Plant Operator Selection System Test Plant Operator Selection System Algebra and Formula Conversion 3 — Questions and Answers
Question 1: Solve for r in the formula A = πr².
- r = A/π
- r = √(A/π) (Correct answer)
- r = √(Aπ)
- r = A²/π
Correct answer: r = √(A/π)
Divide both sides by π, then take the square root: r = √(A/π).
Question 2: If 4x + 12 = 0, what is x?
Correct answer: −3
4x = −12, so x = −3.
Question 3: A tank's volume formula is V = L × W × H. If V = 1,200, L = 10, and W = 6, what is H?
- 10
- 15
- 20 (Correct answer)
- 25
Correct answer: 20
H = V ÷ (L × W) = 1,200 ÷ 60 = 20.
Question 4: Simplify: (3x² × 2x³)
- 5x⁵
- 6x⁶
- 6x⁵ (Correct answer)
- 5x⁶
Correct answer: 6x⁵
Multiply coefficients (3 × 2 = 6) and add exponents (2 + 3 = 5): 6x⁵.
Question 5: Convert 45 feet per minute to feet per hour.
- 450 ft/hr
- 2,700 ft/hr (Correct answer)
- 270 ft/hr
- 750 ft/hr
Correct answer: 2,700 ft/hr
45 ft/min × 60 min/hr = 2,700 ft/hr.
Question 6: If efficiency E = (Output / Input) × 100, and Output = 80 and Input = 120, what is E?
- 50%
- 60%
- 66.7% (Correct answer)
- 75%
Correct answer: 66.7%
E = (80/120) × 100 = 0.6667 × 100 ≈ 66.7%.
Question 7: Rearrange D = M/V to solve for M.
- M = D − V
- M = D + V
- M = D × V (Correct answer)
- M = D/V
Correct answer: M = D × V
Multiply both sides by V: M = D × V.
