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Praxis Middle School Mathematics: Algebra

Expressions, equations, and inequalities for middle school, including what to do when a student's algebra goes wrong.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.Solve 3x + 5 = 20.

  2. 2.Simplify 4x + 3x.

  3. 3.A student expands 2(x + 4) as 2x + 4. What is the expanded form?

  4. 4.Solve x + 3 > 7.

  5. 5.What is the value of 2x − 1 when x = 4?

  6. 6.Which of these is an equation?

  7. 7.Simplify n + n + n.

  8. 8.Solve x/3 = 6.

  9. 9.Solve −2x = 10.

  10. 10.The length of a rectangle is ℓ and the width is w. Which expression is the perimeter?

  11. 11.A pattern starts 3, 7, 11, 15. What is the next term, and what is added each time?

  12. 12.A table shows y = 2x. When x = 5, what is y?

  13. 13.Which relationship is proportional?

  14. 14.Which expression is equivalent to 6x + 9?

  15. 15.A student simplifies 2x + 3 as 5x. What should the teacher point out?

  16. 16.Four more than a number is 11. What is the number?

  17. 17.The inequality x < 2 is graphed on a number line. Which description matches?

  18. 18.Simplify x^2 · x^3.

  19. 19.A student says (2x)^2 = 2x^2. What is (2x)^2?

  20. 20.Solve 5 − x = 2.

  21. 21.Solve 3x − 4 = 11.

  22. 22.A student solves 2x + 1 = 9 and gets x = 5, then does not check. Which check shows the work is off?

  23. 23.Which equation shows the commutative property of addition?

  24. 24.Solve 0.2x = 8.

  25. 25.Which pair is equivalent?

  26. 26.The sum of a number and 6 is at least 10. Which inequality matches?

  27. 27.What is the value of 4a − 2b when a = 3 and b = 5?

  28. 28.A taxi charges $3 plus $2 per mile. Which expression is the cost of m miles?

  29. 29.Solve 8 = 2(x + 1).

  30. 30.Which value of x makes 5x − 5 = 0 true?

  31. 31.A student graphs y = x + 2 and says it is proportional because it is a straight line. What is missing?

  32. 32.Solve x − 9 = −4.

  33. 33.Which expression means 'twice a number, decreased by 7'?

  34. 34.The formula d = 40t gives distance in miles for t hours. What does 40 represent?

  35. 35.Simplify 8y − 3y + 2.

  36. 36.Solve 4(x − 2) = 12.

  37. 37.A student divides only the first term and writes (6x + 9)/3 = 2x + 9. What is the quotient?

  38. 38.Which ordered pair fits y = x − 4?

  39. 39.Solve −3 + x ≤ 2.

  40. 40.A number tripled, then increased by 1, is 16. What is the number?

  41. 41.Which expression is the area of a square with side x + 2, expanded?

  42. 42.A student expands (x + 2)^2 as x^2 + 4. Which product was left out?

  43. 43.Solve x/4 + 1 = 3.

  44. 44.On a graph of a proportional relationship, the point (3, 12) is marked. What is the constant of proportionality?

  45. 45.Which step solves 7x = 21?

  46. 46.A club has n members. Six of them are absent, and the number present is less than 20. Which inequality fits the number present?

  47. 47.What is the slope between (1, 2) and (4, 8), read as a rate of change?

  48. 48.A line falls 3 units for each 1 unit it moves right. What is the slope?

  49. 49.Solve 2(x + 5) = 2x + 10. How many solutions does it have?

  50. 50.Solve 2(x + 5) = 2x + 6. How many solutions does it have?

  51. 51.A recipe uses 2 cups of flour for every 3 cups of oats. Which equation relates flour f to oats a?

  52. 52.Which expression equals 4 − 2(x + 1)?

  53. 53.A student writes 4 − 2(x + 1) as 4 − 2x + 2 and gets 6 − 2x. Where did the sign go wrong?

  54. 54.The y-intercept of y = −2x + 6 is which point?

  55. 55.Solve −2x > 6.

  56. 56.A student divides −2x > 6 by −2 and keeps the > sign, getting x > −3. What is the correction?

