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Fundamentals of Engineering Cheat Sheet 2026

The 30 highest-yield Fundamentals of Engineering facts, distilled from real exam questions. Print it, save it as a PDF, or study it here โ€” free, no sign-up.

110 questions
340 min time limit
70% to pass
  1. Which type of structural analysis method satisfies both equilibrium and compatibility? โ†’ Exact (complete) structural analysis
  2. When comparing two mutually exclusive alternatives using IRR, which approach is correct? โ†’ Calculate the IRR on the incremental cash flow between alternatives
  3. A Carnot engine operates between 800 K and 400 K. What is its maximum theoretical efficiency? โ†’ 50%
  4. What is the coordination number (number of nearest neighbors) for an atom in a face-centered cubic (FCC) structure? โ†’ 12
  5. A 10 kg block rests on a 30ยฐ incline with ฮผ_s = 0.4. What is the maximum static friction force available (g = 9.81 m/sยฒ)? โ†’ 34.0 N
  6. Which integration technique is best suited for โˆซ xยทeหฃ dx? โ†’ Integration by parts
  7. A 500 kg object is accelerated from rest to 20 m/s over 10 seconds on a frictionless surface. What net force is required? โ†’ 1000 N
  8. What's the name for a polymer with characteristics similar to rubber? โ†’ Elastomer
  9. Until a steel contains at least what percentage of chromium, can it be eligible for the stainless prefix? โ†’ 10%
  10. In statistics, what does a p-value less than 0.05 typically indicate? โ†’ The result is statistically significant at the 5% level
  11. A benefit-cost (B/C) ratio greater than 1.0 for a public project indicates: โ†’ Benefits exceed costs and the project is economically justified
  12. Which of the following correctly describes a statically indeterminate structure? โ†’ One where the number of unknowns exceeds the number of equilibrium equations
  13. Which material property describes resistance to permanent deformation under load? โ†’ Hardness
  14. In projectile motion (neglecting air resistance), which component of velocity remains constant? โ†’ Horizontal velocity
  15. The standard deviation of the data set {4, 8, 6, 5, 7} is closest to: โ†’ 1.41
  16. A vector has components Fx = 3 N and Fy = 4 N. What is the magnitude of the resultant force? โ†’ 5 N
  17. In an elastic collision between two objects, which quantities are conserved? โ†’ Both momentum and kinetic energy
  18. In fluid mechanics, the Reynolds number is used to predict flow behavior. Which range typically indicates turbulent flow in a pipe? โ†’ Re > 4000
  19. In probability, if events A and B are mutually exclusive, then P(A โˆช B) equals: โ†’ P(A) + P(B)
  20. What is the hydrostatic pressure at a depth h in a fluid of density ฯ? โ†’ ฯgh
  21. In a series RLC circuit at resonance, what is the impedance? โ†’ Equal to R (purely resistive)
  22. For a body to be in static equilibrium, the sum of all forces and the sum of all moments must each equal: โ†’ Zero
  23. What is the centroid location (ศณ) of a rectangle with height h measured from its base? โ†’ h/2
  24. What is the payback period for a project with an initial cost of $100,000 and uniform annual net cash flow of $25,000? โ†’ 4 years
  25. In an AC circuit, the power factor is defined as: โ†’ Real power divided by apparent power
  26. Which of the following is a thermosetting polymer? โ†’ Epoxy resin
  27. What is the cutoff frequency of a first-order RC low-pass filter with R = 1 kฮฉ and C = 1 ฮผF? โ†’ ~159 Hz
  28. Which method of economic comparison finds the interest rate that makes NPV = 0? โ†’ Internal Rate of Return (IRR)
  29. Which dimensionless number is the ratio of inertial forces to surface tension forces in fluid mechanics? โ†’ Weber number
  30. What is the capital recovery (CR) cost of an asset? โ†’ The equivalent annual cost of owning and financing the asset
Turn these facts into recall:
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