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FE · 7% of the exam

Fundamental Principles practice questions

10 free Fundamental Principles questions for the FE Environmental Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

The core principles behind environmental processes: mass and energy balances, reaction kinetics, reactor behaviour and basic microbiology.

Exam weight
7%
On a real exam
≈ 8 questions
In our bank
42 questions

Topics that come up most

  • Mass and energy balances on control volumes
  • Reaction order and rate constants
  • Ideal reactors: batch, CMFR and plug flow
  • Mass transfer and partitioning between phases
  • Microbial growth and kinetics

How to study it

Work several steady-state mass balance problems with first-order decay in both CMFR and plug-flow reactors until the setup is automatic.

Sample Fundamental Principles questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    A river carrying 10 m³/s at 2 mg/L of a conservative substance receives a 1-m³/s discharge at 24 mg/L. The fully mixed concentration is:

    • A2.2 mg/L
    • B13 mg/L
    • C4 mg/L
    • D26 mg/L
    Show answer and explanation

    Answer: C) 4 mg/L

    • AIncorrect. Include the discharge load.
    • BIncorrect. That's the simple average; weight by flow.
    • CCorrect. (10 × 2 + 1 × 24)/11 = 44/11.
    • DIncorrect. Concentrations don't add.

  2. Question 2

    A river at 10 m³/s and 15 °C receives a 1-m³/s discharge at 37 °C. The fully mixed temperature is:

    • A15 °C
    • B26 °C
    • C17 °C
    • D52 °C
    Show answer and explanation

    Answer: C) 17 °C

    • AIncorrect. Include the warm discharge.
    • BIncorrect. That's the simple average.
    • CCorrect. (10 × 15 + 1 × 37)/11.
    • DIncorrect. Temperatures don't add.

  3. Question 3

    Nitrification needs about 4.57 g of O₂ per g of ammonia-nitrogen. Nitrifying 10 mg/L of NH₄⁺–N needs about:

    • A2.2 mg/L of O₂
    • B45.7 mg/L of O₂
    • C4.57 mg/L of O₂
    • D14.6 mg/L of O₂
    Show answer and explanation

    Answer: B) 45.7 mg/L of O₂

    • AIncorrect. Multiply, don't divide.
    • BCorrect. 10 mg/L × 4.57 g O₂ per g N.
    • CIncorrect. Multiply by 10.
    • DIncorrect. Multiply, don't add.

  4. Question 4

    A wastewater has a 5-day BOD of 200 mg/L and k = 0.23 per day (base e). Its ultimate BOD is about:

    • A137 mg/L, multiplying by 0.683
    • B200 mg/L, the BOD₅
    • C293 mg/L
    • D632 mg/L
    Show answer and explanation

    Answer: C) 293 mg/L

    • AIncorrect. Divide by the exerted fraction.
    • BIncorrect. Ultimate BOD exceeds BOD₅.
    • CCorrect. \(L_0 = BOD_5/(1 - e^{-5k}) = 200/0.683\).
    • DIncorrect. That isn't the calculation.

  5. Question 5

    A completely mixed lake (V = 1,000 m³, Q = 100 m³/day, k = 0.1 per day) receives 1,000 g/day of a decaying pollutant. The steady-state concentration is:

    • A50 mg/L
    • B10 mg/L
    • C1 mg/L
    • D5 mg/L
    Show answer and explanation

    Answer: D) 5 mg/L

    • AIncorrect. Recheck the units: g/m³ = mg/L.
    • BIncorrect. Include decay, kV.
    • CIncorrect. Recheck: 1,000/200.
    • DCorrect. C = W/(Q + kV) = 1,000/(100 + 100) g/m³.

  6. Question 6

    A wastewater has ultimate BOD L₀ = 300 mg/L and k = 0.23 per day (base e). Its 5-day BOD is about:

    • A95 mg/L
    • B205 mg/L
    • C300 mg/L
    • D345 mg/L
    Show answer and explanation

    Answer: B) 205 mg/L

    • AIncorrect. That's the BOD remaining.
    • BCorrect. BOD₅ = L₀(1 − e^(−5k)) = 300(1 − 0.317).
    • CIncorrect. That's the ultimate BOD.
    • DIncorrect. BOD₅ can't exceed L₀.

