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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.

Read the first 7 Ultimate Regents Algebra flashcards as text

  1. A function is defined as f(x) = 3x² - 12x + 9. What are the zeros of this function?

    Answer: x = 1 and x = 3

    Factor out 3 to get 3(x² - 4x + 3) = 3(x - 1)(x - 3), so zeros are x = 1 and x = 3.

  2. The sequence 5, 8, 11, 14, ... is arithmetic. What is the 20th term?

    Answer: 62

    Using aₙ = a₁ + (n-1)d: a₂₀ = 5 + (19)(3) = 5 + 57 = 62.

  3. Which inequality represents the solution to -4x + 7 > 19?

    Answer: x < -3

    Subtracting 7 gives -4x > 12; dividing by -4 (flip inequality) gives x < -3.

  4. If f(x) = 2x + 5 and g(x) = x², what is f(g(3))?

    Answer: 23

    g(3) = 9, then f(9) = 2(9) + 5 = 23.

  5. What is the axis of symmetry of the parabola y = -2x² + 8x - 3?

    Answer: x = 2

    The axis of symmetry is x = -b/(2a) = -8/(2·(-2)) = -8/(-4) = 2.

  6. A student scores 72, 85, 90, and 67 on four tests. What score is needed on the fifth test to have a mean of 80?

    Answer: 86

    Total needed = 5 × 80 = 400; current sum = 314; so 400 - 314 = 86.

  7. Which expression is equivalent to (2x³y²)(3x²y⁴)?

    Answer: 6x⁵y⁶

    Multiply coefficients (2·3 = 6) and add exponents: x³⁺² = x⁵ and y²⁺⁴ = y⁶, giving 6x⁵y⁶.