FE Other Disciplines Cheat Sheet

Math + Statistics

12-20% of exam
Math Toolkit Probability + Statistics Stats Test Picker Math 8-12 questions Stats 6-9 questions

Ethics, Safety, Economics

15-24% of exam
Ethics Rules Safety Thresholds Engineering Economics Economics Picker Exam Day + Handbook

Statics, Dynamics, Strength, Materials

30-47% of exam
Statics Essentials Dynamics Essentials Strength of Materials Materials Mechanics Method Picker

Fluids + Thermal

19-30% of exam
Fluid Mechanics Thermodynamics + Heat Flow + Thermal Picker Fluids 12-18 questions

Chemistry, Controls, Electrical

13-21% of exam
Chemistry Instrumentation + Controls Basic Electrical Smallest Knowledge Areas

Quick Facts

Exam FE Other Disciplines
Owner NCEES
Format CBT at Pearson VUE
Questions 110 total
Exam time 5 hr 20 min
Appointment 5 hr 55 min
Break 25 min scheduled
Fee $225
Testing Year-round, four windows
Attempts Three per 12 months
Result Pass or fail
Reference Onscreen FE Handbook
First-time pass 61%
Blueprint July 2020 specifications

Stats Test Picker QU

Sigma unknown → t distribution
Sigma known → z distribution
Fixed trials, two outcomes → Binomial
Rare events per interval → Poisson
Claim about a mean → Hypothesis test
How well curve fits → R-squared

Math Toolkit QU

Characteristic equation Roots set ODE form
Newton-Raphson Tangent-line root finder
Zero determinant Singular, no inverse
Eigenvalue Scales its eigenvector
Second derivative test Positive means local minimum
Definite integral Signed area under curve
Cross product Moment and normal vectors
Dot product Projection and work
Convergence limit Iteration stops improving

Probability + Statistics QU

t distribution Sigma unknown, small sample
z distribution Sigma known, large sample
Standard error Sigma over root n
Confidence interval Estimate plus margin
Type I error Rejects a true null
Type II error Keeps a false null
Alpha Significance level chosen
R-squared Fraction of variation explained
Binomial Fixed trials, two outcomes
Poisson Rare events per interval

Ethics Priority PR

Public first, client second, self last
Public safety wins Only qualified work Disclose all conflicts Report violations

IRR vs MARR PR

IRR

Computed from cash flows
Present worth is zero
Project's own rate

MARR

Set by the organization
Hurdle for approval
Policy input
Earned vs required

Economics Picker PR

Compare today's dollars → Present worth
Unequal project lives → Annual worth
Is return good enough → IRR versus MARR
Public spending choice → Benefit-cost ratio
Fixed and variable costs → Break-even analysis
Asset writes off value → Depreciation

Ethics Rules PR

First duty Public health, safety, welfare 240.15.A
Judgment overruled Notify client and authority
Truthful documents Objective, relevant, complete
Paid opinions Identify the interested party
Report violations Tell the licensing board
Qualified assignments Only your technical field 240.15.B
Sealing limit No work lacking competence
Confidentiality No disclosure without consent
Conflicts of interest Disclose to employer, client
Gratuities Never from contractors
Peer conduct No false reputation attacks 240.15.C

Exam Clock PR

Agreement 2, tutorial 8, exam 320
Agreement 2 min Tutorial 8 min Exam 5 hr 20 Break 25 min Appointment 5 hr 55

Scheduled vs Unscheduled Break PR

Scheduled

25 minutes allowed
Exam clock pauses
May leave building

Unscheduled

Any time allowed
Exam clock runs
Stay in building
Free time vs cost

Safety Thresholds PR

Oxygen deficient Below 19.5 percent 1910.146
Oxygen enriched Above 23.5 percent
Flammable limit trigger Above 10% of LFL
LFL Leanest burnable mixture
UFL Richest burnable mixture
SDS Chemical hazard data sheet
PPE Last line of defense
Half-life Half the activity remains
Confined space Test, ventilate, then enter
Exposure limit Allowed airborne concentration

Engineering Economics PR

Present worth Cash flows in today's dollars
P/F factor Single future amount discounted
A/P factor Capital recovery per year
IRR Rate zeroing present worth
MARR Minimum acceptable return
Benefit-cost ratio Benefits divided by costs
Break-even point Revenue equals total cost
Sunk cost Spent, never relevant
Straight-line depreciation Equal annual write-off
MACRS Accelerated early deductions
Salvage value End-of-life resale amount

Exam Day + Handbook PR

Arrive early 30 minutes before appointment
Allowed items ID, calculator, locker key
Palm vein scan Each testing room entry
Scratch work Reusable booklets and markers
Onscreen calculator TI-30XS available too
Split screen Question beside searchable handbook
Handbook access Free from MyNCEES account
Half-exam submit No return after submitting
Pretest items Unscored, randomly placed
LOFT delivery Same topics, different questions
Diagnostic report 0-15 scale per area
Units used Both SI and USCS

