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Free SAT Math practice questions

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Algebra

  1. Q1 · Linear equations in one variable · mediumFor what value of k does the equation 5(x-2)+12 = kx+6 have no solution?
  2. Q2 · Linear functions · easyA linear function f satisfies f(2)=15 and f(6)=31. What is the value of f(10)?
  3. Q3 · Linear functions · easyThe function f is defined by f(x) = kx - 4. If the graph of f passes through the point (3, 11), what is the value of k?
  4. Q4 · Systems of two linear equations in two variables · mediumThe system of equations 2x + 5y = 10 and 6x + ky = 30 has infinitely many solutions. What is the value of k?
  5. Q5 · Systems of two linear equations in two variables · easyIf 3x + 2y = 22 and x - 2y = 2, what is the value of x?
  6. Q6 · Linear inequalities in one or two variables · easyWhich of the following is equivalent to -3x + 7 ≤ 22?
  7. Q7 · Systems of two linear equations in two variables · mediumA theater sold 150 tickets for a play, some at $12 for adults and the rest at $7 for children. Total ticket sales were…
  8. Q8 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying x + 3y ≤ 15 and 2x + y ≤ 10, what is the greatest possible value of 3x + 5y?
  9. Q25 · Linear equations in one variable · mediumThe equation kx - 7 = 3x + 2 has exactly one solution for every value of k except one. What is that excluded value of k?
  10. Q27 · Linear equations in two variables · easyWhat is the slope of the line 4x - 2y = 10?
  11. Q28 · Systems of two linear equations in two variables · mediumFor what value of k does the system 2x + 3y = 9 and 4x + ky = 20 have no solution?
  12. Q29 · Linear inequalities in one or two variables · mediumWhat is the solution set of the system x > -3, x ≤ 5, and 2x - 1 < 9?
  13. Q30 · Linear inequalities in one or two variables · easyWhich statement is true about the graph of y ≤ 3x - 2?
  14. Q31 · Linear inequalities in one or two variables · easyA parking garage charges a $5 base fee plus $2.50 for each hour parked. A customer wants to pay no more than $25…
  15. Q57 · Linear equations in two variables · mediumFor every value of k, the line y = k(x-3) + 5 passes through the same fixed point, regardless of the value of k. What…
  16. Q58 · Systems of two linear equations in two variables · mediumThe lines y = 3x - 2 and y = -x + 14 intersect at a point. Is the y-coordinate of that point greater than or less than…
  17. Q59 · Systems of two linear equations in two variables · hardThe system x + y = 10 and x - y = k has a solution in Quadrant I (where both x > 0 and y > 0) for a range of values of…
  18. Q60 · Linear inequalities in one or two variables · mediumThe boundary lines of y ≥ 2x - 4 and y ≤ -x + k intersect at the point where x = 2. What is the value of k?
  19. Q65 · Linear equations in one variable · mediumIf 3(2x+5) - 4 = 17, what is the value of 2x+5?
  20. Q66 · Linear equations in one variable · mediumA car travels at a constant speed of 54 kilometers per hour. How many meters does the car travel in 20 seconds?
  21. Q67 · Linear equations in one variable · mediumA chemist mixes a 10%-acid solution with a 40%-acid solution to create 300 milliliters of a 25%-acid solution. How…
  22. Q68 · Linear functions · easyThe linear function f has a slope of 4. If g(x) = 3f(x) - 7, what is the slope of g?
  23. Q69 · Linear functions · mediumThe function f is defined by f(x) = kx + 5. If the graph of f is perpendicular to the line y = -2x + 3, what is the…
  24. Q70 · Linear functions · easyIf f(x) = 2x + 1 and g(x) = x² - 3, what is the value of f(g(2))?
  25. Q71 · Linear equations in two variables · easyThe line kx + 3y = 15 passes through the point (3, 2). What is the value of k?
  26. Q72 · Linear equations in two variables · mediumFor the line y = 2x + b, if the value of b increases by 4, how does the line's x-intercept change?
  27. Q73 · Systems of two linear equations in two variables · mediumThe equations x + y = 5 and 2x + 2y = 10 describe the same line. If a third equation, x - y = 1, is added to form a…
  28. Q85 · Linear equations in one variable · mediumWhat is the value of x if x/2+13 = 4?
  29. Q86 · Linear equations in one variable · mediumA rectangle's length is 3 more than twice its width. If the perimeter of the rectangle is 54, what is the width?
  30. Q87 · Linear functions · easyThe height of a plant, in centimeters, t months after being planted is modeled by h(t) = 2.5t + 8. What does the value…
  31. Q88 · Linear functions · easyThe table below shows values of a linear function f. | x | f(x) | |---|---| | 1 | 7 | | 3 | 15 | | 5 | ? | What is the…
  32. Q89 · Linear functions · mediumCompany A charges a flat fee of $60 plus $2 per unit produced. Company B charges a flat fee of $20 plus $4 per unit…
  33. Q90 · Linear equations in two variables · mediumThe equation Ax + 4y = 12 represents a line with slope -3/2. What is the value of A?
  34. Q91 · Linear equations in two variables · easyA line has an x-intercept of 4 and a y-intercept of -6. What is the slope of the line?
  35. Q92 · Systems of two linear equations in two variables · easyIf 3x + 2y = 16 and x - 2y = -4, what is the value of x?
  36. Q105 · Linear equations in one variable · mediumThe equation 4(x+3) - 2 = kx + b is true for all values of x. What is the value of k + b?
  37. Q106 · Linear equations in one variable · mediumA number is tripled, then 7 is added to the result, and finally the sum is divided by 2 to get 11. What is the…
  38. Q107 · Linear functions · mediumThe linear function f has a slope of 6. If g(x) = f(2x), what is the slope of g?
  39. Q108 · Linear equations in two variables · easyThe equation 5x + by = 20 has a y-intercept of 4. What is the value of b?
