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Math: Algebra Flashcards

7 cards from real ACT 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. What is the solution to the system of equations: x + y = 7 and x − y = 3?

    Answer: x = 5, y = 2

    Adding the equations gives 2x = 10, so x = 5; substituting back yields y = 2.

  2. Which expression is equivalent to (2x + 3)²?

    Answer: 4x² + 12x + 9

    (2x + 3)² = (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9.

  3. A line passes through the origin and the point (3, 9). What is the equation of the line?

    Answer: y = 3x

    The slope is 9/3 = 3, and since it passes through the origin (b = 0), the equation is y = 3x.

  4. If 2ˣ = 32, what is the value of x?

    Answer: 5

    Since 2⁵ = 32, x = 5.

  5. What is the product of the roots of the equation x² − 7x + 12 = 0?

    Answer: 12

    By Vieta's formulas, the product of the roots equals c/a = 12/1 = 12 (or factor: (x−3)(x−4) = 0, product = 3 × 4 = 12).

  6. If 5 is a solution to the inequality ax > 10, which of the following could be a value of a?

    Answer: 3

    Substituting x = 5 gives 5a > 10, so a > 2; only a = 3 satisfies this condition.

  7. What is the x-intercept of the function f(x) = 4x − 8?

    Answer: 2

    Set f(x) = 0: 4x − 8 = 0, so 4x = 8 and x = 2.