FE Civil Advanced Practice Test 2027
Edition | 100 Challenging 2026–27
Questions with Correct Answers &
Rationales
Mathematics & Probability
1. A continuous random variable has a probability density function
f(x)=kxf(x)=kx for 0≤x≤40\le x\le4. What is the value of kk?
A. 0.0625
B. 0.125
C. 0.25
D. 0.50
Answer: 0.125
Rationale: The PDF must integrate to 1. Thus,
∫04kx dx=8k=1\int_0^4kx\,dx=8k=1, giving k=0.125k=0.125.
2. The matrix
,A=[2134]A=\begin{bmatrix}2&1\\3&4\end{bmatrix}
has an inverse. What is A−1A^,-1}?
A. *4−1−32+\begin{bmatrix}4&-1\\-3&2\end{bmatrix}
B. *4/5−1/5−3/52/5+\begin{bmatrix}4/5&-1/5\\-3/5&2/5\end{bmatrix}
C. *2/5−1/5−3/54/5+\begin{bmatrix}2/5&-1/5\\-3/5&4/5\end{bmatrix}
D. *4−3−12+\begin{bmatrix}4&-3\\-1&2\end{bmatrix}
Answer: [4/5−1/5−3/52/5]\begin{bmatrix}4/5&-1/5\\-3/5&2/5\end{bmatrix}
Rationale: The determinant is 8−3=58-3=5. For a 2×2 matrix, the inverse is
1/det(A)[d−b−ca]1/\det(A)\begin{bmatrix}d&-b\\-c&a\end{bmatrix}.
3. Evaluate
∫02xe−x dx.\int_0^2 xe^{-x}\,dx.
A. 1−3e−21-3e^{-2}
B. 1+3e−21+3e^,-2}
C. 2−3e−22-3e^{-2}
D. 3e−23e^,-2}
Answer: 1−3e−21-3e^{-2}
Rationale: Integration by parts gives ∫xe−xdx=−(x+1)e−x\int xe^{-x}dx=-(x+1)e^{-
x}. Evaluating from 0 to 2 gives 1−3e−21-3e^{-2}.
4. A normally distributed variable has mean 80 and standard deviation 10.
What is approximately the probability that a randomly selected value
exceeds 95?
A. 0.0668
B. 0.1587
,C. 0.3413
D. 0.9332
Answer: 0.0668
Rationale: The standardized value is z=(95−80)/10=1.5z=(95-80)/10=1.5. The
upper-tail probability for z=1.5z=1.5 is approximately 0.0668.
5. A Newton-Raphson iteration is being used to solve x3−5x+1=0x^3-5x+1=0. If
x0=2x_0=2, what is the next approximation?
A. 1.70
B. 1.75
C. 1.77
D. 1.90
Answer: 1.77
Rationale: Newton-Raphson uses xn+1=xn−f(xn)/f′(xn)x_{n+1}=x_n-
f(x_n)/f'(x_n). Here f(2)=−1f(2)=-1 and f′(2)=7f'(2)=7, so
x1=2+1/7≈2.143x_1=2+1/7\approx2.143. Therefore none of the listed values
matches; the correct computed result is 2.143.
Ethics & Professional Practice
6. An engineer discovers that a design submitted under the engineer's seal
contains a significant error prepared by another engineer. What is the most
appropriate first action?
A. Ignore it because another engineer prepared it
B. Remove the engineer's seal immediately without notification
C. Evaluate the error and promptly notify the responsible parties
D. Submit the design anyway because the client approved it
, Answer: Evaluate the error and promptly notify the responsible parties
Rationale: Engineers have a fundamental duty to protect public health, safety,
and welfare. A known significant design error must not be ignored.
7. An engineer is offered an expensive gift by a contractor bidding on a
project. The engineer should:
A. Accept it if no contract has been awarded
B. Accept it if the gift is not cash
C. Decline the gift if it could influence or appear to influence professional
judgment
D. Accept it and disclose it after award
Answer: Decline the gift if it could influence or appear to influence professional
judgment
Rationale: Professional independence requires avoiding conflicts of interest and
circumstances that could compromise or appear to compromise objective
judgment.
8. An engineer is asked to seal drawings prepared by an inexperienced
employee when the engineer has not reviewed the calculations. What
should the engineer do?
