FE Exam Prep: Free Practice Problems and a 12-Week Study Plan
Start your FE exam prep here: 28 original practice problems with full explanations, then a topic map and a 12-week plan for whichever of the seven NCEES disciplines you're taking. To plan first, jump to your discipline's topics or the 12-week schedule.
Practice problems
Original, unofficial starter practice — not NCEES questions or a full-length exam. Use an approved calculator and the FE Reference Handbook.
Problem 1 · Mathematics
A pump delivers liquid at a rate q(t) = 2t + 3, where t is in minutes and q is in liters per minute. How much liquid does it deliver from t = 0 to t = 4 minutes?
- A. 12 L
- B. 16 L
- C. 28 L
- D. 44 L
Answer and explanation
Answer: C. The rate changes with time, so add it up over the interval with an integral: V = ∫₀⁴ (2t + 3) dt = [t² + 3t] from 0 to 4 = 16 + 12 = 28 L. Quick check: the rate climbs steadily from 3 to 11 L/min, so its average is 7 L/min, and 7 × 4 = 28 L.
Common misses: A keeps only the constant 3 L/min part (3 × 4). B keeps only the 2t part (t² at t = 4). D uses the final rate, 11 L/min, as if it applied for all four minutes.
Topic: Subject 1 in every FE specification (Civil: Mathematics and Statistics). Principle: OpenStax Calculus Vol. 1, 5.3 The Fundamental Theorem of Calculus.
Problem 1 is one of 28. Together they sample the four areas that appear on every FE exam (math, probability and statistics, ethics, and engineering economics), plus one problem for each discipline. Subtopics differ: use each problem’s topic note to check its fit with your specification. They're a starting point, not a full-length exam, and your score on them isn't a prediction of your FE result. Use what you miss to decide where your first study weeks go.
Like the real exam, every problem here is all-or-nothing: a "select all that apply" problem only counts if you pick every correct choice and nothing else. (NCEES Examinee Guide, May 2026, p. 11)
Mathematics and units
Problem 1 above starts this group.
Problem 2 · Mathematics
For f(x) = 3x² − 4x + 1, what is the slope of the curve at x = 2?
- A. 5
- B. 8
- C. 12
- D. 2
Answer and explanation
Answer: B. The slope is the derivative. f′(x) = 6x − 4, so f′(2) = 12 − 4 = 8.
Common misses: A is f(2), the height of the curve, not its slope. C is 6x without the −4 term. D differentiates 3x² as 3x, giving 3(2) − 4 = 2.
Topic: Subject 1 in every FE specification. Principle: OpenStax Calculus Vol. 1, 3.3 Differentiation Rules (power, sum, constant-multiple rules).
Problem 3 · Mathematics
What is the determinant of the 2 × 2 matrix with first row (4, −2) and second row (3, 1)?
- A. −2
- B. 10
- C. 4
- D. −10
Answer and explanation
Answer: B. For rows (a, b) and (c, d), the determinant is ad − bc = (4)(1) − (−2)(3) = 4 + 6 = 10.
Common misses: A drops the minus sign on −2 and computes 4 − 6. D reverses the order (bc − ad). C keeps only the main-diagonal product.
Topic: Mathematics: matrix or linear algebra in Chemical, Electrical and Computer, Industrial and Systems, Mechanical, and Other Disciplines; the Civil and Environmental specifications do not explicitly list matrix algebra. Principle: OpenStax College Algebra 2e, 7.8 Solving Systems with Cramer's Rule (2×2 determinant).
Problem 4 · Mathematics
What is the magnitude of the vector 3i + 4j + 12k?
- A. 19
- B. 5
- C. 13
- D. 169
Answer and explanation
Answer: C. Magnitude is the square root of the sum of the squared components: √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.
Common misses: A adds the components. B is the magnitude of 3i + 4j only, ignoring k. D forgets the square root.
Topic: Vector operations: Civil Mathematics and Statistics; Electrical and Computer, Industrial and Systems, and Mechanical Mathematics; Other Disciplines Statics. Principle: OpenStax Calculus Vol. 3, 2.2 Vectors in Three Dimensions (distance in space).
Problem 5 · Mathematics
Solve e^(0.5t) = 4 for t.
- A. 0.69
- B. 2.77
- C. 8.00
- D. 1.39
Answer and explanation
Answer: B. Take the natural log of both sides: 0.5t = ln 4 ≈ 1.38629, so t = (ln 4) ÷ 0.5 ≈ 2.77.
Common misses: D stops at ln 4 and never divides by 0.5. A is ln 2. C treats the equation as 0.5t = 4, skipping the logarithm.
Topic: Subject 1 in every FE specification. Principle: OpenStax College Algebra 2e, 6.6 Exponential and Logarithmic Equations (equations containing e).
Problem 6 · Units and conversions
Select all that apply. Which quantities equal a volumetric flow of 720 L/h?
- A. 0.20 L/s
- B. 0.00020 m³/s
- C. 12 L/min
- D. 0.012 m³/s
Answer and explanation
Answers: A, B, C. 720 L/h ÷ 60 min/h = 12 L/min. Divide by 60 s/min again: 0.20 L/s. Since 1 L = 0.001 m³, that is 0.00020 m³/s. You need all three correct choices and no incorrect choice to get this item right.
Common misses: D equals 12 L/s, not 12 L/min. It skips the minute-to-second step.
Topic: A shared skill used inside the science and engineering subjects of every specification (not a separate NCEES subject). Principle: NIST SP 811, Chapter 5, Table 6 (minute, hour, liter); NIST SP 811, Chapter 4, Table 5 (SI prefixes).
Probability and statistics
Problem 7 · Probability and statistics
A sample of five measurements is 4, 6, 8, 10, and 12 mm. What is the sample standard deviation?
- A. 2.83 mm
- B. 3.16 mm
- C. 10.0 mm
- D. 8.0 mm
Answer and explanation
Answer: B. The mean is 8 mm. The squared deviations are 16, 4, 0, 4, and 16, which add to 40 mm². A sample divides by n − 1: 40 ÷ 4 = 10 mm². The square root gives s = 3.16 mm.
Common misses: A divides by n instead of n − 1 (that's the population formula, 2.83). C is the variance, and variance is in mm², not mm. D is the mean.
Topic: Probability and Statistics in every specification (Civil: Mathematics and Statistics; Industrial and Systems: subject 5). Principle: NIST/SEMATECH e-Handbook, 1.3.5.6 Measures of Scale.
Problem 8 · Probability and statistics
Strengths of a material are normally distributed with a mean of 100 MPa and a standard deviation of 15 MPa. What fraction of specimens exceed 130 MPa?
- A. 0.0228
- B. 0.9772
- C. 0.0455
- D. 0.1587
Answer and explanation
Answer: A. Standardize: z = (130 − 100) ÷ 15 = 2.00. A standard normal table gives an area of 0.47725 between z = 0 and z = 2.00, so the area above z = 2.00 is 0.5 − 0.47725 ≈ 0.0228.
Common misses: B is the area below 130 MPa. C counts both tails (above +2 and below −2). D is the upper tail at z = 1.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, 1.3.6.7.1 Cumulative Distribution Function of the Standard Normal (z = 2.00 row).
Problem 9 · Probability and statistics
Each part from a process is defective with probability 0.10, independently of the others. In a sample of 5 parts, what is the probability that exactly 2 are defective? Enter a decimal to four places.
