100+ Free FE Industrial & Systems Practice Questions

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Question 1

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A solid right circular cone has radius r = 3 m and height h = 6 m. What is its volume?

18π m³

54π m³

36π m³

12π m³

to track

2026 Statistics

Key Facts: FE Industrial & Systems Exam

110

Exam Questions

NCEES

5h 20m

Exam Time

NCEES (6-hour appointment)

$175

Exam Fee

NCEES 2026

Knowledge Areas

NCEES CBT specs

Pearson VUE

Test Provider

NCEES

On-screen

Reference Handbook

Closed book, electronic

FE Industrial & Systems has 110 questions in 5h 20m of testing (6-hour appointment) at Pearson VUE for $175. Highest-weighted areas are Probability & Statistics (10-15 q) and the four 9-14 q blocks: Engineering Economics, Modeling & Quantitative Analysis, Manufacturing/Service/Production, Facilities & Supply Chain, and Quality. Closed book with on-screen NCEES Reference Handbook.

Sample FE Industrial & Systems Practice Questions

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

1A solid right circular cone has radius r = 3 m and height h = 6 m. What is its volume?

A.18π m³

B.54π m³

C.36π m³

D.12π m³

Explanation: Cone volume V = (1/3)πr²h = (1/3)π(3²)(6) = (1/3)π(54) = 18π m³. This formula appears in the analytic-geometry section of the NCEES FE Reference Handbook.

2Evaluate the indefinite integral ∫(6x² + 4x) dx.

A.2x³ + 2x² + C

B.12x + 4 + C

C.6x³ + 4x² + C

D.2x³ + 4x + C

Explanation: Integrating term-by-term using the power rule: ∫6x² dx = 6·(x³/3) = 2x³ and ∫4x dx = 4·(x²/2) = 2x². Adding the constant of integration gives 2x³ + 2x² + C.

3Given the matrices A = [[1,2],[3,4]] and B = [[5,6],[7,8]], what is the (1,1) entry of the product AB?

A.19

B.23

C.5

D.12

Explanation: The (1,1) entry of AB is the dot product of row 1 of A and column 1 of B: (1)(5) + (2)(7) = 5 + 14 = 19. Matrix multiplication is in the linear-algebra section of the FE Reference Handbook.

4Compute the derivative of f(x) = ln(3x²).

A.2/x

B.1/(3x²)

C.6x/(3x²) = 2/x², treated as separate terms

D.3/x

Explanation: Using the chain rule: f'(x) = (1/(3x²))·(6x) = 6x/(3x²) = 2/x. Equivalently, ln(3x²) = ln 3 + 2 ln x, whose derivative is 0 + 2/x = 2/x.

5What is the determinant of the matrix [[2, 5],[1, 3]]?

A.1

B.11

C.6

D.−1

Explanation: For a 2×2 matrix [[a,b],[c,d]], det = ad − bc = (2)(3) − (5)(1) = 6 − 5 = 1. A non-zero determinant means the matrix is invertible.

6Find the geometric series sum 4 + 8 + 16 + 32 + 64.

A.124

B.120

C.128

D.100

Explanation: Geometric series sum Sₙ = a(1−rⁿ)/(1−r) with a = 4, r = 2, n = 5: S = 4(1−32)/(1−2) = 4(31) = 124. Direct addition also gives 4+8+16+32+64 = 124.

7An industrial engineer must compute the surface area swept by rotating a 2 m × 3 m rectangle about its longer side. What is the resulting cylindrical lateral surface area (no caps)?

A.12π m²

B.6π m²

C.18π m²

D.24π m²

Explanation: Rotating a rectangle of width w = 2 m and height h = 3 m about the 3-m side generates a cylinder with radius r = 2 m and height h = 3 m. Lateral surface area = 2πrh = 2π(2)(3) = 12π m².

8A 200 kg crate slides down a frictionless 30° incline. What is its acceleration along the incline (g = 9.81 m/s²)?

A.4.9 m/s²

B.9.81 m/s²

C.8.5 m/s²

D.2.45 m/s²

Explanation: On a frictionless incline, a = g·sin(θ) = 9.81·sin(30°) = 9.81·0.5 ≈ 4.9 m/s². Mass cancels out — acceleration depends only on gravity and incline angle.

9A simple resistive DC circuit has V = 24 V across R = 8 Ω. What is the power dissipated?

A.72 W

B.192 W

C.3 W

D.24 W

Explanation: P = V²/R = (24)²/8 = 576/8 = 72 W. Equivalently, I = V/R = 3 A and P = VI = 24·3 = 72 W. Both forms appear in the NCEES handbook.

10An ideal gas is heated at constant volume. Which thermodynamic quantity must remain ZERO?

A.Work done by the gas

B.Change in internal energy

C.Heat added

D.Change in temperature

Explanation: At constant volume, dV = 0, so boundary work W = ∫P dV = 0. By the first law (Q = ΔU + W), all heat added goes into raising internal energy and temperature.

About the FE Industrial & Systems Exam

The FE Industrial and Systems exam is a 110-question, computer-based test (CBT) administered by NCEES at Pearson VUE centers. It is one of seven FE discipline exams and is designed for graduating industrial/systems engineering students or recent graduates pursuing the EI/EIT designation, the first step toward PE licensure. The exam covers 13 knowledge areas including engineering economics, probability and statistics, modeling and quantitative analysis (LP, queuing, Markov), manufacturing/service systems, supply chain and facilities, human factors and ergonomics, work design, quality (SPC, Six Sigma), and systems engineering. Examinees use an electronic NCEES FE Reference Handbook during the test.

