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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. Which of the following equations represents a parabola with vertex at (-1, 4) that opens downward?

    Answer: y = -(x+1)² + 4

    Vertex form is y = a(x-h)² + k; vertex (-1,4) means h=-1,k=4; opens down means a<0: y = -(x+1)² + 4.

  2. Simplify: (27x⁶)^(1/3)

    Answer: 3x²

    27^(1/3) = 3 and (x⁶)^(1/3) = x², so the answer is 3x².

  3. A function is defined by f(x) = (x² - 4) / (x - 2). What value does f(x) approach as x approaches 2?

    Answer: 4

    Factor numerator as (x-2)(x+2), cancel (x-2), and as x→2 the expression approaches 2+2=4.

  4. The equation x² + y² = 25 represents a circle. Which point lies on this circle?

    Answer: (3, 4)

    Check (3,4): 3² + 4² = 9 + 16 = 25. ✓

  5. If x - 1/x = 3, what is x² + 1/x²?

    Answer: 11

    Square both sides: x² - 2 + 1/x² = 9, so x² + 1/x² = 11.

  6. Which of the following is a solution to |2x - 3| = 7?

    Answer: x = 5

    2x - 3 = 7 gives x = 5; 2x - 3 = -7 gives x = -2. Both 5 and -2 work; x = 5 is listed.

  7. If f(x) = x² + bx + c and the zeros are x = 1 and x = -5, what is the value of c?

    Answer: -5

    c = product of zeros = (1)(-5) = -5 by Vieta's formulas.