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SAT Math: Advanced Math

Quadratics, exponentials, polynomials, and nonlinear functions.

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  1. 1.Which pair of numbers solves the equation x^2 - 5x + 6 = 0?

  2. 2.If 2^x = 32, what is the value of x?

  3. 3.What is the vertex of the graph of y = (x - 2)^2 + 5?

  4. 4.Which product is equal to 49x^2 - 16?

  5. 5.Expand (3x + 2)(x - 4). Which polynomial is the result?

  6. 6.What are the solutions of x^2 + 2x - 15 = 0?

  7. 7.A culture starts with 200 cells and doubles every hour. Which expression is the number of cells after t hours?

  8. 8.What is the minimum value of f(x) = (x + 4)^2 - 9?

  9. 9.For x not equal to 3, which expression equals (x^2 - 9)/(x - 3)?

  10. 10.The graphs of y = x^2 and y = 2x + 3 meet at which two points?

  11. 11.What is the solution of sqrt(2x + 7) = 5?

  12. 12.Which value of x satisfies 3^(x + 1) = 81?

  13. 13.What is the degree of the polynomial 7x^5 - 4x^3 + x - 9?

  14. 14.Which expression is equal to x^2 + 8x + 3?

  15. 15.What are the solutions of 2x^2 - 4x - 6 = 0?

  16. 16.An 80 mg dose is reduced by half every 4 hours. How many milligrams remain after 12 hours?

  17. 17.Which product equals x^2 - 7x + 12?

  18. 18.What is the vertex of y = x^2 - 6x + 4?

  19. 19.Which value equals 16^(3/4)?

  20. 20.The line y = x + 1 meets y = x^2 - 5 at two points. What is the sum of their x-coordinates?

  21. 21.Which expression equals (2x^3)^2 * x^4?

  22. 22.How many distinct real solutions does x^2 + 6x + 10 = 0 have?

  23. 23.Which expression is 12x^3 - 18x^2 + 6x factored completely over the integers?

  24. 24.Which number x makes 5^(2x) = 125 true?

  25. 25.The graph of y = x^2 is moved right 5 units and down 1 unit. Which equation matches the new graph?

  26. 26.For x not equal to 2 or -2, which expression equals 3/(x - 2) + 1/(x + 2)?

  27. 27.Which expression equals sqrt(72) in simplest radical form?

  28. 28.A rectangle has side lengths x + 3 and x - 1, and its area is 45. What is the positive value of x?

  29. 29.If p(x) = 2x^3 - x^2 + 4, what is p(-2)?

  30. 30.Which expression equals 9^x for every x?

  31. 31.At which points does y = (x - 1)(x + 6) meet the x-axis?

  32. 32.Which value equals 8^(2/3)?

  33. 33.Which equation has solutions 4 and -7?

  34. 34.The graphs of y = 3x - 2 and y = x^2 intersect at two points. What is the larger x-coordinate?

  35. 35.For which of these values of x is (x + 4)/(x^2 - 9) undefined?

  36. 36.A sequence starts at f(0) = 5, and each term is 3 times the term before it. What is f(3)?

  37. 37.Which polynomial equals (x + 2)^3?

  38. 38.A ball's height in feet is h(t) = -16t^2 + 48t + 4, with t in seconds. At what time t does the ball reach its highest point?

  39. 39.Which expression equals 5/sqrt(3)?

  40. 40.Which product equals x^3 + 5x^2 + 2x + 10?

  41. 41.If 4^x = 4^3 * 4^5, what is x?

  42. 42.Which values of x satisfy x^2 = 49?

  43. 43.If f(x) = x^2 - 1 and g(x) = x + 4, what is f(g(2))?

  44. 44.Which expression is a factor of x^3 - 6x^2 + 11x - 6?

  45. 45.A town's population is modeled by P(t) = 1200 * (1.04)^t, where t is years after 2020. What does the factor 1.04 mean?

  46. 46.What is the discriminant of 3x^2 - 5x + 1 = 0?

  47. 47.For x not equal to 0 or -2, which expression equals ((x^2 - 4)/x) * (x^2/(x + 2))?

  48. 48.The graph of y = 2(x - 3)^2 + k passes through (4, 9). What is k?

  49. 49.If 4^x = 64, what is x?

  50. 50.What is the sum of the solutions of x^2 - 9x + 14 = 0?

  51. 51.Which of these numbers is in the domain of f(x) = sqrt(x - 6)?

  52. 52.What is (4x^2 - 3x + 1) + (x^2 + 5x - 8)?

  53. 53.An account starts at $500 and doubles every 6 years, with no other deposits. After how many years is it worth $2,000?

  54. 54.What is the equation of the axis of symmetry of y = x^2 + 10x + 21?

  55. 55.Which value equals (1/8)^(-2/3)?

  56. 56.How many real solutions does the system y = x^2 + 1 and y = -2 have?

