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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 x^(3/2)?

    Answer: Both A and C

    x^(3/2) = x^1 · x^(1/2) = x√x, and also x^(3/2) = (x³)^(1/2) = √(x³); both A and C are correct.

  2. The graph of f(x) = x² is shifted 3 units left and 2 units up. What is the new equation?

    Answer: y = (x+3)² + 2

    Shifting left 3 replaces x with (x+3) and shifting up 2 adds 2: y = (x+3)² + 2.

  3. If p(x) = x³ - 2x² - x + 2, which of the following is a factor?

    Answer: x - 2

    p(2) = 8 - 8 - 2 + 2 = 0, so (x-2) is a factor by the Factor Theorem.

  4. What is the product of the complex numbers (3 + 2i) and (1 - i)?

    Answer: 5 - i

    (3+2i)(1-i) = 3 - 3i + 2i - 2i² = 3 - i + 2 = 5 - i (since i² = -1).

  5. The equation y = 2x² - 8x + 6 can be rewritten in vertex form as:

    Answer: y = 2(x-2)² - 2

    Complete the square: y = 2(x²-4x) + 6 = 2(x-2)² - 8 + 6 = 2(x-2)² - 2.

  6. A quadratic equation has roots r₁ and r₂. If r₁ + r₂ = 7 and r₁ · r₂ = 12, which equation has these roots?

    Answer: x² - 7x + 12 = 0

    Using Vieta's formulas: x² - (sum)x + (product) = 0 → x² - 7x + 12 = 0.

  7. For the function f(x) = (x² - 1) / (x² - x - 2), which x-value is a hole (removable discontinuity)?

    Answer: x = 1

    Factor: numerator = (x-1)(x+1), denominator = (x-1)(x+2); (x-1) cancels, creating a hole at x=1.