NCEES Mathematics 3 — Questions and Answers
Question 1: What is the magnitude of the vector v = 3i + 4j?
- 5 (Correct answer)
- 7
- 12
- 25
Correct answer: 5
|v| = √(3² + 4²) = √(9 + 16) = √25 = 5.
Question 2: The Taylor series expansion of e^x centered at x = 0 begins with:
- 1 + x + x²/2! + x³/3! + ... (Correct answer)
- x + x²/2 + x³/3 + ...
- 1 + x + x² + x³ + ...
- 1 - x + x²/2! - x³/3! + ...
Correct answer: 1 + x + x²/2! + x³/3! + ...
The Maclaurin series for e^x is the sum of xⁿ/n! from n=0 to ∞.
Question 3: Which conic section is described by the equation x²/9 + y²/4 = 1?
- Ellipse (Correct answer)
- Hyperbola
- Parabola
- Circle
Correct answer: Ellipse
The equation x²/a² + y²/b² = 1 (with a ≠ b) defines an ellipse.
Question 4: What is the dot product of vectors A = (2, -1, 3) and B = (4, 2, -1)?
- 3 (Correct answer)
- 9
- 15
- -3
Correct answer: 3
A·B = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.
Question 5: What is lim(x→0) [sin(x)/x]?
- 1 (Correct answer)
- 0
- ∞
- Undefined
Correct answer: 1
This is a standard limit; lim(x→0) sin(x)/x = 1.
Question 6: If matrix A is 3×2 and matrix B is 2×4, the product AB has dimensions:
- 3×4 (Correct answer)
- 2×2
- 3×2
- 4×3
Correct answer: 3×4
The resulting matrix has rows from A and columns from B: 3×4.
Question 7: The second derivative test: if f''(c) > 0 at a critical point, then the point is a:
- Local minimum (Correct answer)
- Local maximum
- Inflection point
- Saddle point
Correct answer: Local minimum
A positive second derivative at a critical point indicates the function is concave up, giving a local minimum.
NCEES Mathematics 3
What is the magnitude of the vector v = 3i + 4j?