Fundamentals of Engineering (FE) Civil Exam:
Multiple-Choice Practice Examination with
Verified Questions and Answers | Instant PDF
Study Guide
1. Mathematics — Algebra
A civil engineer needs to solve the equation (3x + 7 = 22). What
is the value of (x)?
A. 3
B. 4
C. 5
D. 7
Rationale: Subtract 7 from both sides to obtain (3x=15). Dividing
both sides by 3 gives (x=5). This is a fundamental algebraic
operation commonly used throughout engineering calculations.
2. Mathematics — Unit Conversion
A concrete slab has an area of 2,500 ft². What is its approximate
area in square meters? Use (1\text{ ft}=0.3048\text{ m}).
,A. 76.2 m²
B. 232.3 m²
C. 304.8 m²
D. 762.0 m²
Rationale: Because area is two-dimensional, the conversion
factor must be squared: (1\text{
ft}^2=(0.3048)^2=0.092903\text{ m}^2). Therefore,
(2,500(0.092903)=232.3\text{ m}^2).
3. Probability and Statistics
A normally distributed population has a mean of 80 and a
standard deviation of 5. What is the z-score corresponding to a
measurement of 90?
A. 0.5
B. 1.0
C. 2.0
D. 2.5
Rationale: The z-score is calculated as (z=(x-\mu)/\sigma). Thus,
(z=(90-80)/5=2.0). The measurement is therefore two standard
deviations above the mean.
4. Mathematics — Calculus
,What is the derivative of (f(x)=4x^3-5x^2+2x)?
A. (12x^2-5x+2)
B. (12x^2-10x+2)
C. (4x^2-10x+2)
D. (12x^3-10x^2+2)
Rationale: Apply the power rule to each term. The derivative of
(4x^3) is (12x^2), the derivative of (-5x^2) is (-10x), and the
derivative of (2x) is 2.
5. Engineering Economics
An engineer deposits $10,000 into an account earning 5%
annual interest, compounded annually. What will the account
contain after 3 years?
A. $10,500
B. $11,025
C. $11,576
D. $11,750
Rationale: The future value is (F=P(1+i)^n). Therefore,
(F=10,000(1.05)^3=11,576.25). Thus, the account will contain
approximately $11,576.
6. Statics — Resultant Force
, Two perpendicular forces of 3 kN and 4 kN act at the same
point. What is the magnitude of their resultant?
A. 1 kN
B. 5 kN
C. 7 kN
D. 12 kN
Rationale: Since the forces are perpendicular, the Pythagorean
theorem applies: (R=\sqrt{3^2+4^2}=5\text{ kN}). The resultant
acts diagonally between the two forces.
7. Statics — Moment
A 500-N force is applied perpendicular to a beam at a distance
of 2 m from a support. What moment does the force produce
about the support?
A. 100 N·m
B. 1,000 N·m
C. 1,500 N·m
D. 2,500 N·m
Rationale: Moment is (M=Fd) when the force is perpendicular to
the moment arm. Thus, (M=(500)(2)=1,000\text{ N·m}).
8. Statics — Equilibrium
Multiple-Choice Practice Examination with
Verified Questions and Answers | Instant PDF
Study Guide
1. Mathematics — Algebra
A civil engineer needs to solve the equation (3x + 7 = 22). What
is the value of (x)?
A. 3
B. 4
C. 5
D. 7
Rationale: Subtract 7 from both sides to obtain (3x=15). Dividing
both sides by 3 gives (x=5). This is a fundamental algebraic
operation commonly used throughout engineering calculations.
2. Mathematics — Unit Conversion
A concrete slab has an area of 2,500 ft². What is its approximate
area in square meters? Use (1\text{ ft}=0.3048\text{ m}).
,A. 76.2 m²
B. 232.3 m²
C. 304.8 m²
D. 762.0 m²
Rationale: Because area is two-dimensional, the conversion
factor must be squared: (1\text{
ft}^2=(0.3048)^2=0.092903\text{ m}^2). Therefore,
(2,500(0.092903)=232.3\text{ m}^2).
3. Probability and Statistics
A normally distributed population has a mean of 80 and a
standard deviation of 5. What is the z-score corresponding to a
measurement of 90?
A. 0.5
B. 1.0
C. 2.0
D. 2.5
Rationale: The z-score is calculated as (z=(x-\mu)/\sigma). Thus,
(z=(90-80)/5=2.0). The measurement is therefore two standard
deviations above the mean.
4. Mathematics — Calculus
,What is the derivative of (f(x)=4x^3-5x^2+2x)?
A. (12x^2-5x+2)
B. (12x^2-10x+2)
C. (4x^2-10x+2)
D. (12x^3-10x^2+2)
Rationale: Apply the power rule to each term. The derivative of
(4x^3) is (12x^2), the derivative of (-5x^2) is (-10x), and the
derivative of (2x) is 2.
5. Engineering Economics
An engineer deposits $10,000 into an account earning 5%
annual interest, compounded annually. What will the account
contain after 3 years?
A. $10,500
B. $11,025
C. $11,576
D. $11,750
Rationale: The future value is (F=P(1+i)^n). Therefore,
(F=10,000(1.05)^3=11,576.25). Thus, the account will contain
approximately $11,576.
6. Statics — Resultant Force
, Two perpendicular forces of 3 kN and 4 kN act at the same
point. What is the magnitude of their resultant?
A. 1 kN
B. 5 kN
C. 7 kN
D. 12 kN
Rationale: Since the forces are perpendicular, the Pythagorean
theorem applies: (R=\sqrt{3^2+4^2}=5\text{ kN}). The resultant
acts diagonally between the two forces.
7. Statics — Moment
A 500-N force is applied perpendicular to a beam at a distance
of 2 m from a support. What moment does the force produce
about the support?
A. 100 N·m
B. 1,000 N·m
C. 1,500 N·m
D. 2,500 N·m
Rationale: Moment is (M=Fd) when the force is perpendicular to
the moment arm. Thus, (M=(500)(2)=1,000\text{ N·m}).
8. Statics — Equilibrium
