Colorado Fundamentals of Engineering
(FE) Examination Practice Exam 2026 |
100 Questions & Answers with Detailed
Rationales | Complete Exam Prep &
Study Guide
1. What is the derivative of f(x)=3x4−5x2+7?
A. 12x3−10x
B. 12x4−10x
C. 3x3−5x
D. 4x3−10x
Answer: 12x3−10x
Rationale: The power rule gives d(xn)/dx=nxn−1. Therefore, 3x4 becomes 12x3,
and −5x2 becomes −10x.
2. Evaluate the integral ∫024xdx.
A. 4
B. 6
C. 8
D. 16
,Answer: 8
Rationale: The integral is 2x2 evaluated from 0 to 2, giving 2(4)−0=8.
3. What is the determinant of the matrix [2134]?
A. 3
B. 5
C. 8
D. 11
Answer: 5
Rationale: For a 2 × 2 matrix, the determinant is ad−bc. Thus, 2(4)−3(1)=5.
4. If z=3+4i, what is the magnitude of z?
A. 3
B. 4
C. 5
D. 7
Answer: 5
Rationale: The magnitude of a complex number a+bi is a2+b2. Thus, 32+42=5.
5. What is the solution to 2x+6=14?
A. 2
B. 4
C. 6
D. 8
Answer: 4
Rationale: Subtracting 6 gives 2x=8, so x=4.
6. A normally distributed variable has a mean of 50 and a standard deviation
of 5. What is its z-score when the value is 60?
,A. 1
B. 2
C. 2.5
D. 10
Answer: 2
Rationale: The z-score is (x−μ)/σ=(60−50)/5=2.
7. If two events are mutually exclusive, what is their joint probability?
A. 0
B. 0.25
C. 0.5
D. 1
Answer: 0
Rationale: Mutually exclusive events cannot occur simultaneously, so their
intersection has probability zero.
8. A machine produces 2% defective parts. If one part is selected randomly,
what is the probability that it is nondefective?
A. 0.02
B. 0.20
C. 0.98
D. 1.02
Answer: 0.98
Rationale: The probability of a nondefective part is the complement of the
defective probability: 1−0.02=0.98.
9. Which ethical principle requires an engineer to place public safety, health,
and welfare first?
, A. Maximizing profit
B. Protecting confidential information
C. Holding paramount the public safety, health, and welfare
D. Minimizing project duration
Answer: Holding paramount the public safety, health, and welfare
Rationale: Fundamental engineering ethics require engineers to prioritize
protection of the public over competing professional or financial interests.
10.An engineer discovers a serious safety defect in a design. What should be
the primary concern?
A. Project profit
B. Public safety
C. Contractor convenience
D. Schedule
Answer: Public safety
Rationale: Protection of public health, safety, and welfare is a fundamental
engineering responsibility.
11.A project costs $10,000 today and returns $12,000 one year later. At a 10%
annual interest rate, what is the approximate net present value?
A. $909
B. $1,000
C. $1,091
D. $2,000
Answer: $909
Rationale: The present value of $12,000 one year later is 12,000/1.10=10,909.
Subtracting the $10,000 initial cost gives approximately $909.
12.What is the simple interest on $5,000 at 6% per year for 3 years?
(FE) Examination Practice Exam 2026 |
100 Questions & Answers with Detailed
Rationales | Complete Exam Prep &
Study Guide
1. What is the derivative of f(x)=3x4−5x2+7?
A. 12x3−10x
B. 12x4−10x
C. 3x3−5x
D. 4x3−10x
Answer: 12x3−10x
Rationale: The power rule gives d(xn)/dx=nxn−1. Therefore, 3x4 becomes 12x3,
and −5x2 becomes −10x.
2. Evaluate the integral ∫024xdx.
A. 4
B. 6
C. 8
D. 16
,Answer: 8
Rationale: The integral is 2x2 evaluated from 0 to 2, giving 2(4)−0=8.
3. What is the determinant of the matrix [2134]?
A. 3
B. 5
C. 8
D. 11
Answer: 5
Rationale: For a 2 × 2 matrix, the determinant is ad−bc. Thus, 2(4)−3(1)=5.
4. If z=3+4i, what is the magnitude of z?
A. 3
B. 4
C. 5
D. 7
Answer: 5
Rationale: The magnitude of a complex number a+bi is a2+b2. Thus, 32+42=5.
5. What is the solution to 2x+6=14?
A. 2
B. 4
C. 6
D. 8
Answer: 4
Rationale: Subtracting 6 gives 2x=8, so x=4.
6. A normally distributed variable has a mean of 50 and a standard deviation
of 5. What is its z-score when the value is 60?
,A. 1
B. 2
C. 2.5
D. 10
Answer: 2
Rationale: The z-score is (x−μ)/σ=(60−50)/5=2.
7. If two events are mutually exclusive, what is their joint probability?
A. 0
B. 0.25
C. 0.5
D. 1
Answer: 0
Rationale: Mutually exclusive events cannot occur simultaneously, so their
intersection has probability zero.
8. A machine produces 2% defective parts. If one part is selected randomly,
what is the probability that it is nondefective?
A. 0.02
B. 0.20
C. 0.98
D. 1.02
Answer: 0.98
Rationale: The probability of a nondefective part is the complement of the
defective probability: 1−0.02=0.98.
9. Which ethical principle requires an engineer to place public safety, health,
and welfare first?
, A. Maximizing profit
B. Protecting confidential information
C. Holding paramount the public safety, health, and welfare
D. Minimizing project duration
Answer: Holding paramount the public safety, health, and welfare
Rationale: Fundamental engineering ethics require engineers to prioritize
protection of the public over competing professional or financial interests.
10.An engineer discovers a serious safety defect in a design. What should be
the primary concern?
A. Project profit
B. Public safety
C. Contractor convenience
D. Schedule
Answer: Public safety
Rationale: Protection of public health, safety, and welfare is a fundamental
engineering responsibility.
11.A project costs $10,000 today and returns $12,000 one year later. At a 10%
annual interest rate, what is the approximate net present value?
A. $909
B. $1,000
C. $1,091
D. $2,000
Answer: $909
Rationale: The present value of $12,000 one year later is 12,000/1.10=10,909.
Subtracting the $10,000 initial cost gives approximately $909.
12.What is the simple interest on $5,000 at 6% per year for 3 years?
