FE Practice

FE Practice Problems: Free Diagnostic + Solved Examples

Page role: This page owns general FE practice intent: free diagnostic routing, solved example habits, and next practice actions. Use discipline study guides for topic planning and handbook/reference guides for lookup workflow.
Quick answer: Start with a short mixed diagnostic, then route practice by discipline and weak topic. This page gives you the free practice entry point, a topic-feedback workflow, and 10 solved FE Electrical and Computer examples that demonstrate how to review an answer instead of just checking whether it is right.
Source note: NCEES publishes the official FE exam format, topic specifications, and calculator policy. Verify your current exam details on the official NCEES FE exam page and scheduling details through Pearson VUE for NCEES. The free-practice routing below uses FE Test Prep's local bank coverage and topic tagging; it is an independent study workflow, not an official NCEES scoring model.

The best FE practice plan is not a random pile of questions. It starts with a diagnostic, identifies weak high-weight topics, then uses solved examples to repair the exact failure mode: concept gap, handbook lookup, calculator setup, unit error, or pacing problem.

FE Practice at a Glance

Current FE format110 questions in 5 hours 20 minutes of exam time
Time5 hours 20 minutes (~2.9 min/question)
Free practice20-question discipline diagnostic with instant topic feedback
Local coverage audit220 public free-practice questions and 9,710 app-view FE/PE questions as of May 23, 2026
ReferenceNCEES FE Reference Handbook (provided digitally)
Best next stepStart with diagnostic feedback, then drill weak high-weight topics.

Choose Your Practice Route

Use the first diagnostic to choose where the next study block should go. The full app keeps topic feedback by discipline so your next set is not just more questions; it is a response to what you missed.

RouteStart hereUse when
FE CivilFree Civil diagnosticWater, geotech, structural, transportation, or construction misses dominate.
FE Electrical and ComputerFree ECE diagnosticCircuits, power, electronics, digital systems, controls, or computer topics are weak.
FE MechanicalFree Mechanical diagnosticThermo, fluids, dynamics, mechanics of materials, or machine design need repair.
FE ChemicalFree Chemical diagnosticBalances, thermo, fluids, heat/mass transfer, or reaction engineering are slow.
FE EnvironmentalFree Environmental diagnosticWater, wastewater, air, groundwater, hydrology, or chemistry topics drive misses.
FE Other DisciplinesFree Other Disciplines diagnosticShared engineering science topics need broad coverage.

Solved FE Electrical and Computer Examples

The 10 problems below are FE Electrical and Computer examples. They are here because they show the review pattern every discipline needs: solve first, reveal the solution, then record the clue, formula source, unit path, calculator step, and wrong-answer trap.

How to use these problems: Try solving each problem on your own before revealing the solution. Time yourself—you should average about 3 minutes per problem on the real exam. Use only the FE Reference Handbook and an NCEES-approved calculator.

Problem 1: Mathematics — Solving a Quadratic Equation

Find all real solutions to the equation 2x2 − 5x − 3 = 0.

  • A) x = 3 and x = −0.5
  • B) x = 3 and x = 0.5
  • C) x = −3 and x = 0.5
  • D) x = −3 and x = −0.5
Show Solution

Answer: A

Apply the quadratic formula with a = 2, b = −5, c = −3:

x = (−b ± √(b2 − 4ac)) / (2a)

Step 1: Compute the discriminant: b2 − 4ac = (−5)2 − 4(2)(−3) = 25 + 24 = 49.

Step 2: Take the square root: √49 = 7.

Step 3: Solve for both roots:

x = (5 + 7) / 4 = 12 / 4 = 3

x = (5 − 7) / 4 = −2 / 4 = −0.5

The solutions are x = 3 and x = −0.5.

Problem 2: Circuit Analysis — KVL and Ohm's Law

A series circuit contains a 12 V DC source, a 4 Ω resistor (R1), and a 6 Ω resistor (R2). What is the voltage drop across R2?