Enter a number.
Answer and explanation
Answer: 0.0729. This is a binomial probability: C(5, 2)(0.10)²(0.90)³ = 10 × 0.01 × 0.729 = 0.0729.
Common misses: 0.00729 forgets the 10 different ways to choose which two parts are defective. 0.01 is the probability that a specified pair is defective; it ignores the three good parts and the different possible pairs.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, Binomial Distribution (probability mass function).
Problem 10 · Probability and statistics
Select all that apply. Which of these are measures of dispersion (spread)?
- A. Range
- B. Median
- C. Variance
- D. Standard deviation
- E. Mode
Answer and explanation
Answers: A, C, D. Range, variance, and standard deviation all describe how spread out the data are. You need all three, and only those three, to get this item right.
Common misses: Median and mode describe the center of the data, not its spread.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, 1.3.5.6 Measures of Scale; NIST/SEMATECH e-Handbook, 1.3.5.1 Measures of Location.
Ethics and professional practice
These follow the NCEES Model Rules, which NCEES publishes as a model for state licensing boards. Your own board's rules govern your actual practice.
Problem 11 · Ethics and professional practice
A licensed engineer recommends adding bracing to a temporary structure. The project manager overrules the recommendation, and the engineer believes workers will be endangered. Under the NCEES Model Rules, what should the engineer do?
- A. Comply, because the manager controls the schedule
- B. Resign without comment
- C. Notify the employer or client and any other appropriate authority
- D. Document the disagreement privately in case of later litigation
Answer and explanation
Answer: C. §240.15 A.3 says that when a licensee's judgment is overruled and public health, safety, or welfare is endangered, the licensee notifies the employer or client and other appropriate authority.
Common misses: A ignores the duty to put public safety first (§240.15 A.1). B and D leave the hazard in place and nobody informed.
Topic: Ethics in every specification (Other Disciplines: Engineering Ethics and Societal Impacts). Principle: NCEES Model Rules, August 2026, §240.15.
Problem 12 · Ethics and professional practice
An engineer designing a building for a client is offered a personal cash gift by a steel supplier in exchange for specifying its product on the same project. Under the NCEES Model Rules, which statement is correct?
- A. Accepting the gift is allowed if the product meets code
- B. Accepting the gift is prohibited, even if the client agrees in writing
- C. It is allowed if the engineer tells the client verbally
- D. It is always allowed because the supplier is not the client
Answer and explanation
Answer: B. §240.15 B.5 prohibits gratuities from contractors, their agents, or other parties in connection with work for employers or clients. The supplier’s personal cash gift is a gratuity tied to the client’s project.
Common misses: A substitutes code compliance for the gratuity rule. C and D do not remove the prohibition. B.7 addresses compensation for professional services from multiple parties; its written-consent condition does not create an exception to B.5.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 13 · Ethics and professional practice
Select all that apply. Under the NCEES Model Rules, which of these are licensee obligations?
- A. Disclose known or potential conflicts of interest to employers or clients
- B. Report to the board knowledge of another person's or firm's violation of the licensing laws or rules
- C. Share a client's proprietary test data with a competitor without the client's consent when no law or rule authorizes or requires disclosure
- D. Refuse gratuities from contractors in connection with work for employers or clients
Answer and explanation
Answers: A, B, D. A is §240.15 B.6. B is §240.15 A.8. D is §240.15 B.5. You need all three, and not C, to get this item right.
Common misses: C breaks §240.15 B.4, which bars revealing information obtained in a professional capacity without prior consent except as authorized or required by law or rules. The option expressly excludes that exception.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 14 · Ethics and professional practice
Under the NCEES Model Rules, what is a licensee's first and foremost responsibility?
- A. Loyalty to the employer
- B. Safeguarding the health, safety, and welfare of the public
- C. Completing work within the contracted budget
- D. Protecting the reputation of the profession
Answer and explanation
Answer: B. §240.15 A.1 states it directly: the first and foremost responsibility is to safeguard the health, safety, and welfare of the public.
Common misses: A, C, and D are real considerations, but none of them outranks public safety.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 15 · Ethics and professional practice
A civil engineer leading a building project is asked to sign and seal the project's electrical drawings. The engineer has no education or experience in electrical design and did not have responsible charge of those drawings. Under the NCEES Model Rules, what is the best course?
- A. Seal them, since the engineer leads the overall project
- B. Seal them with a note stating limited electrical expertise
- C. Decline to seal them; the electrical drawings should be sealed by the licensee responsible for preparing them
- D. Seal them if the deadline would otherwise be missed
Answer and explanation
Answer: C. §240.15 B.2 bars sealing documents in subject matter where the licensee lacks competence, or that were not prepared under their responsible charge. §240.15 B.3 still lets the engineer coordinate the whole project, as long as each technical segment is signed and sealed by the licensee responsible for it.
Common misses: A confuses coordinating a project with sealing every part of it. B: a disclaimer doesn't create competence. D: deadlines don't change the rule.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Engineering economics
Use the factor formulas or the interest tables in your reference handbook. Keep intermediate precision, then round the final answer as the question requests.
Problem 16 · Engineering economics
$10,000 is deposited at 6% interest, compounded annually, with no other deposits or withdrawals. What is it worth after 5 years? Enter to the nearest dollar.
Enter a number in dollars.
Answer and explanation
Answer: $13,382. F = P(1 + i)ⁿ = 10,000 × (1.06)⁵ = $13,382.255776, which rounds to $13,382.
Common misses: $13,000 uses simple interest (6% of $10,000 each year). $13,380 rounds the factor too early. Keep the calculator’s precision until the final answer, then round to the nearest dollar as requested.
Topic: Engineering Economics in every specification (Chemical: Economics). Principle: Penn State EME 460, Nominal, Period, and Effective Interest Rates.
Problem 17 · Engineering economics
A project returns $2,000 at the end of each year for 10 years. At an effective annual interest rate of 8%, what is the present worth of those returns?
- A. $20,000
- B. $13,420
- C. $9,264
- D. $28,973
Answer and explanation
Answer: B. Use the uniform-series present-worth factor: (P/A, 8%, 10) = [(1.08)¹⁰ − 1] ÷ [0.08 × (1.08)¹⁰] ≈ 6.7100814. Then 2,000 × (P/A, 8%, 10) ≈ $13,420.16, or $13,420 to the nearest dollar.
Common misses: A ignores the time value of money. C is the present worth of one $20,000 lump sum at year 10. D is the future worth of the series at year 10.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Compound Interest Formulas III (P/A and A/P factors).
Problem 18 · Engineering economics
A $50,000 machine has a 10-year life and no salvage value. Ignore operating and maintenance costs. At an effective annual interest rate of 10%, what is its equivalent uniform annual cost?
- A. $5,000
- B. $8,137
- C. $3,137
- D. $10,000
Answer and explanation
Answer: B. Use the capital-recovery factor: (A/P, 10%, 10) = [0.10 × (1.10)¹⁰] ÷ [(1.10)¹⁰ − 1] ≈ 0.162745395. Then 50,000 × (A/P, 10%, 10) ≈ $8,137.27, or $8,137 per year to the nearest dollar.
Common misses: A spreads the cost evenly and ignores interest. C uses the sinking-fund factor (A/F ≈ 0.062745395), which converts a future amount, not a present one. D adds $5,000 of simple interest on the original cost to $5,000 of straight-line cost allocation instead of using capital recovery.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Compound Interest Formulas III (P/A and A/P factors); Penn State EME 460, Compound Interest Formulas II (A/F factor).
