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Mathematics and Statistics Flashcards

6 cards from real EIT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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

    Answer: 3x² + 8x - 7

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

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

    Answer: 3.16

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

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

    Answer: 1/(s-a)

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

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

    Answer: Newton-Raphson method

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

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

    Answer: 5

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

  6. In probability, if P(A) = 0.4 and P(B) = 0.3 and A and B are independent, what is P(A∩B)?

    Answer: 0.12

    For independent events, P(A∩B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.