  • A) 4.8 V
  • B) 7.2 V
  • C) 6.0 V
  • D) 5.0 V
Show Solution

Answer: B

Step 1: Find the total resistance: Rtotal = R1 + R2 = 4 + 6 = 10 Ω.

Step 2: Find the current using Ohm's law: I = V / Rtotal = 12 / 10 = 1.2 A.

Step 3: Find the voltage drop across R2: VR2 = I × R2 = 1.2 × 6 = 7.2 V.

You can verify with KVL: VR1 + VR2 = (1.2)(4) + (1.2)(6) = 4.8 + 7.2 = 12 V. ✓

Problem 3: Power Systems — Three-Phase Power Calculation

A balanced three-phase, wye-connected load draws a line current of 10 A from a 480 V (line-to-line) source at a power factor of 0.85 lagging. What is the total real power consumed by the load?

  • A) 4,080 W
  • B) 7,067 W
  • C) 8,314 W
  • D) 4,800 W
Show Solution

Answer: B

For a balanced three-phase system, total real power is given by:

P = √3 × VLL × IL × pf

Step 1: Substitute the given values:

P = √3 × 480 × 10 × 0.85

Step 2: Compute √3 × 480 = 1.732 × 480 = 831.4.

Step 3: Multiply: 831.4 × 10 × 0.85 = 7,067 W (approximately 7.07 kW).

Problem 4: Electronics — Inverting Op-Amp Gain

An inverting op-amp circuit has a feedback resistor Rf = 100 kΩ and an input resistor Rin = 10 kΩ. If the input voltage is Vin = 0.5 V, what is the output voltage? Assume the op-amp is ideal.

  • A) +5.0 V
  • B) −5.0 V
  • C) +0.05 V
  • D) −50.0 V
Show Solution

Answer: B

The closed-loop gain of an inverting op-amp is:

Av = −Rf / Rin

Step 1: Calculate the gain: Av = −100k / 10k = −10.

Step 2: Calculate the output: Vout = Av × Vin = (−10)(0.5) = −5.0 V.

The negative sign confirms the inverting configuration—the output is 180° out of phase with the input.

Problem 5: Digital Systems — Boolean Algebra Simplification

Simplify the Boolean expression: F = A·B + A·B' + A'·B

  • A) F = A + B
  • B) F = A · B
  • C) F = A ⊕ B
  • D) F = A' + B'
Show Solution

Answer: A

Step 1: Group the first two terms, factoring out A:

A·B + A·B' = A·(B + B') = A·1 = A

Step 2: Substitute back into the original expression:

F = A + A'·B

Step 3: Apply the absorption theorem (X + X'Y = X + Y):

F = A + B

You can verify by checking all four input combinations in a truth table—F is 0 only when both A and B are 0.

Tip for digital systems problems: Many Boolean algebra and logic gate questions can be solved faster by building a quick truth table than by algebraic manipulation. If the expression has 2–3 variables, a truth table takes under a minute and eliminates algebraic mistakes.

Problem 6: Signal Processing — Nyquist Sampling Theorem

An analog signal contains frequency components up to 4 kHz. According to the Nyquist-Shannon sampling theorem, what is the minimum sampling rate required to perfectly reconstruct the signal?

  • A) 2 kHz
  • B) 4 kHz
  • C) 8 kHz
  • D) 16 kHz
Show Solution

Answer: C

The Nyquist-Shannon sampling theorem states that to avoid aliasing, the sampling frequency must be at least twice the maximum frequency component of the signal:

fs ≥ 2 × fmax

Step 1: Identify fmax = 4 kHz.

Step 2: Calculate the minimum sampling rate: fs = 2 × 4 kHz = 8 kHz.

Any sampling rate below 8 kHz would cause aliasing, where higher-frequency components fold back into the lower-frequency range and corrupt the reconstructed signal.

Problem 7: Electromagnetics — Parallel-Plate Capacitance

A parallel-plate capacitor has plates of area A = 0.02 m2, a separation of d = 1 mm, and is filled with a dielectric of relative permittivity εr = 4. What is the capacitance? (Use ε0 = 8.854 × 10−12 F/m.)