  7. Question 7

    A bacterial culture in exponential growth doubles every 10 hours. Its specific growth rate is closest to:

    • A6.93 per hour
    • B0.10 per hour
    • C0.030 per hour
    • D0.069 per hour
    Show answer and explanation

    Answer: D) 0.069 per hour

    For exponential growth, N = N0·e^(μt). Setting N/N0 = 2 gives μ = ln 2 / td = 0.693/10 ≈ 0.069 h⁻¹.

    • AIncorrect. This multiplies ln 2 by the doubling time (0.693 × 10) when it should divide by it.
    • BIncorrect. This is just 1/td. It leaves out the ln 2 factor that comes from N = N0·e^(μt) with N/N0 = 2.
    • CIncorrect. This uses log10 2 (0.301) instead of the natural log. The specific growth rate is defined with base-e exponential growth.
    • DCorrect. μ = ln 2 / td = 0.693 / 10 h ≈ 0.069 per hour.

  8. Question 8

    Methane-producing microorganisms (methanogens) in anaerobic digesters are:

    • APhotosynthetic algae
    • BStrict aerobes
    • CStrict anaerobes
    • DViruses
    Show answer and explanation

    Answer: C) Strict anaerobes

    • AIncorrect. They're archaea.
    • BIncorrect. They need anaerobic conditions.
    • CCorrect. Oxygen inhibits them.
    • DIncorrect. They're archaea.

  9. Question 9

    In an aerobic biological reactor, the external substrate has been nearly used up. During the resulting endogenous decay phase, the heterotrophic bacteria mainly:

    • AOxidize their own stored reserves and cell material for maintenance energy
    • BGrow exponentially because there is less competition for the remaining substrate
    • CForm dormant spores, so the oxygen uptake rate drops to zero
    • DSwitch to anaerobic metabolism and release methane as the main end product
    Show answer and explanation

    Answer: A) Oxidize their own stored reserves and cell material for maintenance energy

    Endogenous decay happens when substrate runs out: cells oxidize their own reserves and cell material for maintenance energy, so net biomass declines while oxygen uptake continues.

    • ACorrect. With no external food, cells break down their own reserves and cell material to meet maintenance needs. Net active biomass falls, and the cells keep using oxygen (endogenous respiration).
    • BIncorrect. Exponential (log) growth needs plenty of substrate. When substrate is scarce, growth slows and net biomass declines.
    • CIncorrect. Most wastewater heterotrophs do not form spores, and the cells keep using oxygen to oxidize cell material. That continuing oxygen use is the endogenous respiration rate.
    • DIncorrect. In an aerated reactor, endogenous decay is still aerobic, and its main products are CO2, water and an inert residue. Methane comes from methanogenic archaea under strictly anaerobic conditions.

  10. Question 10

    In a batch culture, bacteria multiply at their maximum rate during the:

    • AStationary phase
    • BLag phase
    • CExponential (log) growth phase
    • DDeath phase
    Show answer and explanation

    Answer: C) Exponential (log) growth phase

    • AIncorrect. Growth equals death then.
    • BIncorrect. Cells are adapting then.
    • CCorrect. Substrate is plentiful.
    • DIncorrect. The population declines then.

Fundamental Principles: FAQs

How much of the FE exam is Fundamental Principles?

Fundamental Principles is 7% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 8 questions. The real exam's exact split varies by form.

What does the Fundamental Principles domain cover?

The core principles behind environmental processes: mass and energy balances, reaction kinetics, reactor behaviour and basic microbiology.

How should I study Fundamental Principles for FE?

Work several steady-state mass balance problems with first-order decay in both CMFR and plug-flow reactors until the setup is automatic.

Where can I practise more Fundamental Principles questions?

This page has 10 free Fundamental Principles questions with answers. The ExamWize FE question bank has 42 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Fundamental Principles exam-ready

The full FE bank has 42 Fundamental Principles questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

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Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.