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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 magnitude of the vector v = 3i + 4j?

    Answer: 5

    |v| = √(3² + 4²) = √(9 + 16) = √25 = 5.

  2. The Taylor series expansion of e^x centered at x = 0 begins with:

    Answer: 1 + x + x²/2! + x³/3! + ...

    The Maclaurin series for e^x is the sum of xⁿ/n! from n=0 to ∞.

  3. Which conic section is described by the equation x²/9 + y²/4 = 1?

    Answer: Ellipse

    The equation x²/a² + y²/b² = 1 (with a ≠ b) defines an ellipse.

  4. What is the dot product of vectors A = (2, -1, 3) and B = (4, 2, -1)?

    Answer: 3

    A·B = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.

  5. What is lim(x→0) [sin(x)/x]?

    Answer: 1

    This is a standard limit; lim(x→0) sin(x)/x = 1.

  6. If matrix A is 3×2 and matrix B is 2×4, the product AB has dimensions:

    Answer: 3×4

    The resulting matrix has rows from A and columns from B: 3×4.

  7. The second derivative test: if f''(c) > 0 at a critical point, then the point is a:

    Answer: Local minimum

    A positive second derivative at a critical point indicates the function is concave up, giving a local minimum.

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