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Algebraic Techniques & Manipulation Flashcards

7 cards from real TMUA 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 Techniques & Manipulation flashcards as text

  1. Simplify: (x² - 9) / (x² - x - 6)

    Answer: (x+3)/(x+2)

    Factor numerator as (x-3)(x+3) and denominator as (x-3)(x+2), then cancel (x-3) to get (x+3)/(x+2).

  2. If p and q are roots of x² - 5x + 3 = 0, find p² + q².

    Answer: 19

    Using p+q=5 and pq=3, p²+q² = (p+q)² - 2pq = 25 - 6 = 19.

  3. Solve for x: |2x - 3| = 7

    Answer: x = 5 or x = -2

    Setting 2x-3=7 gives x=5; setting 2x-3=-7 gives x=-2.

  4. Expand and simplify: (2x + 3)² - (2x - 3)²

    Answer: 24x

    Using difference of squares: [(2x+3)+(2x-3)][(2x+3)-(2x-3)] = (4x)(6) = 24x.

  5. Find all values of k such that x² + kx + 9 = 0 has exactly one real solution.

    Answer: k = ±6

    For one real solution, discriminant = 0: k² - 36 = 0, so k = ±6.

  6. Simplify: (2x³y²)³ / (4x²y)

    Answer: 2x⁷y⁵

    Numerator becomes 8x⁹y⁶; dividing by 4x²y gives 2x⁷y⁵.

  7. If f(x) = x² + 2x - 1, find the value of f(x+1) - f(x).

    Answer: 2x + 3

    f(x+1) = (x+1)²+2(x+1)-1 = x²+4x+2; subtracting f(x) = x²+2x-1 gives 2x+3.