Mechanics Question Load ME

Statics, dynamics, strength: 9-14 each
Statics 9-14 Dynamics 9-14 Strength 9-14 Materials 6-9

Statics vs Dynamics ME

Statics

Body at rest
Forces sum zero
Reactions and friction

Dynamics

Body accelerating
Force equals ma
Energy and momentum
Equilibrium vs motion

Mechanics Method Picker ME

Speeds and distances → Work-energy ( No time needed )
Collision or impact → Impulse-momentum ( Use restitution )
Support reactions → 2D equilibrium ( Three equations )
All truss members → Method of joints
One member force → Method of sections ( Cut through it )
Beam internal forces → Shear-moment diagrams
Slender column load → Euler buckling ( End factor K )
Combined stress state → Mohr's circle ( Principal stresses )
Area property needed → Parallel axis theorem

Largest Knowledge Areas ME

Fluid Mechanics 12-18 questions Biggest
Statics 9-14 questions
Dynamics 9-14 questions
Strength of Materials 9-14 questions
Thermodynamics, Heat Transfer 9-14 questions
Mathematics 8-12 questions

Stress Formula Trio ME

Axial P/A, bending Mc/I, torsion Tr/J
Axial P over A Bending Mc over I Torsion Tr over J Shear VQ over Ib

Mass vs Area Inertia ME

Mass moment

Units kg m squared
Resists angular acceleration
Used in rotation

Area moment

Units length fourth
Describes area distribution
Used in bending
Rotation vs bending

Statics Essentials ME

2D equilibrium Three independent equations
Determinate structure Unknowns match equations
Free-body diagram Isolate body, show forces
Method of joints Two equations per joint
Method of sections Cut through wanted member
Zero-force member Unloaded two-member joint
Couple Pure moment, no resultant
Centroid Area balance point
Parallel axis theorem Add A times d squared
Static friction Maximum equals mu N

Dynamics Essentials ME

Newton's second law Force equals mass acceleration
Work-energy principle Net work changes kinetic energy
Impulse-momentum Force times time
Restitution e Separation over approach speed
Plastic impact e equals zero
Elastic impact e equals one
Normal acceleration Speed squared over radius
Mass moment of inertia Resists angular acceleration
Natural frequency Root of k over m
Kinetic friction Constant while sliding

Strength of Materials ME

Axial stress P over A
Axial deformation PL over AE
Bending stress Mc over I
Torsional stress Tr over J
Transverse shear VQ over Ib
Hooke's law Stress equals E strain
Euler buckling Slender column critical load
Effective length K Depends on end restraint
Mohr's circle radius Maximum in-plane shear
Superposition Add elastic load effects
Factor of safety Strength over actual stress
Stress concentration Notch raises local stress

Materials ME

Lever rule Phase fractions from tie-line
Eutectic point Liquid becomes two solids
Quenching Fast cooling makes martensite
Tempering Reheat to regain toughness
0.2 percent offset Yield without sharp point
Modulus of elasticity Elastic slope, stiffness
Hardness Resistance to indentation
Fatigue Failure from cyclic loading
Creep Slow strain, hot and loaded
Brittle fracture Breaks with little strain

Biggest Areas TH

Fluids 12-18 tops every knowledge area
Fluids 12-18 Thermal 9-14 Mechanics trio 9-14 Math 8-12

Laminar vs Turbulent TH

Laminar

Re below about 2100
Friction factor 64 over Re
Smooth ordered layers

Turbulent

Re above about 4000
Moody diagram needed
Mixing eddies
Viscous vs inertial

Flow + Thermal Picker TH

Pressure at depth → Hydrostatics ( Gauge pressure )
Ideal streamline problem → Bernoulli ( No friction )
Pipe head loss → Darcy-Weisbach ( Need friction factor )
Laminar friction factor → 64 over Re
Turbulent friction factor → Moody diagram ( Relative roughness )
Open channel flow → Manning's equation
Heat through wall → Fourier conduction ( Thermal resistance )
Surface to moving fluid → Convection ( h not material )
Hot surface, no medium → Stefan-Boltzmann ( Absolute temperature )
Gas near saturation → Compressibility z

Fluid Mechanics TH

Hydrostatic pressure Density times g times depth
Continuity AV constant if incompressible
Bernoulli heads Pressure, velocity, elevation
Reynolds number Inertial over viscous forces
Laminar pipe flow Below about Re 2100
Darcy-Weisbach Head loss from friction
Laminar friction factor 64 over Reynolds number
Moody diagram Turbulent friction factor
Manning's equation Open-channel flow velocity
Froude number Inertia over gravity
Mach number Speed over sound speed
Pitot tube Measures stagnation pressure
Venturi meter Flow from pressure drop
Ideal gas law pV equals nRT
Compressibility z Real gas correction