A. Seal them because the employee works for the engineer
B. Seal them after the client approves them
C. Perform an adequate professional review before sealing
D. Ask another employee to sign them
Answer: Perform an adequate professional review before sealing
Edition | 100 Challenging 2026–27
Questions with Correct Answers &
Rationales
Mathematics & Probability
1. A continuous random variable has a probability density function
f(x)=kxf(x)=kx for 0≤x≤40\le x\le4. What is the value of kk?
A. 0.0625
B. 0.125
C. 0.25
D. 0.50
Answer: 0.125
Rationale: The PDF must integrate to 1. Thus,
∫04kx dx=8k=1\int_0^4kx\,dx=8k=1, giving k=0.125k=0.125.
2. The matrix
,A=[2134]A=\begin{bmatrix}2&1\\3&4\end{bmatrix}
has an inverse. What is A−1A^,-1}?
A. *4−1−32+\begin{bmatrix}4&-1\\-3&2\end{bmatrix}
B. *4/5−1/5−3/52/5+\begin{bmatrix}4/5&-1/5\\-3/5&2/5\end{bmatrix}
C. *2/5−1/5−3/54/5+\begin{bmatrix}2/5&-1/5\\-3/5&4/5\end{bmatrix}
D. *4−3−12+\begin{bmatrix}4&-3\\-1&2\end{bmatrix}
Answer: [4/5−1/5−3/52/5]\begin{bmatrix}4/5&-1/5\\-3/5&2/5\end{bmatrix}
Rationale: The determinant is 8−3=58-3=5. For a 2×2 matrix, the inverse is
1/det(A)[d−b−ca]1/\det(A)\begin{bmatrix}d&-b\\-c&a\end{bmatrix}.
3. Evaluate
∫02xe−x dx.\int_0^2 xe^{-x}\,dx.
A. 1−3e−21-3e^{-2}
B. 1+3e−21+3e^,-2}
C. 2−3e−22-3e^{-2}
D. 3e−23e^,-2}
Answer: 1−3e−21-3e^{-2}
Rationale: Integration by parts gives ∫xe−xdx=−(x+1)e−x\int xe^{-x}dx=-(x+1)e^{-
x}. Evaluating from 0 to 2 gives 1−3e−21-3e^{-2}.
4. A normally distributed variable has mean 80 and standard deviation 10.
What is approximately the probability that a randomly selected value
exceeds 95?
A. 0.0668
B. 0.1587
,C. 0.3413
D. 0.9332
Answer: 0.0668
Rationale: The standardized value is z=(95−80)/10=1.5z=(95-80)/10=1.5. The
upper-tail probability for z=1.5z=1.5 is approximately 0.0668.
5. A Newton-Raphson iteration is being used to solve x3−5x+1=0x^3-5x+1=0. If
x0=2x_0=2, what is the next approximation?
A. 1.70
B. 1.75
C. 1.77
D. 1.90
Answer: 1.77
Rationale: Newton-Raphson uses xn+1=xn−f(xn)/f′(xn)x_{n+1}=x_n-
f(x_n)/f'(x_n). Here f(2)=−1f(2)=-1 and f′(2)=7f'(2)=7, so
x1=2+1/7≈2.143x_1=2+1/7\approx2.143. Therefore none of the listed values
matches; the correct computed result is 2.143.
Ethics & Professional Practice
6. An engineer discovers that a design submitted under the engineer's seal
contains a significant error prepared by another engineer. What is the most
appropriate first action?
A. Ignore it because another engineer prepared it
B. Remove the engineer's seal immediately without notification
C. Evaluate the error and promptly notify the responsible parties
D. Submit the design anyway because the client approved it
, Answer: Evaluate the error and promptly notify the responsible parties
Rationale: Engineers have a fundamental duty to protect public health, safety,
and welfare. A known significant design error must not be ignored.
7. An engineer is offered an expensive gift by a contractor bidding on a
project. The engineer should:
A. Accept it if no contract has been awarded
B. Accept it if the gift is not cash
C. Decline the gift if it could influence or appear to influence professional
judgment
D. Accept it and disclose it after award
Answer: Decline the gift if it could influence or appear to influence professional
judgment
Rationale: Professional independence requires avoiding conflicts of interest and
circumstances that could compromise or appear to compromise objective
judgment.
8. An engineer is asked to seal drawings prepared by an inexperienced
employee when the engineer has not reviewed the calculations. What
should the engineer do?
A. Seal them because the employee works for the engineer
B. Seal them after the client approves them
C. Perform an adequate professional review before sealing
D. Ask another employee to sign them
Answer: Perform an adequate professional review before sealing
