FreeExam

STAAR Algebra I

One hundred eight questions on linear equations, systems, quadratics, exponents, and sequences.

These questions are original. This is not an official STAAR test, and FreeExam is not affiliated with the Texas Education Agency.

  1. 1.Solve 3x + 7 = 22.

  2. 2.One fourth of a number, decreased by 3, is 5. What is the number?

  3. 3.Five times the quantity x minus 2 equals 35. Find x.

  4. 4.What is x if (2/3)x = 10?

  5. 5.If 4x − 9 = 3, what is x?

  6. 6.For which x is (2x + 6)/5 equal to 4?

  7. 7.Half of a number plus 3 equals 11. What is the number?

  8. 8.Find the solution of 6x + 1 = 19.

  9. 9.The equation 5x + 4 = 2x + 19 has what solution?

  10. 10.Find x in 8 − 3x = 2x + 18.

  11. 11.Which x makes 4(x + 3) equal 2(x + 11)?

  12. 12.Collect like terms in 7x − 6 = 4x + 15 and solve.

  13. 13.Solve 2(3x − 1) = 5x + 8.

  14. 14.What x satisfies x/2 + 5 = x − 1?

  15. 15.Solve −2x > 8.

  16. 16.Which solution set matches 3x − 5 ≤ 16?

  17. 17.Solve −4(x + 1) < 12.

  18. 18.What values of x satisfy 5 − x ≥ 2?

  19. 19.Solve 2x + 7 > 5x − 2.

  20. 20.Which inequality is equivalent to x/3 − 4 ≤ 2?

  21. 21.A rectangle has a perimeter of 44 cm. Its length is 4 cm more than twice its width. What is the width?

  22. 22.A rectangle's length is three times its width. Shorten the length by 4 cm and lengthen the width by 4 cm, and the figure is a square. What was the width before the change?

  23. 23.Two numbers add to 36. The larger is 4 less than three times the smaller. What is the smaller number?

  24. 24.One plumber charges a $45 visit fee plus $30 an hour. Another charges a $75 visit fee plus $20 an hour. After how many hours are the two charges equal?

  25. 25.A jar holds 18 coins, and every coin is either a nickel or a dime. The coins are worth $1.20 altogether. How many dimes are in the jar?

  26. 26.A ramp on a grid runs from (1, 2) to (5, 10), in meters. What is the slope?

  27. 27.A thermometer reading is recorded as (−2, 5) and later as (4, −1), with hours first and degrees second. What is the rate of change in degrees per hour?

  28. 28.What is the slope of the line through (3, 7) and (3, 12)?

  29. 29.A drone moves from (0, −4) to (6, 8) on a coordinate grid. What is the slope of its path?

  30. 30.On a map grid, a trail passes through (−5, −3) and (−1, 9). What is the trail's slope?

  31. 31.In the equation y = −3x + 8, what is the y-intercept?

  32. 32.A line has slope 2 and crosses the y-axis at −5. Which equation matches that line?

  33. 33.What does the 6 tell you in y = (1/4)x + 6?

  34. 34.Which equation has a slope of 0?

  35. 35.A kayak rental costs C = 8h + 12 dollars for h hours. What does the 8 represent?

  36. 36.A line rises 3 units for each 1 unit it moves right, and it passes through (2, 5). Which equation matches the line?

  37. 37.Water in a tank follows a line of slope −2 through (4, 3), with x in hours and y in liters. Which equation fits?

  38. 38.Use slope 4 and the point (−2, 1) to choose the line's equation.

  39. 39.A horizontal line passes through (5, −2). Which equation describes it?

  40. 40.Which equation has slope 5 and contains the point (−1, −3)?

  41. 41.Two lines are y = 2x + 1 and y = x + 6. Where do they meet?

  42. 42.Substitute y = 3x − 4 into x + y = 12. What is the solution?

  43. 43.Use x = y − 3 to solve 2x + y = 12.

  44. 44.The system is y = −x + 7 and 3x + y = 15. Which ordered pair is the solution?

  45. 45.Find the intersection of y = 4x and 2x + y = 18.

  46. 46.Add the equations 2x + y = 11 and x − y = 1. What solution do you get?

  47. 47.Solve 3x + 2y = 16 and 3x − 2y = 8 by adding them.

  48. 48.Subtract 2x + y = 9 from 4x + y = 13, then find the solution.

  49. 49.The system is 5x + 2y = 20 and x + 2y = 12. Which pair solves both equations?

  50. 50.Add 2x + 3y = 12 and 4x − 3y = 6. What is the solution?

  51. 51.The system is y = 2x + 3 and y = 2x − 1. How many solutions does it have?

