100+ Free FE Chemical Practice Questions

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Question 1

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Evaluate the indefinite integral of (3x^2 + 2x - 5) dx.

x^3 + x^2 - 5x + C

6x + 2 + C

x^3 + 2x^2 - 5x + C

3x^3 + x^2 - 5x + C

to track

2026 Statistics

Key Facts: FE Chemical Exam

110

Exam Questions

NCEES FE Chemical CBT specs

5h 20m

Exam Time

NCEES

$175

Exam Fee

NCEES

~73%

First-Time Pass Rate

NCEES discipline data

Knowledge Areas

FE Chemical CBT specs

v10.6

FE Reference Handbook

NCEES (2025)

FE Chemical is a 110-question CBT delivered in a 6-hour appointment (5h 20m of testing plus tutorial and an optional 25-minute break). The $175 NCEES fee is paid at registration and the exam is administered at Pearson VUE test centers. The current July 2020 specifications remain in effect for 2026, and candidates work from the on-screen FE Reference Handbook v10.6. Heaviest content blocks are Material/Energy Balances (10-15 questions), Fluid Mechanics, Thermodynamics, Heat Transfer, and Mass Transfer/Separation (each 8-12 questions).

Sample FE Chemical Practice Questions

Try these sample questions to test your FE Chemical exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the indefinite integral of (3x^2 + 2x - 5) dx.

A.x^3 + x^2 - 5x + C

B.6x + 2 + C

C.x^3 + 2x^2 - 5x + C

D.3x^3 + x^2 - 5x + C

Explanation: Integrate term-by-term: integral of 3x^2 is x^3, integral of 2x is x^2, integral of -5 is -5x. Add the constant of integration C, giving x^3 + x^2 - 5x + C.

2A first-order ODE dy/dx = ky has y(0) = 100. If k = -0.05 min^-1, what is y at x = 20 min?

A.50.0

B.36.79

C.60.65

D.73.58

Explanation: Solution to dy/dx = ky is y = y0 e^(kx). With y0 = 100, k = -0.05, x = 20: y = 100 e^(-1.0) = 100 (0.3679) = 36.79.

3Use the Newton-Raphson method to perform one iteration on f(x) = x^2 - 5 starting from x0 = 2. What is x1?

A.2.25

B.2.50

C.2.236

D.1.75

Explanation: Newton-Raphson: x1 = x0 - f(x0)/f'(x0). f(2) = -1, f'(2) = 2x = 4. x1 = 2 - (-1)/4 = 2 + 0.25 = 2.25.

4What is the Laplace transform of f(t) = e^(-3t)?

A.1/(s+3)

B.1/(s-3)

C.3/(s^2+9)

D.s/(s^2+9)

Explanation: L{e^(-at)} = 1/(s + a). With a = 3, L{e^(-3t)} = 1/(s + 3). This is a standard Laplace transform pair listed in the FE Reference Handbook.

5Given two equations: 2x + y = 7 and x - y = 2, solve for x.

A.3

B.1

C.5

D.9

Explanation: Add the two equations: (2x + y) + (x - y) = 7 + 2, giving 3x = 9, so x = 3. Then y = x - 2 = 1; check: 2(3) + 1 = 7 (OK).

6A measurement is 12.345 g with uncertainty +/- 0.01 g. How many significant figures should be reported?

A.3

B.4

C.5

D.6

Explanation: The uncertainty +/- 0.01 g controls the last reported digit. Reporting 12.35 g (or 12.34 g) carries 4 significant figures, matching the precision of the measurement to the hundredths place.

7A quality engineer collects 30 viscosity readings with mean 50 cP and sample standard deviation 4 cP. What is the 95% confidence interval for the population mean (use z = 1.96)?

A.50 +/- 0.73

B.50 +/- 1.43

C.50 +/- 7.84

D.50 +/- 4.00

Explanation: CI = mean +/- z * (s / sqrt(n)) = 50 +/- 1.96 * (4 / sqrt(30)) = 50 +/- 1.96 * 0.7303 = 50 +/- 1.43 cP. With n = 30 the z-approximation is acceptable.

