PRE CALCULUS Advanced Topics 4

Question 1

What is the dot product of vectors u = ⟨2, −1⟩ and v = ⟨4, 3⟩?

Accepted Answer

5

Answer

u · v = (2)(4) + (−1)(3) = 8 − 3 = 5.

Question 2

What is the period of the function f(x) = sin(3x)?

Accepted Answer

2π/3

Answer

The period of sin(bx) is 2π/b, so for b=3 the period is 2π/3.

Question 3

Which test can confirm that a power series converges?

Accepted Answer

Ratio Test

Answer

The Ratio Test evaluates lim|aₙ₊₁/aₙ| and determines convergence when the limit is less than 1.

Question 4

The eccentricity of an ellipse satisfies which condition?

Accepted Answer

0 < e < 1

Answer

For an ellipse, the eccentricity e = c/a lies strictly between 0 and 1.

Question 5

What is the value of i⁴ where i = √(−1)?

Accepted Answer

1

Answer

i²=−1, so i⁴=(i²)²=(−1)²=1.

PRE CALCULUS Practice Test