IB Mathematics 5

Question 1

How many distinct arrangements are there of the letters in the word STATISTICS?

Accepted Answer

50400

Answer

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]?

Accepted Answer

5

Answer

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?

Accepted Answer

4

Answer

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?

Accepted Answer

[[ −2, 1], [3/2, −1/2]]

Answer

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?

Accepted Answer

12x² − 6

Answer

f'(x) = 4x³ − 6x; f''(x) = 12x² − 6.

IB - International Baccalaureate Practice Test