A solid right circular cone has radius r = 3 m and height h = 6 m. What is its volume?
Mathematics
Question · Easy
Where does this beam break first?
Short
Evaluate the indefinite integral ∫(6x² + 4x) dx.
Chapter 1: Exam Overview, CBT Strategy & Handbook Navigation
1.1 FE Industrial Exam Structure, CBT Logistics, and Pacing
Study guide
Given the matrices A = [[1,2],[3,4]] and B = [[5,6],[7,8]], what is the (1,1) entry of the product AB?
Engineering Exam Prep Podcast
Listen on Spotify
Podcast
Compute the derivative of f(x) = ln(3x²).
What is the determinant of the matrix [[2, 5],[1, 3]]?
Question · Medium
Fishbone diagram, x-rayed
Find the geometric series sum 4 + 8 + 16 + 32 + 64.
1.2 Using the NCEES FE Reference Handbook and Approved Calculators
An 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)?
Question · Hard
A 200 kg crate slides down a frictionless 30° incline. What is its acceleration along the incline (g = 9.81 m/s²)?
Engineering Sciences
A simple resistive DC circuit has V = 24 V across R = 8 Ω. What is the power dissipated?
OSHA noise limits
An ideal gas is heated at constant volume. Which thermodynamic quantity must remain ZERO?
Chapter 2: Mathematics for Industrial Engineers
2.1 Analytic Geometry, Coordinate Systems, and Trigonometry
Water flows through a 0.05 m diameter pipe at 2 m/s. What is the volumetric flow rate?
Under the NCEES Model Rules, an engineer's PARAMOUNT obligation is to:
Ethics And Professional Practice
An engineer is offered a 'finder's fee' by a vendor for steering a client toward that vendor's product. Under NCEES Model Rules, the engineer should:
The longest way home
An EI (Engineer Intern) prepares plans that will be sealed by a licensed PE. What is required for the PE to seal them?
2.2 Calculus: Differential, Integral, and Series Approximations
An industrial engineer discovers that a client's product violates an OSHA regulation. The client refuses to fix it. What is the engineer's most ethically correct action under NCEES rules?
Which contract type places the MOST cost risk on the contractor (and least on the owner)?
Compute the present worth of $10,000 received 5 years from now at 8% annual interest, compounded annually.
Engineering Economics
What uniform annual payment over 4 years at 6% is equivalent to a present value of $20,000?
2.3 Linear Algebra: Matrix Operations, Systems of Equations, and Vectors
Project A: invest $50,000 today, return $80,000 in year 5. Project B: invest $50,000 today, return $15,000/year for years 1–5. At MARR = 10%, which has the higher net present worth (NPW)?
A nominal annual rate of 12% compounded monthly corresponds to what effective annual rate?
A factory has fixed cost FC = $50,000/yr, variable cost v = $20/unit, and selling price p = $45/unit. What is the break-even production quantity?
Equipment cost $100,000, salvage $20,000, useful life 5 years. Compute year-1 depreciation by the straight-line method.
Chapter 3: Engineering Sciences Core
3.1 Thermodynamics Fundamentals and Fluid Flow Principles
Under MACRS, which property class typically applies to manufacturing equipment?
Two mutually exclusive projects: A: −$10k, +$13k @ year 1 (IRR 30%); B: −$10k, +$25k @ year 5 (IRR 20%). At MARR = 10%, by INCREMENTAL ROR analysis you should choose:
Inflation rate f = 4%, real interest rate i = 6%. What is the market (combined) interest rate?
Bag A holds 3 red and 7 blue balls. You draw two without replacement. P(both red) =
Probability And Statistics
3.2 Statics, Dynamics, and Mechanics of Materials Core
How many distinct ways can a committee of 3 be selected from 8 candidates (order doesn't matter)?
X is normal with μ = 50, σ = 5. Approximately what fraction of values fall between 40 and 60?
A sample of 25 yields x̄ = 100 with known σ = 10. Construct a 95% confidence interval for μ.
A test of H₀: μ = 50 vs H₁: μ ≠ 50 with α = 0.05 yields p = 0.03. The correct conclusion is:
3.3 Electrical Circuits, DC/AC Analysis, and Power in Industrial Systems
Linear regression of y on x yields a correlation coefficient r = −0.85. What does this indicate?
An ANOVA F-test compares three group means. F-statistic = 4.2, F-critical (α = 0.05) = 3.5. Conclusion?
Type I error in hypothesis testing is:
An exponentially distributed time-to-failure has mean 100 hours. What is the probability the device survives at least 50 hours?
Chapter 4: Ethics and Professional Practice
4.1 NCEES Model Rules of Professional Conduct and Technical Society Ethics
Loading more…