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Mathematics Flashcards

7 cards from real NCEES 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 determinant of the matrix [[3, 1], [2, 4]]?

    Answer: 10

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

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

    Answer: 9x² - 12x + 2

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

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

    Answer: 1/(s-2)

    L{e^(at)} = 1/(s - a), so L{e^(2t)} = 1/(s - 2).

  4. Which of the following is the general solution to dy/dx = ky?

    Answer: y = Ce^(kx)

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

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

    Answer: 5 and 3

    A diagonal matrix has eigenvalues equal to its diagonal entries.

  6. Evaluate the integral ∫₀^π sin(x) dx.

    Answer: 2

    ∫₀^π sin(x) dx = [-cos(x)]₀^π = -cos(π) + cos(0) = 1 + 1 = 2.

  7. A geometric series has first term a = 4 and common ratio r = 0.5. What is the sum to infinity?

    Answer: 8

    S∞ = a/(1 - r) = 4/(1 - 0.5) = 4/0.5 = 8.

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