USA · National Council of Examiners for Engineering and Surveying · licensing
Computer-based at Pearson VUE, 110 questions, 6-hour appointment (5 h 20 min exam time, 25-minute break). Reference handbook supplied on screen.
The official FE page was read for the question count and appointment length; it lists Environmental among the FE disciplines. The knowledge-area list here is from general knowledge of the FE Environmental specification and was not re-read. First step to licensure as a PE.
Official source: https://ncees.org/exams/fe-exam/
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. What is the ionic strength of a 0.01 M CaCl2 solution?
A. 0.03 M
I = ½(0.01 × 2² + 0.02 × 1²) = ½(0.04 + 0.02) = 0.03 M. 0.01 is the salt concentration; 0.02 ignores charge squared for Ca; 0.05 omits the ½.
Environmental Chemistry · Chemical bonding, concentration units, activity and ionic strength
2. Using the empirical biomass formula C5H7O2N (molar mass 113 g/mol), what percentage of dry cell mass is nitrogen?
B. 12.4 per cent
N = 14/113 = 12.4%. 53.1% is carbon (60/113); 28.3% is oxygen (32/113); 6.2% is hydrogen (7/113).
Environmental Microbiology · Cell chemistry: proteins, nucleic acids, lipids, polysaccharides
3. What is the determinant of the matrix [[3, 2], [1, 4]]?
D. 10
det = 3 × 4 − 2 × 1 = 10. 14 adds the products; 2 and −10 are sign or order slips.
Mathematics & Statistics for Environmental Science · Linear algebra: matrices, linear systems, eigenvalues
4. Station X (normal annual rainfall 1000 mm) is missing a storm record. Three nearby stations with normals [800, 1200, 1100] mm recorded [60, 90, 80] mm. Using the normal ratio method, estimate X's rainfall.
A. 74.2 mm
P_x = (N_x/n) sum(P_i/N_i) = (1000/3)(0.0750 + 0.0750 + 0.0727) = 74.2. The arithmetic mean ignores normals.
Hydrology & Water Resources for Environmental Scientists · Precipitation, infiltration, evapotranspiration and runoff
5. Using the Streeter-Phelps equation with L0 = 10.0 mg/L, D0 = 1.0 mg/L, kd = 0.2/day and kr = 0.4/day, what is the oxygen deficit after 2 days of travel?
D. 2.66 mg/L
D = (0.2 x 10 / 0.2)(e^-0.4 - e^-0.8) + 1.0 e^-0.8 = 2.21 + 0.45 = 2.66. Omitting the initial-deficit term or its decay gives the wrong values.
Water Quality & Agricultural Non-point Source Pollution · River pollution and the oxygen sag curve
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