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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 y-intercept of the line 3x − 4y = 12?

    Answer: −3

    Set x = 0 and solve: −4y = 12, so y = −3.

  2. Simplify: (3x²y)(4xy³)

    Answer: 12x³y⁴

    Multiply coefficients (3 × 4 = 12) and add exponents for matching bases (x²⁺¹ = x³, y¹⁺³ = y⁴).

  3. If a² − b² = 21 and a − b = 3, what is the value of a + b?

    Answer: 7

    Factor using difference of squares: (a − b)(a + b) = 21, so 3(a + b) = 21, giving a + b = 7.

  4. What is the solution set for the inequality 2x − 5 > 9?

    Answer: x > 7

    Add 5 to both sides to get 2x > 14, then divide by 2 to get x > 7.

  5. A quadratic equation has a = 1, b = −6, and c = 9. How many real solutions does it have?

    Answer: Exactly one real solution

    The discriminant b² − 4ac = 36 − 36 = 0, which means exactly one real (repeated) solution: x = 3.

  6. Which equation represents a line parallel to y = 2x + 5?

    Answer: y = 2x − 1

    Parallel lines have equal slopes; y = 2x − 1 has the same slope of 2 as the given line.

  7. If p(x) = x³ − 4x, what is the value of p(−2)?

    Answer: 0

    p(−2) = (−2)³ − 4(−2) = −8 + 8 = 0.