Fundamentals of Engineering (FE) Chemical Exam

Fundamentals of Engineering (FE)
Chemical Exam
Question 1. What is the solution to the equation 2x + 5 = 11?


A) x = 1


B) x = 2


C) x = 3


D) x = 4


Answer: C


Explanation: Subtract 5 from both sides: 2x = 6, then divide both sides

by 2: x = 3.




Question 2. Which of the following is equivalent to sin²θ + cos²θ?


A) 1


B) 0

,Fundamentals of Engineering (FE)
Chemical Exam
C) sinθ


D) cosθ


Answer: A


Explanation: This is the fundamental Pythagorean identity for all real θ.




Question 3. The derivative of f(x) = x² with respect to x is:


A) 2x


B) x


C) x²


D) 2


Answer: A


Explanation: The power rule gives df/dx = 2x.

,Fundamentals of Engineering (FE)
Chemical Exam

Question 4. Which of the following is the solution to the system of

linear equations: x + y = 3, x - y = 1?


A) x = 1, y = 2


B) x = 2, y = 1


C) x = 3, y = 0


D) x = 0, y = 3


Answer: B


Explanation: Adding equations yields 2x = 4, so x = 2, then y = 1.




Question 5. The integral ∫0¹ x dx equals:


A) 1

, Fundamentals of Engineering (FE)
Chemical Exam
B) 1/2


C) 1/3


D) 2


Answer: B


Explanation: The integral of x is (1/2)x², so from 0 to 1 it's (1/2)(1² - 0²) =

1/2.




Question 6. Which method is best for solving a nonhomogeneous first-

order linear differential equation?


A) Separation of variables


B) Integrating factor


C) Laplace transform


D) Power series