FE Exam flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax² + bx + c = 0, x = [−b ± √(b² − 4ac)]/(2a). The discriminant b² − 4ac gives two real roots if positive, one repeated root if zero, and a complex-conjugate pair if negative.

L'Hôpital's rule

When the limit of f(x)/g(x) takes the indeterminate form 0/0 or ∞/∞, the limit equals the limit of f'(x)/g'(x), provided that the latter limit exists.

Integration by parts

∫u dv = uv − ∫v du. Choose u as the factor that simplifies when differentiated, such as ln x or xⁿ, and let dv be the remaining part that is easy to integrate.

Dot product of vectors

A·B = |A||B|cos θ = AₓBₓ + A_yB_y + A_zB_z. It equals zero when the vectors are perpendicular and gives the component of one vector along the other.

Bayes' theorem

P(A|B) = P(B|A)·P(A)/P(B). It updates a prior probability P(A) with new evidence B, where the denominator is the total probability of the evidence.

Binomial distribution mean

For n independent trials each with success probability p, the binomial mean is np and the variance is np(1 − p); the standard deviation is the square root of that variance.

Standard error of the mean

SE = s/√n, where s is the sample standard deviation and n is the sample size. It estimates how widely sample means scatter about the true population mean.

Type I and Type II errors

A Type I error rejects a true null hypothesis and occurs with probability α, the chosen significance level. A Type II error fails to reject a false null, with probability β.

Capital recovery factor

A = P·[i(1 + i)ⁿ]/[(1 + i)ⁿ − 1]. It converts a present sum into an equivalent uniform end-of-period payment over n periods at interest rate i per period.

Effective annual interest rate

For a nominal rate r compounded m times per year, i_eff = (1 + r/m)^m − 1. As m becomes large the value approaches e^r − 1, the continuous-compounding limit.

Net present worth

Discount every cash flow to time zero using NPW = Σ CF_t/(1 + i)^t. A positive result means the project earns more than the minimum attractive rate of return.

Paramount professional obligation

Under the NSPE Fundamental Canons, engineers hold the safety, health, and welfare of the public paramount, perform services only in their areas of competence, and issue only objective, truthful public statements.

Signing and sealing limits

Engineers may sign and seal only documents they personally prepared or that were prepared under their direct supervisory control, and only for work within their demonstrated technical competence.

Conflict of interest disclosure

Engineers must disclose to clients or employers any known or potential conflict, such as a financial interest in a supplier, and may not take pay from more than one party for the same service without consent.

Static equilibrium conditions

A rigid body at rest satisfies ΣF = 0 and ΣM = 0 taken about any convenient point. In two dimensions these give three independent scalar equations for three unknowns.

Axial deformation formula

δ = FL/(AE), where F is the axial load, L the member length, A the cross-sectional area, and E the elastic modulus. It requires linear-elastic material and constant load and section.

Parallel axis theorem

I = I_c + A·d², where I_c is the moment of inertia about the centroidal axis parallel to the axis of interest, A the area, and d the perpendicular distance between the two axes.

Zero-force truss members

At a joint having only two non-collinear members and no external load or reaction, both members carry zero force; with three members where two are collinear, the third is zero.

Poisson's ratio

ν = −ε_lateral/ε_axial under uniaxial loading. Most metals fall near 0.25 to 0.35, and the value cannot exceed 0.5 for an isotropic material that preserves volume behavior.

Yield strength by offset method

On an engineering stress-strain curve, yield strength is found by drawing a line parallel to the elastic slope at 0.2 percent strain and reading the stress where it meets the curve.

Lever rule phase fractions

In a two-phase region, the mass fraction of a phase equals the length of the tie-line segment on the opposite side of the alloy composition divided by the total tie-line length.

Reynolds number criterion

Re = ρVD/μ = VD/ν. For flow in a circular pipe, Re below roughly 2100 indicates laminar flow, Re above roughly 4000 indicates turbulent flow, with transition between them.

Bernoulli equation

P/γ + V²/(2g) + z = constant along a streamline for steady, incompressible, frictionless flow. Each term is energy per unit weight, expressed as a head of fluid.

Buoyant force

By Archimedes' principle, F_b = γ·V_displaced, the weight of the displaced fluid. A floating body displaces a volume whose weight equals the body's own weight.

Carnot efficiency

η_max = 1 − T_L/T_H for a reversible engine operating between reservoirs at absolute temperatures T_L and T_H. No real engine between those reservoirs can exceed this value.

Steam quality

Quality x is the mass fraction of vapor in a saturated liquid-vapor mixture. Mixture properties follow v = v_f + x(v_g − v_f) and h = h_f + x·h_fg.

Isentropic ideal-gas relations

For an ideal gas with constant specific heats undergoing an isentropic process, T₂/T₁ = (P₂/P₁)^((k−1)/k) and P·v^k = constant, where k = c_p/c_v.

Thevenin equivalent circuit

Any linear two-terminal network can be replaced by a voltage source V_th in series with R_th, where V_th is the open-circuit voltage and R_th the resistance seen with independent sources deactivated.

RC time constant

In a series resistor-capacitor circuit, τ = RC is the time to reach about 63.2 percent of the total voltage change; after roughly five time constants the transient is essentially finished.

Balanced three-phase power

For a balanced three-phase load, P = √3·V_L·I_L·cos θ, where V_L and I_L are line voltage and line current and θ is the angle between phase voltage and phase current.

Hierarchy of hazard controls

Control effectiveness runs from elimination and substitution, through engineering controls and administrative controls, down to personal protective equipment, which is the least reliable option.

OSHA noise exposure limit

The permissible exposure limit is 90 dBA as an 8-hour time-weighted average, with an action level of 85 dBA and a 5 dB exchange rate that halves allowable exposure time.