Heat Transfer Modes TH

Conduction k, convection h, radiation sigma
Conduction needs material Convection needs flow Radiation needs no medium

First vs Second Law TH

First law

Energy bookkeeping
Allows any direction
Heat plus work

Second law

Entropy increases
Sets allowed direction
Caps efficiency
Amount vs direction

Thermodynamics + Heat TH

First law Energy is conserved
Second law Entropy sets direction
Carnot efficiency 1 minus Tcold over Thot
Absolute temperature Kelvin or Rankine
Enthalpy Internal energy plus pv
Quality x Vapor fraction in mixture
Adiabatic No heat transfer
Isentropic Adiabatic and reversible
Conduction Fourier through solid material
Thermal resistance Thickness over kA
Convection h times area times deltaT
Radiation Fourth power of temperature
Stefan-Boltzmann sigma 5.67e-8 W per m2K4
Psychrometrics Moist air properties
Combustion products CO2, CO, NOx, particulates

Accuracy vs Precision EL

Accuracy

Close to true value
Systematic bias
Fixed by calibration

Precision

Readings repeat closely
Random scatter
Improved by averaging
Correct vs consistent

Smallest Knowledge Areas EL

Instrumentation and Controls 4-6 questions Smallest
Chemistry 5-8 questions
Ethics, Societal Impacts 5-8 questions
Probability and Statistics 6-9 questions
Safety, Health, Environment 6-9 questions
Engineering Economics 6-9 questions
Materials 6-9 questions
Basic Electrical Engineering 6-9 questions

Series vs Parallel EL

Series

Same current everywhere
Resistances add
Voltage divides

Parallel

Same voltage across
Conductances add
Current divides
Shared current vs voltage

Chemistry EL

pH Negative log hydrogen ion
pH plus pOH Equals 14 at 25C
Neutral solution pH 7 at 25C
Oxidation Loses electrons at anode
Reduction Gains electrons at cathode
Galvanic corrosion Active metal corrodes first
Le Chatelier Shift opposes imposed change
Stoichiometry Mole ratios from equation
Limiting reactant Runs out first
Buffer Resists pH change

Instrumentation + Controls EL

Nyquist criterion Sample above twice frequency
Aliasing Undersampling fakes low frequency
A/D conversion Analog signal to digital
Resolution Bits across full scale
Accuracy Closeness to true value
Precision Repeatability of readings
Low-pass filter Removes high-frequency noise
Amplification Raises weak signal level
Thermocouple Voltage from junction temperature
Strain gauge Resistance changes with strain
Logic diagram AND, OR, NOT gates

Basic Electrical EL

Ohm's law V equals I times R
KCL Node currents sum zero
KVL Loop voltages sum zero
Series resistors Resistances add directly
Parallel resistors Conductances add directly
RMS sinusoid Peak over root 2
Impedance Resistance plus reactance
Power factor Cosine of phase angle
Three-phase power Root3 times VL IL pf
Capacitor Blocks DC, stores charge
Inductor Opposes current change
Wattmeter Reads real power

Common Traps

Mass vs weight

Mass is kg or slug ≠ Weight is newtons or lbf

Stress vs strain

Stress is force per area ≠ Strain is deformation ratio

Friction factor source

Laminar uses 64 over Re ≠ Turbulent needs Moody diagram

Absolute vs gauge

Carnot needs absolute temperature ≠ Hydrostatics gives gauge pressure

Sunk vs future cost

Sunk costs are ignored ≠ Future costs drive decisions

Type I vs Type II

Type I rejects true null ≠ Type II keeps false null

Anode vs cathode

Oxidation occurs at anode ≠ Reduction occurs at cathode

Break clocks differ

Scheduled break pauses clock ≠ Unscheduled break burns time

Score reporting

Result is pass/fail ≠ Diagnostic scale is 0-15

Last Minute

1. 110 questions, 5 hr 20 min
2. Appointment runs 5 hr 55 min
3. Fluid Mechanics largest: 12-18 questions
4. Statics, dynamics, strength: 9-14 each
5. Instrumentation smallest: 4-6 questions
6. Public safety outranks client wishes
7. Bending stress = Mc over I
8. Laminar pipe flow below Re 2100
9. Carnot needs absolute temperature
10. IRR must exceed MARR
11. RMS = peak over root 2
12. pH plus pOH equals 14
13. Oxygen below 19.5% is deficient
14. One approved calculator only
15. Handbook is onscreen and searchable
16. Result is pass or fail

FE Other Disciplines

Practice Questions 100 questions Study Guide 73 topics Cheat Sheet 182 facts Flashcards 50 cards Shorts 4 short s Free CE Podcast