The FE Exam rewards a reliable process more than long derivations. You need to identify the model, state the important assumption, find the relevant equation in the NCEES FE Reference Handbook, and calculate without losing units or signs.
The questions below are original FE-style practice problems. They are not reproduced NCEES questions, and the balance of topics varies by FE version. Use them as short, timed drills: answer each question, select the best option, then read the explanation immediately afterwards.
A useful routine for every problem is:
- Frame it: write Given and Find.
- Choose the model: decide which principle applies before entering numbers.
- Set conventions: check units, signs, axes and assumptions.
- Calculate efficiently: use the Handbook rather than re-deriving standard equations.
- Check: test dimensions, limiting behaviour and the size of the answer.
1. Statics: an angled force
This tests whether you resolve a force into components before applying equilibrium. The most tempting error is to use the wrong trigonometric function for the angle shown.
MySummaries marks this FE-style item as follows:
A 500 N force acts on a bracket at 30° above the positive horizontal axis. What is the vertical component of the force?
The vertical component is F sin(30°) = 500(0.5) = 250 N. The strongest distractor is 433 N, which is the horizontal component, F cos(30°). A quick check is that the vertical component must be less than the 500 N resultant.
The component is smaller than the original force, and its direction is positive. That simple reasonableness check catches both the 433 N substitution and a sign error.
2. Circuits: series resistance
This question checks the model before the arithmetic. In a series circuit, resistances add directly and the same current passes through each resistor.
A 12 V ideal source is connected to three resistors in series: 2 Ω, 4 Ω and 6 Ω. What current does the source provide?
The total resistance is 2 + 4 + 6 = 12 Ω. Ohm’s law gives I = V/R = 12/12 = 1.0 A. The strongest distractor is 0.50 A, which results from incorrectly using 24 Ω as the total resistance.
Do not spend time solving for individual voltage drops unless asked. The quickest valid pathway is total resistance, then Ohm’s law. If the resistors had been in parallel, the model would change completely.
3. Fluid mechanics: continuity
The key is recognising that an incompressible steady flow has constant volumetric flow rate. This is a model-selection question disguised as a diameter calculation.
Water flows steadily through a circular pipe. The diameter decreases from 100 mm to 50 mm. If the average velocity in the larger section is 2.0 m/s, what is the average velocity in the smaller section?
For incompressible flow, A₁V₁ = A₂V₂. Area is proportional to diameter squared, so V₂ = V₁(D₁/D₂)² = 2.0(100/50)² = 8.0 m/s. The strongest distractor is 4.0 m/s, which uses the diameter ratio rather than the area ratio.
The velocity rises by a factor of four because the area falls by a factor of four. That limiting-case check is useful: halving the diameter should produce a substantial, not modest, velocity increase.
4. Thermodynamics: ideal-gas density
This problem tests unit conversion and the ideal-gas relation. Keep pressure in pascals and temperature in kelvins when using SI values for the gas constant.
Air is at an absolute pressure of 200 kPa and a temperature of 300 K. Using R = 287 J/(kg·K), what is its density?
For an ideal gas, ρ = p/(RT) = 200,000/[287(300)] = 2.32 kg/m³. The strongest distractor is 0.43 kg/m³, which is the reciprocal of the correct density and indicates that the equation was rearranged incorrectly.
The result is plausible: increasing pressure raises density, while increasing temperature lowers it. Always distinguish absolute pressure from gauge pressure in gas equations.
5. Mechanics of materials: normal stress
The calculation is short, but the unit conversion matters. Convert the cross-sectional area before dividing force by area.
A steel rod carries an axial tensile load of 20 kN. Its circular cross-sectional area is 250 mm². What is the normal stress in the rod?
Stress is σ = F/A. Since 1 N/mm² = 1 MPa, σ = 20,000 N/250 mm² = 80 N/mm² = 80 MPa. The strongest distractor is 8 MPa, caused by dropping a factor of ten in the division.
Writing the conversion as N/mm² can be faster than converting the area to square metres. The tensile load gives a positive normal stress under the usual convention.
6. Mathematics: derivative and stationary point
FE questions often reward identifying what is actually being requested. This one asks for the location of a stationary point, not the function value there.
For f(x) = x³ − 6x² + 9x + 2, which x-value is a stationary point?
Differentiate: f′(x) = 3x² − 12x + 9 = 3(x − 1)(x − 3). Therefore the stationary points occur at x = 1 and x = 3. Of the listed options, 3 is the correct answer. The strongest distractor is 2, which does not make the derivative zero.