Questions

110 scored questions

Time Limit

5 hours 20 minutes

Passing Score

Scaled (NCEES does not publish a fixed percentage)

Exam Fee

$175 (NCEES (Pearson VUE))

FE Industrial & Systems Exam Content Outline

6-9 q

Mathematics

Analytic geometry, calculus (derivatives, integrals, series), and linear algebra (matrix operations, vectors)

4-6 q

Engineering Sciences

Thermodynamics and fluid mechanics; statics, dynamics, and materials; electricity and electrical circuits

4-6 q

Ethics and Professional Practice

NCEES Model Rules, codes of ethics, agreements and contracts, professional/legal responsibility, public protection

9-14 q

Engineering Economics

Time value of money, alternatives evaluation (PW, EAC, IRR), cost analyses (break-even, sunk, replacement), depreciation and taxes (MACRS)

10-15 q

Probability and Statistics

Probabilities, distributions, central limit theorem, confidence intervals, hypothesis testing, regression, design of experiments (ANOVA)

9-14 q

Modeling and Quantitative Analysis

Data and analytics, linear programming and optimization (LP, IP, sensitivity), stochastic models (queuing M/M/1, Markov, simulation)

8-12 q

Engineering Management

Planning and motivation, project management (PERT/CPM, earned value, agile), KPIs/balanced scorecard, decision trees and risk

9-14 q

Manufacturing, Service, and Production Systems

Manufacturing processes, throughput and line balancing, forecasting, MRP and aggregate planning, lean systems

9-14 q

Facilities and Supply Chain

Layout types and from/to charts, capacity and material handling, supply chain design and distribution networks

8-12 q

Human Factors, Ergonomics, and Safety

Displays/controls, OSHA workplace hazards and noise PEL, ergonomics (NIOSH lifting equation, RULA/REBA, anthropometry, macroergonomics)

7-11 q

Work Design

Methods analysis and motion economy, time study and predetermined time systems (MTM, MOST), work sampling, learning curves

9-14 q

Quality

Six Sigma DMAIC, TQM, QFD, Taguchi loss function, fishbone, control charts (X-bar/R, p, c, np), process capability Cp/Cpk, OC curves

8-12 q

Systems Engineering, Analysis, and Design

Requirements analysis, functional analysis and configuration management, FMEA and fault trees, life-cycle cost, reliability (MTTF, MTBF, series/parallel)

How to Pass the FE Industrial & Systems Exam

What You Need to Know

Passing score: Scaled (NCEES does not publish a fixed percentage)
Exam length: 110 questions
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 Industrial & Systems Study Tips from Top Performers

1Download and study the NCEES FE Reference Handbook (free from MyNCEES) — every exam formula is in it, but only if you know where to look

2Buy and complete the official NCEES FE Industrial practice exam — it sets the bar for question style and difficulty

3Drill engineering economics — present worth, EAC, IRR, and incremental ROR consistently appear

4Practice queuing M/M/1 (Lq, Wq, ρ) and basic Markov chain stationary distributions until they're automatic

5Memorize the EOQ, line-balancing, and break-even formulas — they're high-yield calculation questions

6Be fluent in control-chart limits (X-bar UCL = μ + 3σ/√n, p-chart UCL with binomial SE) and Cp/Cpk

7Review NIOSH lifting equation logic (LI = Load/RWL) and the OSHA hierarchy of hazard controls

8Practice time-study calculations: standard time = observed × performance rating × (1 + allowance)

9Re-read NCEES Model Rules of Professional Conduct — ethics questions are gimmes if you know them

10Take at least one full-length 110-question timed simulation to build pacing (~3 min per question)

Frequently Asked Questions

How many questions are on the FE Industrial and Systems exam?

110 multiple-choice questions delivered as a computer-based test (CBT) at Pearson VUE. The 6-hour appointment includes an 8-minute tutorial, 5 hours 20 minutes of exam time, a 25-minute scheduled break, and a brief survey.

What does the FE Industrial exam cost?

The NCEES exam fee is $175 in 2026. Some state licensing boards add a separate application fee. Pearson VUE rescheduling fees may apply if you change your appointment within the cutoff window.

What topics carry the most weight?

Probability and Statistics is the largest single area (10-15 questions). Five other areas — Engineering Economics, Modeling and Quantitative Analysis, Manufacturing/Service/Production, Facilities and Supply Chain, and Quality — each contribute 9-14 questions, so together they make up roughly half the exam.

Is the FE Industrial exam open book?

It is closed book, but NCEES provides a searchable electronic FE Reference Handbook on screen. Practicing with the digital handbook (free download from MyNCEES) is essential — knowing where each formula lives saves test time.

What calculator is allowed?

Only NCEES-approved calculators: Casio FX-115 series, HP 33s/35s, and TI-30X/TI-36X series. An on-screen calculator is also provided. Confirm the current approved list at ncees.org before exam day.

How do FE Industrial pass rates compare to other FE disciplines?

FE Industrial first-time pass rates typically run in the high 50s to mid 60s percent — broadly in line with the all-disciplines average. Pass rates depend heavily on whether candidates work through the NCEES practice exam and the FE Reference Handbook.