FE Exam Flashcards

Q: What topics do these FE flashcards cover?

These cards review discipline-neutral FE fundamentals: math, probability and statistics, ethics, engineering economics, statics and dynamics, mechanics of materials, materials and chemistry, fluids, thermodynamics and heat transfer, electrical circuits, reference-handbook use, units, and calculator strategy.

Q: Are FE flashcards enough by themselves?

Flashcards are useful for formulas, concepts, and decision rules, but the FE also requires problem solving. Pair these cards with timed practice problems, reference-handbook lookup drills, and an NCEES-approved calculator you know well.

Q: Can I bring my own reference materials to the FE exam?

No. The FE exam provides an on-screen searchable NCEES FE Reference Handbook. You should practice finding formulas and tables in that handbook before exam day rather than relying on personal notes.

Q: What is the FE retake policy?

NCEES retake eligibility is controlled by testing-window rules rather than a universal fixed day wait. Local licensing-board rules may also apply, so confirm current eligibility in your MyNCEES account before scheduling another attempt.

Question 1

What is the best way to use the FE Reference Handbook during study?

Accepted Answer

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.

Question 2

Why should FE candidates practice with their approved calculator only?

Accepted Answer

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.

Question 3

What unit habit prevents many FE mistakes?

Accepted Answer

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.

Question 4

When should you flag an FE problem and move on?

Accepted Answer

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.

Question 5

Derivative meaning on the FE

Accepted Answer

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.

Question 6

Definite integral meaning on the FE

Accepted Answer

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.

Question 7

How do determinants help identify a unique solution?

Accepted Answer

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.

Question 8

Euler's method setup

Accepted Answer

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.

Question 9

Laplace transforms in engineering problems

Accepted Answer

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.

Question 10

Expected value

Accepted Answer

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.

Question 11

Standard deviation versus variance

Accepted Answer

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.

Question 12

Normal distribution z-score

Accepted Answer

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.

Question 13

Regression residual

Accepted Answer

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.

Question 14

Primary ethical duty of an engineer

Accepted Answer

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.

Question 15

What should an engineer do when asked to approve work outside their competence?

Accepted Answer

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.

Question 16

Conflict of interest

Accepted Answer

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.

Question 17

What if a design condition threatens public safety?

Accepted Answer

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.

Question 18

Present worth

Accepted Answer

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.

Question 19

Annual worth

Accepted Answer

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.

Question 20

Benefit-cost ratio

Accepted Answer

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.

Question 21

Sunk cost

Accepted Answer

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.

Question 22

Straight-line depreciation

Accepted Answer

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.

Question 23

Particle equilibrium

Accepted Answer

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.

Question 24

Rigid-body equilibrium in 2D

Accepted Answer

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.

Question 25

Moment of a force

Accepted Answer

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.

Question 26

Static friction limit

Accepted Answer

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.

Question 27

Constant-acceleration kinematics

Accepted Answer

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.

Question 28

Work-energy principle

Accepted Answer

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.

Question 29

Impulse-momentum principle

Accepted Answer

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.

Question 30

Normal stress

Accepted Answer

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.

Question 31

Hooke's law for axial loading

Accepted Answer

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.

Question 32

Flexure formula

Accepted Answer

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.

Question 33

Torsion in a circular shaft

Accepted Answer

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.

Question 34

Euler buckling

Accepted Answer

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.

Question 35

Ductility

Accepted Answer

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.

Question 36

Toughness

Accepted Answer

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.

Question 37

Cold working

Accepted Answer

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

Question 38

Balancing chemical equations

Accepted Answer

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

Question 39

Gauge pressure versus absolute pressure

Accepted Answer

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.

Question 40

Continuity equation

Accepted Answer

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.

Question 41

Bernoulli equation assumptions

Accepted Answer

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.

Question 42

Reynolds number

Accepted Answer

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.

Question 43

Hydrostatic pressure

Accepted Answer

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.

Question 44

First law of thermodynamics for a closed system

Accepted Answer

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.

Question 45

Thermal efficiency

Accepted Answer

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.

Question 46

Coefficient of performance

Accepted Answer

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.

Question 47

Conduction, convection, and radiation

Accepted Answer

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.

Question 48

Ohm's law and power checks

Accepted Answer

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.

Question 49

Kirchhoff's laws

Accepted Answer

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.

Question 50

AC power factor

Accepted Answer

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.

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