Question 1.
a) A credit union pays interest of 10% per annum compounded monthly on a certain savings plan. If $10000 is deposited in such a plan and the interest is left to accumulate, how much is in the account after 2 years?
b) Solve the following equation: $5^x \cdot 2^{\frac{2x-1}{x+1}} = 50$.

Question 2.
Given the following function $f(x) = \frac{3x+2}{x-1}$
a) Find the inverse function of $f$.
b) Find the average rate of change of $f$ from $x_0$ to $x_0 + h$, where $h$ is real.

Question 3.
The area of the opening of a rectangular window is to be 143 square feet. If the length is to be 2 feet more than the width, what are the dimensions?

Question 4.
Solve the following system of linear equations

Question 5.
Let

and

where $I$ is the identity matrix of size 2.

a) Find inverse of $A$
b) Find $B$
c) Find $\det(B)$

Question 6.
Let

where $m \in \mathbb{R}$.

a) Find $m$ such that $B$ is invertible
b) Find the inverse of $B$ when $m = 0$

Question 7.
One group of people purchased 20 hot dogs and 10 soft drinks at a cost of $85.00. A second bought 8 hot dogs and 3 soft drinks at a cost of $32.50. What is the cost of a single hot dog? A single soft drink?

Question 8.
Maximize $z = 4x + 7y$ subject to $x \ge 0$, $y \ge 0$, $x + y \ge 4$, $x + y \le 10$, $x + 2y \ge 6$

Question 9.
a) Given the following polynomial $f(x) = x^4 - 2x^3 + 6x^2 - 2x + 5$. Note that $f(x) = 0$ has a solution $x = i$. Find all remaining solutions.
b) Show the following number $z = (2 + 2i)^6$ in the form of $a + bi$.

Question 10.
Let $A, B$ be two square matrices of size $n$ such that $AB - A - B = 0$. Prove that $AB = BA$