EMS Math-Science Cross-Curricular Lessons 2 — Questions and Answers
Question 1: An EMS auditor calculates that a facility emits 450 kg of NOx per month. If the regulatory limit is 5,000 kg per year, what percentage of the annual limit is the facility using monthly?
- 9% (Correct answer)
- 10.8%
- 8.1%
- 11%
Correct answer: 9%
450 kg ÷ (5,000 kg ÷ 12 months) = 450 ÷ 416.7 ≈ 108%; 450 ÷ 5,000 = 9% of the annual limit.
Question 2: Which scientific principle explains why dissolved oxygen (DO) levels in a receiving water body decrease after an industrial facility discharges warm effluent?
- Henry's Law — gas solubility decreases as temperature increases (Correct answer)
- Boyle's Law — pressure reduces oxygen dissolution
- Dalton's Law — partial pressure of oxygen drops
- Le Chatelier's Principle — equilibrium shifts to produce less O₂
Correct answer: Henry's Law — gas solubility decreases as temperature increases
Henry's Law states that gas solubility in liquids decreases with increasing temperature, reducing DO when warm effluent is discharged.
Question 3: A facility tracks VOC emissions quarterly (in tonnes): Q1=12, Q2=15, Q3=18, Q4=11. What is the standard deviation closest to?
- 2.9 (Correct answer)
- 3.5
- 4.1
- 2.5
Correct answer: 2.9
Mean=14; deviations squared: 4, 1, 16, 9; variance=7.5; SD=√7.5≈2.74, closest to 2.9 among the options.
Question 4: During an EMS audit, an auditor notes pH readings of 6.2, 6.5, 6.8, and 7.1 in a treatment pond over four days. What does an upward pH trend most likely indicate in a biological treatment system?
- Increasing microbial activity consuming CO₂ (Correct answer)
- Decreasing temperature reducing acid production
- Higher heavy metal concentrations
- Rising BOD load entering the system
Correct answer: Increasing microbial activity consuming CO₂
Aerobic microbial metabolism consumes CO₂, raising pH, so an upward trend indicates increasing biological activity.
Question 5: A company reduces energy consumption from 10,000 GJ to 8,500 GJ per year. Using an emission factor of 56 kg CO₂/GJ, what is the annual CO₂ reduction in metric tonnes?
- 84 t CO₂ (Correct answer)
- 840 t CO₂
- 8.4 t CO₂
- 8,400 t CO₂
Correct answer: 84 t CO₂
Reduction = 1,500 GJ × 56 kg CO₂/GJ = 84,000 kg = 84 metric tonnes CO₂.
Question 6: An EMS auditor reviews a site's stormwater runoff coefficient. If 60% of a 2-hectare impervious surface generates runoff during a 25 mm rainfall event, what volume of stormwater (m³) must the retention pond manage?
- 300 m³ (Correct answer)
- 30 m³
- 3,000 m³
- 500 m³
Correct answer: 300 m³
Volume = 0.6 × 20,000 m² × 0.025 m = 300 m³ (2 ha = 20,000 m²).
Question 7: Which mathematical relationship best describes the logarithmic scale used when measuring sound pressure levels in an EMS noise impact assessment?
- dB = 10 × log₁₀(I/I₀) (Correct answer)
- dB = I/I₀
- dB = ln(I × I₀)
- dB = 20 × (I − I₀)
Correct answer: dB = 10 × log₁₀(I/I₀)
Sound intensity level in decibels is calculated as 10 times the base-10 logarithm of the ratio of measured intensity to reference intensity.
EMS Math-Science Cross-Curricular Lessons 2
An EMS auditor calculates that a facility emits 450 kg of NOx per month.
If the regulatory limit is 5,000 kg per year, what percentage of the annual limit is the facility using monthly?