200+ Free FE Exam Practice Questions

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Question 1

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What is the derivative of f(x) = 3x³ + 2x² - 5x + 7?

9x² + 4x - 5

9x³ + 4x² - 5x

6x² + 4x - 5

x³ + x² - 5x + C

to track

2026 Statistics

Key Facts: FE Exam Exam

~70%

Avg. Pass Rate

Varies by discipline

110

Exam Questions

NCEES

200-300 hrs

Study Time

Recommended

5h 20m

Exam Duration

NCEES

$175

Exam Fee

NCEES

Open Book

Reference Handbook

On-screen

The FE exam has 110 questions in 5 hours 20 minutes (including break). Pass rates vary by discipline (50-80%). The exam is open-book with a searchable NCEES reference handbook on-screen.

Sample FE Exam Practice Questions

Try these sample questions to test your FE Exam exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 200+ question experience with AI tutoring.

1What is the derivative of f(x) = 3x³ + 2x² - 5x + 7?

A.9x² + 4x - 5

B.9x³ + 4x² - 5x

C.6x² + 4x - 5

D.x³ + x² - 5x + C

Explanation: To find the derivative, apply the power rule: d/dx(xⁿ) = nxⁿ⁻¹. For 3x³: 3 × 3x² = 9x². For 2x²: 2 × 2x = 4x. For -5x: -5 × 1 = -5. The constant 7 disappears. Therefore, f'(x) = 9x² + 4x - 5.

2Evaluate the definite integral ∫₀² (4x + 3) dx.

A.14

B.10

C.16

D.8

Explanation: Using the power rule for integration: ∫(4x + 3)dx = 2x² + 3x + C. Evaluating from 0 to 2: [2(2)² + 3(2)] - [2(0)² + 3(0)] = [8 + 6] - [0] = 14.

3Solve the system of linear equations: 2x + 3y = 12 and x - y = 1.

A.x = 3, y = 2

B.x = 4, y = 1

C.x = 2, y = 3

D.x = 1, y = 4

Explanation: From the second equation: x = y + 1. Substituting into the first: 2(y + 1) + 3y = 12, so 2y + 2 + 3y = 12, thus 5y = 10, and y = 2. Therefore x = 2 + 1 = 3.

4What is the general solution to the differential equation dy/dx = 2x?

A.y = x² + C

B.y = 2x² + C

C.y = x²/2 + C

D.y = 2x + C

Explanation: Integrating both sides: ∫dy = ∫2x dx, so y = x² + C, where C is the constant of integration. This is the general solution to this first-order ordinary differential equation.

5A matrix A has eigenvalues λ₁ = 2 and λ₂ = 5. What is the determinant of A?

A.10

B.7

C.3

D.Cannot be determined

Explanation: For a square matrix, the determinant equals the product of all eigenvalues. Therefore, det(A) = λ₁ × λ₂ = 2 × 5 = 10. This is a fundamental property connecting eigenvalues to the determinant.

6Using Euler's method with step size h = 0.5, approximate y(1) for dy/dx = x + y, given y(0) = 1.

A.2.5

B.2.0

C.3.0

D.1.75

Explanation: Euler's method: yₙ₊₁ = yₙ + h·f(xₙ, yₙ). Step 1 (x=0 to 0.5): y₁ = 1 + 0.5(0 + 1) = 1.5. Step 2 (x=0.5 to 1.0): y₂ = 1.5 + 0.5(0.5 + 1.5) = 1.5 + 1.0 = 2.5.

7Find the inverse Laplace transform of F(s) = 1/(s² + 4).

A.(1/2)sin(2t)

B.cos(2t)

C.sin(2t)

D.(1/2)cos(2t)

Explanation: Using the standard Laplace transform pair: L⁻¹{a/(s² + a²)} = sin(at). Here we have 1/(s² + 4) = 1/(s² + 2²), which equals (1/2) × 2/(s² + 2²). Therefore, L⁻¹{1/(s² + 4)} = (1/2)sin(2t).

8What is the Fourier series representation of a square wave with period 2π and amplitude 1?

A.(4/π)[sin(t) + (1/3)sin(3t) + (1/5)sin(5t) + ...]

B.(4/π)[cos(t) + (1/3)cos(3t) + (1/5)cos(5t) + ...]

C.(2/π)[sin(t) + sin(2t) + sin(3t) + ...]

D.(4/π)[sin(t) - (1/2)sin(2t) + (1/3)sin(3t) - ...]

Explanation: An odd square wave has only sine terms with odd harmonics. The coefficient aₙ = 4/(nπ) for odd n. The series is (4/π)[sin(t) + (1/3)sin(3t) + (1/5)sin(5t) + ...]. This is a standard Fourier series result for square waves.

9A fair die is rolled. What is the probability of rolling a number greater than 4?

A.1/3

B.1/2

C.1/6

D.2/3

Explanation: The favorable outcomes are 5 and 6, which is 2 outcomes out of 6 possible outcomes. Therefore, P(>4) = 2/6 = 1/3.

10The mean of a data set is 50 and the standard deviation is 5. What percentage of data falls within one standard deviation of the mean (assuming normal distribution)?

A.68%

B.95%

C.99.7%

D.50%

Explanation: According to the empirical rule (68-95-99.7 rule) for normal distributions, approximately 68% of data falls within one standard deviation of the mean (between μ-σ and μ+σ).

About the FE Exam Exam

The FE exam is the first step toward Professional Engineer (PE) licensure. It is offered in seven disciplines: Chemical, Civil, Electrical/Computer, Environmental, Industrial/Systems, Mechanical, and Other Disciplines. Passing earns the Engineer Intern (EI) designation.

Questions

110 scored questions

Time Limit

5 hours 20 minutes

Passing Score

Scaled (varies by discipline)

Exam Fee

$175 (National Council of Examiners for Engineering and Surveying (NCEES))

FE Exam Exam Content Outline

25%

Mathematics & Statistics

Calculus, differential equations, linear algebra, probability, statistics, numerical methods

20%

Engineering Sciences

Statics, dynamics, mechanics of materials, fluid mechanics, thermodynamics, heat transfer

20%

Discipline-Specific Topics

Topics specific to chosen discipline (Civil, Mechanical, Electrical, Chemical, etc.)

15%

Ethics & Professional Practice

NCEES Model Rules, professional ethics, licensure, public safety obligations

10%

Engineering Economics

Time value of money, present/future worth, annual cost, rate of return, benefit-cost

10%

Computational Tools

Spreadsheet analysis, programming concepts, numerical methods, reference handbook usage

How to Pass the FE Exam Exam

What You Need to Know

Passing score: Scaled (varies by discipline)
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 Exam Study Tips from Top Performers

1Study with the NCEES FE Reference Handbook — know where every formula is located

2Focus on math, engineering sciences, and discipline-specific content

3Practice with an NCEES-approved calculator exclusively

4Take the NCEES official practice exam

5Build time management — approximately 3 minutes per question

6Review engineering economics: PV, FV, annual worth, rate of return

Frequently Asked Questions

What is the FE exam pass rate?

Pass rates vary: FE Civil ~67%, FE Mechanical ~72%, FE Electrical ~65%, FE Chemical ~75%, FE Other ~55%.

Which discipline should I take?

Take the discipline matching your degree. If no match, consider FE Other Disciplines. The discipline doesn't need to match your PE license.

Can I use a calculator?

Only NCEES-approved: Casio FX-115 series and TI-30X/TI-36X series. An on-screen calculator is also provided.

How long should I study?

Most study 200-300 hours over 2-4 months. Focus on the NCEES FE Reference Handbook.