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Math-Science Cross-Curricular Lessons Flashcards

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

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  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?

    Answer: 9%

    450 kg ÷ (5,000 kg ÷ 12 months) = 450 ÷ 416.7 ≈ 108%; 450 ÷ 5,000 = 9% of the annual limit.

  2. Which scientific principle explains why dissolved oxygen (DO) levels in a receiving water body decrease after an industrial facility discharges warm effluent?

    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.

  3. A facility tracks VOC emissions quarterly (in tonnes): Q1=12, Q2=15, Q3=18, Q4=11. What is the standard deviation closest to?

    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.

  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?

    Answer: Increasing microbial activity consuming CO₂

    Aerobic microbial metabolism consumes CO₂, raising pH, so an upward trend indicates increasing biological activity.

  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?

    Answer: 84 t CO₂

    Reduction = 1,500 GJ × 56 kg CO₂/GJ = 84,000 kg = 84 metric tonnes CO₂.

  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?

    Answer: 300 m³

    Volume = 0.6 × 20,000 m² × 0.025 m = 300 m³ (2 ha = 20,000 m²).

  7. Which mathematical relationship best describes the logarithmic scale used when measuring sound pressure levels in an EMS noise impact assessment?

    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.