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Algebraic Equations and Functions Flashcards

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

Read the first 7 Algebraic Equations and Functions flashcards as text

  1. Solve the system: x + y = 10 and x - y = 4. What is x?

    Answer: 7

    Adding the equations gives 2x = 14, so x = 7.

  2. Factor completely: x² - 9.

    Answer: (x - 3)(x + 3)

    This is a difference of squares: x² - 9 = (x - 3)(x + 3).

  3. If f(x) = x² - 4x + 4, what are the roots?

    Answer: x = 2 (double)

    x² - 4x + 4 = (x - 2)², so x = 2 is a repeated root.

  4. Simplify: (2x³)(3x²).

    Answer: 6x⁵

    Multiply coefficients (2·3 = 6) and add exponents (3 + 2 = 5) to get 6x⁵.

  5. If 3^x = 81, what is x?

    Answer: 4

    Since 81 = 3⁴, x = 4.

  6. What is the y-intercept of f(x) = -2x + 7?

    Answer: 7

    The y-intercept occurs at x = 0, giving f(0) = 7.

  7. Solve for x: (x/3) + 2 = 6.

    Answer: 12

    Subtract 2 to get x/3 = 4, then multiply by 3 to get x = 12.