Problem 19 · Engineering economics
Equipment costs $80,000, has a 6-year life, and has an $8,000 salvage value. Using straight-line depreciation, what is its book value at the end of year 3?
- A. $40,000
- B. $44,000
- C. $36,000
- D. $56,000
Answer and explanation
Answer: B. Annual depreciation = (80,000 − 8,000) ÷ 6 = $12,000. After 3 years: 80,000 − 3 × 12,000 = $44,000.
Common misses: A ignores salvage: 80,000 − 3 × (80,000 ÷ 6) = $40,000. C is the depreciation taken so far, not the book value. D is the book value after only 2 years.
Topic: Engineering Economics in every specification. Principle: Penn State EME 801, Depreciation Accounting (straight-line formula and book value).
Problem 20 · Engineering economics
A loan is quoted at 12% per year, compounded monthly. What is the effective annual interest rate?
- A. 12.00%
- B. 12.68%
- C. 1.00%
- D. 12.36%
Answer and explanation
Answer: B. The monthly rate is 12% ÷ 12 = 1%. Effective annual rate = (1.01)¹² − 1 ≈ 0.1268, or 12.68%.
Common misses: A is the nominal rate. C is the monthly rate. D is what semiannual compounding would give: (1.06)² − 1.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Nominal, Period, and Effective Interest Rates.
Problem 21 · Engineering economics
A product has fixed costs of $40,000 per year, sells for $25 per unit, and has a variable cost of $15 per unit. How many units must be sold each year to break even?
- A. 1,600
- B. 2,667
- C. 4,000
- D. 1,000
Answer and explanation
Answer: C. Each unit contributes $25 − $15 = $10 toward fixed costs. Break-even = 40,000 ÷ 10 = 4,000 units.
Common misses: A divides fixed costs by the price. B divides by the variable cost. D divides by 40, adding the price and variable cost instead of subtracting them.
Topic: Engineering Economics in every specification. Principle: OpenStax Principles of Managerial Accounting, 3.2 Calculate a Break-Even Point.
One problem for each discipline
Do the one for your exam. The others are optional: each tests a principle that also shows up on other FE exams.
Problem 22 · Chemical · Thermodynamics
A fixed amount of an ideal gas occupies 0.60 m³ at 200 kPa absolute and 300 K. Its volume changes to 0.40 m³ and its temperature to 360 K. What is the final absolute pressure?
- A. 160 kPa
- B. 240 kPa
- C. 300 kPa
- D. 360 kPa
Answer and explanation
Answer: D. For a fixed amount of ideal gas, p₁V₁/T₁ = p₂V₂/T₂. So p₂ = 200 × (0.60 ÷ 0.40) × (360 ÷ 300) = 200 × 1.5 × 1.2 = 360 kPa absolute. The pressure is absolute and the temperatures are in kelvins, which is what the relation needs.
Common misses: A flips the volume ratio. B accounts only for the temperature change. C accounts only for the volume change.
Topic: FE Chemical, subject 7: Thermodynamics. Principle: OpenStax University Physics Vol. 2, 2.1 Molecular Model of an Ideal Gas.
Problem 23 · Civil · Statics
A horizontal beam is 6 m long, with a pin support at the left end and a roller at the right end. Its only load is 12 kN downward, 2 m from the left support. Ignore the beam's weight. What is the upward reaction at the right support?
- A. 4 kN
- B. 6 kN
- C. 8 kN
- D. 24 kN
Answer and explanation
Answer: A. Take moments about the left support so the left reaction drops out: R_right × 6 − 12 × 2 = 0, so R_right = 4 kN. Check with vertical force balance: the left reaction is 12 − 4 = 8 kN.
Common misses: B assumes the load sits at midspan. C is the left reaction, not the one asked for. D is the load's moment (24 kN·m) reported as a force.
Topic: FE Civil, subject 4: Statics. Principle: OpenStax University Physics Vol. 1, 12.1 Conditions for Static Equilibrium.
Problem 24 · Electrical and Computer · Circuit Analysis (DC and AC Steady State)
An ideal 12 V DC source is connected across a 6 Ω resistor and a 3 Ω resistor in parallel. What total current does the source supply?
- A. 1.33 A
- B. 6.00 A
- C. 2.00 A
- D. 4.00 A
Answer and explanation
Answer: B. 1/R_eq = 1/6 + 1/3 = 1/2, so R_eq = 2 Ω and I = 12 ÷ 2 = 6 A. Another way: each branch sees 12 V, so the branch currents are 2 A and 4 A, which add to 6 A.
Common misses: A treats the resistors as if they were in series (12 ÷ 9). C and D are the individual branch currents, not the total.
Topic: FE Electrical and Computer, subject 6: Circuit Analysis (DC and AC Steady State). Principle: OpenStax University Physics Vol. 2, 10.2 Resistors in Series and Parallel.
Problem 25 · Environmental · Water and Wastewater
A discharge has a constant flow of 1,500 m³/day and a constant concentration of 20 mg/L of a dissolved substance. What mass of that substance passes the sampling point each day? Enter the value in kg/day.
Enter a number in kg/day.
Answer and explanation
Answer: 30 kg/day. Mass rate = flow × concentration: 1,500 m³/day × 1,000 L/m³ × 20 mg/L × (1 kg ÷ 1,000,000 mg) = 30 kg/day.
Common misses: 30,000 treats grams as kilograms. 0.030 skips the cubic-meter-to-liter conversion.
Topic: FE Environmental, subject 12: Water and Wastewater. Principle: NIST SP 811, Chapter 5, Table 6 (minute, hour, liter); NIST SP 811, Chapter 4, Table 5 (SI prefixes).
Problem 26 · Industrial and Systems · Systems Engineering, Analysis, and Design
A system needs both component A and component B to work for the whole mission. Their probabilities of surviving the mission are 0.98 and 0.95. Failures are independent, the first failure stops the system, and nothing is replaced. What is the probability the system completes the mission?
- A. 93.0%
- B. 93.1%
- C. 96.5%
- D. 99.9%
Answer and explanation
Answer: B. Both must survive, so this is a series system: R = 0.98 × 0.95 = 0.931, or 93.1%. Multiplying is valid because the failures are independent.
Common misses: A subtracts both failure chances from 1 and double-counts the case where both fail. C averages the two. D is the chance that at least one survives, which is the parallel case, not this one.
Topic: FE Industrial and Systems, subject 13: Systems Engineering, Analysis, and Design. Principle: NIST/SEMATECH e-Handbook, 8.1.8.2 Series model.
Problem 27 · Mechanical · Thermodynamics
A closed system receives 150 kJ of heat and does 40 kJ of work on its surroundings. Changes in kinetic and potential energy are negligible. What is the change in its internal energy? Enter a signed value in kJ.
Enter a number in kJ.
Answer and explanation
Answer: +110 kJ. With heat into the system positive and work done by the system positive, ΔU = Q − W = 150 − 40 = +110 kJ. Internal energy goes up.
Common misses: +190 treats the outgoing work as energy added. −110 reverses the direction of the net energy flow.
Topic: FE Mechanical, subject 11: Thermodynamics. Principle: OpenStax University Physics Vol. 2, 3.3 First Law of Thermodynamics.
