Math Exam Notes for 11th Grade Advanced - Paper Section

Question 1

Converting Rectangular Equation to Polar Form

The task is to convert the given rectangular equation to polar form:

$(x-2)^2 + y^2 = 4$

Question 2

Complex Number in Polar and Rectangular Forms

Given the complex number:

$z = 5\sqrt{3} + 5i$

Part a: Expressing in Polar Form

Express the complex number $z$ in polar form.

Part b: Finding and Expressing in Rectangular Form

Find $(5\sqrt{3} + 5i)^3$ and express the result in rectangular form.

Question 3

Finding the Fifth Term of a Sequence

Find the fifth term of the sequence where:

$a<em>{n+1} = 2a</em>n + n, a_1 = -1, n \geq 1$

Question 4

Finding Arithmetic Means in a Sequence

Find the arithmetic means in the following arithmetic sequence:

182, ___, ___, ___, ___, ___, 104

Question 5

Finding the 8th Term of a Binomial Expansion

Find the 8th term of the binomial expansion:

$(3a - 2b)^8$