EIT Mathematics and Statistics

Question 1

What is the derivative of f(x) = x³ + 4x² - 7x + 2?

Accepted Answer

3x² + 8x - 7

Answer

Using the power rule, the derivative of x³ + 4x² - 7x + 2 is 3x² + 8x - 7.

Question 2

A dataset has values 4, 8, 6, 10, 12. What is the standard deviation?

Accepted Answer

3.16

Answer

The mean is 8, sum of squared deviations is 40, variance is 8, so standard deviation = √8 ≈ 3.16.

Question 3

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

Accepted Answer

1/(s-a)

Answer

The Laplace transform of e^(at) is 1/(s-a), valid for s > a.

Question 4

Which numerical method uses the formula xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) to find roots?

Accepted Answer

Newton-Raphson method

Answer

The Newton-Raphson method iteratively refines root estimates using the function and its derivative.

Question 5

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

Accepted Answer

5

Answer

The determinant of a 2×2 matrix [[a,b],[c,d]] is ad - bc = (2)(4) - (3)(1) = 8 - 3 = 5.

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