KENTUCKY PROFESSIONAL ENGINEER
FUNDAMENTALS OF ENGINEERING EXAM
QUESTIONS AND CORRECT ANSWERS (VERIFIED
ANSWERS) Q&A 2027 |INSTANT DOWNLOAD PDF
1. If f(x)=3x2−4x+5f(x)=3x^2-4x+5, what is f′(x)f'(x)?
A. 6x−46x-4
B. 3x−43x-4
C. 6x+46x+4
D. 3x2−43x^2-4
Answer: A. 6x−46x-4
Rationale: Applying the power rule,
d(3x2)/dx=6xd(3x^2)/dx=6x, d(−4x)/dx=−4d(-4x)/dx=-4, and the
derivative of a constant is zero.
2. What is the integral of 2x+32x+3 with respect to xx?
A. x2+3x+Cx^2+3x+C
B. 2x2+3x+C2x^2+3x+C
C. x2+3+Cx^2+3+C
D. 2x+3+C2x+3+C
Answer: A. x2+3x+Cx^2+3x+C
Rationale: Integrating 2x2x gives x2x^2, while integrating 3
gives 3x3x.
,3. What is the determinant of the matrix
[2314]\begin{bmatrix}2&3\\1&4\end{bmatrix}?
A. 5
B. 8
C. 11
D. 14
Answer: A. 5
Rationale: The determinant is ad−bc=(2)(4)−(3)(1)=8−3=5ad-
bc=(2)(4)-(3)(1)=8-3=5.
4. What is the positive root of x2−9=0x^2-9=0?
A. 1
B. 3
C. 6
D. 9
Answer: B. 3
Rationale: x2=9x^2=9, so x=±3x=\pm3. The positive root is 3.
5. What is the value of sin30∘\sin 30^\circ?
A. 0
B. 0.5
,C. 0.707
D. 1
Answer: B. 0.5
Rationale: The standard trigonometric value of
sin30∘\sin30^\circ is 0.5.
6. If y=e2xy=e^{2x}, what is dy/dxdy/dx?
A. e2xe^{2x}
B. 2e2x2e^{2x}
C. xe2xxe^{2x}
D. 2xex2xe^x
Answer: B. 2e2x2e^{2x}
Rationale: By the chain rule, the derivative of e2xe^{2x} is
2e2x2e^{2x}.
7. What is the mean of 4, 6, 8, and 12?
A. 6
B. 7
C. 7.5
D. 8
Answer: C. 7.5
Rationale: The mean is
(4+6+8+12)/4=30/4=7.5(4+6+8+12)/4=30/4=7.5.
, 8. A fair six-sided die is rolled once. What is the probability of
obtaining a 4?
A. 1/21/2
B. 1/31/3
C. 1/61/6
D. 1/121/12
Answer: C. 1/61/6
Rationale: There is one favorable outcome among six equally
likely outcomes.
9. Which statistical measure is most directly affected by an
extreme outlier?
A. Median
B. Mean
C. Mode
D. Range midpoint
Answer: B. Mean
Rationale: The arithmetic mean uses every observation and
therefore can be strongly influenced by unusually large or small
values.
FUNDAMENTALS OF ENGINEERING EXAM
QUESTIONS AND CORRECT ANSWERS (VERIFIED
ANSWERS) Q&A 2027 |INSTANT DOWNLOAD PDF
1. If f(x)=3x2−4x+5f(x)=3x^2-4x+5, what is f′(x)f'(x)?
A. 6x−46x-4
B. 3x−43x-4
C. 6x+46x+4
D. 3x2−43x^2-4
Answer: A. 6x−46x-4
Rationale: Applying the power rule,
d(3x2)/dx=6xd(3x^2)/dx=6x, d(−4x)/dx=−4d(-4x)/dx=-4, and the
derivative of a constant is zero.
2. What is the integral of 2x+32x+3 with respect to xx?
A. x2+3x+Cx^2+3x+C
B. 2x2+3x+C2x^2+3x+C
C. x2+3+Cx^2+3+C
D. 2x+3+C2x+3+C
Answer: A. x2+3x+Cx^2+3x+C
Rationale: Integrating 2x2x gives x2x^2, while integrating 3
gives 3x3x.
,3. What is the determinant of the matrix
[2314]\begin{bmatrix}2&3\\1&4\end{bmatrix}?
A. 5
B. 8
C. 11
D. 14
Answer: A. 5
Rationale: The determinant is ad−bc=(2)(4)−(3)(1)=8−3=5ad-
bc=(2)(4)-(3)(1)=8-3=5.
4. What is the positive root of x2−9=0x^2-9=0?
A. 1
B. 3
C. 6
D. 9
Answer: B. 3
Rationale: x2=9x^2=9, so x=±3x=\pm3. The positive root is 3.
5. What is the value of sin30∘\sin 30^\circ?
A. 0
B. 0.5
,C. 0.707
D. 1
Answer: B. 0.5
Rationale: The standard trigonometric value of
sin30∘\sin30^\circ is 0.5.
6. If y=e2xy=e^{2x}, what is dy/dxdy/dx?
A. e2xe^{2x}
B. 2e2x2e^{2x}
C. xe2xxe^{2x}
D. 2xex2xe^x
Answer: B. 2e2x2e^{2x}
Rationale: By the chain rule, the derivative of e2xe^{2x} is
2e2x2e^{2x}.
7. What is the mean of 4, 6, 8, and 12?
A. 6
B. 7
C. 7.5
D. 8
Answer: C. 7.5
Rationale: The mean is
(4+6+8+12)/4=30/4=7.5(4+6+8+12)/4=30/4=7.5.
, 8. A fair six-sided die is rolled once. What is the probability of
obtaining a 4?
A. 1/21/2
B. 1/31/3
C. 1/61/6
D. 1/121/12
Answer: C. 1/61/6
Rationale: There is one favorable outcome among six equally
likely outcomes.
9. Which statistical measure is most directly affected by an
extreme outlier?
A. Median
B. Mean
C. Mode
D. Range midpoint
Answer: B. Mean
Rationale: The arithmetic mean uses every observation and
therefore can be strongly influenced by unusually large or small
values.
