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Exam Review

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 review concepts for the FE Exam exam. 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) = 3x^3 + 2x^2 - 5x + 7?
A.9x^2 + 4x - 5
B.9x^3 + 4x^2 - 5x
C.6x^2 + 4x - 5
D.x^3 + x^2 - 5x + C
Explanation: To find the derivative, apply the power rule: d/dx(x^n) = nx^(n-1). For 3x^3: 3 x 3x^2 = 9x^2. For 2x^2: 2 x 2x = 4x. For -5x: -5 x 1 = -5. The constant 7 disappears. Therefore, f'(x) = 9x^2 + 4x - 5.
2Evaluate the definite integral integral_0^2 (4x + 3) dx.
A.14
B.10
C.16
D.8
Explanation: Using the power rule for integration: integral (4x + 3)dx = 2x^2 + 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 = x^2 + C
B.y = 2x^2 + C
C.y = x^2/2 + C
D.y = 2x + C
Explanation: Integrating both sides: integral dy = integral 2x dx, so y = x^2 + 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 lambda_1 = 2 and lambda_2 = 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) = lambda_1 x lambda_2 = 2 x 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: y_(n+1) = y_n + h.f(x_n, y_n). Step 1 (x=0 to 0.5): y_1 = 1 + 0.5(0 + 1) = 1.5. Step 2 (x=0.5 to 1.0): y_2 = 1.5 + 0.5(0.5 + 1.5) = 1.5 + 1.0 = 2.5.
7Find the inverse Laplace transform of F(s) = 1/(s^2 + 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/(s^2 + a^2)} = sin(at). Here we have 1/(s^2 + 4) = 1/(s^2 + 2^2), which equals (1/2) x 2/(s^2 + 2^2). Therefore, L^(-1){1/(s^2 + 4)} = (1/2)sin(2t).
8What is the Fourier series representation of a square wave with period 2pi and amplitude 1?
A.(4/pi)[sin(t) + (1/3)sin(3t) + (1/5)sin(5t) + ...]
B.(4/pi)[cos(t) + (1/3)cos(3t) + (1/5)cos(5t) + ...]
C.(2/pi)[sin(t) + sin(2t) + sin(3t) + ...]
D.(4/pi)[sin(t) - (1/2)sin(2t) + (1/3)sin(3t) - ...]
Explanation: An odd square wave has only sine terms with odd harmonics. The coefficient a_n = 4/(npi) for odd n. The series is (4/pi)[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 mu-sigma and mu+sigma).

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.

Exam sponsor: National Council of Examiners for Engineering and Surveying (NCEES). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

110 questions

Time Limit

5 hours 20 minutes

Passing Score

Scaled (varies by discipline)

Exam / Certification Fees

$175

Exam sponsor website

Reported exam pass rate: ~70%. varies by discipline (50-80%) This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

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

Preparing for 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 / certification fees: $175 Official sources

Using Our Practice Resources

  • Work through all 200 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

FE Exam: Suggested Study Strategy

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.