100+ Free FE Mechanical Practice Questions

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Question 1

Score: 0/0

Evaluate the limit lim(x→0) (sin 3x)/(5x).

3/5

5/3

to track

2026 Statistics

Key Facts: FE Mechanical Exam

110

Exam Questions

NCEES

5h 20m

Testing Time

NCEES

$175

Exam Fee

NCEES

~65%

Pass Rate (first-time)

NCEES Jan 2026

Knowledge Areas

NCEES FE Mechanical CBT specs

Pearson VUE

Exam Provider

NCEES

FE Mechanical is a 110-question CBT delivered in 5 hours 20 minutes of testing time (6-hour total appointment) with a $175 NCEES fee. The exam uses the NCEES FE Reference Handbook on-screen, an NCEES-approved calculator, and the current FE Mechanical CBT specifications. Pass rates for first-time takers are approximately 65%. Largest content areas are Dynamics/Vibrations, Fluid Mechanics, Thermodynamics, and Mechanical Design (each 9-14 questions). Passing earns the EI/EIT designation in most jurisdictions.

Sample FE Mechanical Practice Questions

Try these sample questions to test your FE Mechanical exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the limit lim(x→0) (sin 3x)/(5x).

A.0

B.3/5

C.1

D.5/3

Explanation: Apply L'Hopital's rule or the standard limit sin(ax)/x → a as x→0. Then (sin 3x)/(5x) = (1/5)·(sin 3x)/x → (1/5)·3 = 3/5.

2Find the derivative dy/dx of y = x^2 · ln(x).

A.2x · ln(x)

B.x + 2x · ln(x)

C.x(1 + 2 ln x)

D.2x/x

Explanation: Use the product rule: dy/dx = (2x)·ln(x) + x^2·(1/x) = 2x ln x + x = x(1 + 2 ln x). Always combine like terms when factoring is possible.

3Solve the ODE dy/dx + 2y = 0 with y(0) = 5.

A.y = 5e^(2x)

B.y = 5e^(-2x)

C.y = 5 - 2x

D.y = 2e^(-5x)

Explanation: This is a separable / first-order linear ODE. Separating: dy/y = -2 dx, so ln|y| = -2x + C, giving y = A e^(-2x). With y(0) = 5, A = 5. Hence y = 5 e^(-2x).

4Two vectors A = 3i + 4j and B = i - 2j. Compute A · B.

A.-5

B.5

C.11

D.-11

Explanation: Dot product: A · B = (3)(1) + (4)(-2) = 3 - 8 = -5. The dot product yields a scalar that captures co-directional magnitude.

5Evaluate ∫(0 to 2) (3x^2 + 2) dx.

A.10

B.12

C.14

D.16

Explanation: Antiderivative is x^3 + 2x. Evaluating: (8 + 4) - (0 + 0) = 12. Always check by plugging in both bounds.

6The eigenvalues of the matrix [[4, 2],[1, 3]] are:

A.1 and 6

B.2 and 5

C.3 and 4

D.0 and 7

Explanation: Characteristic equation: (4-λ)(3-λ) - 2 = λ^2 - 7λ + 10 = 0. Factor: (λ-2)(λ-5) = 0, giving λ = 2 or λ = 5. Always check by trace = sum and determinant = product.

7Apply Newton's method to find a root of f(x) = x^2 - 5 starting at x0 = 2. What is x1?

A.2.20

B.2.25

C.2.30

D.2.50

Explanation: Newton iteration: x1 = x0 - f(x0)/f'(x0). f(2) = -1, f'(x) = 2x → f'(2) = 4. So x1 = 2 - (-1)/4 = 2 + 0.25 = 2.25.

8What is the Laplace transform of f(t) = e^(-3t)?

A.1/(s+3)

B.1/(s-3)

C.s/(s+3)

D.3/(s+3)

Explanation: From the standard table, L{e^(at)} = 1/(s-a). With a = -3, this gives 1/(s+3). The Laplace transform requires s > -a for convergence.

9A discrete random variable X has P(X=0) = 0.3, P(X=1) = 0.5, and P(X=2) = 0.2. Find E[X].

A.0.7

B.0.9

C.1.0

D.1.2

Explanation: Expected value: E[X] = Σ x·P(x) = 0·0.3 + 1·0.5 + 2·0.2 = 0.5 + 0.4 = 0.9. The probabilities must sum to 1 (verified: 0.3+0.5+0.2 = 1.0).

10The mean of a normal distribution is 50 and the standard deviation is 10. What is the probability that a sample is between 40 and 60? (use 68-95-99.7 rule)

A.~50%

B.~68%

C.~95%

D.~99.7%

Explanation: The interval [μ-σ, μ+σ] = [40, 60] is exactly ±1 standard deviation. By the empirical rule for a normal distribution, ≈68.27% of data falls within ±1σ.

About the FE Mechanical Exam

The FE Mechanical exam is one of seven NCEES Fundamentals of Engineering discipline exams and is the first national licensure step toward becoming a Professional Engineer (PE). It is a 110-question computer-based exam covering 15 mechanical engineering knowledge areas including statics, dynamics, mechanics of materials, fluid mechanics, thermodynamics, heat transfer, mechanical design, and controls. Most candidates take it during their senior year of an EAC/ABET-accredited engineering program or shortly after graduation.

Assessment

110 multiple-choice computer-based questions with on-screen NCEES FE Reference Handbook

Time Limit

5 hours 20 minutes

Passing Score

Scaled cut score (NCEES does not publish a fixed percentage)

Exam Fee

$175 (NCEES (Pearson VUE))

FE Mechanical Exam Content Outline

8-12 questions

Mathematics

Analytic geometry, calculus, ordinary differential equations, linear algebra, vector analysis, and numerical methods.

