PRE CALCULUS Advanced Topics 2

Question 1

What is the polar form of the complex number 1 + i?

Accepted Answer

√2(cos 45° + i sin 45°)

Answer

The modulus is √(1²+1²)=√2 and the argument is arctan(1/1)=45°, giving √2(cos45°+i sin45°).

Question 2

Which conic section is represented by the equation x²/9 - y²/4 = 1?

Accepted Answer

Hyperbola

Answer

The standard form x²/a² - y²/b² = 1 with opposite signs defines a hyperbola.

Question 3

What is the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + …?

Accepted Answer

3/2

Answer

For |r|<1, S = a/(1−r) = 1/(1−1/3) = 1/(2/3) = 3/2.

Question 4

Which expression equals log₂(8) + log₂(4)?

Accepted Answer

5

Answer

log₂(8)=3 and log₂(4)=2, so their sum is 5.

Question 5

The parametric equations x = 3cos(t), y = 3sin(t) describe which curve?

Accepted Answer

A circle of radius 3

Answer

Since x²+y²=9cos²t+9sin²t=9, the curve is a circle with radius 3.

PRE CALCULUS Practice Test