Problem 28 · Other Disciplines · Dynamics
A 20 kg cart has two horizontal forces on it: 100 N to the right and 40 N to the left. What is its horizontal acceleration?
- A. 2 m/s² to the left
- B. 3 m/s² to the right
- C. 5 m/s² to the right
- D. 7 m/s² to the right
Answer and explanation
Answer: B. Take right as positive. F_net = 100 − 40 = 60 N, so a = F_net ÷ m = 60 ÷ 20 = 3 m/s² to the right.
Common misses: A uses only the 40 N resisting force. C ignores the resisting force. D adds the two forces instead of subtracting.
Topic: FE Other Disciplines, subject 9: Dynamics. Principle: OpenStax University Physics Vol. 1, 5.3 Newton's Second Law.
Read all 28 answers and explanations
Problem 1 · Mathematics
Answer: C. The rate changes with time, so add it up over the interval with an integral: V = ∫₀⁴ (2t + 3) dt = [t² + 3t] from 0 to 4 = 16 + 12 = 28 L. Quick check: the rate climbs steadily from 3 to 11 L/min, so its average is 7 L/min, and 7 × 4 = 28 L.
Common misses: A keeps only the constant 3 L/min part (3 × 4). B keeps only the 2t part (t² at t = 4). D uses the final rate, 11 L/min, as if it applied for all four minutes.
Topic: Subject 1 in every FE specification (Civil: Mathematics and Statistics). Principle: OpenStax Calculus Vol. 1, 5.3 The Fundamental Theorem of Calculus.
Problem 2 · Mathematics
Answer: B. The slope is the derivative. f′(x) = 6x − 4, so f′(2) = 12 − 4 = 8.
Common misses: A is f(2), the height of the curve, not its slope. C is 6x without the −4 term. D differentiates 3x² as 3x, giving 3(2) − 4 = 2.
Topic: Subject 1 in every FE specification. Principle: OpenStax Calculus Vol. 1, 3.3 Differentiation Rules (power, sum, constant-multiple rules).
Problem 3 · Mathematics
Answer: B. For rows (a, b) and (c, d), the determinant is ad − bc = (4)(1) − (−2)(3) = 4 + 6 = 10.
Common misses: A drops the minus sign on −2 and computes 4 − 6. D reverses the order (bc − ad). C keeps only the main-diagonal product.
Topic: Mathematics: matrix or linear algebra in Chemical, Electrical and Computer, Industrial and Systems, Mechanical, and Other Disciplines; the Civil and Environmental specifications do not explicitly list matrix algebra. Principle: OpenStax College Algebra 2e, 7.8 Solving Systems with Cramer's Rule (2×2 determinant).
Problem 4 · Mathematics
Answer: C. Magnitude is the square root of the sum of the squared components: √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.
Common misses: A adds the components. B is the magnitude of 3i + 4j only, ignoring k. D forgets the square root.
Topic: Vector operations: Civil Mathematics and Statistics; Electrical and Computer, Industrial and Systems, and Mechanical Mathematics; Other Disciplines Statics. Principle: OpenStax Calculus Vol. 3, 2.2 Vectors in Three Dimensions (distance in space).
Problem 5 · Mathematics
Answer: B. Take the natural log of both sides: 0.5t = ln 4 ≈ 1.38629, so t = (ln 4) ÷ 0.5 ≈ 2.77.
Common misses: D stops at ln 4 and never divides by 0.5. A is ln 2. C treats the equation as 0.5t = 4, skipping the logarithm.
Topic: Subject 1 in every FE specification. Principle: OpenStax College Algebra 2e, 6.6 Exponential and Logarithmic Equations (equations containing e).
Problem 6 · Units and conversions
Answers: A, B, C. 720 L/h ÷ 60 min/h = 12 L/min. Divide by 60 s/min again: 0.20 L/s. Since 1 L = 0.001 m³, that is 0.00020 m³/s. You need all three correct choices and no incorrect choice to get this item right.
Common misses: D equals 12 L/s, not 12 L/min. It skips the minute-to-second step.
Topic: A shared skill used inside the science and engineering subjects of every specification (not a separate NCEES subject). Principle: NIST SP 811, Chapter 5, Table 6 (minute, hour, liter); NIST SP 811, Chapter 4, Table 5 (SI prefixes).
Problem 7 · Probability and statistics
Answer: B. The mean is 8 mm. The squared deviations are 16, 4, 0, 4, and 16, which add to 40 mm². A sample divides by n − 1: 40 ÷ 4 = 10 mm². The square root gives s = 3.16 mm.
Common misses: A divides by n instead of n − 1 (that's the population formula, 2.83). C is the variance, and variance is in mm², not mm. D is the mean.
Topic: Probability and Statistics in every specification (Civil: Mathematics and Statistics; Industrial and Systems: subject 5). Principle: NIST/SEMATECH e-Handbook, 1.3.5.6 Measures of Scale.
Problem 8 · Probability and statistics
Answer: A. Standardize: z = (130 − 100) ÷ 15 = 2.00. A standard normal table gives an area of 0.47725 between z = 0 and z = 2.00, so the area above z = 2.00 is 0.5 − 0.47725 ≈ 0.0228.
Common misses: B is the area below 130 MPa. C counts both tails (above +2 and below −2). D is the upper tail at z = 1.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, 1.3.6.7.1 Cumulative Distribution Function of the Standard Normal (z = 2.00 row).
Problem 9 · Probability and statistics
Answer: 0.0729. This is a binomial probability: C(5, 2)(0.10)²(0.90)³ = 10 × 0.01 × 0.729 = 0.0729.
Common misses: 0.00729 forgets the 10 different ways to choose which two parts are defective. 0.01 is the probability that a specified pair is defective; it ignores the three good parts and the different possible pairs.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, Binomial Distribution (probability mass function).
Problem 10 · Probability and statistics
Answers: A, C, D. Range, variance, and standard deviation all describe how spread out the data are. You need all three, and only those three, to get this item right.
Common misses: Median and mode describe the center of the data, not its spread.
Topic: Probability and Statistics in every specification. Principle: NIST/SEMATECH e-Handbook, 1.3.5.6 Measures of Scale; NIST/SEMATECH e-Handbook, 1.3.5.1 Measures of Location.
Problem 11 · Ethics and professional practice
Answer: C. §240.15 A.3 says that when a licensee's judgment is overruled and public health, safety, or welfare is endangered, the licensee notifies the employer or client and other appropriate authority.
Common misses: A ignores the duty to put public safety first (§240.15 A.1). B and D leave the hazard in place and nobody informed.
Topic: Ethics in every specification (Other Disciplines: Engineering Ethics and Societal Impacts). Principle: NCEES Model Rules, August 2026, §240.15.
Problem 12 · Ethics and professional practice
Answer: B. §240.15 B.5 prohibits gratuities from contractors, their agents, or other parties in connection with work for employers or clients. The supplier’s personal cash gift is a gratuity tied to the client’s project.
Common misses: A substitutes code compliance for the gratuity rule. C and D do not remove the prohibition. B.7 addresses compensation for professional services from multiple parties; its written-consent condition does not create an exception to B.5.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 13 · Ethics and professional practice
Answers: A, B, D. A is §240.15 B.6. B is §240.15 A.8. D is §240.15 B.5. You need all three, and not C, to get this item right.