4-6 questions

Probability and Statistics

Measures of central tendency and dispersion, probability distributions, expected value, hypothesis testing, regression.

3-5 questions

Computational Tools

Spreadsheets, structured programming concepts, numerical methods, and reference handbook navigation.

3-5 questions

Ethics and Professional Practice

NCEES Model Rules, public welfare obligations, conflicts of interest, intellectual property, and licensure responsibilities.

3-5 questions

Engineering Economics

Time value of money, present/future worth, annual cost, rate of return, depreciation, and benefit-cost analysis.

5-8 questions

Electricity and Magnetism

DC and AC circuit fundamentals, three-phase power, motors, transformers, and basic electromagnetics.

8-12 questions

Statics

Force resultants, equilibrium, free body diagrams, frames and trusses, centroids, moments of inertia, and friction.

9-14 questions

Dynamics, Kinematics, and Vibrations

Particle and rigid-body kinematics, Newton's laws, work-energy, impulse-momentum, free and forced vibrations, transmissibility.

8-12 questions

Mechanics of Materials

Axial and torsional stress, bending and shear in beams, Mohr's circle, deflections, columns and Euler buckling, fatigue.

6-9 questions

Material Properties and Processing

Material classes and properties, stress-strain behavior, heat treatment, manufacturing processes, hardness, and corrosion.

9-14 questions

Fluid Mechanics

Fluid statics, Bernoulli equation, Reynolds number, pipe flow and Darcy-Weisbach, control volume momentum, pumps, NPSH.

9-14 questions

Thermodynamics

First and second laws, ideal gas, properties, power and refrigeration cycles (Otto, Diesel, Brayton, Rankine), psychrometrics.

5-8 questions

Heat Transfer

Conduction, convection, radiation, fins, and basic heat exchanger analysis (LMTD, effectiveness-NTU).

4-7 questions

Measurements, Instrumentation, and Controls

Sensors, signal conditioning, uncertainty propagation, transfer functions, time/frequency response, basic feedback control.

9-14 questions

Mechanical Design and Analysis

Shaft design, fasteners and welds, bearings (L10 life), gears, springs, pressure vessels, design for fatigue and static loading.

How to Pass the FE Mechanical Exam

What You Need to Know

Passing score: Scaled cut score (NCEES does not publish a fixed percentage)
Assessment: 110 multiple-choice computer-based questions with on-screen NCEES FE Reference Handbook
Time limit: 5 hours 20 minutes
Exam fee: $175

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

FE Mechanical Study Tips from Top Performers

1Download the current NCEES FE Reference Handbook and practice with it open during every study session — handbook lookup speed determines exam pacing.

2Allocate study time proportionally: spend the most hours on Dynamics/Vibrations, Fluid Mechanics, Thermodynamics, Mechanical Design, Statics, and Mechanics of Materials.

3Memorize the few formulas the handbook does NOT include explicitly (e.g., basic vector identities, trigonometric values).

4Practice unit conversions in both SI and US customary; FE Mechanical mixes both systems freely.

5Use only an NCEES-approved calculator (Casio FX-115, TI-30X/36X, or HP 35s) and learn its statistical and equation-solver functions cold.

6Work full-length 110-question timed practice exams at least twice — pace target is roughly 3 minutes per question with handbook lookup.

7Review the NCEES Model Rules and ethics scenarios; ethics questions reward the answer that prioritizes public health, safety, and welfare.

8Master the section-modulus, area, and moment-of-inertia tables in the handbook so you don't recompute them under time pressure.

9Build intuition for pump/turbine power calculations (P = ρgQh / η) and three-phase electrical power (P = √3 V I cosφ) — both appear repeatedly.

10Take the official NCEES FE Mechanical practice exam late in your prep to calibrate against actual question difficulty and on-screen format.

Frequently Asked Questions

How many questions are on the FE Mechanical exam?

The FE Mechanical exam has 110 multiple-choice questions delivered as a computer-based test. The total appointment is 6 hours, including a tutorial and a 25-minute scheduled break, leaving 5 hours 20 minutes of actual testing time. NCEES uses an on-screen reference handbook and accepts only NCEES-approved calculators (Casio FX-115 series, TI-30X, TI-36X, or HP 35s).

What is the FE Mechanical pass rate?

NCEES reported approximately 65% first-time pass rate for FE Mechanical in early 2026. Pass rates are higher for those who test within 12 months of graduation from an EAC/ABET-accredited program. Repeat-taker rates are typically 30-40%. NCEES does not publish a fixed numeric cut score — results are reported as pass/fail.

Which content areas have the most questions on FE Mechanical?

The largest sections are Dynamics/Kinematics/Vibrations, Fluid Mechanics, Thermodynamics, and Mechanical Design and Analysis — each with 9-14 questions. Statics and Mechanics of Materials each have 8-12. Together these six areas account for over half the exam, so they should receive the heaviest study focus.

How much does the FE Mechanical exam cost?

The NCEES exam fee is $175. State licensing boards may charge an additional application or processing fee that varies by jurisdiction. The fee covers a single attempt; retakes are $175 each. Pearson VUE does not charge an additional test-center fee.

How long should I study for FE Mechanical?

Most candidates spend 150-300 hours of focused preparation over 2-4 months. Recent graduates from ABET-accredited programs may need less time because the material is fresh. The most important resource is the NCEES FE Reference Handbook — practice every problem with the on-screen handbook open to build lookup speed.

Can I take FE Mechanical even if my degree is not in mechanical engineering?

Yes. NCEES does not require the FE discipline to match your degree. However, FE Mechanical assumes baseline familiarity with mechanical engineering coursework (thermodynamics, fluid mechanics, machine design). Candidates with non-mechanical backgrounds often choose FE Other Disciplines instead, which has broader content.