FE Other Disciplines (NCEES Fundamentals of Engineering)

The FE Other Disciplines exam is NCEES's general Fundamentals of Engineering test, the first step toward PE licensure for engineers whose field is not covered by a discipline-specific FE. It is a 110-question, 6-hour computer-based exam grounded in the free FE Reference Handbook.

Updated for 2026 · 423 practice questions with answers & explanations

110

exam questions

360 min

time limit

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What the FE Other Disciplines (NCEES Fundamentals of Engineering) exam covers

12%

Fluid Mechanics

Statics

Dynamics

Strength of Materials

Thermodynamics and Heat Transfer

Mathematics

Probability and Statistics

Safety, Health, and Environment

Engineering Economics

Materials

Basic Electrical Engineering

Chemistry

Engineering Ethics and Societal Impacts

Instrumentation and Controls

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Sample FE Other Disciplines (NCEES Fundamentals of Engineering) questions

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Mathematics
1. What is the derivative of f(x) = 3x^3 - 5x evaluated at x = 2?
- a.31Correct
- b.27
- c.36
- d.19
Why: Differentiate term by term: f'(x) = 9x^2 - 5. At x = 2, f'(2) = 9(4) - 5 = 36 - 5 = 31. The power rule d/dx(x^n) = n·x^(n-1) is the core single-variable calculus tool tested on the FE.
Mathematics
2. What is the determinant of the 2x2 matrix [[4, 3], [2, 5]]?
- a.26
- b.7
- c.20
- d.14Correct
Why: For a 2x2 matrix [[a, b], [c, d]], the determinant is ad - bc. Here (4)(5) - (3)(2) = 20 - 6 = 14. Determinants indicate whether a linear system has a unique solution (nonzero determinant).
Mathematics
3. Evaluate the definite integral of sin(x) from 0 to pi.
- a.1
- b.2Correct
- c.pi
- d.0
Why: The antiderivative of sin(x) is -cos(x). Evaluating from 0 to pi gives [-cos(pi)] - [-cos(0)] = -(-1) - (-(1)) = 1 + 1 = 2. This is a standard application of the Fundamental Theorem of Calculus.
Probability and Statistics
4. Two fair six-sided dice are rolled. What is the probability that the sum equals 7?
- a.1/12
- b.1/9
- c.1/8
- d.1/6Correct
Why: There are 36 equally likely outcomes. The combinations summing to 7 are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes. Probability = 6/36 = 1/6. Seven is the most likely sum for two dice.
Probability and Statistics
5. Find the sample standard deviation of the data set 2, 4, 6, 8, 10.
- a.3.16Correct
- b.6.32
- c.2.83
- d.10
Why: The mean is 6. Deviations are -4, -2, 0, 2, 4; squared they are 16, 4, 0, 4, 16 summing to 40. Sample variance divides by (n - 1) = 4, giving 10; the standard deviation is sqrt(10) = 3.16. Dividing by n-1 (not n) gives the unbiased SAMPLE estimate.
Chemistry
6. What is the pH of a 0.001 M solution of the strong acid HCl?
- a.3Correct
- b.2
- c.11
- d.1
Why: HCl fully dissociates, so [H+] = 0.001 = 1x10^-3 M. pH = -log10[H+] = -log10(10^-3) = 3. A pH below 7 is acidic, consistent with an acid solution.

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