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Ultimate Regents Algebra Flashcards

7 cards from real Regents 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 ball is thrown upward. Its height h (feet) after t seconds is h = -16t² + 64t + 5. What is the maximum height?

    Answer: 69 feet

    Vertex at t = -64/(2·(-16)) = 2; h(2) = -16(4) + 64(2) + 5 = -64 + 128 + 5 = 69 feet.

  2. What is the domain of f(x) = √(x - 4)?

    Answer: x ≥ 4

    The radicand must be non-negative: x - 4 ≥ 0, so x ≥ 4.

  3. Which value of x satisfies 2^(x+1) = 32?

    Answer: 4

    Since 32 = 2⁵, we have 2^(x+1) = 2⁵, so x + 1 = 5 and x = 4.

  4. A data set has a mean of 50 and standard deviation of 5. Which score is 2 standard deviations above the mean?

    Answer: 60

    Two standard deviations above the mean: 50 + 2(5) = 60.

  5. Solve for x: (x + 3)/(x - 2) = 4

    Answer: x = 11/3

    Cross-multiply: x + 3 = 4(x - 2) → x + 3 = 4x - 8 → 11 = 3x → x = 11/3.

  6. The scatter plot of a data set shows a strong negative correlation. Which correlation coefficient best represents this?

    Answer: r = -0.92

    A strong negative correlation is represented by a value of r close to -1, such as -0.92.

  7. What is the product of (3 + 2i)(3 - 2i)?

    Answer: 13

    Using difference of squares: (3)² - (2i)² = 9 - 4i² = 9 - 4(-1) = 9 + 4 = 13.