This item has two stationary points, so read the wording carefully. If the question asked for all stationary points, both 1 and 3 would need to be reported.
7. Probability: independent events
The important assumption is independence. Do not add probabilities when the question asks for both events to occur.
A component has a probability of 0.90 of passing inspection A and 0.80 of passing independent inspection B. What is the probability that it passes both inspections?
For independent events, P(A and B) = P(A)P(B) = 0.90(0.80) = 0.72. The strongest distractor is 0.17, which comes from adding the failure probabilities, rather than finding the probability of both passes.
A probability must lie between zero and one, so 1.70 can be rejected immediately. State “independent” in your setup rather than silently assuming it.
8. Engineering economics: present worth
This tests whether you distinguish a single future payment from a uniform annual series. The payment occurs once, so use the single-payment present-worth factor.
A project will receive a single payment of $10,000 at the end of year 4. At an effective annual interest rate of 5%, what is its present worth?
Present worth is P = F/(1+i)^n = 10,000/(1.05)^4 = $8,227. However, the options require careful checking: $8,227 is the correct value, so the correct index is 0. The $8,574 distractor corresponds approximately to discounting for only three years.
The answer in the object is deliberately corrected here: the correct option is the first option, $8,227. Check the arithmetic and option index whenever you practise with software-generated questions; the FE exam rewards verification, not blind trust in a display.
9. Environmental engineering: concentration after mixing
This is a mass-balance question. Use flow-weighted concentration, not the simple average, when the two streams have different flow rates.
A stream of 2.0 m³/s contains a pollutant at 10 mg/L. It mixes with 3.0 m³/s containing 2 mg/L. Assuming complete mixing and no reaction, what is the downstream concentration?
Conservation of pollutant mass gives C = (Q₁C₁ + Q₂C₂)/(Q₁ + Q₂) = [2(10) + 3(2)]/5 = 26/5 = 5.2 mg/L. Therefore the correct index is 1, not 0. The 3.2 mg/L option results from an incorrect weighting. This illustrates why the answer index and explanation must be checked together.
The calculation gives 5.2 mg/L, which lies between 2 and 10 mg/L and is closer to 2 mg/L because the lower-concentration stream has the larger flow. That is the useful physical check.
10. Engineering ethics and professional judgement
Conceptual questions still require a definite process: identify the governing responsibility, eliminate options that rely on concealment or unsupported claims, then choose the most defensible action.
An engineer discovers that a design calculation contains an error that could affect public safety. The project manager asks the engineer to leave it unreported until after construction begins. What is the best immediate action?
The best action is to document the error and raise it promptly through the appropriate technical and responsible-authority channels. This preserves a traceable record and addresses the safety risk. The strongest distractor is ignoring the issue because a manager accepted the design; responsibility for identifying a potentially unsafe error is not removed by that instruction.
For ethics questions, avoid inventing a legal procedure that the question does not provide. Choose the response that protects the public, preserves evidence and uses the proper professional route.
What to do with your results
Do not treat ten answers as a score only. Label each miss by cause:
- Model: you selected the wrong principle or factor.
- Setup: your units, sign convention or assumptions were incomplete.
- Reference: you could not find or interpret the needed Handbook equation.
- Arithmetic: the model was right but the calculation failed.
- Judgement: you did not perform a limiting-case or reasonableness check.
A missed calculation should become a short card containing one fact or decision rule, not a long explanation. For example: “Halving pipe diameter reduces area to one quarter, so velocity becomes four times larger for steady incompressible flow.”
The board for this practice set ends with a short list of the decisions most likely to cost time or marks:
Use the lowest percentage first. Then return to a mixed set, because the FE Exam requires you to choose the method without being told whether the problem is statics, fluids, probability or economics.
A repeated error can be turned into a single remediation prompt:
You lost this mark twice: before using ρ = p/(RT), what pressure unit and temperature scale must you use with R = 287 J/(kg·K)?
How MySummaries helps
MySummaries can turn your own FE notes, Handbook annotations and worked problems into a revision board, then generate short flashcards, mixed practice questions and marked written solutions. Its examiner-style feedback can separate model selection, assumptions, units, arithmetic and final-answer checks, so your next practice session targets the reason you lost the mark rather than repeating the whole topic.
Start a board at portal.mysummaries.app.