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Advanced Math Flashcards

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

Read the first 7 Advanced Math flashcards as text

  1. Which of the following is equivalent to (x² - 9) / (x - 3) for x ≠ 3?

    Answer: x + 3

    Factor the numerator as (x-3)(x+3), then cancel (x-3) to get x+3.

  2. If f(x) = 3x² - 2x + 1, what is f(-2)?

    Answer: 17

    f(-2) = 3(4) - 2(-2) + 1 = 12 + 4 + 1 = 17.

  3. The function g(x) = x² - 6x + 8 has zeros at x = 2 and x = 4. What is the vertex of g(x)?

    Answer: (3, -1)

    The vertex x-coordinate is the midpoint of the zeros: (2+4)/2 = 3, and g(3) = 9 - 18 + 8 = -1.

  4. Which expression is equivalent to (2x³y²)(3xy⁴)?

    Answer: 6x⁴y⁶

    Multiply coefficients (2×3=6) and add exponents: x^(3+1)=x⁴ and y^(2+4)=y⁶, giving 6x⁴y⁶.

  5. If 2^(x+1) = 32, what is the value of x?

    Answer: 4

    32 = 2⁵, so 2^(x+1) = 2⁵ means x+1 = 5, giving x = 4.

  6. What are the solutions to 2x² + x - 6 = 0?

    Answer: x = -3/2 and x = 2

    Factor as (2x - 3)(x + 2) = 0, giving x = 3/2 or x = -2; wait — actually (2x+3)(x-2)=0 gives x=-3/2 or x=2.

  7. If h(x) = √(4x - 8), what is the domain of h?

    Answer: x ≥ 2

    The radicand must be non-negative: 4x - 8 ≥ 0 → x ≥ 2.