Common misses: C breaks §240.15 B.4, which bars revealing information obtained in a professional capacity without prior consent except as authorized or required by law or rules. The option expressly excludes that exception.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 14 · Ethics and professional practice
Answer: B. §240.15 A.1 states it directly: the first and foremost responsibility is to safeguard the health, safety, and welfare of the public.
Common misses: A, C, and D are real considerations, but none of them outranks public safety.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 15 · Ethics and professional practice
Answer: C. §240.15 B.2 bars sealing documents in subject matter where the licensee lacks competence, or that were not prepared under their responsible charge. §240.15 B.3 still lets the engineer coordinate the whole project, as long as each technical segment is signed and sealed by the licensee responsible for it.
Common misses: A confuses coordinating a project with sealing every part of it. B: a disclaimer doesn't create competence. D: deadlines don't change the rule.
Topic: Ethics in every specification. Principle: NCEES Model Rules, August 2026, §240.15.
Problem 16 · Engineering economics
Answer: $13,382. F = P(1 + i)ⁿ = 10,000 × (1.06)⁵ = $13,382.255776, which rounds to $13,382.
Common misses: $13,000 uses simple interest (6% of $10,000 each year). $13,380 rounds the factor too early. Keep the calculator’s precision until the final answer, then round to the nearest dollar as requested.
Topic: Engineering Economics in every specification (Chemical: Economics). Principle: Penn State EME 460, Nominal, Period, and Effective Interest Rates.
Problem 17 · Engineering economics
Answer: B. Use the uniform-series present-worth factor: (P/A, 8%, 10) = [(1.08)¹⁰ − 1] ÷ [0.08 × (1.08)¹⁰] ≈ 6.7100814. Then 2,000 × (P/A, 8%, 10) ≈ $13,420.16, or $13,420 to the nearest dollar.
Common misses: A ignores the time value of money. C is the present worth of one $20,000 lump sum at year 10. D is the future worth of the series at year 10.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Compound Interest Formulas III (P/A and A/P factors).
Problem 18 · Engineering economics
Answer: B. Use the capital-recovery factor: (A/P, 10%, 10) = [0.10 × (1.10)¹⁰] ÷ [(1.10)¹⁰ − 1] ≈ 0.162745395. Then 50,000 × (A/P, 10%, 10) ≈ $8,137.27, or $8,137 per year to the nearest dollar.
Common misses: A spreads the cost evenly and ignores interest. C uses the sinking-fund factor (A/F ≈ 0.062745395), which converts a future amount, not a present one. D adds $5,000 of simple interest on the original cost to $5,000 of straight-line cost allocation instead of using capital recovery.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Compound Interest Formulas III (P/A and A/P factors); Penn State EME 460, Compound Interest Formulas II (A/F factor).
Problem 19 · Engineering economics
Answer: B. Annual depreciation = (80,000 − 8,000) ÷ 6 = $12,000. After 3 years: 80,000 − 3 × 12,000 = $44,000.
Common misses: A ignores salvage: 80,000 − 3 × (80,000 ÷ 6) = $40,000. C is the depreciation taken so far, not the book value. D is the book value after only 2 years.
Topic: Engineering Economics in every specification. Principle: Penn State EME 801, Depreciation Accounting (straight-line formula and book value).
Problem 20 · Engineering economics
Answer: B. The monthly rate is 12% ÷ 12 = 1%. Effective annual rate = (1.01)¹² − 1 ≈ 0.1268, or 12.68%.
Common misses: A is the nominal rate. C is the monthly rate. D is what semiannual compounding would give: (1.06)² − 1.
Topic: Engineering Economics in every specification. Principle: Penn State EME 460, Nominal, Period, and Effective Interest Rates.
Problem 21 · Engineering economics
Answer: C. Each unit contributes $25 − $15 = $10 toward fixed costs. Break-even = 40,000 ÷ 10 = 4,000 units.
Common misses: A divides fixed costs by the price. B divides by the variable cost. D divides by 40, adding the price and variable cost instead of subtracting them.
Topic: Engineering Economics in every specification. Principle: OpenStax Principles of Managerial Accounting, 3.2 Calculate a Break-Even Point.
Problem 22 · Thermodynamics
Answer: D. For a fixed amount of ideal gas, p₁V₁/T₁ = p₂V₂/T₂. So p₂ = 200 × (0.60 ÷ 0.40) × (360 ÷ 300) = 200 × 1.5 × 1.2 = 360 kPa absolute. The pressure is absolute and the temperatures are in kelvins, which is what the relation needs.
Common misses: A flips the volume ratio. B accounts only for the temperature change. C accounts only for the volume change.
Topic: FE Chemical, subject 7: Thermodynamics. Principle: OpenStax University Physics Vol. 2, 2.1 Molecular Model of an Ideal Gas.
Problem 23 · Statics
Answer: A. Take moments about the left support so the left reaction drops out: R_right × 6 − 12 × 2 = 0, so R_right = 4 kN. Check with vertical force balance: the left reaction is 12 − 4 = 8 kN.
Common misses: B assumes the load sits at midspan. C is the left reaction, not the one asked for. D is the load's moment (24 kN·m) reported as a force.
Topic: FE Civil, subject 4: Statics. Principle: OpenStax University Physics Vol. 1, 12.1 Conditions for Static Equilibrium.
Problem 24 · Circuit Analysis (DC and AC Steady State)
Answer: B. 1/R_eq = 1/6 + 1/3 = 1/2, so R_eq = 2 Ω and I = 12 ÷ 2 = 6 A. Another way: each branch sees 12 V, so the branch currents are 2 A and 4 A, which add to 6 A.
Common misses: A treats the resistors as if they were in series (12 ÷ 9). C and D are the individual branch currents, not the total.
Topic: FE Electrical and Computer, subject 6: Circuit Analysis (DC and AC Steady State). Principle: OpenStax University Physics Vol. 2, 10.2 Resistors in Series and Parallel.
Problem 25 · Water and Wastewater
Answer: 30 kg/day. Mass rate = flow × concentration: 1,500 m³/day × 1,000 L/m³ × 20 mg/L × (1 kg ÷ 1,000,000 mg) = 30 kg/day.
Common misses: 30,000 treats grams as kilograms. 0.030 skips the cubic-meter-to-liter conversion.
Topic: FE Environmental, subject 12: Water and Wastewater. Principle: NIST SP 811, Chapter 5, Table 6 (minute, hour, liter); NIST SP 811, Chapter 4, Table 5 (SI prefixes).
Problem 26 · Systems Engineering, Analysis, and Design
Answer: B. Both must survive, so this is a series system: R = 0.98 × 0.95 = 0.931, or 93.1%. Multiplying is valid because the failures are independent.
Common misses: A subtracts both failure chances from 1 and double-counts the case where both fail. C averages the two. D is the chance that at least one survives, which is the parallel case, not this one.
Topic: FE Industrial and Systems, subject 13: Systems Engineering, Analysis, and Design. Principle: NIST/SEMATECH e-Handbook, 8.1.8.2 Series model.
Problem 27 · Thermodynamics
Answer: +110 kJ. With heat into the system positive and work done by the system positive, ΔU = Q − W = 150 − 40 = +110 kJ. Internal energy goes up.
Common misses: +190 treats the outgoing work as energy added. −110 reverses the direction of the net energy flow.
Topic: FE Mechanical, subject 11: Thermodynamics. Principle: OpenStax University Physics Vol. 2, 3.3 First Law of Thermodynamics.