  40. Q109 · Linear equations in two variables · mediumA line has a slope of 2 and passes through the midpoint of the segment connecting (2,3) and (6,9). What is the…
  41. Q110 · Linear equations in two variables · mediumWhich equation represents the same line as 2x + 3y = 12?
  42. Q111 · Linear equations in two variables · easyThe equation 4x + 5y = 100 models the cost, in dollars, of buying x notebooks at $4 each and y folders at $5 each, for…
  43. Q112 · Systems of two linear equations in two variables · easyThe system 2x + ky = 14 and x - y = 1 has solution (5, 4). What is the value of k?
  44. Q113 · Systems of two linear equations in two variables · mediumIf 1/3x + 1/2y = 7 and x + y = 15, what is the value of y?
  45. Q125 · Linear functions · mediumA model predicts that a company's monthly sales, in units, will be 50t + 200, where t is the number of months since…
  46. Q126 · Linear inequalities in one or two variables · easyAn elevator can carry at most 2,000 pounds. If the average person weighs 165 pounds, what is the maximum number of…
  47. Q127 · Linear inequalities in one or two variables · mediumWhich inequality is equivalent to |x - 5| ≤ 3?
  48. Q128 · Linear inequalities in one or two variables · mediumA region in the coordinate plane is defined by x ≥ 0, y ≥ 0, and x + y ≤ 10. Which statement must be true for every…
  49. Q129 · Linear inequalities in one or two variables · mediumFor the system x > k and x < 10 to have at least one solution, k must be less than what value?
  50. Q130 · Linear functions · easyA linear function g satisfies g(-3) = 4 and g(1) = 16. What is the value of g(4)?
  51. Q145 · Linear equations in one variable · mediumFor what values of k and c does the equation 5(x-2)+12 = kx+c have infinitely many solutions?
  52. Q146 · Linear inequalities in one or two variables · mediumWhich of the following is equivalent to -2(x-3) > 10?
  53. Q147 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying x + y ≥ 6 and 2x + y ≥ 10, what is the smallest possible value of 4x + 3y?
  54. Q148 · Linear functions · mediumThe function f is defined by f(x) = ax + b. If f(1) = 5 and f(3) = 13, what is the value of a + b?
  55. Q149 · Systems of two linear equations in two variables · mediumAn investor puts a total of $8,000 into two accounts, one earning 4% annual interest and the other earning 7% annual…
  56. Q150 · Systems of two linear equations in two variables · hardThe line kx + my = 26 passes through the point (3, 4) and the equation kx + 4my = 22 (using the same k and m) is…
  57. Q166 · Linear equations in one variable · mediumA coffee shop blends a $8-per-pound coffee with a $14-per-pound coffee to create 20 pounds of a blend costing $11 per…
  58. Q167 · Linear equations in one variable · mediumAn isosceles triangle has two equal sides that are each 3 more than the length of the base. If the perimeter of the…
  59. Q168 · Linear inequalities in one or two variables · easyWhich statement is true about the graph of y < 2x + 3?
  60. Q169 · Linear equations in two variables · mediumWhat is the y-intercept of the line 3x - 5y = 20?
  61. Q170 · Systems of two linear equations in two variables · mediumThe system ax + 3y = 12 and 4x + by = 24 has infinitely many solutions. If a = 2, what is the value of b?
  62. Q171 · Linear functions · mediumA rideshare service charges a base fee of $4 plus $2.50 per mile. A taxi charges a base fee of $10 plus $1.50 per…
  63. Q186 · Linear inequalities in one or two variables · mediumA parking lot must hold no fewer than 50 cars and no more than 120 cars at any time. What is the width of the range of…
  64. Q187 · Linear functions · easyThe function f is defined by f(x) = kx + 7. If the graph of f is parallel to the line y = 5x - 2, what is the value of…
  65. Q188 · Systems of two linear equations in two variables · easyThe system 3x + ky = 21 and x + y = 7 has solution (4, 3). What is the value of k?
  66. Q189 · Linear equations in two variables · easyThe equation 6x + 4y = 84 models a budget split between two categories of spending. If y = 6, what is the value of x?
  67. Q190 · Linear functions · mediumThe linear function f has a slope of -4. If g(x) = -2f(x) + 5, what is the slope of g?
  68. Q191 · Linear inequalities in one or two variables · mediumA thermostat is set so that the temperature T, in degrees Celsius, satisfies -5 ≤ T ≤ 30. If an additional rule…
  69. Q205 · Linear equations in one variable · mediumWhat is the value of x if (3x+1)/(5) - 2 = 6?
  70. Q206 · Linear equations in one variable · mediumIf 2(3x-1)+7 = 23, what is the value of 3x - 1?
  71. Q207 · Linear inequalities in one or two variables · easyWhich of the following is equivalent to -x/3 ≤ 4?
  72. Q208 · Linear equations in two variables · easyA line has an x-intercept of -3 and a y-intercept of 9. What is the slope of the line?
  73. Q209 · Systems of two linear equations in two variables · easyIf 2x + 3y = 19 and 4x - 3y = 5, what is the value of 6x?
  74. Q210 · Linear functions · easyA linear function h satisfies h(-2) = 10 and h(3) = 0. What is the value of h(6)?
  75. Q211 · Linear equations in two variables · mediumThe equation 6x + Ay = 18 represents a line with slope -2. What is the value of A?
  76. Q225 · Systems of two linear equations in two variables · mediumA concert sold 300 tickets, some at $15 for general admission and the rest at $20 for VIP. Total ticket sales were…
  77. Q226 · Linear inequalities in one or two variables · easyA delivery van can carry at most 5,000 pounds. If each package weighs 210 pounds on average, what is the maximum…
  78. Q227 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying x + 2y ≤ 12 and 3x + y ≤ 16, what is the greatest possible value of 2x + 3y?
  79. Q228 · Linear equations in two variables · easyWhat is the slope of the line 5x - 3y = 21?
  80. Q229 · Linear functions · easyA linear function p satisfies p(0) = 6 and p(4) = 22. What is the value of p(10)?
  81. Q230 · Linear inequalities in one or two variables · easyA moving truck rental costs no more than $150 per day. The base fee is $40, plus $22 per hour of use. What is the…
  82. Q231 · Linear equations in one variable · mediumA number is doubled, then 5 is subtracted from the result, and finally the difference is divided by 3 to get 7. What…
  83. Q245 · Linear equations in one variable · mediumFor what value of k does the equation 6(x-1) + 9 = kx + 7 have no solution?