  57. 57.Which rule fits the sequence 5, 8, 11, 14?

  58. 58.Which equation is equivalent to x + 8 = 14?

  59. 59.Tickets cost $6 each. A fee of $2 is added to the order. Which equation gives the cost c of t tickets?

  60. 60.What is the value of −3x + 4 when x = −2?

  61. 61.A student evaluates −3x + 4 at x = −2 by computing −3 × −2 as −6. What is the value?

  62. 62.Which expression is 'a number squared' for the number n, rather than twice the number?

  63. 63.Factor 10x + 15 by taking out the greatest common factor.

  64. 64.A car uses 2 gallons every 50 miles. Which equation gives gallons g for m miles?

  65. 65.In the equation c = 6t + 2, which quantity is independent if tickets are chosen first?

  66. 66.A table shows (x, y) pairs (0, 0), (2, 6), and (4, 12). Which equation fits?

  67. 67.Solve 9 − 2x = 1.

  68. 68.Which inequality has the same solutions as x + 1 ≥ 4?

  69. 69.The expression 5(n − 2) represents which situation?

  70. 70.What is the slope of y = 4?

  71. 71.What is the slope of the line x = −1?

  72. 72.A savings account starts with $20 and adds $5 each week. Which equation gives the amount a after w weeks?

  73. 73.Using a = 5w + 20, how much is in the account after 4 weeks?

  74. 74.Which equation matches 'a number divided by 5 is 7'?

  75. 75.Solve n/5 = 7.

  76. 76.The points (0, 1) and (2, 5) are on a line. What is the slope?

  77. 77.A line has slope 2 and y-intercept 1. Which equation matches?

  78. 78.Which ordered pair is a solution of x + y = 6?

  79. 79.The equations are y = x + 1 and y = 4. What is x?

  80. 80.A rectangle's length is 3 more than its width w. Which expression is the length?

  81. 81.That rectangle has perimeter 26. Which equation finds the width?

  82. 82.Solve 2w + 2(w + 3) = 26.

  83. 83.Which expression equals −(3x − 5)?

  84. 84.A student writes −(3x − 5) as −3x − 5. What was missed?

  85. 85.A sequence starts at 4 and adds 3 each time. What is the 10th term?

  86. 86.Which pairs (x, y) show a proportional relationship?

  87. 87.Solve 6 + x/2 = 10.

  88. 88.The inequality −4 ≤ x < 1 includes which number?

  89. 89.Which property justifies 4 + (x + 2) = (4 + x) + 2?

  90. 90.A phone plan costs $15 plus $0.10 per minute. What is the cost of 30 minutes?

  91. 91.Simplify 3(2x − 1) − 4x.

  92. 92.A student leaves 6x − 3 − 4x uncombined. What is the simplified form?

  93. 93.Which equation has no solution?

  94. 94.Three consecutive integers start at n and add to 33. Which equation fits?

  95. 95.From n + (n + 1) + (n + 2) = 33, what is n?

  96. 96.A graph of distance versus time is a straight line through the origin. What does that say?

  97. 97.Solve 5(x − 1) = 5x − 5. What is true?

  98. 98.Which expression is the cost of p pounds of apples at $1.50 per pound?

  99. 99.A student writes the apple cost as 1.50 + p. For 4 pounds, what is the actual cost?

  100. 100.The solution of an inequality is x ≥ −2. Which number is not a solution?

  101. 101.Rewrite y − 3 = 2(x − 1) so that y is alone.

  102. 102.A student rewrites y − 3 = 2(x − 1) as y = 2x − 2 and forgets to add 3. What is the equation?

  103. 103.How many terms are in 4x + 7?

  104. 104.A store doubles a price p and then takes off $3. Which expression is the sale price?

  105. 105.A student uses 2(p − 3) for 'double the price, then take off $3.' What does that expression do?

  106. 106.The class looks at 4x + 4 = 4(x + 1). What should students conclude?

  107. 107.A student solves 2x + 6 = 14 by dividing every term by 2 and getting x + 3 = 7. Is that step valid?

  108. 108.A budget equation is 12 = 3(x − 1). A student distributes first and gets 12 = 3x − 3. What is x?