Problem 28 · Dynamics
Answer: B. Take right as positive. F_net = 100 − 40 = 60 N, so a = F_net ÷ m = 60 ÷ 20 = 3 m/s² to the right.
Common misses: A uses only the 40 N resisting force. C ignores the resisting force. D adds the two forces instead of subtracting.
Topic: FE Other Disciplines, subject 9: Dynamics. Principle: OpenStax University Physics Vol. 1, 5.3 Newton's Second Law.
What your results mean
A count of right answers here tells you how you did on these 28 problems. That's it. NCEES doesn't publish a passing score: it converts the number you get right into a scaled score and compares it with a minimum standard set by subject-matter experts (NCEES exam scoring). So there's no honest way to turn "19 of 28" into "ready" or "not ready."
What the results are good for:
- Missed two or more in one shared area? Put that area first in week 2 of the plan below.
- Got it right but it took a while? Treat that as a miss for planning. Slow is a real problem on a timed exam.
- Missed your discipline's problem? That's one data point, not a verdict. The full subject list for your exam is in the next section.
Choose your discipline
The NCEES Fundamentals of Engineering (FE) exam has 110 questions, but there are seven different exams, and you take one of them: Chemical, Civil, Electrical and Computer, Environmental, Industrial and Systems, Mechanical, or Other Disciplines. Each has its own official specification listing its subjects and how many questions each subject gets (NCEES FE exam page). All seven specifications currently linked from the NCEES FE page took effect with the July 2020 exams.
Which one should you take? Usually the one that best matches your degree and coursework. FE Other Disciplines is a separate exam built on broad engineering fundamentals (statics, fluids, thermo, electrical basics, and more). It isn't a common section everyone takes. If your degree doesn't line up neatly with one of the six named exams, compare its subject list with your coursework. Before you register, confirm your board's requirements through the state selector on the NCEES FE exam page.
The shared areas, exam by exam
Four areas appear on all seven exams. How many questions they get varies a lot:
| FE exam | Mathematics | Probability and statistics | Ethics | Engineering economics | Shared areas together (of 110) |
|---|---|---|---|---|---|
| Chemical | 6–9 | 4–6 | 3–5 | 4–6 (listed as "Economics") | 17–26 |
| Civil | 8–12 (listed as "Mathematics and Statistics") | included with math | 4–6 | 5–8 | 17–26 |
| Electrical and Computer | 11–17 | 4–6 | 4–6 | 5–8 | 24–37 |
| Environmental | 5–8 | 4–6 | 5–8 | 5–8 | 19–30 |
| Industrial and Systems | 6–9 | 10–15 | 4–6 | 9–14 | 29–44 |
| Mechanical | 6–9 | 4–6 | 4–6 | 4–6 | 18–27 |
| Other Disciplines | 8–12 | 6–9 | 5–8 (listed as "Engineering Ethics and Societal Impacts") | 6–9 | 25–38 |
The ranges come straight from each NCEES specification. The last column is our arithmetic: we added the low ends and the high ends. These are outer bounds from the published ranges, not a fixed count or a promise that both extremes occur on actual forms. A bigger number doesn't mean harder questions. The takeaway: if you're taking Industrial and Systems, the "shared" areas are a big chunk of your exam, not a warm-up.
Your exam's full subject list and study passes
Find your exam below. Every numbered subject in the official specification is listed with its question range; open the linked PDF for its detailed subtopics. We've grouped the subjects into four study passes (A–D) for the 12-week plan; the grouping follows NCEES's own subject order. It's our planning aid. It isn't NCEES's question order, and the four passes aren't equal in size.
FE Chemical
Official FE Chemical specification (PDF) · Largest areas: Material/Energy Balances (10–15), then Fluid Mechanics/Dynamics, Thermodynamics, Heat Transfer, and Mass Transfer and Separation (8–12 each).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (6–9) · Probability and Statistics (4–6) · Engineering Sciences (4–6) · Materials Science (4–6) · Chemistry and Biology (7–11) |
| B | Fluid Mechanics/Dynamics (8–12) · Thermodynamics (8–12) · Material/Energy Balances (10–15) · Heat Transfer (8–12) |
| C | Mass Transfer and Separation (8–12) · Solids Handling (3–5) · Chemical Reaction Engineering (7–11) · Economics (4–6) · Process Design (7–11) |
| D | Process Control (4–6) · Safety, Health, and Environment (5–8) · Ethics and Professional Practice (3–5) |
FE Civil
Official FE Civil specification (PDF) · Largest areas: Water Resources and Environmental Engineering, Structural Engineering, and Geotechnical Engineering (10–15 each), then Transportation Engineering (9–14).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics and Statistics (8–12) · Ethics and Professional Practice (4–6) · Engineering Economics (5–8) |
| B | Statics (8–12) · Dynamics (4–6) · Mechanics of Materials (7–11) · Materials (5–8) |
| C | Fluid Mechanics (6–9) · Surveying (6–9) · Water Resources and Environmental Engineering (10–15) |
| D | Structural Engineering (10–15) · Geotechnical Engineering (10–15) · Transportation Engineering (9–14) · Construction Engineering (8–12) |
FE Electrical and Computer
Official FE Electrical and Computer specification (PDF) · Largest areas: Mathematics and Circuit Analysis (11–17 each), then Power Systems and Digital Systems (8–12 each).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (11–17) · Probability and Statistics (4–6) · Ethics and Professional Practice (4–6) · Engineering Economics (5–8) |
| B | Properties of Electrical Materials (4–6) · Circuit Analysis (DC and AC Steady State) (11–17) · Linear Systems (5–8) · Signal Processing (5–8) |
| C | Electronics (7–11) · Power Systems (8–12) · Electromagnetics (4–6) · Control Systems (6–9) · Communications (5–8) |
| D | Computer Networks (4–6) · Digital Systems (8–12) · Computer Systems (5–8) · Software Engineering (4–6) |
FE Environmental
Official FE Environmental specification (PDF) · Largest areas: Fluid Mechanics and Hydraulics and Water and Wastewater (12–18 each), then Surface Water Resources and Hydrology (9–14).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (5–8) · Probability and Statistics (4–6) · Ethics and Professional Practice (5–8) · Engineering Economics (5–8) |
| B | Fundamental Principles (7–11) · Environmental Chemistry (7–11) · Health Hazards and Risk Assessment (4–6) · Fluid Mechanics and Hydraulics (12–18) · Thermodynamics (3–5) |
| C | Surface Water Resources and Hydrology (9–14) · Groundwater, Soils, and Sediments (8–12) · Water and Wastewater (12–18) |
| D | Air Quality and Control (8–12) · Solid and Hazardous Waste (7–11) · Energy and Environment (4–6) |
FE Industrial and Systems
Official FE Industrial and Systems specification (PDF) · Largest areas: Probability and Statistics (10–15), then Engineering Economics, Modeling and Quantitative Analysis, Manufacturing/Service/Production Systems, Facilities and Supply Chain, and Quality (9–14 each).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (6–9) · Engineering Sciences (4–6) · Ethics and Professional Practice (4–6) |
| B | Engineering Economics (9–14) · Probability and Statistics (10–15) · Modeling and Quantitative Analysis (9–14) |
| C | Engineering Management (8–12) · Manufacturing, Service, and Other Production Systems (9–14) · Facilities and Supply Chain (9–14) |
| D | Human Factors, Ergonomics, and Safety (8–12) · Work Design (7–11) · Quality (9–14) · Systems Engineering, Analysis, and Design (8–12) |
FE Mechanical
Official FE Mechanical specification (PDF) · Largest areas: Dynamics/Kinematics/Vibrations, Fluid Mechanics, Thermodynamics, and Mechanical Design and Analysis (10–15 each).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (6–9) · Probability and Statistics (4–6) · Ethics and Professional Practice (4–6) · Engineering Economics (4–6) · Electricity and Magnetism (5–8) |
| B | Statics (9–14) · Dynamics, Kinematics, and Vibrations (10–15) · Mechanics of Materials (9–14) · Material Properties and Processing (7–11) |
| C | Fluid Mechanics (10–15) · Thermodynamics (10–15) · Heat Transfer (7–11) |
| D | Measurements, Instrumentation, and Controls (5–8) · Mechanical Design and Analysis (10–15) |
FE Other Disciplines
Official FE Other Disciplines specification (PDF) · Largest area: Fluid Mechanics (12–18), then Statics, Dynamics, Strength of Materials, and Thermodynamics and Heat Transfer (9–14 each).