  84. Q246 · Linear inequalities in one or two variables · easyWhich of the following is equivalent to -3x + 5 ≤ 20?
  85. Q247 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying 2x + y ≤ 14 and x + 3y ≤ 17, what is the greatest possible value of 3x + 2y?
  86. Q248 · Linear equations in two variables · easyThe line kx + 3y = 29 passes through the point (2, 5). What is the value of k?
  87. Q249 · Linear equations in one variable · mediumA square has a side length of 2x + 3. If the perimeter of the square is 68, what is the value of x?
  88. Q250 · Linear inequalities in one or two variables · mediumWhat is the smallest integer value of x that satisfies both x > -3 and 2x - 7 > 5?
  89. Q251 · Linear functions · easyA linear function q satisfies q(-1) = 12 and q(2) = 3. What is the value of q(5)?
  90. Q265 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying x + y ≤ 8 and 3x + y ≤ 16, what is the greatest possible value of x + 2y?
  91. Q267 · Linear functions · mediumThe function f is defined by f(x) = kx - 3. If the graph of f is perpendicular to the line y = 1/4x + 2, what is the…
  92. Q268 · Systems of two linear equations in two variables · easyThe system 5x + ky = 29 and x - y = 1 has solution (3, 2). What is the value of k?
  93. Q269 · Linear equations in one variable · mediumA regular pentagon has a side length of 3x - 2. If the perimeter of the pentagon is 80, what is the value of x?
  94. Q270 · Linear functions · easyThe linear function f has a slope of 7. If g(x) = 4f(x) - 9, what is the slope of g?
  95. Q271 · Linear inequalities in one or two variables · easyWhich statement is true about the graph of y ≥ -2x + 6?
  96. Q285 · Linear equations in one variable · mediumThe equation 4(x+2) - 5 = kx + b is true for all values of x. What is the value of k + b?
  97. Q286 · Systems of two linear equations in two variables · easyThe system 4x + ky = 48 and 2x - y = 8 has solution (6, 4). What is the value of k?
  98. Q287 · Linear inequalities in one or two variables · hardFor x ≥ 0 and y ≥ 0 satisfying x + 3y ≤ 17 and 2x + y ≤ 14, what is the greatest possible value of 4x + 3y?
  99. Q288 · Linear functions · easyA linear function r satisfies r(-4) = 20 and r(2) = 2. What is the value of r(6)?
  100. Q289 · Linear equations in two variables · mediumThe equation 8x + Ay = 24 represents a line with slope -4. What is the value of A?
  101. Q290 · Linear equations in two variables · easyA line has an x-intercept of 5 and a y-intercept of -10. What is the slope of the line?
  102. Q291 · Linear inequalities in one or two variables · easyWhich of the following is equivalent to -4x + 9 ≥ 25?
  103. Q305 · Linear equations in one variable · mediumWhat is the value of x if (4x-3)/(7) + 2 = 9?
  104. Q306 · Systems of two linear equations in two variables · easyThe system 3x + ky = 33 and x - y = 4 has solution (7, 3). What is the value of k?
  105. Q307 · Linear functions · easyA linear function s satisfies s(-2) = 15 and s(3) = 0. What is the value of s(7)?
  106. Q308 · Linear inequalities in one or two variables · easyA shipping company charges no more than $80 per package. The base fee is $15, plus $6.50 per pound. What is the…
  107. Q309 · Linear equations in two variables · easyWhat is the slope of the line 7x - 2y = 18?
  108. Q321 · Systems of two linear equations in two variables · hardThe system kx + 4y = 20 and 3x + 2y = 10 has infinitely many solutions. What is the value of k?
  109. Q322 · Linear inequalities in one or two variables · hardFor x + y ≤ 20 and x - y ≥ 4, what is the largest integer value of y for which a valid value of x exists?
  110. Q323 · Linear equations in two variables · hardA line has slope 2k - 1 and passes through the points (1, 1) and (3, k+5). What is the value of k?
  111. Q324 · Systems of two linear equations in two variables · hardThe system 4x + ky = 8 and 2x + 3y = m has no solution when k = 6 and m = 5. For which value of m would the system…

Advanced Math

  1. Q9 · Equivalent expressions · mediumThe function f(x) = x² - 8x + 19 is equivalent to which of the following, where the minimum value of f is visible…
  2. Q10 · Nonlinear equations in one variable · mediumFor what positive value of k does the equation x² - kx + 9 = 0 have exactly one real solution?
  3. Q11 · Nonlinear equations in one variable · hardThe equation x² - 7x + c = 0 has two real solutions that differ by 3. What is the value of c?
  4. Q12 · Nonlinear equations in one variable · mediumWhat value of x satisfies 8^x+1 = 32^x-2?
  5. Q13 · Nonlinear functions · mediumA ball's height in feet after t seconds is modeled by h(t) = -16t² + 64t + 5. What is the maximum height the ball…
  6. Q14 · Nonlinear functions · easyA city's population is modeled by P(t) = 24,000(0.92)^t, where t is the number of years after 2020. According to this…
  7. Q15 · Nonlinear functions · easyThe variable y varies inversely with x. When x=3, y=8. What is the value of y when x=12?
  8. Q16 · Equivalent expressions · easyIf (x+3)(x-5) = x² + bx + c for all values of x, what is the value of b?
  9. Q26 · Nonlinear equations in one variable · mediumIf |2x - 5| = 11 and x is negative, what is the value of x?
  10. Q32 · Equivalent expressions · easyFor x ≠ 4, which expression is equivalent to (x² - 16)/(x - 4)?
  11. Q33 · Nonlinear equations in one variable · mediumWhat is the solution to √(2x+3) = x, after rejecting any extraneous candidate?
  12. Q34 · Nonlinear equations in one variable · mediumWhat is the sum of all values of x that satisfy 2^x²-5x = 2^-6?
  13. Q35 · Systems of equations in two variables · hardFor what value of k is the line y = 2x + k tangent to the parabola y = x² - 4x + 7?
