Math + Statistics
12-20%of exam
Ethics, Safety, Economics
15-24%of exam
Statics, Dynamics, Strength, Materials
30-47%of exam
Fluids + Thermal
19-30%of exam
Chemistry, Controls, Electrical
13-21%of exam
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
- 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
- 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
- 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
Public first, client second, self last
Public safety winsOnly qualified workDisclose all conflictsReport violations
IRR vs MARR
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
- 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
- First duty
- Public health, safety, welfare240.15.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 field240.15.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 attacks240.15.C
Exam Clock
Agreement 2, tutorial 8, exam 320
Agreement 2 minTutorial 8 minExam 5 hr 20Break 25 minAppointment 5 hr 55
Scheduled vs Unscheduled Break
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
- Oxygen deficient
- Below 19.5 percent1910.146
- 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
- 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
- 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
Statics, dynamics, strength: 9-14 each
Statics 9-14Dynamics 9-14Strength 9-14Materials 6-9
Statics vs Dynamics
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
- 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
- Fluid Mechanics
- 12-18 questionsBiggest
- 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
Axial P/A, bending Mc/I, torsion Tr/J
Axial P over ABending Mc over ITorsion Tr over JShear VQ over Ib
Mass vs Area Inertia
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
- 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
- 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
- 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
- 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
Fluids 12-18 tops every knowledge area
Fluids 12-18Thermal 9-14Mechanics trio 9-14Math 8-12
Laminar vs Turbulent
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
- 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
- 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
Conduction k, convection h, radiation sigma
Conduction needs materialConvection needs flowRadiation needs no medium
First vs Second Law
First law
- Energy bookkeeping
- Allows any direction
- Heat plus work
Second law
- Entropy increases
- Sets allowed direction
- Caps efficiency
Amount vs direction
Thermodynamics + Heat
- 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
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
- Instrumentation and Controls
- 4-6 questionsSmallest
- 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
Series
- Same current everywhere
- Resistances add
- Voltage divides
Parallel
- Same voltage across
- Conductances add
- Current divides
Shared current vs voltage
Chemistry
- 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
- 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
- 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
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