.A water-level model at Lake Anna is f(x) = 3 * 2^x + 1. Which set is the range?

  63. 63.A fountain curve at the University of Virginia is y = (x - 3)^2 + 4. How is this graph related to y = x^2?

  64. 64.A cable model over a cove at Claytor Lake is y = (x + 2)^2 - 5. What is the vertex?

  65. 65.A curve sketched for Natural Tunnel is y = x^2 - 6x + 5. What is the equation of its axis of symmetry?

  66. 66.A ferry-cost model in Gloucester is y = x^2 + 4x + 7. What is the minimum value of y?

  67. 67.Along a Reston bike path, a practice model uses f(x) = x^2. What is the average rate of change from x = 1 to x = 4?

  68. 68.A graphing sheet in Bristol uses f(x) = x^4 - 3x^2. Which symmetry description is correct?

  69. 69.Seats in a Salem auditorium form an arithmetic sequence with 7 seats in row 1 and 4 more seats in each later row. How many seats are in row 6?

  70. 70.A Petersburg fundraiser starts at 3 dollars on day 1, and each day's gift is double the day before. How many dollars does the model give on day 5?

  71. 71.A Manassas club collects stamps in the arithmetic pattern 5, 8, 11, and so on. What is the sum of the first 8 terms?

  72. 72.Ticket requests in Portsmouth form the geometric sequence 6, 12, 24, 48. What is the sum of these four terms?

  73. 73.Rows of chairs in Rockbridge County follow 11, 15, 19, 23, and so on. Which formula gives the nth term?

  74. 74.A display at Nauticus in Norfolk starts with 5 lights on panel 1, and each later panel has 3 times as many lights as the panel before it. How many lights are on panel 4?

  75. 75.A scoring sheet in Woodstock asks for the sum from k = 1 to k = 4 of (2k + 1). What is that sum?

  76. 76.A booth at a Chincoteague carnival has 4 red tokens, 5 blue tokens, and 3 green tokens. One token is drawn at random. What is the probability that it is green?

  77. 77.A Richmond forecast model assigns probability 0.3 to rain during a Saturday market. What is the probability that it does not rain?

  78. 78.At a school fair in Hopewell, a spinner lands on red with probability 1/3, and an independent fair coin lands on heads with probability 1/2. What is the probability of red and heads?

  79. 79.A box in a Roanoke classroom holds 5 algebra cards and 3 geometry cards. Two cards are drawn at random without replacement. What is the probability that both are algebra cards?

  80. 80.Eight student guides are available at Monticello, and 3 will be chosen for one tour. Order does not matter. How many groups of 3 are possible?

  81. 81.Montpelier will hang 3 different portraits in a row, chosen from 7 available portraits. Order matters. How many hangings are possible?

  82. 82.An Alexandria club has 6 seniors and 4 juniors. A president is chosen at random, and then a secretary is chosen from those who remain. What is the probability that both officers are seniors?

  83. 83.Practice scores in a Falls Church class are modeled with mean 80 and standard deviation 5. What is the z-score of a practice score of 90?

  84. 84.A Virginia Beach class reviews a normal curve. About what percent of the data in a normal distribution lie within one standard deviation of the mean?

  85. 85.A practice-score model in Fairfax has mean 100 and standard deviation 15. What is the z-score of a score of 70?

  86. 86.At a Middleburg bakery, y varies directly with x. When x = 4, y = 18. What is y when x = 10?

  87. 87.In a Danville shop model, y varies inversely with x. When x = 6, y = 8. What is y when x = 4?

  88. 88.For a planter comparison in Crozet, y varies jointly with x and z. When x = 2 and z = 3, y = 24. What is y when x = 5 and z = 2?

  89. 89.A drop model at Natural Bridge uses y = sqrt(x - 5). Which set is the domain?

  90. 90.A Carytown shop uses f(x) = x - 4 and g(x) = 3x. Which expression equals g(f(x))?

  91. 91.A plat in Fauquier County shows the ratio 5/(3 - sqrt(2)). Which equivalent expression has a rational denominator?

  92. 92.A garden plan in Bedford divides x^2 - 5x + 6 by x - 2. What is the quotient?

  93. 93.Students in Front Royal divide x^2 + 3x + 5 by x + 1. What is the remainder?

  94. 94.A square garden in Goochland has side length 2x - 3. Which polynomial is the area?

  95. 95.Two planters in Orange are compared by the volume expression 27x^3 - 8. Which factorization is correct?

  96. 96.A path length in Appomattox satisfies x^2 - 4x - 5 = 0. What is the positive solution?

  97. 97.A savings plan in Colonial Heights uses 3x - 4 > 11, where x is the number of weeks. Which solution set is correct?

  98. 98.A greenhouse in Christiansburg keeps a reading x in the band -2 < 2x + 4 <= 10. Which inequality is equivalent?

  99. 99.A distance from a marker in Warrenton is modeled by |x + 2| = -5. What is the solution set?

  100. 100.On a map of Shenandoah County, 2 inches represent 15 miles. How many miles do 6 inches represent?

  101. 101.Visitor counts at Grayson Highlands are modeled by f(x) = (x - 2)(x + 5). What is the positive zero of f?

  102. 102.A fountain arc in Farmville follows f(x) = 2(x - 3)^2 + 5. What is the y-intercept?

  103. 103.A print-shop cost in Emporia is f(x) = (x - 1)^2. On which interval is f increasing?

  104. 104.A garden club in Charlottesville compares models for a clover patch. Which equation represents exponential growth?

  105. 105.A number puzzle in Ashland uses log_2(x + 1) = 4. What is x?

  106. 106.A count in Spotsylvania triples at each step and begins 2, 6, 18, 54, and so on. Which term equals 486?

  107. 107.A carnival spinner in Kilmarnock has 8 equal sections: 3 red, 2 gold, and 3 blue. What is the probability of landing on red or gold?

  108. 108.A lunch line in Henrico offers 3 soups and 5 sandwiches. A meal is one soup paired with one sandwich. How many different meals are possible?