  57. 57.Which product equals 8x^3 - 27?

  58. 58.What are the solutions of (x - 5)^2 = 9?

  59. 59.For x and y not equal to 0, which expression equals (12x^5 y^2)/(3x^2 y)?

  60. 60.What is the vertex of g(x) = 3(x + 1)^2 + 6?

  61. 61.A quadratic has zeros at x = -2 and x = 5, and its value at x = 0 is -10. Which equation matches?

  62. 62.Find x when 10^(x - 2) = 1000.

  63. 63.Which point lies on the graph of y = 2^(x - 3)?

  64. 64.What is the product of the solutions of 2x^2 - 8x + 6 = 0?

  65. 65.Which value equals sqrt(50) * sqrt(2)?

  66. 66.Which of these values of x must be excluded from (x^2 + x)/(x^2 - x)?

  67. 67.A water arc is modeled by h(x) = -(1/2)(x - 8)^2 + 12, where h is height in feet. What is the greatest height?

  68. 68.What is the solution of sqrt(3x - 2) = x - 2?

  69. 69.Which monomial equals 5x^2 * 4x^3?

  70. 70.The graphs of y = x^2 - 4 and y = 5 meet at two points. What is the positive x-coordinate of those points?

  71. 71.Which expression equals (x + 3)^2 - (x - 3)^2?

  72. 72.A sample's mass in grams is m = 64 * (1/2)^(d/5), where d is the number of days. What is the mass after 15 days?

  73. 73.When (x - 2)(2x + 1)(x + 4) is expanded, what is the leading term?

  74. 74.Which product of linear factors equals x^2 - 4x - 12?

  75. 75.Which expression equals x^(1/2) * x^(3/2)?

  76. 76.Which of these values of a makes the graph of y = a(x - 1)^2 + 4 open downward?

  77. 77.What is the solution of 4/(x - 1) = 2, where x is not 1?

  78. 78.What is the solution of x^2 + 6x + 9 = 0?

  79. 79.A population is modeled by P = 800 * (1.5)^t. What is P when t = 2?

  80. 80.What is (5x^3 + 2x - 1) - (3x^3 - x + 4)?

  81. 81.For x not equal to 5, which expression equals (2x^2 - 10x)/(x - 5)?

  82. 82.The graphs of y = -x + 6 and y = x^2 intersect where x satisfies which equation?

  83. 83.Which number equals (3 * 10^4) * (2 * 10^3)?

  84. 84.What is the range of f(x) = -2(x + 5)^2 + 3?

  85. 85.Which value of k makes x^2 - 12x + k a perfect square trinomial?

  86. 86.If x^(3/2) = 8 and x > 0, what is x?

  87. 87.A square patio has area 144 square meters. Each side is lengthened by the same amount, and the new area is 196 square meters. By how many meters was each side lengthened?

  88. 88.For f(x) = -4x^3 + x, what happens to f(x) as x increases without bound?

  89. 89.For x not equal to -2, which expression equals (x^2 - 4)/(x^2 + 4x + 4)?

  90. 90.Find x if 4^(x + 1) = 8^(x - 1).

  91. 91.What is the y-coordinate of the vertex of y = -x^2 + 8x - 5?

  92. 92.Which value equals (sqrt(5))^4?

  93. 93.A box has volume V = x(x + 2)(x + 3). Which polynomial equals V?

  94. 94.The amount of a substance is N(t) = 40 * (1/2)^(t/8), with t in hours. The amount is multiplied by 1/2 every how many hours?

  95. 95.One solution of 5x^2 + 2x - 3 = 0 is x = -1. What is the other solution?

  96. 96.How is the graph of y = x^2 + 7 related to the graph of y = x^2?

  97. 97.For x not equal to 0, what is the quotient when 6x^3 + 3x^2 - 9x is divided by 3x?

  98. 98.For the system x^2 + y^2 = 25 and y = x + 1, what is the sum of the y-coordinates of the real solutions?

  99. 99.Which value equals 4^(-2)?

  100. 100.Which product equals 2x^2 + 7x + 3?

  101. 101.The function f(x) = a * b^x passes through (0, 6) and (1, 18). What is a?

  102. 102.A rectangle's length is 3 meters more than its width, and its area is 108 square meters. What is the width in meters?

  103. 103.Which expression equals 1/(sqrt(7) - 2)?

  104. 104.For f(x) = x^2, what is the average rate of change from x = 1 to x = 4?

  105. 105.Which expression equals (a^2 b^3)^2 for all a and b?

  106. 106.Tickets sell according to n = 200 - 4p, where p is the price in dollars. Revenue is R = p * n. Which price gives the greatest revenue?

  107. 107.Squaring both sides of 2 + sqrt(x) = x produces the candidates x = 1 and x = 4. Which of those values solves the original equation?

  108. 108.The function f is defined by f(x) = 3^(x - 1). If f(k) = 81, what is k?