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{n+1} = 2an + 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