NCEES Mathematics 2 — Questions and Answers
Question 1: What is the determinant of the matrix [[3, 1], [2, 4]]?
- 10 (Correct answer)
- 14
- 8
- 12
Correct answer: 10
det = (3)(4) - (1)(2) = 12 - 2 = 10.
Question 2: A function f(x) = 3x³ - 6x² + 2x - 5. What is f'(x)?
- 9x² - 12x + 2 (Correct answer)
- 9x² - 6x + 2
- 3x² - 12x + 2
- 9x² - 12x - 5
Correct answer: 9x² - 12x + 2
Differentiating term by term: 9x² - 12x + 2.
Question 3: What is the Laplace transform of f(t) = e^(2t)?
- 1/(s-2) (Correct answer)
- 1/(s+2)
- 2/s²
- s/(s-2)
Correct answer: 1/(s-2)
L{e^(at)} = 1/(s - a), so L{e^(2t)} = 1/(s - 2).
Question 4: Which of the following is the general solution to dy/dx = ky?
- y = Ce^(kx) (Correct answer)
- y = kx + C
- y = Ce^(-kx)
- y = Cx^k
Correct answer: y = Ce^(kx)
Separating variables and integrating gives y = Ce^(kx).
Question 5: The eigenvalues of the matrix [[5, 0], [0, 3]] are:
- 5 and 3 (Correct answer)
- 8 and 0
- 15 and 0
- 4 and 4
Correct answer: 5 and 3
A diagonal matrix has eigenvalues equal to its diagonal entries.
Question 6: Evaluate the integral ∫₀^π sin(x) dx.
- 2 (Correct answer)
- 0
- 1
- π
Correct answer: 2
∫₀^π sin(x) dx = [-cos(x)]₀^π = -cos(π) + cos(0) = 1 + 1 = 2.
Question 7: A geometric series has first term a = 4 and common ratio r = 0.5. What is the sum to infinity?
- 8 (Correct answer)
- 4
- 6
- 2
Correct answer: 8
S∞ = a/(1 - r) = 4/(1 - 0.5) = 4/0.5 = 8.
NCEES Mathematics 2
What is the determinant of the matrix [[3, 1], [2, 4]]?