Practice Test Geeks(MPT) UCF Math Placement Test Practice Test
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Case Analysis Flashcards

7 cards from real MPT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A piecewise function is defined as f(x) = 3x + 1 if x < 2, and f(x) = x² - 1 if x ≥ 2. What is f(2) + f(0)?

    Answer: 4

    f(2) = 2² - 1 = 3 (x ≥ 2 case), and f(0) = 3(0) + 1 = 1 (x < 2 case), so f(2) + f(0) = 4.

  2. Solve the absolute value inequality |2x - 4| > 6 and express as a compound inequality.

    Answer: x 5

    Split into 2x - 4 > 6 (giving x > 5) or 2x - 4 5.

  3. A function g(x) = |x + 3| - |x - 1|. What is g(-5)?

    Answer: -4

    g(-5) = |-5 + 3| - |-5 - 1| = |-2| - |-6| = 2 - 6 = -4.

  4. For what values of x does the piecewise function h(x) = x² if x ≤ 0, and h(x) = 2x if x > 0 satisfy h(x) = 4?

    Answer: x = -2 and x = 2

    For x ≤ 0: x² = 4 gives x = -2 (valid); for x > 0: 2x = 4 gives x = 2 (valid), so both solutions exist.

  5. A grading scale assigns A if s ≥ 90, B if 80 ≤ s < 90, and C if 70 ≤ s < 80. Which grade does a score of s = 80 receive?

    Answer: B

    Since 80 ≤ 80 < 90, the score satisfies the B condition.

  6. What is the number of solutions to |x² - 4| = 0?

    Answer: 2

    The absolute value equals zero only when x² - 4 = 0, giving x = 2 or x = -2, so there are 2 solutions.

  7. The function f(x) = (x² - 9)/(x - 3) for x ≠ 3. What value should be assigned at x = 3 to make f continuous?

    Answer: 6

    Factor: (x² - 9)/(x - 3) = x + 3 for x ≠ 3; as x → 3 the limit is 3 + 3 = 6.