  14. Q36 · Nonlinear functions · easyThe function f is defined by f(x) = (x-3)(x+7). What is the sum of the zeros of f?
  15. Q37 · Nonlinear functions · mediumIf f(2) = 9, and g(x) = f(x-3) + 4, what is the value of g(5)?
  16. Q38 · Nonlinear functions · easyWhat is the equation of the horizontal asymptote of f(x) = (3x+6)/(x-5)?
  17. Q61 · Equivalent expressions · hardLet u = x² - 1. If u² - 7u + 10 = 0, how many distinct real values of x satisfy this equation?
  18. Q62 · Equivalent expressions · mediumIf x + y = 7 and xy = 10, what is the value of x² + y²?
  19. Q63 · Nonlinear equations in one variable · hardWhat is the sum of all real solutions to x^4 - 13x² + 36 = 0?
  20. Q64 · Systems of equations in two variables · hardA circle is defined by x² + y² = 25. A line given by y = x + 1 intersects the circle at two points, forming a chord.…
  21. Q74 · Equivalent expressions · mediumIn the expansion of (x+5)(2x-3), what is the coefficient of the x term?
  22. Q75 · Equivalent expressions · mediumWhich expression is equivalent to x^3/2 for x > 0?
  23. Q76 · Equivalent expressions · mediumWhen the polynomial x³ - 2x² + 5 is divided by x - 1, what is the remainder?
  24. Q77 · Nonlinear equations in one variable · mediumWhat is the solution to x+2/x-3 = 5/x-3?
  25. Q78 · Nonlinear equations in one variable · mediumHow many real solutions does the equation |3x - 6| = 2x have?
  26. Q79 · Nonlinear equations in one variable · hardThe polynomial x³ - 7x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?
  27. Q80 · Nonlinear functions · hardA quantity triples every 6 years. What is the growth factor for a 2-year period, rounded to the nearest hundredth?
  28. Q81 · Nonlinear functions · mediumThe function f(x) = (x-2)²(x+3) has a zero at x=2. What is the behavior of the graph of f at this zero?
  29. Q82 · Nonlinear functions · mediumFor the function f(x) = (x²-9)/(x-3), what occurs at x=3?
  30. Q93 · Equivalent expressions · mediumWhat is the product of the two solutions to x² - 5x - 24 = 0?
  31. Q94 · Equivalent expressions · mediumFor which values of x is the expression (x²-4)/(x²-2x) undefined?
  32. Q95 · Nonlinear equations in one variable · mediumThe equation 2^x = x + 5 can be solved by finding the x-coordinates where the graphs of y=2^x and y=x+5 intersect. How…
  33. Q96 · Systems of equations in two variables · mediumIf x² + y = 10 and x² - y = 4, what is the value of y?
  34. Q97 · Systems of equations in two variables · mediumHow many real solutions does the system y = -x² + 4x + 1 and y = x - 2 have?
  35. Q98 · Systems of equations in two variables · mediumThe equations x² - 5x + 6 = 0 and x² + kx - 12 = 0 share x=3 as a common root. What is the value of k?
  36. Q99 · Nonlinear functions · easyA parabola has zeros at x=-2 and x=8. What is the x-coordinate of the vertex of the parabola?
  37. Q100 · Nonlinear equations in one variable · mediumFor what negative value of k does the equation x² + kx + 16 = 0 have exactly one real solution?
  38. Q114 · Systems of equations in two variables · hardThe circle x² + y² = 8 is tangent to the line y = x + k for a positive value of k. What is that value of k?
  39. Q115 · Systems of equations in two variables · mediumThe graphs of y = x² and y = 3x + 4 intersect at two points. What is the sum of the x-coordinates of these two points?
  40. Q116 · Systems of equations in two variables · mediumIf x + y = 8 and xy = 12, what is the value of x² + y²?
  41. Q117 · Nonlinear equations in one variable · mediumThe equation 3^x = x + 10 has a positive real solution. Between which two consecutive integers does this positive…
  42. Q118 · Systems of equations in two variables · mediumThe system x² + y² = 25 and y = x - 1 has two solutions. Which solution satisfies the additional constraint x > 0?
  43. Q131 · Nonlinear equations in one variable · mediumFor how many integer values of k between -6 and 6, inclusive, does the equation x² + kx + 9 = 0 have exactly one real…
  44. Q132 · Nonlinear equations in one variable · hardFor what values of k does the equation x² + kx + 9 = 0 have two distinct real solutions?
  45. Q133 · Nonlinear functions · mediumA company's monthly revenue, in dollars, from selling x units of a product is modeled by R(x) = -5x² + 200x. How many…
  46. Q134 · Nonlinear functions · easyThe value of an investment, in dollars, after t years is modeled by V(t) = 5000(1.06)^t. According to this model, by…
  47. Q135 · Equivalent expressions · mediumWhat is the minimum value of the function f(x) = x² - 6x + 5?
  48. Q136 · Nonlinear equations in one variable · hardThe equation x² - bx + 24 = 0 has two real solutions whose difference is 5. What is the value of b, given that both…
  49. Q151 · Nonlinear equations in one variable · mediumWhat value of x satisfies 4^x-1 = 8^x+2?
  50. Q152 · Nonlinear functions · mediumA factory's daily production cost, in dollars, for producing x units is modeled by C(x) = 2x² - 40x + 500. How many…
  51. Q153 · Equivalent expressions · mediumWhat is the maximum value of the function f(x) = -x² + 10x - 21?
  52. Q154 · Nonlinear functions · easyWhat is the equation of the vertical asymptote of f(x) = (2x+3)/(x-7)?
  53. Q155 · Nonlinear functions · hardFor the function f(x) = ((x-2)(x+3))/((x-2)(x-5)), which statement correctly describes its behavior at x=2 and x=5?
  54. Q156 · Nonlinear equations in one variable · mediumHow many valid solutions does the equation √(x+10) = x - 2 have, after rejecting any extraneous candidates?
  55. Q157 · Nonlinear equations in one variable · hardThe polynomial x³ - 4x² - 7x + 10 has x=1 as one of its roots. What is the product of the other two roots?