8A continuous reactor produces 5% off-spec product. In a random sample of 4 batches, what is the probability that exactly 1 is off-spec? (binomial distribution)

A.0.171

B.0.050

C.0.200

D.0.815

Explanation: P(X=1) = C(4,1) * 0.05^1 * 0.95^3 = 4 * 0.05 * 0.857 = 0.1715, or about 17.1%.

9An x-bar control chart uses 3-sigma limits. Sigma of the process is 2.0 and the target mean is 100. What are the upper and lower control limits for samples of size n = 4?

A.UCL = 106, LCL = 94

B.UCL = 103, LCL = 97

C.UCL = 102, LCL = 98

D.UCL = 112, LCL = 88

Explanation: Standard error of the sample mean = sigma / sqrt(n) = 2 / sqrt(4) = 1.0. UCL = 100 + 3(1) = 103; LCL = 100 - 3(1) = 97.

10Two events A and B are independent with P(A) = 0.3 and P(B) = 0.4. What is P(A and B)?

A.0.12

B.0.70

C.0.58

D.0.30

Explanation: For independent events, P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

About the FE Chemical Exam

The NCEES FE Chemical exam is the discipline-specific Fundamentals of Engineering exam for chemical engineers pursuing Engineer Intern (EI/EIT) status and, ultimately, the PE Chemical license. The current July 2020 CBT specifications cover 17 knowledge areas spanning math, engineering sciences, chemistry/biology, fluid mechanics, thermodynamics, material/energy balances, heat and mass transfer, reaction engineering, process design and control, safety, economics, and ethics. The exam is closed-book except for the on-screen NCEES FE Reference Handbook (v10.6, effective 2025).

Assessment

110 computer-based questions with the on-screen NCEES FE Reference Handbook (v10.6)

Time Limit

5 hours 20 minutes

Passing Score

Scaled cut score (NCEES does not publish a fixed percentage)

Exam Fee

$175 (NCEES (Pearson VUE))

FE Chemical Exam Content Outline

6-9 questions

Mathematics

Analytic geometry, calculus, differential equations, numerical methods (Newton-Raphson, Taylor series), linear algebra, accuracy/precision, significant figures.

4-6 questions

Probability and Statistics

Discrete and continuous distributions, expected value, hypothesis testing, ANOVA, central tendency, regression, control charts.

4-6 questions

Engineering Sciences

Basic dynamics (force, mass, momentum), work-energy-power, electricity and circuits (Ohm's law, Kirchhoff's laws).

4-6 questions

Materials Science

Chemical/electrical/mechanical/physical properties, ferrous/nonferrous metals, corrosion mechanisms and control, polymers, ceramics, composites.

7-11 questions

Chemistry and Biology

Inorganic chemistry (molarity, normality, pH/pK, redox, electrochemistry), organic chemistry, analytical chemistry, biochemistry, microbiology, bioprocessing/fermentation.

8-12 questions

Fluid Mechanics/Dynamics

Fluid properties, Reynolds number, mechanical energy balance, Bernoulli, laminar/turbulent flow, pumps and compressors, flow measurement, compressible and non-Newtonian flow.

8-12 questions

Thermodynamics

Pure-component and mixture properties, steam tables, T-s/P-h/x-y diagrams, first/second laws, cycles (power, refrigeration, heat pump), phase and chemical equilibrium, heats of reaction.

10-15 questions

Material/Energy Balances

Steady- and unsteady-state mass balances, energy balances, recycle/bypass, reactive systems, combustion calculations.

8-12 questions

Heat Transfer

Conduction (Fourier law), convection (natural and forced, Nusselt correlations), radiation, overall U, fouling, heat-exchanger design (LMTD, NTU, double-pipe, shell-and-tube).

8-12 questions

Mass Transfer and Separation

Molecular diffusion, convective mass transfer, distillation, absorption, extraction, membranes, McCabe-Thiele equilibrium-stage methods, NTU/HETP/HTU.

3-5 questions

Solids Handling

Particle-size distributions, surface and bulk forces, crushing and grinding, crystallization, pneumatic conveying, slurries, hoppers, tanks.

7-11 questions

Chemical Reaction Engineering

Rate laws and order, Arrhenius rate constant, conversion/yield/selectivity, batch/CSTR/PFR/semi-batch design, series and parallel reactions, catalysis.

4-6 questions

Economics

Time value of money (PW, AW, FW, ROR), break-even and benefit-cost, expected value/risk, depreciation, project comparison with unequal lives, discounted cash flow.

