New Jersey Fundamentals of Engineering
FE Exam-Practice Questions And Correct
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Rationales 2026-2027 Q&A | Instant
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1. Evaluate the expression 3𝑥 2 − 4𝑥 + 7when 𝑥 = 3.
A. 22
B. 24
C. 26
D. 28
Correct Answer: C. 22
Rationale: Substituting 𝑥 = 3gives 3(32 ) − 4(3) + 7 = 27 − 12 + 7 = 22. Therefore, the
correct answer is 22, corresponding to option A.
2. A force of 500 N acts on an area of 0.025 m². What pressure does it produce?
A. 10,000 Pa
B. 15,000 Pa
C. 20,000 Pa
D. 25,000 Pa
Correct Answer: C. 20,000 Pa
Rationale: Pressure is force divided by area. Thus, 𝑃 = 500/0.025 = 20,000 Pa.
3. A vehicle travels 180 km in 2.5 hours. What is its average speed?
A. 60 km/h
B. 72 km/h
C. 75 km/h
D. 80 km/h
Correct Answer: B. 72 km/h
Rationale: Average speed equals distance divided by time. Therefore, 𝑣 = 180/2.5 =
72 km/h.
4. What is the derivative of 𝑓(𝑥) = 4𝑥 3 − 5𝑥 2 + 2𝑥 − 8?
,A. 12𝑥 2 − 10𝑥 + 2
B. 12𝑥 3 − 10𝑥 + 2
C. 4𝑥 2 − 5𝑥 + 2
D. 12𝑥 2 − 5𝑥 + 2
Correct Answer: A. 12𝑥 2 − 10𝑥 + 2
Rationale: Apply the power rule to each polynomial term. The derivative of 4𝑥 3 is 12𝑥 2 , the
derivative of −5𝑥 2 is −10𝑥, and the derivative of 2𝑥is 2.
2
5. Evaluate the definite integral ∫0 3 𝑥 2 𝑑𝑥.
A. 4
B. 6
C. 8
D. 12
Correct Answer: C. 8
Rationale: The antiderivative is 𝑥 3 . Evaluating at the limits gives 23 − 03 = 8.
6. A right triangle has perpendicular sides of 6 m and 8 m. What is the hypotenuse length?
A. 9 m
B. 10 m
C. 12 m
D. 14 m
Correct Answer: B. 10 m
Rationale: By the Pythagorean theorem, 𝑐 = √62 + 82 = √100 = 10 m.
7. Solve the equation 5𝑥 − 12 = 28.
A. 6
B. 7
C. 8
D. 9
Correct Answer: C. 8
Rationale: Add 12 to both sides to obtain 5𝑥 = 40. Dividing by 5 gives 𝑥 = 8.
8. A vector has components 𝐴𝑥 = 3and 𝐴𝑦 = 4. What is its magnitude?
A. 4
B. 5
C. 6
D. 7
,Correct Answer: B. 5
Rationale: The magnitude is √𝐴2𝑥 + 𝐴𝑦2 = √32 + 42 = 5.
9. What is the slope of the line passing through (2, 3)and (6, 11)?
A. 1
B. 2
C. 3
D. 4
Correct Answer: B. 2
Rationale: The slope is (11 − 3)/(6 − 2) = 8/4 = 2.
10. What is the solution to the system 𝑥 + 𝑦 = 10and 𝑥 − 𝑦 = 4?
A. 𝑥 = 6, 𝑦 = 4
B. 𝑥 = 7, 𝑦 = 3
C. 𝑥 = 8, 𝑦 = 2
D. 𝑥 = 5, 𝑦 = 5
Correct Answer: B. 𝑥 = 7, 𝑦 = 3
Rationale: Adding the equations gives 2𝑥 = 14, so 𝑥 = 7. Substituting into 𝑥 + 𝑦 = 10gives
𝑦 = 3.
11. What is the value of log10 (1000)?
A. 1
B. 2
C. 3
D. 10
Correct Answer: C. 3
Rationale: Since 103 = 1000, the base-10 logarithm of 1000 is 3.
4 2
12. What is the determinant of the matrix [ ]?
3 5
A. 8
B. 10
C. 14
D. 26
Correct Answer: C. 14
Rationale: For a 2 × 2matrix, the determinant is 𝑎𝑑 − 𝑏𝑐. Thus, 4(5) − 2(3) = 20 − 6 =
14.
, 13. Convert 25°C to kelvins.
A. 248.15 K
B. 273.15 K
C. 298.15 K
D. 310.15 K
Correct Answer: C. 298.15 K
Rationale: Kelvin temperature equals Celsius temperature plus 273.15. Therefore, 𝑇 = 25 +
273.15 = 298.15 K.
14. What is the value of sin 30∘ ?
A. 0.250
B. 0.500
C. 0.707
D. 0.866
Correct Answer: B. 0.500
Rationale: The sine of 30 degrees is exactly 1/2, or 0.500.
15. A circle has a radius of 4 m. What is its area?
A. 8𝜋 m2
B. 12𝜋 m2
C. 16𝜋 m2
D. 32𝜋 m2
Correct Answer: C. 16𝜋 m2
Rationale: The area of a circle is 𝐴 = 𝜋𝑟 2 . Substituting 𝑟 = 4gives 𝐴 = 16𝜋 m2,
approximately 50.27 m².
16. What is the second derivative of 𝑓(𝑥) = 2𝑥 4 ?
A. 8𝑥 3
B. 12𝑥 2
C. 24𝑥 2
D. 24𝑥 3
Correct Answer: C. 24𝑥 2
Rationale: The first derivative is 8𝑥 3 . Differentiating again gives 24𝑥 2 .
