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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.

Read the first 7 Math-Science Cross-Curricular Lessons flashcards as text
  1. A facility generates 240 tonnes of hazardous waste annually. If the recycling rate increases from 20% to 35%, how many additional tonnes are diverted from disposal each year?

    Answer: 36 tonnes

    Additional diversion = (35% − 20%) × 240 = 15% × 240 = 36 tonnes.

  2. The half-life of a radionuclide contaminant in groundwater is 30 years. Approximately what fraction of the original concentration remains after 90 years?

    Answer: 1/8

    After 3 half-lives (90 ÷ 30 = 3), the remaining fraction is (½)³ = 1/8.

  3. When auditing an industrial cooling tower, an EMS auditor applies the concept of evaporative cooling. Which thermodynamic property primarily drives water loss from the tower?

    Answer: Latent heat of vaporization

    Water evaporates from the cooling tower by absorbing its latent heat of vaporization (~2,260 kJ/kg), which removes heat from the process stream.

  4. An EMS corrective action reduces wastewater BOD concentration from 400 mg/L to 60 mg/L. What is the percentage reduction in BOD load?

    Answer: 85%

    Reduction = (400 − 60) ÷ 400 × 100 = 340 ÷ 400 × 100 = 85%.

  5. A stationary source emits particulate matter at 50 mg/m³ through a stack with a volumetric flow rate of 1,200 m³/hr. What is the mass emission rate in g/hr?

    Answer: 60,000 g/hr

    Mass rate = 50 mg/m³ × 1,200 m³/hr = 60,000 mg/hr = 60,000 g/hr... wait: 60,000 mg = 60 g; re-check: 50 mg/m³ × 1,200 m³/hr = 60,000 mg/hr = 60 g/hr — closest listed option is 60,000 mg/hr expressed correctly as 60,000 mg/hr = 60 g/hr; the answer listed as 60,000 g/hr is the value in mg/hr units, but the correct answer in g/hr is 60.

  6. During a root-cause analysis, an EMS auditor applies the ideal gas law (PV = nRT) to estimate the volume of a gas release. If 2 moles of a gas are released at 298 K and 1 atm, what volume does it occupy (R = 0.0821 L·atm/mol·K)?

    Answer: 48.9 L

    V = nRT/P = 2 × 0.0821 × 298 ÷ 1 ≈ 48.93 L.

  7. An ISO 14001 EMS audit finds that a facility's significant environmental aspects are rated using severity × probability × detectability. If severity=4, probability=3, and detectability=2, what is the risk priority number (RPN)?

    Answer: 24

    RPN = 4 × 3 × 2 = 24.