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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.

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  1. A polynomial p(x) satisfies p(2) = 0. Which of the following must be a factor of p(x)?

    Answer: x - 2

    By the Factor Theorem, if p(2) = 0, then (x - 2) is a factor of p(x).

  2. What is the sum of all solutions to x² - 5x + 6 = 0?

    Answer: 5

    By Vieta's formulas, the sum of roots = -b/a = 5/1 = 5.

  3. Which of the following is equivalent to (x + 3)² - 4?

    Answer: x² + 6x + 5

    Expand (x+3)² - 4 = x² + 6x + 9 - 4 = x² + 6x + 5.

  4. For what value of k does the equation x² + kx + 16 = 0 have exactly one real solution?

    Answer: 8

    For one solution the discriminant = 0: k² - 4(16) = 0 → k² = 64 → k = 8.

  5. The graph of y = a(x - h)² + k passes through (0, 5) with vertex at (2, 1). What is the value of a?

    Answer: 1

    Substituting (0,5): 5 = a(0-2)² + 1 = 4a + 1, so 4a = 4 and a = 1.

  6. Which expression is equivalent to (x² + 2x - 8) / (x + 4)?

    Answer: x - 2

    Factor numerator as (x+4)(x-2), then cancel (x+4) to get x-2.

  7. If f(x) = x³ - x and g(x) = x + 2, what is f(g(1))?

    Answer: 24

    g(1) = 3, then f(3) = 27 - 3 = 24.