  56. Q158 · Equivalent expressions · hardWhich expression is equivalent to x^-2/3 for x > 0?
  57. Q172 · Equivalent expressions · mediumWhat is the sum of the two solutions to x² - 5x - 24 = 0?
  58. Q173 · Nonlinear functions · easyThe function f is defined by f(x) = (x-3)(x+7). What is the product of the zeros of f?
  59. Q174 · Nonlinear functions · easyThe variable y varies inversely with x. When x=4, y=5. What is the value of y when x=10?
  60. Q175 · Nonlinear equations in one variable · mediumWhat is the larger of the two solutions to |4x - 8| = 3x?
  61. Q176 · Systems of equations in two variables · mediumIf x² + y = 21 and x² - y = 11, what is the positive value of x?
  62. Q177 · Systems of equations in two variables · mediumThe equations x² - 4x - 5 = 0 and x² + kx - 15 = 0 share x = 5 as a common root. What is the value of k?
  63. Q178 · Equivalent expressions · hardFor x ≠ 2 and x ≠ -2, which expression is equivalent to (x^4 - 16)/(x² - 4)?
  64. Q179 · Equivalent expressions · mediumIf x + y = 9 and xy = 14, what is the value of (x-y)²?
  65. Q180 · Equivalent expressions · mediumIf (x+2)(x-4) = x² + bx + c for all values of x, what is the value of b + c?
  66. Q185 · Nonlinear equations in one variable · mediumIf |3x + 1| = 13 and x is positive, what is the value of x?
  67. Q192 · Nonlinear equations in one variable · mediumWhat is the sum of all real solutions to 3^x² - 2x = 3^8?
  68. Q193 · Equivalent expressions · mediumWhen the polynomial x³ + 3x² - x + 2 is divided by x - 2, what is the remainder?
  69. Q194 · Nonlinear functions · mediumThe function f(x) = (x-1)³(x+4) has a zero at x=1. What is the behavior of the graph of f at this zero?
  70. Q195 · Nonlinear equations in one variable · mediumWhat is the solution to (3x+1)/(x-4) = 2, given that x ≠ 4?
  71. Q196 · Nonlinear equations in one variable · hardThe equation x² - 9x + c = 0 has two real solutions that differ by 5. What is the value of c?
  72. Q197 · Nonlinear functions · easyA radioactive sample's mass, in grams, after t hours is modeled by M(t) = 1000(0.85)^t. According to this model, by…
  73. Q198 · Equivalent expressions · mediumWhat is the value of 8^2/3?
  74. Q201 · Nonlinear functions · hardA radioactive substance decays by 10% every hour. Starting with 1,000 grams, after how many whole hours does the…
  75. Q212 · Nonlinear equations in one variable · hardFor what values of k does the equation x² + kx + 16 = 0 have two distinct real solutions?
  76. Q213 · Nonlinear functions · mediumA company's daily profit, in dollars, is modeled by P(x) = -3x² + 150x - 800, where x is the number of units sold. How…
  77. Q214 · Equivalent expressions · easyWhat is the x-coordinate of the vertex of the graph of f(x) = x² + 12x + 40?
  78. Q215 · Nonlinear functions · easyThe variable y varies inversely with x. When x=6, y=8. What is the value of y when x=16?
  79. Q216 · Nonlinear equations in one variable · mediumWhat value of x satisfies 9^x+2 = 27^x-1?
  80. Q217 · Systems of equations in two variables · mediumThe graphs of y = x² - 3 and y = 4x - 3 intersect at two points. What is the product of the x-coordinates of these two…
  81. Q218 · Nonlinear equations in one variable · hardThe polynomial x³ - 2x² - 5x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?
  82. Q232 · Equivalent expressions · easyWhat is the y-intercept of the graph of f(x) = x² - 8x + 21?
  83. Q233 · Nonlinear equations in one variable · hardThe equation x² - 11x + c = 0 has two real solutions that differ by 7. What is the value of c?
  84. Q234 · Nonlinear functions · easyThe function f is defined by f(x) = (x+5)(x-9). What is the sum of the zeros of f?
  85. Q235 · Nonlinear equations in one variable · hardThe polynomial x³ + 2x² - 5x - 6 has x = 2 as one of its roots. What is the sum of the other two roots?
  86. Q236 · Equivalent expressions · hardWhich expression is equivalent to x^-3/2 for x > 0?
  87. Q237 · Systems of equations in two variables · mediumIf x² + y = 13 and x² - y = 5, what is the product of the two possible values of x?
  88. Q238 · Nonlinear functions · easyA car's value, in dollars, after t years is modeled by V(t) = 28,000(0.82)^t. By what percent does the car's value…
  89. Q252 · Nonlinear functions · mediumA ball's height in feet after t seconds is modeled by h(t) = -16t² + 96t + 10. What is the maximum height the ball…
  90. Q253 · Nonlinear functions · easyThe variable y varies inversely with x. When x=4, y=15. What is the value of y when x=20?
  91. Q254 · Equivalent expressions · mediumWhat is the product of the two solutions to x² - 2x - 35 = 0?
  92. Q255 · Nonlinear equations in one variable · mediumWhat value of x satisfies 5^x+3 = 25^x-2?
  93. Q256 · Nonlinear equations in one variable · hardThe equation x² - 13x + c = 0 has two real solutions that differ by 3. What is the value of c?
  94. Q257 · Nonlinear functions · easyWhat is the equation of the vertical asymptote of f(x) = (5x-2)/(x+6)?
  95. Q258 · Equivalent expressions · mediumIf (x-6)(x+2) = x² + bx + c for all values of x, what is the value of b - c?
  96. Q266 · Equivalent expressions · easyIf (x-4)(x+9) = x² + bx + c for all values of x, what is the value of c?
  97. Q272 · Equivalent expressions · mediumThe function f(x) = x² - 4x - 5 can be written in vertex form as f(x) = (x-h)² + k. What is the value of h + k?
