FE Exam study guide
FE Exam · Work through your exam, one topic at a time.
The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a licensed professional engineer (P.E.). It is designed for recent graduates and for students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program. The FE Exam study guide has 10 sections and about 2,964 words.
01Mathematics
The FE mathematics scope is broad but shallow: vector algebra (dot and cross products, projections, unit vectors), analytic geometry (lines, planes, conics, distance formulas), single- and multivariable calculus (partial derivatives, multiple integrals, divergence, curl, line and surface integrals), linear algebra (matrix arithmetic, determinants, inverse, eigenvalues, solving linear systems by elimination), ordinary differential equations (separable, first-order linear with integrating factor, second-order constant-coefficient), and numerical methods (Newton-Raphson, trapezoidal and Simpson's rules, Euler's method). Mixing degrees and radians: derivatives and series for trig functions assume radians.
278 words, about 1 min02Probability and Statistics
Know the standard distributions and when each applies: binomial (fixed n, independent trials, constant p), Poisson (counts per unit time or space), normal (with z-scores and the empirical 68/95/99.7 rule), exponential (time between Poisson events), and the hypergeometric idea of sampling without replacement. Be fluent in combinations and permutations, conditional probability, independence, Bayes' theorem, expected value and variance, standard error, confidence intervals, hypothesis testing (Type I vs Type II error, p-value logic), and simple linear regression (slope, correlation coefficient, coefficient of determination).
289 words, about 1 min03Engineering Economics
The core is the time value of money: single-payment factors (P/F, F/P), uniform-series factors (P/A, A/P, A/F, F/A), gradient and geometric-gradient factors, and the correct compounding convention (discrete annual vs nominal rate with m periods, effective annual rate = (1 + r/m)^m - 1). Then build cash flows and compare alternatives using present worth, annual worth, future worth, internal rate of return, payback period, and benefit-cost ratio.
306 words, about 2 min04Ethics and Professional Practice
Know the structure of professional regulation: the state licensing board, the NCEES Model Law and Model Rules, the path to licensure (ABET-accredited degree, FE and PE exams, qualifying experience), comity, and the engineer's seal and signature. Study the canons: holding public health, safety and welfare paramount; competence in the field of practice; avoiding conflicts of interest; refusing and reporting bribery or improper gifts; preserving confidentiality of client information; objectivity and truthfulness in reports and testimony; and obligations to the profession through continuing education and mentoring.
323 words, about 2 min05Engineering Mechanics
Statics: free-body diagrams, equilibrium in two and three dimensions, support reactions (pin, roller, fixed), truss analysis by joints and sections, zero-force member identification, frames and machines, friction (static, kinetic, impending motion, belt friction), centroids, centers of mass, and area moments of inertia including the parallel-axis theorem. Dynamics: particle and rigid-body kinematics (rectilinear, curvilinear, rotational, relative motion), Newton's second law in normal/tangential and cylindrical coordinates, work-energy, impulse-momentum, impact and restitution, and basic vibration.
275 words, about 1 min06Materials Science
Stress and strain in tension, compression and shear; the engineering stress-strain curve (proportional limit, elastic modulus, yield strength by the 0.2% offset method, ultimate tensile strength, fracture strain, toughness as area under the curve); Poisson's ratio and the relation G = E/[2(1 + nu)]; thermal expansion strain; hardness scales and their approximate correlation with strength; fatigue (S-N curves, endurance limit, stress concentration factors); creep and elevated-temperature behavior; ductile versus brittle fracture; phase diagrams and the iron-carbon system; heat treatment (annealing, quenching, tempering); corrosion mechanisms and protection; and properties of polymers, ceramics and composites. Engineering stress uses the original area; true stress uses the instantaneous area.
303 words, about 2 min07Fluid Mechanics
Fluid properties (density, specific weight, viscosity, surface tension, vapor pressure), hydrostatic pressure distribution and manometry, forces on plane and curved submerged surfaces, buoyancy and stability, continuity and the Bernoulli/energy equation with head losses, the Reynolds number and laminar/turbulent classification, Darcy-Weisbach friction factors (Moody chart, laminar f = 64/Re), minor losses, pipe networks and parallel/series piping, pump and system curves (head, efficiency, NPSH, cavitation), open-channel flow (Manning's equation, Froude number), orifice and weir flow, and drag on immersed bodies. Gauge versus absolute pressure: Bernoulli works consistently in either, but vapor-pressure comparisons need absolute.
282 words, about 1 min08Thermodynamics
Properties and state (ideal gas law, compressibility, saturated and superheated tables, quality), the first law for closed systems (Q - W = delta U) and open systems (steady-flow energy equation with enthalpy), boundary work, specific heats and the relation cp - cv = R, polytropic processes, the second law and entropy, Carnot efficiency, Rankine and Brayton cycles with their efficiency-improving modifications (reheat, regeneration, superheat), refrigeration and heat pumps with COP, psychrometrics (dry-bulb, wet-bulb, humidity ratio, dew point), combustion basics, and heat transfer by conduction (Fourier), convection (Newton's law of cooling) and radiation (Stefan-Boltzmann). Sign convention: work done by the system is positive in most FE texts -- check the convention implied by the answer choices.
292 words, about 1 min09Electrical and Computer Engineering
Circuit fundamentals: Ohm's law, series/parallel reduction, Kirchhoff's current and voltage laws, node and mesh analysis, superposition, Thevenin and Norton equivalents, maximum power transfer. AC: phasors, impedance of R, L and C, RMS versus peak values, real/reactive/apparent power, power factor and correction, three-phase relationships (line vs phase voltage and current, total power = sqrt(3) V L I L cos theta), transformers and turns ratio, and DC/AC motor basics.
299 words, about 1 min10Safety, Health, and Environment
The hierarchy of controls (elimination, substitution, engineering controls, administrative controls, PPE -- in that order of preference), hazard identification and risk assessment (risk as probability times consequence), job hazard analysis, lockout/tagout, confined-space entry, machine guarding, electrical safety, fall protection, and fire prevention. Industrial hygiene: routes of exposure, air sampling, time-weighted averages, permissible exposure limits and threshold limit values, noise exposure in dBA and the 5 dB exchange rate, heat stress, and ventilation.
317 words, about 2 min