NCEES Mathematics 5

Question 1

Using Simpson's 1/3 rule with n = 2 intervals to approximate ∫₀² x² dx gives:

Accepted Answer

2.667

Answer

Simpson's rule: (h/3)[f(0)+4f(1)+f(2)] = (1/3)[0+4+4] = 8/3 ≈ 2.667, matching the exact value.

Question 2

What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

Accepted Answer

2

Answer

Row reduction shows only 2 linearly independent rows (the third is a linear combination of the first two), so rank = 2.

Question 3

In numerical integration, increasing the number of subintervals generally:

Accepted Answer

Decreases the truncation error

Answer

More subintervals means smaller step sizes, reducing truncation (approximation) error.

Question 4

The solution to the linear system Ax = b using Gaussian elimination requires the matrix A to be:

Accepted Answer

Non-singular (invertible)

Answer

Gaussian elimination finds a unique solution only when A is non-singular (det ≠ 0).

Question 5

The Poisson distribution is most appropriate for modeling:

Accepted Answer

Number of events in a fixed interval of time or space

Answer

The Poisson distribution models the count of rare, independent events occurring in a fixed interval.

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