  98. Q273 · Nonlinear equations in one variable · mediumWhat is the sum of all real solutions to |5x - 10| = 3x?
  99. Q274 · Equivalent expressions · mediumWhen the polynomial x³ + 4x² - 2x + 1 is divided by x - 1, what is the remainder?
  100. Q275 · Nonlinear functions · easyA bacteria population is modeled by N(t) = 500(1.12)^t, where t is measured in hours. By what percent does the…
  101. Q276 · Nonlinear equations in one variable · hardThe polynomial x³ - 3x² - 6x + 8 has x = 1 as one of its roots. What is the sum of the other two roots?
  102. Q277 · Nonlinear functions · mediumA company's cost, in dollars, to produce x units is modeled by C(x) = 3x² - 60x + 800. How many units should be…
  103. Q278 · Systems of equations in two variables · mediumThe graphs of y = x² + 2 and y = 6x - 4 intersect at two points. What is the sum of the x-coordinates of these two…
  104. Q292 · Nonlinear equations in one variable · hardThe equation x² - 10x + c = 0 has two real solutions that differ by 4. What is the value of c?
  105. Q293 · Nonlinear equations in one variable · hardThe polynomial x³ + x² - 10x + 8 has x = 1 as one of its roots. What is the sum of the other two roots?
  106. Q294 · Nonlinear functions · easyThe variable y varies inversely with x. When x=7, y=10. What is the value of y when x=14?
  107. Q295 · Equivalent expressions · mediumWhat is the sum of the two solutions to x² - 3x - 40 = 0?
  108. Q296 · Nonlinear functions · easyWhat is the equation of the horizontal asymptote of f(x) = (7x-3)/(2x+5)?
  109. Q297 · Nonlinear functions · mediumA farmer has 200 feet of fencing to enclose a rectangular garden, using the fencing for all four sides. If A(w) =…
  110. Q298 · Equivalent expressions · easyFor x ≠ 6, which expression is equivalent to (x² - 36)/(x - 6)?
  111. Q310 · Nonlinear equations in one variable · hardThe polynomial x³ - 4x² - x + 4 has x = 1 as one of its roots. What is the sum of the other two roots?
  112. Q311 · Nonlinear functions · easyThe variable y varies inversely with x. When x=6, y=9. What is the value of y when x=18?
  113. Q312 · Equivalent expressions · mediumWhat is the product of the two solutions to x² + 3x - 40 = 0?
  114. Q313 · Nonlinear functions · easyWhat is the equation of the vertical asymptote of f(x) = (2x+9)/(x-4)?
  115. Q314 · Nonlinear equations in one variable · hardThe equation x² - 15x + c = 0 has two real solutions that differ by 7. What is the value of c?

Problem-Solving and Data Analysis

  1. Q17 · Percentages · easyAfter a 15% discount, a jacket costs $68. What was the original price of the jacket, before the discount?
  2. Q18 · One-variable data: distributions and measures of center and spread · mediumThe mean of 9 numbers is 42. A 10th number is added to the list, and the mean of all 10 numbers becomes 44. What is…
  3. Q19 · Probability and conditional probability · mediumA survey of pet ownership and car ownership among 120 people found: 45 own both a car and a pet, 30 own a car but no…
  4. Q20 · Two-variable data: models and scatterplots · easyThe equation C = 3.5g + 40 models the total cost C, in dollars, of a rental car after driving g gallons' worth of…
  5. Q39 · Percentages · mediumA price is increased by 20% and then the new price is decreased by 25%. What is the overall percent change from the…
  6. Q40 · One-variable data: distributions and measures of center and spread · mediumA data set consists of the values 12, 15, 18, 22, and 25. If the values 1 and 100 are added to the data set, what is…
  7. Q41 · Probability and conditional probability · mediumThe probability of rain on any given day this week is 0.3, independent of other days. What is the probability of at…
  8. Q48 · Ratios, rates, proportional relationships, and units · mediumA car travels 120 miles in 2 hours, then travels an additional 180 miles in 3 hours. What is the car's average speed…
  9. Q49 · Ratios, rates, proportional relationships, and units · mediumWorking at the same rate, 4 workers can paint a fence in 10 hours. How many hours would it take 8 workers, working at…
  10. Q50 · Ratios, rates, proportional relationships, and units · easyA physicist wants to compute the density of an object, defined as mass divided by volume. Which expression could…
  11. Q51 · Inference from sample statistics and margin of error · mediumSurvey A estimates that 52% of a population supports a proposal, with a margin of error of 4 percentage points. Survey…
  12. Q52 · Inference from sample statistics and margin of error · mediumA random sample of 400 voters found that 55% favor a candidate, with a reported margin of error of 3 percentage…
  13. Q53 · Inference from sample statistics and margin of error · hardA random sample of 1,000 adults found that 40% own a particular type of car, with a margin of error of 3 percentage…
  14. Q54 · Evaluating statistical claims: observational studies and experiments · mediumA researcher observes that, among adults who were not randomly assigned to groups, those who exercise regularly have…
  15. Q55 · Evaluating statistical claims: observational studies and experiments · mediumA researcher wants to test whether a new fertilizer increases plant growth. Instead of using two separate groups of…
  16. Q56 · Evaluating statistical claims: observational studies and experiments · hardA researcher studying successful startup companies that are still operating after 10 years finds that a high…
  17. Q119 · Ratios, rates, proportional relationships, and units · easyA water pump moves water at a rate of 15 gallons per minute. At this rate, how many gallons does the pump move in one…
  18. Q120 · Ratios, rates, proportional relationships, and units · easyOn a map, the scale is 1 inch represents 25 miles. If two cities are 3.5 inches apart on the map, what is the actual…
  19. Q121 · Ratios, rates, proportional relationships, and units · easyThe variable y varies directly with x. When x=6, y=18. What is the value of y when x=15?
