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Ultimate Regents Algebra Flashcards

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

Read the first 7 Ultimate Regents Algebra flashcards as text

  1. A store marks up items 40% from cost. If an item costs $80, what is the selling price?

    Answer: $112

    Selling price = 80 + 0.40(80) = 80 + 32 = $112.

  2. Which equation represents a line perpendicular to y = (1/3)x + 5?

    Answer: y = -3x + 2

    Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 1/3 is -3.

  3. Simplify: (4x² - 9) ÷ (2x + 3)

    Answer: 2x - 3

    Factor the numerator as a difference of squares: (2x+3)(2x-3); cancel (2x+3) to get 2x - 3.

  4. A geometric sequence has first term 4 and common ratio 3. What is the 5th term?

    Answer: 324

    aₙ = a₁ · rⁿ⁻¹; a₅ = 4 · 3⁴ = 4 · 81 = 324.

  5. Which system of inequalities is graphed by the region below y = x + 2 AND above y = -x?

    Answer: y -x

    Below y = x + 2 means y -x.

  6. The population of a town is modeled by P = 12000(1.03)^t where t is years. After how many years will the population exceed 16,000?

    Answer: About 10 years

    Solving 12000(1.03)^t > 16000 gives (1.03)^t > 4/3; taking logarithms gives t > log(4/3)/log(1.03) ≈ 9.7, so about 10 years.

  7. What is the range of the function f(x) = |x| - 3?

    Answer: y ≥ -3

    Since |x| ≥ 0 for all x, f(x) = |x| - 3 ≥ -3, so the range is y ≥ -3.