20242025 Common Fundamentals of Engineering (FE) questions and answers covering a range
of topics—from mathematics and engineering mechanics to thermodynamics, circuits, materials,
and ethics. These questions are representative of the types of problems you may encounter on the
FE exam.
1. Algebraic Manipulation
Which of the following expressions is equivalent to (2x−3)2(2x - 3)^2?
A) 4x2−94x^2 - 9
B) 4x2−12x+94x^2 - 12x + 9
C) 4x2+94x^2 + 9
D) 2x2−3x2x^2 - 3x
Answer: B) 4x2−12x+94x^2 - 12x + 9
2. Quadratic Equation
Solve the quadratic equation:
x2−5x+6=0x^2 - 5x + 6 = 0
A) x=2x = 2 and x=3x = 3
B) x=−2x = -2 and x=−3x = -3
C) x=1x = 1 and x=6x = 6
D) x=−1x = -1 and x=−6x = -6
Answer: A) x=2x = 2 and x=3x = 3
3. Calculus – Derivative
Find the derivative of f(x)=3x3−4x+5f(x)=3x^3 - 4x + 5.
A) 9x2−49x^2 - 4
B) 9x2+49x^2 + 4
C) 3x2−43x^2 - 4
D) 9x2−4x9x^2 - 4x
Answer: A) 9x2−49x^2 - 4
4. Calculus – Integration
Evaluate the definite integral:
∫012x dx\int_0^1 2x \, dx
, A) 1
B) 2
C) 12\frac{1}{2}
D) 0
Answer: A) 1
Explanation: ∫012x dx=x2∣01=12−0=1\int_0^1 2x\,dx = \left. x^2 \right|_0^1 = 1^2 - 0 = 1.
5. Differential Equations
Solve the differential equation dydx=3y\frac{dy}{dx} = 3y with initial condition y(0)=2y(0)=2.
A) y=2e3xy = 2e^{3x}
B) y=2ex/3y = 2e^{x/3}
C) y=2exy = 2e^x
D) y=2e3/xy = 2e^{3/x}
Answer: A) y=2e3xy = 2e^{3x}
6. Linear Algebra
Given the 2×22 \times 2 matrix
A=[2345],A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix},
what is the determinant of AA?
A) −2-2
B) 2
C) −1-1
D) 1
Answer: A) −2-2
Explanation: det(A)=2⋅5−3⋅4=10−12=−2\det(A)=2\cdot5-3\cdot4=10-12=-2.
7. Probability and Statistics
What is the probability of obtaining exactly 2 heads when flipping a fair coin 3 times?
A) 12\frac{1}{2}
B) 13\frac{1}{3}
C) 38\frac{3}{8}
D) 14\frac{1}{4}
Answer: C) 38\frac{3}{8}
Explanation: C(3,2)=3C(3,2)=3 outcomes out of 23=82^3=8 total outcomes.
of topics—from mathematics and engineering mechanics to thermodynamics, circuits, materials,
and ethics. These questions are representative of the types of problems you may encounter on the
FE exam.
1. Algebraic Manipulation
Which of the following expressions is equivalent to (2x−3)2(2x - 3)^2?
A) 4x2−94x^2 - 9
B) 4x2−12x+94x^2 - 12x + 9
C) 4x2+94x^2 + 9
D) 2x2−3x2x^2 - 3x
Answer: B) 4x2−12x+94x^2 - 12x + 9
2. Quadratic Equation
Solve the quadratic equation:
x2−5x+6=0x^2 - 5x + 6 = 0
A) x=2x = 2 and x=3x = 3
B) x=−2x = -2 and x=−3x = -3
C) x=1x = 1 and x=6x = 6
D) x=−1x = -1 and x=−6x = -6
Answer: A) x=2x = 2 and x=3x = 3
3. Calculus – Derivative
Find the derivative of f(x)=3x3−4x+5f(x)=3x^3 - 4x + 5.
A) 9x2−49x^2 - 4
B) 9x2+49x^2 + 4
C) 3x2−43x^2 - 4
D) 9x2−4x9x^2 - 4x
Answer: A) 9x2−49x^2 - 4
4. Calculus – Integration
Evaluate the definite integral:
∫012x dx\int_0^1 2x \, dx
, A) 1
B) 2
C) 12\frac{1}{2}
D) 0
Answer: A) 1
Explanation: ∫012x dx=x2∣01=12−0=1\int_0^1 2x\,dx = \left. x^2 \right|_0^1 = 1^2 - 0 = 1.
5. Differential Equations
Solve the differential equation dydx=3y\frac{dy}{dx} = 3y with initial condition y(0)=2y(0)=2.
A) y=2e3xy = 2e^{3x}
B) y=2ex/3y = 2e^{x/3}
C) y=2exy = 2e^x
D) y=2e3/xy = 2e^{3/x}
Answer: A) y=2e3xy = 2e^{3x}
6. Linear Algebra
Given the 2×22 \times 2 matrix
A=[2345],A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix},
what is the determinant of AA?
A) −2-2
B) 2
C) −1-1
D) 1
Answer: A) −2-2
Explanation: det(A)=2⋅5−3⋅4=10−12=−2\det(A)=2\cdot5-3\cdot4=10-12=-2.
7. Probability and Statistics
What is the probability of obtaining exactly 2 heads when flipping a fair coin 3 times?
A) 12\frac{1}{2}
B) 13\frac{1}{3}
C) 38\frac{3}{8}
D) 14\frac{1}{4}
Answer: C) 38\frac{3}{8}
Explanation: C(3,2)=3C(3,2)=3 outcomes out of 23=82^3=8 total outcomes.
