FE Exam 2026 Latest Comprehensive Study Guide with Practice Questions

FE Exam 2026 Latest Comprehensive Study
Guide with Practice Questions
Seven FE Exam Disciplines:
• FE Chemical
• FE Civil Engineering
• FE Electrical and Computer
• FE Environmental Engineering
• FE Industrial and Systems
• FE Mechanical
• FE Other Disciplines
Core Topics Across All Disciplines:
• Mathematics and Statistics (8-12 questions)
• Ethics and Professional Practice (4-6 questions)
• Engineering Economics (5-8 questions)
• Discipline-specific technical topics
2026 Updates:
• FE Reference Handbook Version 10.6 effective July 2026
• Year-round CBT format with continuous testing availability
• Scaled scoring with no published fixed passing percentage


SECTION 1: MATHEMATICS (Questions 1-12)


Question 1
What is the derivative of f(x) = 3x⁴ + 2x³ - 5x + 7?

,A) 12x³ + 6x² - 5
B) 12x³ + 6x² + 5
C) 3x³ + 2x² - 5
D) 12x³ + 2x² - 5
Correct Answer: A
Rationale: Using the power rule: d/dx(xⁿ) = nxⁿ⁻¹. f'(x) = 3(4x³) + 2(3x²) - 5(1) + 0
= 12x³ + 6x² - 5. The derivative of a constant (7) is zero. Option B has the wrong
sign for the constant term. Option C incorrectly applies the power rule. Option D
has an incorrect coefficient for the x² term.


Question 2
Evaluate the integral: ∫(6x² - 4x + 3) dx
A) 2x³ - 2x² + 3x + C
B) 2x³ - 4x² + 3x + C
C) 6x³ - 2x² + 3x + C
D) 3x³ - 2x² + 3x + C
Correct Answer: A
Rationale: Using the power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C. ∫6x² dx =
6(x³/3) = 2x³. ∫(-4x) dx = -4(x²/2) = -2x². ∫3 dx = 3x. Therefore, the integral is 2x³ -
2x² + 3x + C. Option B has the wrong coefficient for the x² term. Option C
incorrectly integrates the first term. Option D incorrectly applies the coefficient to
the first term.


Question 3
What is the determinant of the matrix [[3, 1], [2, 4]]?
A) 10
B) 14
C) 5
D) 12
Correct Answer: A

,Rationale: For a 2×2 matrix [[a, b], [c, d]], the determinant is ad - bc. det = (3)(4) -
(1)(2) = 12 - 2 = 10. Option B (14) is the sum of the diagonal elements. Option C
(5) is the difference of the off-diagonal elements. Option D (12) is only the product
of the first diagonal.


Question 4
Solve for x: log₂(x) + log₂(x - 2) = 3
A) x = 4
B) x = 6
C) x = 8
D) x = 2
Correct Answer: A
Rationale: Using the logarithm product rule: log₂(x) + log₂(x-2) = log₂[x(x-2)] = 3.
Therefore, x(x-2) = 2³ = 8. x² - 2x - 8 = 0 → (x - 4)(x + 2) = 0 → x = 4 or x = -2.
Since logarithms are only defined for positive arguments, x = -2 is extraneous. x =
4. Option B (6) is incorrect. Option C (8) is incorrect. Option D (2) would make
log₂(0) undefined.


Question 5
What is the Laplace transform of f(t) = 3e^(-2t)?
A) 3/(s+2)
B) 3/(s-2)
C) 3s/(s+2)
D) 3/(s²+4)
Correct Answer: A
Rationale: The Laplace transform of e^(at) is 1/(s-a). For e^(-2t), a = -2, so L{e^(-
2t)} = 1/(s+2). Therefore, L{3e^(-2t)} = 3/(s+2). Option B is incorrect because it
uses the wrong sign. Option C is the transform of 3e^(-2t) with an extra s factor.
Option D is the transform of sin(2t).

, Question 6
The probability of an event occurring is 0.3. What is the probability that the event
does NOT occur?
A) 0.3
B) 0.7
C) 1.0
D) 0.0
Correct Answer: B
Rationale: The probability of the complement of an event is 1 - P(event). 1 - 0.3
= 0.7. This is a fundamental probability concept: the sum of the probabilities of an
event and its complement equals 1. Option A is the probability of the event itself.
Option C is the probability of certainty. Option D is the probability of
impossibility.


Question 7
What is the mean of the data set: 4, 8, 6, 10, 12?
A) 6
B) 8
C) 10
D) 9
Correct Answer: B
Rationale: The mean is the sum of all values divided by the number of values.
Sum = 4 + 8 + 6 + 10 + 12 = 40. Number of values = 5. Mean = 40/5 = 8. Option A
(6) is the median of the data set (when sorted: 4, 6, 8, 10, 12). Option C (10) is one
of the values. Option D (9) is incorrect.


Question 8
What is the derivative of y = ln(x² + 1)?
A) 2x/(x²+1)
B) 1/(x²+1)