IB Mathematics 5 — Questions and Answers
Question 1: How many distinct arrangements are there of the letters in the word STATISTICS?
- 50400 (Correct answer)
- 3628800
- 604800
- 25200
Correct answer: 50400
STATISTICS has 10 letters: S×3, T×3, A×1, I×2, C×1; arrangements = 10!/(3!·3!·2!) = 3628800/72 = 50400.
Question 2: What is the value of lim(x→0) [sin(5x)/x]?
- 5 (Correct answer)
- 1
- 0
- ∞
Correct answer: 5
Using lim(x→0) sin(kx)/x = k, the limit equals 5.
Question 3: The equation x² + y² − 6x + 4y − 3 = 0 represents a circle. What is its radius?
- 4 (Correct answer)
- 3
- 16
- √13
Correct answer: 4
Completing the square: (x−3)² + (y+2)² = 16, so radius = 4.
Question 4: If the matrix A = [[1, 2], [3, 4]], what is A⁻¹?
- [[ −2, 1], [3/2, −1/2]] (Correct answer)
- [[4, −2], [−3, 1]]
- [[1/4, 1/2], [3/4, 1]]
- [[−4, 2], [3, −1]]
Correct answer: [[ −2, 1], [3/2, −1/2]]
det(A) = −2; A⁻¹ = (1/−2)[[4,−2],[−3,1]] = [[−2, 1],[3/2, −1/2]].
Question 5: What is the second derivative of f(x) = x⁴ − 3x²?
- 12x² − 6 (Correct answer)
- 4x³ − 6x
- 12x² − 3
- x⁴ − 6
Correct answer: 12x² − 6
f'(x) = 4x³ − 6x; f''(x) = 12x² − 6.
Question 6: A binomial experiment has n = 10 trials and probability of success p = 0.3. What is the expected number of successes?
- 3 (Correct answer)
- 7
- 0.3
- 2.1
Correct answer: 3
For a binomial distribution, E(X) = np = 10 × 0.3 = 3.
Question 7: Which expression is equivalent to log(a²/b³)?
- 2log(a) − 3log(b) (Correct answer)
- 2log(a) + 3log(b)
- log(2a) − log(3b)
- log(a²) · log(b³)
Correct answer: 2log(a) − 3log(b)
Using log rules: log(a²/b³) = log(a²) − log(b³) = 2log(a) − 3log(b).
IB Mathematics 5
How many distinct arrangements are there of the letters in the word STATISTICS?