17. An arithmetic sequence begins 5, 9, 13, 17. What is its tenth term?
A. 37
B. 39
FE Exam-Practice Questions And Correct
Answers (Verified Answers) Plus
Rationales 2026-2027 Q&A | Instant
Download Pdf
1. Evaluate the expression 3𝑥 2 − 4𝑥 + 7when 𝑥 = 3.
A. 22
B. 24
C. 26
D. 28
Correct Answer: C. 22
Rationale: Substituting 𝑥 = 3gives 3(32 ) − 4(3) + 7 = 27 − 12 + 7 = 22. Therefore, the
correct answer is 22, corresponding to option A.
2. A force of 500 N acts on an area of 0.025 m². What pressure does it produce?
A. 10,000 Pa
B. 15,000 Pa
C. 20,000 Pa
D. 25,000 Pa
Correct Answer: C. 20,000 Pa
Rationale: Pressure is force divided by area. Thus, 𝑃 = 500/0.025 = 20,000 Pa.
3. A vehicle travels 180 km in 2.5 hours. What is its average speed?
A. 60 km/h
B. 72 km/h
C. 75 km/h
D. 80 km/h
Correct Answer: B. 72 km/h
Rationale: Average speed equals distance divided by time. Therefore, 𝑣 = 180/2.5 =
72 km/h.
4. What is the derivative of 𝑓(𝑥) = 4𝑥 3 − 5𝑥 2 + 2𝑥 − 8?
,A. 12𝑥 2 − 10𝑥 + 2
B. 12𝑥 3 − 10𝑥 + 2
C. 4𝑥 2 − 5𝑥 + 2
D. 12𝑥 2 − 5𝑥 + 2
Correct Answer: A. 12𝑥 2 − 10𝑥 + 2
Rationale: Apply the power rule to each polynomial term. The derivative of 4𝑥 3 is 12𝑥 2 , the
derivative of −5𝑥 2 is −10𝑥, and the derivative of 2𝑥is 2.
2
5. Evaluate the definite integral ∫0 3 𝑥 2 𝑑𝑥.
A. 4
B. 6
C. 8
D. 12
Correct Answer: C. 8
Rationale: The antiderivative is 𝑥 3 . Evaluating at the limits gives 23 − 03 = 8.
6. A right triangle has perpendicular sides of 6 m and 8 m. What is the hypotenuse length?
A. 9 m
B. 10 m
C. 12 m
D. 14 m
Correct Answer: B. 10 m
Rationale: By the Pythagorean theorem, 𝑐 = √62 + 82 = √100 = 10 m.
7. Solve the equation 5𝑥 − 12 = 28.
A. 6
B. 7
C. 8
D. 9
Correct Answer: C. 8
Rationale: Add 12 to both sides to obtain 5𝑥 = 40. Dividing by 5 gives 𝑥 = 8.
8. A vector has components 𝐴𝑥 = 3and 𝐴𝑦 = 4. What is its magnitude?
A. 4
B. 5
C. 6
D. 7
,Correct Answer: B. 5
Rationale: The magnitude is √𝐴2𝑥 + 𝐴𝑦2 = √32 + 42 = 5.
9. What is the slope of the line passing through (2, 3)and (6, 11)?
A. 1
B. 2
C. 3
D. 4
Correct Answer: B. 2
Rationale: The slope is (11 − 3)/(6 − 2) = 8/4 = 2.
10. What is the solution to the system 𝑥 + 𝑦 = 10and 𝑥 − 𝑦 = 4?
A. 𝑥 = 6, 𝑦 = 4
B. 𝑥 = 7, 𝑦 = 3
C. 𝑥 = 8, 𝑦 = 2
D. 𝑥 = 5, 𝑦 = 5
Correct Answer: B. 𝑥 = 7, 𝑦 = 3
Rationale: Adding the equations gives 2𝑥 = 14, so 𝑥 = 7. Substituting into 𝑥 + 𝑦 = 10gives
𝑦 = 3.
11. What is the value of log10 (1000)?
A. 1
B. 2
C. 3
D. 10
Correct Answer: C. 3
Rationale: Since 103 = 1000, the base-10 logarithm of 1000 is 3.
4 2
12. What is the determinant of the matrix [ ]?
3 5
A. 8
B. 10
C. 14
D. 26
Correct Answer: C. 14
Rationale: For a 2 × 2matrix, the determinant is 𝑎𝑑 − 𝑏𝑐. Thus, 4(5) − 2(3) = 20 − 6 =
14.
, 13. Convert 25°C to kelvins.
A. 248.15 K
B. 273.15 K
C. 298.15 K
D. 310.15 K
Correct Answer: C. 298.15 K
Rationale: Kelvin temperature equals Celsius temperature plus 273.15. Therefore, 𝑇 = 25 +
273.15 = 298.15 K.
14. What is the value of sin 30∘ ?
A. 0.250
B. 0.500
C. 0.707
D. 0.866
Correct Answer: B. 0.500
Rationale: The sine of 30 degrees is exactly 1/2, or 0.500.
15. A circle has a radius of 4 m. What is its area?
A. 8𝜋 m2
B. 12𝜋 m2
C. 16𝜋 m2
D. 32𝜋 m2
Correct Answer: C. 16𝜋 m2
Rationale: The area of a circle is 𝐴 = 𝜋𝑟 2 . Substituting 𝑟 = 4gives 𝐴 = 16𝜋 m2,
approximately 50.27 m².
16. What is the second derivative of 𝑓(𝑥) = 2𝑥 4 ?
A. 8𝑥 3
B. 12𝑥 2
C. 24𝑥 2
D. 24𝑥 3
Correct Answer: C. 24𝑥 2
Rationale: The first derivative is 8𝑥 3 . Differentiating again gives 24𝑥 2 .
17. An arithmetic sequence begins 5, 9, 13, 17. What is its tenth term?
A. 37
B. 39
