Free FE Exam Flashcards

Use it while solving every practice problem. The goal is not to memorize every equation, but to recognize which section contains the needed formula, table, or property data and find it quickly under exam timing.

Speed on the FE depends on muscle memory. Matrix solving, statistics functions, complex numbers, unit conversions, and equation solving are only useful if you can run them quickly on the exact calculator model you will bring.

Write units through the calculation and convert before substituting. Mixed systems, squared or cubed dimensions, gauge versus absolute pressure, and kN versus N are common sources of wrong numerical answers.

Flag it when you do not know the setup after a short attempt, when the handbook lookup is taking too long, or when algebra becomes messy. Easy points across the exam are worth more than over-investing in one problem.

A derivative is an instantaneous rate of change or slope. In engineering problems it may represent velocity from position, acceleration from velocity, marginal cost from cost, or a local linear approximation.

A definite integral accumulates a quantity over an interval. It can represent area, displacement from velocity, work from force over distance, volume from cross-sectional area, or total probability from a density function.

For a square linear system, a nonzero determinant means the coefficient matrix is invertible and the system has one unique solution. A zero determinant signals dependence or inconsistency and needs more analysis.

Euler's method advances an approximate solution with y_next = y_current + h f(x_current, y_current). It is a first-order numerical method, so smaller step sizes generally improve accuracy but require more steps.

Laplace transforms convert differential equations into algebraic equations in the s-domain. They are especially useful for linear systems, circuit transients, controls, and initial-condition problems.

Expected value is the long-run weighted average of a random variable. Multiply each outcome by its probability and sum the products; for continuous variables, integrate x times the probability density.

Variance measures average squared spread from the mean. Standard deviation is the square root of variance and has the same units as the measured data, which makes it easier to interpret in engineering context.

A z-score standardizes a value as z = (x - mean) / standard deviation. It tells how many standard deviations the value is above or below the mean and lets you use standard normal tables.

A residual is observed value minus predicted value. Residual patterns can reveal a poor model fit, nonlinearity, outliers, changing variance, or missing variables even when the regression equation looks plausible.

The engineer's highest obligation is protection of public health, safety, and welfare. Employer loyalty, client confidentiality, budget pressure, and schedule goals are subordinate to that duty.

Decline, obtain qualified review, or limit approval to the portion they are competent to judge. Signing or sealing work without adequate knowledge misleads the public and creates professional liability.

A conflict exists when personal, financial, or organizational interests could affect professional judgment. The ethical response is disclosure to affected parties and removal or consent before proceeding.

Raise the concern through appropriate channels, document the technical basis, refuse to endorse unsafe work, and escalate to proper authorities if the danger is not corrected.

Present worth converts future cash flows to an equivalent value at time zero using an interest rate. It is useful for comparing alternatives with different timing on one common economic basis.

Annual worth converts costs and benefits into an equivalent uniform yearly amount. It is useful when alternatives have different service lives and can be repeated under comparable conditions.

Benefit-cost ratio compares equivalent benefits to equivalent costs. A ratio greater than 1 indicates benefits exceed costs for the stated assumptions, but mutually exclusive choices still require careful incremental comparison.

A sunk cost has already occurred and cannot be recovered. It should not affect an economic choice between future alternatives, even though it may feel psychologically important.

Straight-line depreciation spreads depreciable value evenly over the asset life: annual depreciation equals cost minus salvage value divided by useful life. It is simple and appears often in FE economics problems.

For a particle in equilibrium, the vector sum of forces is zero. In two dimensions, write separate equations for horizontal and vertical components before solving unknown forces.

A planar rigid body in static equilibrium must satisfy sum of forces in x equals zero, sum of forces in y equals zero, and sum of moments about any point equals zero.

A moment measures rotational tendency and equals force times perpendicular distance to the line of action. Choosing the moment point to eliminate unknown reactions usually simplifies equilibrium equations.

Static friction adjusts up to a maximum value of mu_s times the normal force. Use equality only at impending motion; otherwise friction may be less than the maximum.

Use constant-acceleration equations only when acceleration is actually constant. Match the equation to the missing variable so you avoid unnecessary algebra, especially when time is not given.

The net work done on a body equals its change in kinetic energy. It is often faster than force-acceleration equations when displacement, speed, springs, gravity, or friction are involved.

Impulse equals change in momentum. It is the natural tool for impacts, short-duration forces, collisions, and problems where force varies over time but the net impulse is known.

Average normal stress equals axial force divided by cross-sectional area. Tension and compression use the same magnitude formula, but the sign convention and deformation direction differ.

Within the linear elastic range, stress equals elastic modulus times strain. For a prismatic axial member, deformation is commonly found from force times length divided by area times modulus.

Bending stress varies linearly with distance from the neutral axis and is commonly written as sigma = M c / I at the extreme fiber. Larger section moment of inertia reduces bending stress.

Shear stress in a circular shaft increases with radius and is largest at the outer surface. The common form is tau = T r / J, where J is the polar moment of inertia.

Long slender columns can fail by instability before material yield. Critical load depends strongly on effective length, end conditions, elastic modulus, and the least area moment of inertia.

Ductility is the ability to plastically deform before fracture. It is often indicated by percent elongation or reduction in area and is important when visible yielding before failure is desired.

Toughness is the ability to absorb energy before fracture. It differs from strength: a very strong material can still be brittle if it absorbs little energy before breaking.

Cold working plastically deforms metal below its recrystallization temperature. It typically increases strength and hardness while reducing ductility because dislocation movement becomes more difficult.

Balanced chemical equations conserve atoms and charge. On FE chemistry problems, balance the reaction before using stoichiometric ratios, oxidation states, or limiting-reactant logic.

Gauge pressure is measured relative to local atmospheric pressure. Absolute pressure is measured relative to vacuum. Use absolute pressure in gas-law and thermodynamic property relationships unless told otherwise.

Continuity expresses conservation of mass. For steady incompressible flow, area times average velocity is constant along a streamtube, so smaller flow area means higher velocity.

The basic Bernoulli equation assumes steady, incompressible, inviscid flow along a streamline with no pump, turbine, or head loss terms. Real pipe systems often need energy additions and losses included.

Reynolds number compares inertial effects to viscous effects. It helps classify flow behavior and decide whether laminar formulas, turbulent correlations, or transitional caution are appropriate.

In a stationary fluid of constant density, pressure increases linearly with depth. The pressure force on a submerged plane acts at the center of pressure, not necessarily at the centroid.

Energy conservation for a closed system relates heat transfer, work, and change in system energy. Be consistent with the sign convention used by the formula in the reference handbook.

Thermal efficiency compares useful work output to heat input for a heat engine. It must be less than the reversible limit for the same temperature reservoirs and cannot exceed 100 percent.

COP measures refrigeration or heat-pump benefit per unit work input. For a refrigerator the desired effect is heat removed from the cold space; for a heat pump it is heat delivered to the warm space.

Conduction transfers heat through material, convection transfers heat between a surface and moving fluid, and radiation transfers heat by electromagnetic emission. Many FE heat-transfer problems combine two or more modes.

Ohm's law relates voltage, current, and resistance. Power checks such as P = V I, P = I squared R, and P = V squared over R help verify whether a circuit answer is physically reasonable.

Kirchhoff's current law applies conservation of charge at a node. Kirchhoff's voltage law applies conservation of energy around a closed loop. Define current directions and voltage polarities before writing equations.

Power factor is the ratio of real power to apparent power and equals the cosine of the phase angle for sinusoidal loads. Low power factor means more current is required for the same real power.