IB Mathematics 2

Question 1

A geometric sequence has first term 5 and common ratio 2. What is the sum of the first 8 terms?

Accepted Answer

1275

Answer

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)?

Accepted Answer

3/(3x + 1)

Answer

By the chain rule, d/dx[ln(3x+1)] = 3/(3x+1).

Question 3

What is the value of ∫₀² (3x² − 2x) dx?

Accepted Answer

4

Answer

[x³ − x²] from 0 to 2 = (8 − 4) − 0 = 4.

Question 4

A matrix A = [[2, 1], [5, 3]]. What is det(A)?

Accepted Answer

1

Answer

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)?

Accepted Answer

0.2

Answer

For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.

IB - International Baccalaureate Practice Test