7-11 questions

Process Design

PFDs and P&IDs, equipment selection and scale-up, cost estimation with cost indices, sustainability and inherently safer design, ASTM/ISO/OSHA design standards.

4-6 questions

Process Control

First- and second-order dynamics, gains and time constants, transfer functions, stability, PID tuning, feedback/feedforward/cascade/ratio, sensors, control valves, DCS/PLC.

5-8 questions

Safety, Health, and Environment

SDS hazards (flammability/LFL-UFL, toxicity), industrial hygiene, HAZOP and LOPA, fault/event-tree analysis, relief and overpressure, RCRA/CWA/EPA waste rules, runaway-reaction control.

3-5 questions

Ethics and Professional Practice

NCEES Model Rules, codes of ethics, contracts and NDAs, public health and welfare obligations, intellectual property (patents, trademarks, trade secrets, copyright).

How to Pass the FE Chemical Exam

What You Need to Know

Passing score: Scaled cut score (NCEES does not publish a fixed percentage)
Assessment: 110 computer-based questions with the on-screen NCEES FE Reference Handbook (v10.6)
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 Chemical Study Tips from Top Performers

1Anchor your plan around the 17 NCEES knowledge areas, not generic chemical engineering topics - the specifications PDF lists exact subtopics that get tested.

2Drill open-system first-law and steady-state mass/energy balances until reactive systems and recycle/bypass loops feel routine - they show up across many sections.

3Practice locating equations in the on-screen FE Reference Handbook v10.6 - speed of lookup matters more than memorization in a CBT environment.

4Master one Antoine, Raoult, and McCabe-Thiele workflow end-to-end so VLE and distillation questions become pattern recognition.

5Build fluency with LMTD, NTU, and overall U for heat-exchanger sizing, plus Nusselt correlations for forced and natural convection.

6Memorize Arrhenius, batch/CSTR/PFR design equations, and how to apply them to first- and second-order kinetics; reactor problems repeat in different wrappers.

7Review NCEES-approved calculators (Casio FX-115, TI-30X/36X, HP 33s/35s) and bring spare batteries to test day.

8Skim a process-safety primer covering LFL/UFL, HAZOP, LOPA, and overpressure relief - safety questions are easy points if you know the vocabulary.

9Refresh engineering economics formulas (P/F, P/A, A/F, A/P) and depreciation methods - 4-6 economics questions are usually quick wins.

10Take at least one full timed 5h 20m simulation using only the FE Reference Handbook to build pacing and stamina.

Frequently Asked Questions

What is the FE Chemical exam pass rate in 2026?

NCEES reports first-time pass rates around 73% for FE Chemical, making it consistently one of the higher-passing FE disciplines. Repeat-taker pass rates are lower (typically 35-45%). Pass rates are scaled, not percentage-based, so NCEES does not publish a fixed cut score.

How long is the FE Chemical exam?

The exam itself is 5 hours and 20 minutes long, but the total Pearson VUE appointment is 6 hours. That includes an 8-minute tutorial, the testing window, and an optional 25-minute scheduled break that does not count against your test time.

Which FE Reference Handbook version is used in 2026?

NCEES is using FE Reference Handbook version 10.6 in 2026 (released July 2025). The handbook is delivered as a searchable PDF on-screen during the exam. Practice with the same version you will see on test day - formula locations and notation differ slightly from earlier editions.

What does the FE Chemical exam cost?

The NCEES exam fee is $175, paid directly to NCEES at registration. Some state boards charge an additional application fee on top of the NCEES fee, and a few jurisdictions require board pre-approval before you can register. The $175 is also the retake fee per attempt.

What calculator is allowed on the FE Chemical exam?

Only NCEES-approved models: Casio FX-115 series, Hewlett Packard HP 33s and HP 35s, and Texas Instruments TI-30X and TI-36X series. An on-screen calculator is also provided at the test center. Personal smartphones, laptops, and reference books are not permitted.

What are the heaviest topics on FE Chemical?

Material/Energy Balances is the largest single area at 10-15 questions. Four other domains each carry 8-12 questions: Fluid Mechanics, Thermodynamics, Heat Transfer, and Mass Transfer/Separation. Together, these five blocks make up roughly half the exam, so they should anchor your study plan.