| Pass | Subjects (number of questions) |
|---|---|
| A | Mathematics (8–12) · Probability and Statistics (6–9) · Chemistry (5–8) · Instrumentation and Controls (4–6) |
| B | Engineering Ethics and Societal Impacts (5–8) · Safety, Health, and Environment (6–9) · Engineering Economics (6–9) · Statics (9–14) |
| C | Dynamics (9–14) · Strength of Materials (9–14) · Materials (6–9) |
| D | Fluid Mechanics (12–18) · Basic Electrical Engineering (6–9) · Thermodynamics and Heat Transfer (9–14) |
How to use the ranges: they tell you what the exam covers, not where you need work. A big subject you already know well may only need upkeep. A small subject you've forgotten can still need a full session. Combine the ranges with what you actually miss.
Your 12-week FE study plan
Assumes about 8 hours a week (96 hours total), for someone who finished most of the relevant coursework. That's our planning estimate, not an NCEES requirement or a promise that 96 hours is enough. If a pass runs long, give it another week instead of skipping what you haven't learned.
A typical week: four 1-hour weekday sessions plus two 2-hour weekend sessions. Move the hours wherever they fit.
| Week | Focus | What to do | Done when |
|---|---|---|---|
| 1 | Set up and sample | Open your exam's specification and get the free FE Reference Handbook through MyNCEES (see the handbook section below). Confirm your calculator is on NCEES's approved list. Work the shared-area problems whose topic notes fit your specification plus your discipline's problem, using only the handbook and calculator. Skim one unfamiliar topic from each study pass. | You have your full subject list, an error log started, and your next 11 weeks on the calendar. |
| 2–3 | Pass A | For each subject: 20 minutes finding it in the handbook and reading the variable definitions, then problems from your own coursework, textbooks, or other legal sources, then corrections. Give more time to subjects with bigger ranges and to the ones you missed in week 1. | Every Pass A subject has been practiced, and anything shaky is on your error log. |
| 4–5 | Pass B | Same routine. At the end of week 5, redo every Pass A problem you missed without looking at the solution. | Pass B covered; old misses retried. |
| 6–7 | Pass C | Same routine. Each week, include a mixed set of 10–15 problems from passes A and B. | Pass C covered; earlier passes still warm. |
| 8–9 | Pass D | Same routine. At the end of week 9, check every subject in your specification against your log. | Every subject visited; remaining gaps named. |
| 10 | Repair | Spend 4 hours on your two biggest gaps, 2 hours on mixed problems from all passes, and 2 hours on handbook searches and calculator steps that slowed you down. | Your two biggest gaps are smaller or have extra time scheduled. |
| 11 | Pacing practice | Two 30-problem blocks using discipline-matched problems from your coursework or other authorized sources, the handbook PDF, and your calculator: 90 minutes per block, then 5 hours total reviewing misses and slow problems. These are pacing drills, not full-length simulations. | You know your real pace and what slows you down. |
| 12 | Taper and logistics | Light mixed practice. Redo old misses without solutions. Check your ID, calculator model, appointment time, and route. No new topics in the last few days. | Your ID, calculator, appointment, and travel plan are checked. |
Pacing math: 5 hours 20 minutes is 320 minutes for 110 questions, about 2 minutes 55 seconds per question on average. That's an average, not a budget for each question; an easy item may take less time and a multi-step item more.
Before a pacing drill, review NCEES’s explanation of alternative item types. This starter set uses single-answer, multiple-correct, and numeric-response formats; it does not reproduce the official testing interface.
If your situation is different
- About 4 hours a week: stretch each week of the plan across two weeks. That's the same work over 24 weeks.
- About 12 hours a week: use the eight-week allocation below to keep the same 96-hour budget. Only do this if your setup work goes well; faster calendars don't shrink what you need to learn.
- Several years out of school: add 2–4 weeks before Pass A to rebuild math and the foundations your specification lists. Push the end date rather than switching disciplines to dodge a weak subject.
- Retaking after a fail: NCEES sends a diagnostic report showing your relative strengths and weaknesses by subject (NCEES exam scoring). Put your weakest subjects first within each pass, but still check the rest of your specification; the report doesn't list every concept you missed.
Eight-week allocation at 12 hours per week
This redistributes the main plan without dropping a study pass. The hours are planning estimates, not required study times.
| Week | Allocation | Total |
|---|---|---|
| 1 | Setup and sampling: 8 h; Pass A: 4 h | 12 h |
| 2 | Pass A: 12 h | 12 h |
| 3 | Pass B: 12 h | 12 h |
| 4 | Pass B: 4 h; Pass C: 8 h | 12 h |
| 5 | Pass C: 8 h; Pass D: 4 h | 12 h |
| 6 | Pass D: 12 h | 12 h |
| 7 | Repair: 8 h; pacing and review: 4 h | 12 h |
| 8 | Pacing and review: 4 h; taper and logistics: up to 8 h | Up to 12 h |
The 96 hours are reserved study capacity. The taper is deliberately light; do not fill unused hours simply to hit the total.
Practice with the handbook you'll get on exam day
On exam day, NCEES gives you the reference handbook on screen as a searchable PDF, and that's your only reference. You search it with a search box on the left side of the screen; Ctrl+F doesn't work. (NCEES Examinee Guide, May 2026, p. 10) You can't bring your own.
Get the same handbook free through your MyNCEES account. Use the version NCEES shows for your exam date. You can print it for personal study, but not share or post it. (NCEES help: exam reference handbooks)
The handbook lists formulas and tables. It doesn't show you how to set up a problem. That part comes from practice. Here's a routine for every practice problem:
- Name the unknown and its units before you search.
- Name the idea that governs it: accumulation, equilibrium, circuit reduction, time value of money, an energy balance.
- Search a short term, not the problem's wording. Try concept names such as "capital recovery" rather than a dollar amount from the problem. At home, use your PDF viewer's search, knowing the exam's search box is a different tool.
- Read the variable definitions and conditions before plugging in. Is that the sample or the population formula? Gauge or absolute pressure?
- Log the search term that worked next to the topic in your error log.
