Regents Ultimate Regents Algebra 5 — Questions and Answers
Question 1: A store marks up items 40% from cost. If an item costs $80, what is the selling price?
- $112 (Correct answer)
- $120
- $48
- $100
Correct answer: $112
Selling price = 80 + 0.40(80) = 80 + 32 = $112.
Question 2: Which equation represents a line perpendicular to y = (1/3)x + 5?
- y = -3x + 2 (Correct answer)
- y = (1/3)x - 2
- y = 3x + 5
- y = -(1/3)x + 2
Correct answer: y = -3x + 2
Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 1/3 is -3.
Question 3: Simplify: (4x² - 9) ÷ (2x + 3)
- 2x - 3 (Correct answer)
- 2x + 3
- 4x - 9
- 2x
Correct answer: 2x - 3
Factor the numerator as a difference of squares: (2x+3)(2x-3); cancel (2x+3) to get 2x - 3.
Question 4: A geometric sequence has first term 4 and common ratio 3. What is the 5th term?
- 324 (Correct answer)
- 243
- 108
- 256
Correct answer: 324
aₙ = a₁ · rⁿ⁻¹; a₅ = 4 · 3⁴ = 4 · 81 = 324.
Question 5: Which system of inequalities is graphed by the region below y = x + 2 AND above y = -x?
- y < x + 2 and y > -x (Correct answer)
- y > x + 2 and y < -x
- y ≤ x + 2 and y ≥ -x
- y < x + 2 and y < -x
Correct answer: y < x + 2 and y > -x
Below y = x + 2 means y < x + 2, and above y = -x means y > -x.
Question 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?
- About 10 years (Correct answer)
- About 5 years
- About 15 years
- About 3 years
Correct 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.
Question 7: What is the range of the function f(x) = |x| - 3?
- y ≥ -3 (Correct answer)
- y ≤ -3
- All real numbers
- y ≥ 3
Correct answer: y ≥ -3
Since |x| ≥ 0 for all x, f(x) = |x| - 3 ≥ -3, so the range is y ≥ -3.
Regents Ultimate Regents Algebra 5
A store marks up items 40% from cost.
If an item costs $80, what is the selling price?