  • A) 177 pF
  • B) 708 pF
  • C) 1.77 nF
  • D) 354 pF
Show Solution

Answer: B

The capacitance of a parallel-plate capacitor is:

C = ε0 × εr × A / d

Step 1: Substitute the values:

C = (8.854 × 10−12)(4)(0.02) / 0.001

Step 2: Compute the numerator: 8.854 × 10−12 × 4 × 0.02 = 7.083 × 10−13.

Step 3: Divide by d: 7.083 × 10−13 / 10−3 = 7.083 × 10−10 F.

Step 4: Convert: 7.083 × 10−10 F ≈ 708 pF.

Problem 8: Control Systems — Transfer Function Stability

A system has the open-loop transfer function G(s) = 10 / (s2 + 5s + 6). What are the poles of this system, and is it stable?

  • A) Poles at s = −2, −3; stable
  • B) Poles at s = 2, 3; unstable
  • C) Poles at s = −1, −6; stable
  • D) Poles at s = −2, 3; unstable
Show Solution

Answer: A

The poles are the roots of the denominator polynomial s2 + 5s + 6 = 0.

Step 1: Factor the denominator: s2 + 5s + 6 = (s + 2)(s + 3).

Step 2: Set each factor to zero: s = −2 and s = −3.

Step 3: Check stability: A linear time-invariant (LTI) system is stable if and only if all poles have negative real parts. Both −2 and −3 are negative, so the system is stable.

On the s-plane, both poles lie in the left-half plane (LHP), confirming BIBO stability.

Tip for control systems problems: When asked about stability, check the poles first. Factor the denominator polynomial (or use the quadratic formula), then check if all real parts are negative. For the FE exam, most stability problems can be solved by factoring alone—Routh-Hurwitz is only needed for higher-order systems.

Problem 9: Probability — Independent Events

A circuit board undergoes two independent quality tests. The probability of passing Test 1 is 0.95, and the probability of passing Test 2 is 0.90. What is the probability that a randomly selected board passes both tests?

  • A) 0.855
  • B) 0.925
  • C) 0.950
  • D) 0.810
Show Solution

Answer: A

For two independent events, the probability that both occur is the product of their individual probabilities:

P(A ∩ B) = P(A) × P(B)

Step 1: Identify the probabilities: P(Test 1) = 0.95, P(Test 2) = 0.90.

Step 2: Multiply: P(both) = 0.95 × 0.90 = 0.855.

There is an 85.5% chance that a board passes both tests. Note that this is lower than either individual probability—adding more independent tests always reduces the overall pass rate.

Problem 10: Engineering Economics — Present Worth Analysis

A piece of equipment costs $10,000 today and generates annual savings of $3,000 for 5 years. If the interest rate is 8% per year, what is the net present worth (NPW) of this investment?

  • A) $1,978
  • B) $5,000
  • C) $2,485
  • D) −$1,978
Show Solution

Answer: A

The net present worth is calculated as:

NPW = −Initial Cost + Annual Savings × (P/A, i, n)

where (P/A, i, n) is the present worth of an annuity factor.

Step 1: Compute the P/A factor:

(P/A, 8%, 5) = [(1 + 0.08)5 − 1] / [0.08 × (1 + 0.08)5]

Step 2: Calculate (1.08)&sup5; = 1.4693.

Step 3: Substitute: (P/A) = (1.4693 − 1) / (0.08 × 1.4693) = 0.4693 / 0.11755 = 3.9927.

Step 4: Compute NPW: NPW = −$10,000 + $3,000 × 3.9927 = −$10,000 + $11,978 = $1,978.

Since NPW > 0, the investment is economically justified at an 8% interest rate.


How Should You Use These Practice Problems?

A good FE practice set should do more than tell you whether you were right. Use each problem to build a repeatable exam routine: read the units, find the handbook section, calculate cleanly, and decide whether your answer is reasonable.