  20. Q137 · Ratios, rates, proportional relationships, and units · mediumCar A travels 250 miles using 10 gallons of gas. Car B travels 300 miles using 15 gallons of gas. Which car has the…
  21. Q138 · Ratios, rates, proportional relationships, and units · easyA metal sample has a density of 8 grams per cubic centimeter. What is the mass, in grams, of a 25 cubic centimeter…
  22. Q139 · Ratios, rates, proportional relationships, and units · mediumA recipe for 4 servings requires 2 cups of flour. If the recipe is first scaled to make 10 servings, and then that…
  23. Q140 · Ratios, rates, proportional relationships, and units · mediumStore A sells a 12-ounce bottle of juice for $3.60. Store B sells a 20-ounce bottle of the same juice for $5.60. Which…
  24. Q159 · Percentages · mediumIn a survey, support for a proposal increased from 40% to 46%. What is the increase in PERCENTAGE POINTS, and what is…
  25. Q160 · Percentages · mediumAn item originally costs $80. A store marks up the price by 25%, then later offers a 20% discount off the marked-up…
  26. Q161 · Percentages · easyA student measures the length of a table as 47 centimeters. The actual length is 50 centimeters. What is the percent…
  27. Q165 · Ratios, rates, proportional relationships, and units · mediumA runner moves at a constant speed of 15 miles per hour. What is this speed in feet per second? (1 mile = 5,280 feet)
  28. Q181 · Percentages · easyA school has 800 students, and 320 of them participate in the science club. What percent of the students participate…
  29. Q182 · Percentages · mediumA restaurant bill, including an 8% tax, totals $70.20. What was the pre-tax amount of the bill, in dollars?
  30. Q199 · Percentages · mediumA chemist has 20 liters of a solution that is 30% salt. How many liters of pure water must be added to dilute the…
  31. Q200 · Percentages · easyA town's population grew from 400 to 500 over one year. What was the percent growth rate?
  32. Q219 · One-variable data: distributions and measures of center and spread · mediumThe mean of 6 numbers is 40. If the number 10 is removed from the list, what is the mean of the remaining 5 numbers?
  33. Q220 · One-variable data: distributions and measures of center and spread · mediumA data set has a range of 25. If every value in the data set is multiplied by 3, what is the range of the new data set?
  34. Q221 · One-variable data: distributions and measures of center and spread · mediumA data set has a standard deviation of 4. If every value in the data set is multiplied by 3, what is the standard…
  35. Q239 · One-variable data: distributions and measures of center and spread · mediumClass A has a mean test score of 78 with a standard deviation of 5. Class B has a mean test score of 78 with a…
  36. Q240 · One-variable data: distributions and measures of center and spread · mediumA data set of 9 employee salaries has a median of $52,000. If the highest salary in the data set is replaced with a…
  37. Q241 · Two-variable data: models and scatterplots · mediumA linear model predicts a plant's height, in centimeters, as h(w) = 2.5w + 8, where w is the number of weeks since…
  38. Q259 · Two-variable data: models and scatterplots · mediumA linear model predicts that a company will sell 50 units in a given month. The company actually sold 42 units that…
  39. Q260 · Two-variable data: models and scatterplots · mediumA linear model was used to predict the weight of four different animals based on their length. The residuals (actual…
  40. Q261 · Two-variable data: models and scatterplots · easyA line of best fit for a data set is given by y = 2.5x + 30, where x represents years of experience and y represents…
  41. Q279 · Two-variable data: models and scatterplots · easyA scatterplot shows that as the number of hours studied increases, exam scores tend to increase as well, with the…
  42. Q280 · Two-variable data: models and scatterplots · mediumA researcher fits a linear model to a data set. When the residuals are plotted against the x-values, they show a clear…
  43. Q281 · Probability and conditional probability · easyThe probability that it rains on a given day is 0.4, and the probability that a certain sports team wins on a given…
  44. Q299 · Two-variable data: models and scatterplots · mediumTwo stores each fit a linear model relating advertising spending to monthly sales. Store A's model has a slope of 3.5,…
  45. Q300 · Probability and conditional probability · mediumA bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn at random without replacement. What is the…
  46. Q301 · Probability and conditional probability · mediumIn a survey, 50% of respondents said they like coffee, 40% said they like tea, and 20% said they like both. What…
  47. Q302 · Probability and conditional probability · easyA factory finds that 3% of its manufactured parts are defective. In a batch of 2,000 parts, how many parts would be…
  48. Q315 · Probability and conditional probability · easyThe probability that a customer buys a coffee is 0.6, and the probability that a customer buys a pastry is 0.5,…
  49. Q316 · One-variable data: distributions and measures of center and spread · mediumA data set has a standard deviation of 6. If a constant value of 10 is added to every value in the data set, what is…
  50. Q317 · One-variable data: distributions and measures of center and spread · mediumA histogram shows that 12 students scored between 70 and 80 on a test, and 8 students scored between 80 and 90. Based…
  51. Q325 · Percentages · hardA price is increased by 25%. By what percent must the new price then be decreased so that the final price equals the…
  52. Q326 · Inference from sample statistics and margin of error · hardSurvey A samples 2,000 people and reports a margin of error of 2 percentage points. Survey B samples 500 people and…
  53. Q327 · Probability and conditional probability · hardA game costs $5 to play. A player wins $20 with probability 0.1, wins $8 with probability 0.3, and wins nothing…
  54. Q328 · Probability and conditional probability · hardA factory's Machine A produces 60% of all units with a 3% defect rate, and Machine B produces the remaining 40% with a…

Geometry and Trigonometry

  1. Q21 · Lines, angles, and triangles · mediumIn a triangle, one exterior angle measures 140°. The two remote interior angles measure 3x° and (2x+10)°. What is the…
  2. Q22 · Right triangles and trigonometry · easyA right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
  3. Q23 · Circles · easyA circle is defined by the equation (x+2)² + (y-6)² = 81. What is the radius of the circle?
  4. Q24 · Circles · easyA circle has radius 12. What is the area of a sector with a central angle of 60°?
  5. Q42 · Lines, angles, and triangles · hardTriangle ABC is similar to triangle DEF, with vertex A corresponding to D, B to E, and C to F. If AB = 8, BC = 12, and…
  6. Q43 · Right triangles and trigonometry · hardA right triangle has legs of length 6 and 8 and a hypotenuse of length 10. What is the length of the altitude drawn…
  7. Q44 · Circles · hardA circle has radius 13. A chord of the circle has length 24. What is the distance from the center of the circle to the…
  8. Q45 · Area and volume · mediumA cylinder has radius 3 and height 8. A cone with radius 6 has the same volume as the cylinder. What is the height of…
  9. Q46 · Area and volume · mediumA closed rectangular box has length 4, width 5, and height 6. If the top face of the box is removed, what is the total…
  10. Q47 · Area and volume · hardThe volume of a cube increases by 72.8% after each edge of the cube is scaled by the same factor. By what percent does…
  11. Q83 · Lines, angles, and triangles · mediumTwo sides of a triangle have lengths 7 and 12. Which of the following is a possible length for the third side?
