IB Mathematics 4

Question 1

What is the sum to infinity of the geometric series 12 + 4 + 4/3 + … ?

Accepted Answer

18

Answer

r = 1/3 and a = 12; S∞ = a/(1−r) = 12/(1 − 1/3) = 12/(2/3) = 18.

Question 2

Which of the following is the derivative of y = e^(2x) · cos(x)?

Accepted Answer

2e^(2x)cos(x) − e^(2x)sin(x)

Answer

By the product rule: dy/dx = 2e^(2x)cos(x) + e^(2x)(−sin(x)) = e^(2x)(2cos(x) − sin(x)).

Question 3

What is the area enclosed between y = x² and y = x over the interval where they intersect?

Accepted Answer

1/6

Answer

Intersect at x = 0 and x = 1; area = ∫₀¹ (x − x²) dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6.

Question 4

The complex number z = 3 + 4i. What is |z|?

Accepted Answer

5

Answer

|z| = √(3² + 4²) = √(9 + 16) = √25 = 5.

Question 5

A Poisson random variable X has mean λ = 3. What is P(X = 0)?

Accepted Answer

e⁻³

Answer

P(X = 0) = e^(−λ)·λ⁰/0! = e^(−3).

IB - International Baccalaureate Practice Test