  • Practice in short timed bursts. Work 10-question sets at roughly 30 minutes, then review immediately while the reasoning is still fresh.
  • Use the NCEES FE Reference Handbook. During the actual exam, you will have access to a searchable PDF of the handbook. Practice finding formulas in it rather than memorizing everything.
  • Review your mistakes carefully. When you get a problem wrong, identify whether the error was conceptual, computational, or due to a misread. Each type requires a different fix.
  • Track your performance by topic. If you consistently miss the same topic family, allocate more study time there before adding more random problems.
  • Rework your misses without the answer visible. Reading a solution feels productive, but solving the same setup cold is what turns it into memory.

What Topics Do These Solved Examples Cover?

The solved examples above are mostly FE Electrical and Computer examples, so they touch these ECE topic areas:

  • Mathematics (11%)
  • Probability and Statistics (4%)
  • Ethics and Professional Practice (4%)
  • Engineering Economics (4%)
  • Properties of Electrical Materials (4%)
  • Engineering Sciences (4%)
  • Circuit Analysis (DC and AC) (12%)
  • Linear Systems (5%)
  • Signal Processing (6%)
  • Electronics (8%)
  • Power Systems (8%)
  • Electromagnetics (5%)
  • Control Systems (6%)
  • Communications (5%)
  • Computer Networks (5%)
  • Digital Systems (9%)

The 10 problems above touch several high-weight ECE categories. To fully prepare, route into your own FE discipline and practice across the official topic list for that exam. The value of the examples is the review method: solve, inspect the official reference path, check the calculator workflow, and record the miss pattern.

Don't skip engineering economics: Present worth, annual cost, and rate-of-return problems are among the most formulaic on the entire FE exam. The P/A, P/F, and A/P factor equations are in the reference handbook—learn to find them quickly and these become efficient scoring opportunities.

Essential Study Tools

Having the right tools makes a significant difference in your practice sessions:

  • TI-36X Pro Scientific Calculator — The most capable NCEES-approved calculator. Practice with it during every problem session so you are fluent on exam day.
  • NCEES FE Reference Handbook — The exact reference provided during the exam. Solve every practice problem with it open.

What Should You Do Next?

These 10 problems are only a doorway into the exam. Build readiness with mixed sets across your discipline, then use every missed question to update your formula lookup, calculator habit, or concept map.

Continue your FE practice:

How many problems to doPractice strategyBest FE Exam Prep Books🔢 Calculator Guide✅ Exam Day ChecklistGuide for Returning Engineers

Use the matching FE Handbook 10.6 page guide Map your official NCEES topic list to high-value FE Handbook 10.6 page ranges and verified page starts from practice misses. It does not reproduce the handbook; it helps you navigate your official NCEES copy faster. Start with the discipline page-guide hub.
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Frequently Asked Questions

How many FE practice problems should I do?

Many candidates use 300–600 reviewed problems as a working range, but the better target is topic coverage, miss-log improvement, and timed-set stability. Start with a diagnostic, then put more reviewed reps into weak high-weight topics.

What types of FE practice questions should I use?

Use a mix of multiple-choice, numeric, fill-in-the-blank, multi-select, point-and-click/hotspot, drag-and-drop, and discipline-specific calculation questions. Good practice should include solved steps, why-wrong review, calculator workflow, and topic feedback.

Disclaimer: This content is for educational purposes only and is not affiliated with, endorsed by, or sponsored by NCEES. "FE" and "Fundamentals of Engineering" are trademarks of NCEES. Always refer to the official NCEES website for the most current exam specifications and policies.

Ready for More Practice?

Want a realistic dry run? Take our free timed 20-question diagnostic — it mirrors FE pacing and ends with an instant per-topic feedback report showing exactly which topics to drill next. No email required.

These 10 examples are only a taste. Practice with discipline routing, detailed solutions, topic tagging, calculator help, and handbook-aware review so every missed question creates a next action.

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