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  • Question:
    Which of the following is a factored form of the expression 6x2 + x - 2?

    (a) (3x + 2)(2x - 1)
    (b) (2x + 2)(3x - 1)
    (c) (3x + 2)(2x + 1)
    (d) (3x - 2)(2x - 1)
    (e) (2x + 2)(3x - 2)

    Answer: 6x2 + x - 2 = 6x2 + 4x - 3x - 2 = 2x(3x + 2) - (3x + 2) =
    = (3x + 2)(2x - 1).


  • Question: Mr Jones plans to drive 660 miles at an average speed of 60 miles/hour. How many miles per hour faster needs he to average, while driving, to reduce his total time by 1 hour?

    (a) 5
    (b) 6
    (c) 7
    (d) 8
    (e) 9

    • Answer:
      At 60 miles/hour, the trip would take 660/60 = 11 hours. A 10 hours trip would require a speed of 660/10 = 66 miles/hour.
      The answer to the question is 66miles/hour - 60 miles/hour = 6 miles/hour.


    • Question: What is the length of side b in the triangle below?
      Figure not drawn to scale
      act test, geometry?

      (a) 2
      (b) 3
      (c) 4
      (d) 5
      (e) 6

    • Answer: sin(30o) = b/c.
      1/2 = b/c.
      b = 3.

    • Question #6: The parabola in the figure below is described by the equation: x2 + bx + c = 0. Which of the following inequalities is true?
      act, function, graph, parabola

      (a) b > 0 and 4c < b2
      (b) b > 0 and 4c < b
      (c) b > 0 and 4c > b2
      (d) b < 0 and 4c < b2
      (e) b < 0 and c > 4b2

      • Answer: The coordinates of the vertex of the parabola are
        (-b/2, c - b2/4) .
        From the given graph, both the x and y coordinates of the vertex are negative, so:
        -b/2 < 0 and c - b2/4 < 0
        This means that b > 0 and 4c < b2 is the correct answer.
    • ACT Sample Questions
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