  52. 52.The equation 4x − 2y = 6 rewrites as y = 2x − 3. The second line is y = 2x + 1. Which statement is true?

  53. 53.What is the solution of 3x + y = 5 and 6x + 2y = 8?

  54. 54.Solve x + 2y = 4 and 2x + 4y = 6.

  55. 55.How many solutions do y = 3x − 2 and 6x − 2y = 4 have?

  56. 56.Which statement describes the system 2x + y = 7 and 4x + 2y = 14?

  57. 57.Because 3x − 3y = 15 is 3 times x − y = 5, what is the solution of the system?

  58. 58.How are the graphs of y = −x + 4 and 2x + 2y = 8 related?

  59. 59.Which set of points has a constant rate of change?

  60. 60.Which table is not linear?

  61. 61.Every row of a table fits one equation: (0, −2), (2, 4), (4, 10), and (6, 16). Which equation is it?

  62. 62.A baker lists loaves made on four days in a row. Which list goes up by the same amount each day?

  63. 63.Which graph does not show y as a function of x?

  64. 64.Which set of ordered pairs is not a function?

  65. 65.A graph includes the points (3, 1) and (3, 6). Why does that keep the graph from being a function of x?

  66. 66.Which graph fails the vertical line test?

  67. 67.A rule is f(x) = 3x − 4. What is f(5)?

  68. 68.g(x) = x² − 2x. What is g(4)?

  69. 69.h(x) = −2x + 9. What is h(−3)?

  70. 70.The price of t pounds of nails is p(t) = 4t + 1 dollars. For what t is the price $21?

  71. 71.A function is defined by k(x) = 5 − x². Find k(3).

  72. 72.Compute 2³ × 2⁴ by writing out the factors of 2.

  73. 73.Compute (3²)³ by first finding 3² and then cubing that value.

  74. 74.Compute 5⁶ ÷ 5⁴ by canceling factors of 5.

  75. 75.Compute (2 × 5)³.

  76. 76.4³ ÷ 4³ equals 4⁰. What is that value?

  77. 77.Write 2⁻³ as a fraction by expanding the positive power in the denominator.

  78. 78.Simplify 3⁴ × 3² ÷ 3³ by combining the powers, then evaluate.

  79. 79.What is 10³ × 10²?

  80. 80.Expand (x + 3)(x + 4).

  81. 81.Expand (x − 5)(x + 2).

  82. 82.Expand (2x + 1)(x + 6).

  83. 83.Expand (x − 4)².

  84. 84.Expand (3x − 2)(x − 5).

  85. 85.Which product is equal to x² + 5x + 6?

  86. 86.Factor x² − 7x + 12.

  87. 87.Factor x² + 2x − 15.

  88. 88.Factor x² − 9x + 20.

  89. 89.Solve x² − 5x + 6 = 0 by factoring.

  90. 90.Solve x² + 6x + 8 = 0 by factoring.

  91. 91.Solve x² − 4x − 12 = 0 by factoring.

  92. 92.Solve 2x² + 7x + 3 = 0 by factoring.

  93. 93.Use the quadratic formula to solve x² − 6x + 5 = 0.

  94. 94.Use the quadratic formula to solve x² + 2x − 8 = 0.

  95. 95.Use the quadratic formula to solve 2x² − 4x − 6 = 0.

  96. 96.Use the quadratic formula to solve x² − 4x − 5 = 0.

  97. 97.A lab culture starts with 3 cells and doubles every hour. How many cells are there after 4 hours?

  98. 98.A stack starts with 5 cards. Each minute the stack is tripled. How many cards are there after 3 minutes?

  99. 99.An account starts with $200 and the balance doubles each year. What is the balance after 3 years?

  100. 100.A video has 4 views at noon, and the view count triples every hour. How many views are there at 4 p.m.?

  101. 101.An arithmetic sequence starts at 7 and increases by 4. What is the 10th term?

  102. 102.The sequence 12, 9, 6, 3, … decreases by the same amount each time. What is the 8th term?

  103. 103.An arithmetic sequence starts at 5 and increases by 6. Which term equals 41?

  104. 104.In week 1, Nia saves $8. Each later week she saves $5 more than the week before. How much does she save in week 9?

  105. 105.A geometric sequence starts at 3, and each term is twice the term before it. What is the 6th term?

  106. 106.A geometric sequence starts at 64, and each term is half of the term before it. What is the 5th term?

  107. 107.The sequence 5, 15, 45, … multiplies by the same number each time. What is the 5th term?

  108. 108.A geometric sequence starts at 2, and each term is 4 times the term before it. What is the 4th term?