NCEES Mathematics 2

Question 1

What is the determinant of the matrix [[3, 1], [2, 4]]?

Accepted Answer

10

Answer

det = (3)(4) - (1)(2) = 12 - 2 = 10.

Question 2

A function f(x) = 3x³ - 6x² + 2x - 5. What is f'(x)?

Accepted Answer

9x² - 12x + 2

Answer

Differentiating term by term: 9x² - 12x + 2.

Question 3

What is the Laplace transform of f(t) = e^(2t)?

Accepted Answer

1/(s-2)

Answer

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?

Accepted Answer

y = Ce^(kx)

Answer

Separating variables and integrating gives y = Ce^(kx).

Question 5

The eigenvalues of the matrix [[5, 0], [0, 3]] are:

Accepted Answer

5 and 3

Answer

A diagonal matrix has eigenvalues equal to its diagonal entries.

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