Forms A–B · First edition

FE Other Disciplines Practice Exam

110 original four-choice problems mapped to the current FE Other Disciplines knowledge areas, with complete worked solutions.

See 2 forms — USD 29 each Free practice PDF · 14 problems Read free problems

Statics, dynamics, strength of materials, fluid mechanics, and thermodynamics and heat transfer account for 51 of the 110 problems here, with fluid mechanics the single heaviest area at 12 problems.

Problems: 110 per form
Free problems: 14
Forms: 2

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Practice Exam, Form A

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110 original problems and complete worked solutions
Answer key and knowledge-area score sheet
127-page immediate private PDF download

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Practice Exam, Form B

USD29

110 original problems and complete worked solutions
Answer key and knowledge-area score sheet
102-page immediate private PDF download

14-day full refund · 90-day download access

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Form A

127 pages · Version 1.0.0

FE Other Disciplines Form A: A worked-solution page from the current release — **Worked solution**Form A · direct PDF render

FE Other Disciplines Form A: The knowledge-area score sheet included in the PDF — **Score sheet**Form A · direct PDF render

Form B

102 pages · Version 1.0.0

FE Other Disciplines Form B: A worked-solution page from the current release — **Worked solution**Form B · direct PDF render

FE Other Disciplines Form B: The knowledge-area score sheet included in the PDF — **Score sheet**Form B · direct PDF render

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Try a complete mathematics problem

Water drains from an inverted right circular cone, apex down, having a top radius of 3.0 m and a height of 6.0 m. The discharge is steady at 0.25 m $^{3}$ /s. When the water depth is 4.0 m, the rate of fall of the free surface is most nearly:

(A)0.0050 m/s
(B)0.0088 m/s
(C)0.0199 m/s
(D)0.0597 m/s

Show worked solution

Answer: (C)

The free surface falls about 0.0199 m/s, since at a depth of 4.0 m its area is only $4 π$ m $^{2}$ .

Geometric similarity ties the surface radius to the depth, reducing the volume to a single variable.

r = \frac{h}{2}

V = \frac{1}{3} π r^{2} h = \frac{π h ^{3}}{12}

Differentiating volume with respect to depth produces the instantaneous free-surface area, the only geometry the drain rate responds to.

\frac{d V}{d t} = \frac{π h ^{2}}{4} \cdot \frac{d h}{d t}

At 4.0 m depth the surface radius is 2.0 m and the surface area is $4 π$ m $^{2}$ , so the level drops at

\frac{d h}{d t} = \frac{0.25}{4 π} = 0.0199 m/s

FE Reference Handbook — Mathematics: Mensuration of Areas and Volumes, Right Circular Cone; Differential Calculus, The Chain Rule

Why the other choices appear

(A)Sets the surface radius equal to the depth, $r = h = 4.0$ m, giving $0.25/ (16 π) = 0.0050$ m/s.
(B)Uses the fixed 3.0 m top radius as the surface radius, giving $0.25/ (9 π) = 0.0088$ m/s.
(D)Divides the volume by the depth instead of differentiating, taking $d V / d h = π h^{2} /12 = 4.19$ m $^{2}$ and giving 0.0597 m/s.

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What each download contains

Edition: First edition
Form A: 127 pages · Version 1.0.0
Form B: 102 pages · Version 1.0.0
Questions: 110 original problems per form
Coverage: 14 knowledge areas
Question type: Four-choice, single-answer
Format: Print-ready PDF, US Letter

Built against the NCEES FE Other Disciplines specifications effective July 2020, current as of July 2026. Official exam format and appointment facts are available from NCEES. This printable form does not reproduce the Pearson VUE interface or interactive alternative item types.

Knowledge-area coverage

Knowledge area	Form A	NCEES range
Mathematics	9	8-12
Probability and Statistics	7	6-9
Chemistry	6	5-8
Instrumentation and Controls	5	4-6
Engineering Ethics and Societal Impacts	5	5-8
Safety, Health, and Environment	6	6-9
Engineering Economics	7	6-9
Statics	10	9-14
Dynamics	10	9-14
Strength of Materials	10	9-14
Materials	7	6-9
Fluid Mechanics	12	12-18
Basic Electrical Engineering	7	6-9
Thermodynamics and Heat Transfer	9	9-14

Verification and corrections

Original problems, checked by a second calculation route

Every answer is reproduced with an alternate formula, a limiting case, a dimensional check, or a direct recomputation before publication. Official examination questions are confidential and are not reproduced or paraphrased.

Confirmed errors are published as versioned corrections. Buyers can re-download the corrected release at no charge. Read the full editorial method.

For a repeat attempt

Close the weak areas before another USD 225 appointment

FE Other Disciplines repeat examinees passed at 29% versus 61% for first-time examinees in the cited NCEES data. Use the form's score sheet beside your diagnostic report, then read the FE Other Disciplines retake plan or compare FE pass rates by discipline.

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Questions about the PDF

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EngineerProof is not affiliated with, endorsed by, or sponsored by NCEES. FE and NCEES are registered trademarks of the National Council of Examiners for Engineering and Surveying, used solely to identify the examination for which these study materials are relevant. All problems and solutions in this publication are original works.

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No. This is a printable four-choice PDF. It does not include the Pearson VUE interface or interactive alternative item types such as point-and-click and drag-and-drop.

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