IB Mathematics 2 — Questions and Answers
Question 1: A geometric sequence has first term 5 and common ratio 2. What is the sum of the first 8 terms?
- 1275 (Correct answer)
- 1280
- 635
- 255
Correct answer: 1275
Using S_n = a(r^n - 1)/(r - 1): S_8 = 5(2^8 - 1)/(2 - 1) = 5(255) = 1275.
Question 2: If f(x) = ln(3x + 1), what is f'(x)?
- 3/(3x + 1) (Correct answer)
- 1/(3x + 1)
- 3 ln(3x + 1)
- 1/(3x)
Correct answer: 3/(3x + 1)
By the chain rule, d/dx[ln(3x+1)] = 3/(3x+1).
Question 3: What is the value of ∫₀² (3x² − 2x) dx?
- 4 (Correct answer)
- 8
- 6
- 2
Correct answer: 4
[x³ − x²] from 0 to 2 = (8 − 4) − 0 = 4.
Question 4: A matrix A = [[2, 1], [5, 3]]. What is det(A)?
- 1 (Correct answer)
- 11
- −1
- 6
Correct answer: 1
det(A) = (2)(3) − (1)(5) = 6 − 5 = 1.
Question 5: The probability that event A occurs is 0.4 and event B occurs is 0.5. If A and B are independent, what is P(A ∩ B)?
- 0.2 (Correct answer)
- 0.9
- 0.1
- 0.45
Correct answer: 0.2
For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.
Question 6: What is the equation of the line passing through (1, 2) and (3, 8)?
- y = 3x − 1 (Correct answer)
- y = 2x + 1
- y = 3x + 1
- y = 2x − 1
Correct answer: y = 3x − 1
Slope = (8−2)/(3−1) = 3; using point (1,2): y − 2 = 3(x − 1) → y = 3x − 1.
Question 7: In a right triangle, the two legs measure 6 and 8. What is the length of the hypotenuse?
- 10 (Correct answer)
- 12
- 14
- √(100)
Correct answer: 10
By the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.
IB Mathematics 2
A geometric sequence has first term 5 and common ratio 2.
What is the sum of the first 8 terms?