Five-minute drill: open your handbook and find (1) the uniform-series present-worth factor, (2) the sample standard deviation formula, (3) the standard normal table, (4) the ethics section, and (5) the section for your largest discipline subject. Time yourself. Repeat in week 10 and see how much faster you are.
Turn misses into your next session
After a missed or slow problem, write down what stopped a clean solution. Then fix that cause, not just that problem.
| Problem and topic | Result | Cause | Next task | Retry |
|---|---|---|---|---|
| Example: Problem 23, Civil Statics | Picked 8 kN, the left reaction | Setup: solved for the wrong unknown | Label both supports, circle the asked-for reaction, then solve a new beam with an off-center load | Date, result, anything still wrong |
| Your row | Right / wrong / skipped; time | Concept / setup / units / calculator / reading / handbook lookup | One specific action | Date and notes |
| Cause | What fixes it |
|---|---|
| Concept | Explain the governing idea in your own words, check when it applies, then solve a fresh example. |
| Setup | List the givens, the unknown, and the equation before you touch a number. Draw the system. |
| Units | Write the conversion as a chain of fractions and cancel the units on paper. |
| Calculator | Redo the exact keystrokes. Check parentheses, scientific notation, and degree/radian mode. |
| Reading | Underline what's actually asked and any word that changes the assumptions ("sample," "absolute," "net"). |
| Handbook lookup | Practice finding the topic and reading its definitions without solving anything. |
Check the exam details before you book
These booking notes follow the U.S. NCEES process; your selected licensing board controls eligibility.
| Detail | FE exam |
|---|---|
| Questions | 110 |
| Exam time | 5 hours 20 minutes, plus a 25-minute scheduled break |
| Full appointment | The May 2026 Examinee Guide lists 5 hr 55 min; the FE webpage lists 6 hours. The guide includes a 2-minute nondisclosure agreement and an 8-minute tutorial. |
| Fee | $225, paid to NCEES (your board may charge its own application fee) |
| Where and when | Computer-based, at NCEES-approved Pearson test centers, year-round |
| Results | Pass or fail; the Examinee Guide and NCEES scoring page say typically 7–10 days |
Sources: NCEES FE exam page; NCEES Examinee Guide, May 2026, pp. 3, 9, 14 and 16; NCEES exam scoring. For arrival and scheduling, follow your appointment confirmation and the guide’s instruction to arrive 30 minutes early. Some state-specific blocks on the FE webpage describe results as 7–10 business days; these are estimates, not a guaranteed release date.
Rules to know before exam day:
- You can't go back to the first half. The exam has two sections. After about half the questions, you review and submit them, and they're locked. You get the full exam time at the start; the sections aren't timed separately. The break comes after you submit the first section. Flag and review before you submit. (Examinee Guide, pp. 11–12)
- Not every question is single-answer. Expect multiple-correct, point-and-click, drag-and-drop, and fill-in-the-blank questions too. None of them give partial credit. (Examinee Guide, p. 11)
- Never leave a question blank. Your score is based on correct answers, with nothing taken off for wrong ones. (NCEES exam scoring)
- Bring one approved calculator. The guide directs you to “Calculator Policy” at the bottom of the NCEES exams page to check your exact model. An on-screen TI-30XS is also available during the exam (Examinee Guide, p. 8). Practice on the model you'll bring.
- Scratch-work materials are provided: two reusable booklets and three markers, with replacement booklets available if you ask (Examinee Guide, pp. 9–10).
- Bring an accepted physical, current photo ID: government-issued ID from the country where you test, an international travel passport in Roman characters from your country of citizenship, or a U.S. military ID. It must show an expiration date, your name, date of birth, recognizable photo, and signature; valid U.S. military IDs may omit the signature. First and last names must match your appointment confirmation. Student IDs and digital IDs aren't accepted (Examinee Guide, p. 8).
- Need to move your appointment? The normal rule is to reschedule or cancel at least 48 hours ahead; Pearson charges $50. Canceling the appointment does not also cancel your NCEES registration: follow the separate registration-cancellation process when seeking a registration refund. The guide explains documented emergency exceptions (Examinee Guide, pp. 4 and 6–7).
- Need accommodations? Ask during registration. NCEES then emails you the next steps. The exam stays on hold while the request is decided, so resolve it before scheduling (Examinee Guide, p. 3).
Common questions about FE exam prep
What score do I need to pass? NCEES doesn't publish one. Your correct answers become a scaled score that's compared with a minimum standard, and you get pass or fail (NCEES exam scoring). Anyone quoting you an exact passing percentage is guessing.
What happens if I fail? You get a diagnostic report by subject. NCEES allows one attempt per testing window and no more than three in any 12 months; some boards are stricter. The windows are January–March, April–June, July–September, and October–December (Examinee Guide, p. 5). Use the retake adjustment in the plan above.
Can I take the FE before I graduate? NCEES designs the FE for recent graduates and students close to finishing an EAC/ABET-accredited engineering degree (NCEES FE exam page). Whether you can sit for it, and whether you need to apply to your board first, depends on your state. Check through the FE page's state selector or the NCEES licensing board directory.
Does passing make me an EIT or a PE? Passing the FE is not a PE license; NCEES describes it as generally the first step toward becoming a licensed professional engineer (NCEES FE exam page). EIT or EI certification follows your board's process. Titles like engineer-in-training (EIT) or engineer intern (EI), and the steps after the FE, are set by your state board, so check with them through the NCEES licensing board directory.
Which specification should I use? Use the specification linked for your discipline on the NCEES FE exam page. The seven PDFs checked for this guide are effective beginning with the July 2020 examinations. Before your test, revisit that page and the current Examinee Guide; a date on a prep resource is not an exam-version rule.
What can I use for free study? The handbook is free, your discipline's specification lists its subjects and subtopics, and your old coursework and textbooks are full of problems. The OpenStax chapters and NIST explanations linked under these questions also provide free concept review. Practice problems with the handbook open, then fix what you miss.
Sources and verification
Last verified: October 5, 2026. We checked the NCEES FE exam page, all seven linked FE specifications, the May 2026 Examinee Guide, NCEES's scoring and handbook-access instructions, and the August 2026 Model Rules passages used in the ethics items. The teaching principles were checked against the sources linked beneath the problems, and numerical answers were recalculated.
AI-assisted tools were used to develop and check this content. This is editorial source checking, not professional engineering review.
Official sources:
- NCEES: FE exam
- NCEES Examinee Guide, May 2026 (PDF) · current guide landing page
- NCEES: Exam scoring
- NCEES: Exams page, including calculator policy
- NCEES help: Exam reference handbooks
- FE specifications, effective July 2020: Chemical · Civil · Electrical and Computer · Environmental · Industrial and Systems · Mechanical · Other Disciplines
- NCEES Model Rules, August 2026 (PDF)
- NCEES member licensing board directory
- NCEES exam prep errata
Teaching sources for each problem are linked directly beneath it. How we check exam facts: our methodology. Found an error? Our corrections log explains how to report it.
Written by the Castleport Test Prep Editorial Team.
Castleport Test Prep is an independent exam prep publisher, not affiliated with, endorsed by, or approved by the National Council of Examiners for Engineering and Surveying (NCEES), Pearson VUE, or any state engineering licensing board. The practice problems on this page are original and unofficial; they are not NCEES exam questions. Exam and credential names identify their subjects; trademarks belong to their respective owners. This resource doesn't guarantee an exam result or determine eligibility or licensure.