  12. Q84 · Lines, angles, and triangles · mediumTwo similar triangles have corresponding side lengths in the ratio 2:5. If the smaller triangle has area 16, what is…
  13. Q101 · Area and volume · easyA cylinder and a cone have the same radius and the same height. What is the ratio of the cylinder's volume to the…
  14. Q102 · Lines, angles, and triangles · easyAn isosceles triangle has a vertex angle of 40°, formed by its two equal sides. What is the measure of each base angle?
  15. Q103 · Right triangles and trigonometry · easyIn a right triangle, angle A is one of the acute angles. The side opposite angle A has length 5, and the hypotenuse…
  16. Q104 · Circles · easyA circle has radius 9. What is the length of an arc with a central angle of 80°, in terms of π? (Enter your answer as…
  17. Q122 · Area and volume · easyTwo similar rectangular gardens have corresponding side lengths in the ratio 3:4. What is the ratio of their areas?
  18. Q123 · Area and volume · mediumTwo similar solids have corresponding linear dimensions in the ratio 2:5. If the volume of the smaller solid is 40,…
  19. Q124 · Area and volume · mediumA square has side length 10. A circle with radius 3 is cut out from the center of the square. In terms of π, what is…
  20. Q141 · Area and volume · easyA triangle has vertices at (0,0), (6,0), and (0,8). What is the area of the triangle?
  21. Q142 · Area and volume · easyA circular pie chart has a total area of 48 square inches. If one sector of the chart represents a central angle of…
  22. Q143 · Lines, angles, and triangles · mediumThe three angles of a triangle measure x°, 2x°, and (3x-30)°. What is the value of x?
  23. Q144 · Area and volume · hardA cube with edge length 5 is painted on all six faces, then cut into 125 unit cubes (each with edge length 1). How…
  24. Q162 · Lines, angles, and triangles · mediumA line passes through the points (1,2) and (5,10). A second line passes through the points (0,6) and (4,4). What is…
  25. Q163 · Lines, angles, and triangles · easyIn a triangle, a midsegment (connecting the midpoints of two sides) has length 7. What is the length of the side of…
  26. Q164 · Circles · mediumThe equation x² + y² - 6x + 8y - 11 = 0 represents a circle. What is the radius of this circle?
  27. Q183 · Right triangles and trigonometry · easyIn a 30-60-90 triangle, the side opposite the 30° angle has length 6. What is the length of the hypotenuse?
  28. Q184 · Right triangles and trigonometry · easyIn a 45-45-90 triangle, each leg has length 7. What is the length of the hypotenuse? (Enter your answer as a…
  29. Q202 · Lines, angles, and triangles · mediumTwo parallel lines are cut by a transversal. One of the angles formed measures 65°. What is the measure of the…
  30. Q203 · Lines, angles, and triangles · mediumIn triangle ABC, segment DE is drawn parallel to side BC, with D on side AB and E on side AC. If AD = 4, DB = 6, and…
  31. Q204 · Right triangles and trigonometry · mediumTwo right triangles are similar, with corresponding angle A in each triangle. In the smaller triangle, (A) = 3/5. What…
  32. Q222 · Right triangles and trigonometry · mediumA person standing 50 feet from the base of a tower observes the top of the tower at an angle of elevation of 40°. To…
  33. Q223 · Right triangles and trigonometry · mediumIn a right triangle, one acute angle measures 35°. If (35°) = (x°), what is the value of x?
  34. Q224 · Right triangles and trigonometry · easyPoints A(0,0) and B(8,6) are graphed in the coordinate plane. What is the distance from A to B?
  35. Q242 · Right triangles and trigonometry · hardIn a right triangle, the side opposite an acute angle has length x, and the hypotenuse has length x + 7. If the sine…
  36. Q243 · Circles · easyA circle centered at the origin passes through the point (3, 4). What is the radius of the circle?
  37. Q244 · Circles · mediumA triangle is inscribed in a circle such that one side of the triangle is a diameter of the circle. What must be true…
  38. Q262 · Circles · mediumA circle has center (2, 3). A line is tangent to the circle at the point (2, 8). What is the slope of the tangent line?
  39. Q263 · Circles · mediumIn a circle, a central angle measures 80°. What is the measure of an inscribed angle that intercepts the same arc?
  40. Q264 · Circles · hardThe circle x² + y² = 32 is tangent to the line y = x + k for a positive value of k. What is that value of k?
  41. Q282 · Circles · easyA circle is defined by the equation (x-5)² + (y+2)² = 49. What is the radius of the circle?
  42. Q283 · Right triangles and trigonometry · easyA right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
  43. Q284 · Lines, angles, and triangles · mediumIn a triangle, one exterior angle measures 135°. The two remote interior angles measure 4x° and (2x+15)°. What is the…
  44. Q303 · Lines, angles, and triangles · mediumTwo sides of a triangle have lengths 9 and 15. What is the smallest possible integer length for the third side?
  45. Q304 · Lines, angles, and triangles · mediumIn a triangle, one exterior angle measures 150°. The two remote interior angles measure 3x° and (x+30)°. What is the…
  46. Q318 · Circles · easyA circle is defined by the equation (x-1)² + (y+5)² = 100. What is the radius of the circle?
  47. Q319 · Area and volume · mediumTwo similar rectangular fields have corresponding side lengths in the ratio 4:7. If the smaller field has area 32…
  48. Q320 · Right triangles and trigonometry · easyA right triangle has legs of length 8 and 15. What is the length of the hypotenuse?