EIT Mathematics and Statistics 1 — Questions and Answers
Question 1: What is the derivative of f(x) = x³ + 4x² - 7x + 2?
- 3x² + 8x - 7 (Correct answer)
- 3x² + 4x - 7
- x² + 8x - 7
- 3x³ + 8x - 7
Correct answer: 3x² + 8x - 7
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?
- 2.83
- 3.16 (Correct answer)
- 2.56
- 3.46
Correct answer: 3.16
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)?
- 1/(s+a)
- 1/(s-a) (Correct answer)
- a/(s²+a²)
- s/(s²+a²)
Correct answer: 1/(s-a)
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?
- Bisection method
- Secant method
- Newton-Raphson method (Correct answer)
- Fixed-point iteration
Correct answer: Newton-Raphson method
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]]?
- 5 (Correct answer)
- 11
- 8
- 14
Correct answer: 5
The determinant of a 2×2 matrix [[a,b],[c,d]] is ad - bc = (2)(4) - (3)(1) = 8 - 3 = 5.
Question 6: In probability, if P(A) = 0.4 and P(B) = 0.3 and A and B are independent, what is P(A∩B)?
- 0.70
- 0.12 (Correct answer)
- 0.10
- 0.58
Correct answer: 0.12
For independent events, P(A∩B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
EIT Mathematics and Statistics 1
What is the derivative of f(x) = x³ + 4x² - 7x + 2?