1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x -2 y &=& 3 \\ -2 x +2y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=-1, y=\frac{-1}{2} $$

2.	Differentiation A Differentiate the following equation: $$\sqrt{\exp\left(\frac{1}{x}\right)}$$ Correct Answer $$\frac{(-\sqrt{\exp\left(\frac{1}{x}\right)})}{2{x}^{2}}$$

3.	Differentiation A Differentiate the following equation: $$\sqrt{\sin\left(x\right) - \cos\left(x\right)}$$ Correct Answer $$\frac{\cos\left(x\right) + \sin\left(x\right)}{2\sqrt{\sin\left(x\right) - \cos\left(x\right)}}$$

4.

Differentiation B Differentiate the following equation: $$\frac{\sqrt{x}\ln\left(x\right)}{\exp\left(\frac{-2}{x}\right)}$$ Correct Answer $$\frac{\frac{\ln\left(x\right)}{2\sqrt{x}} + \frac{1}{\sqrt{x}}}{\exp\left(\frac{-2}{x}\right)} - \frac{2\ln\left(x\right)}{{x}^{1.5}\exp\left(\frac{-2}{x}\right)}$$

5.	Integration Please carry out the following integral: $$ \int \sqrt{-6x} dx$$ Correct Answer $$ \frac{(-{\left((-6)x\right)}^{\frac{3}{2}})}{9} $$

6.	Integration Please carry out the following integral: $$ \int \sqrt{-4x} dx$$ Correct Answer $$ \frac{(-{\left((-4)x\right)}^{\frac{3}{2}})}{6} $$

7.	Consider the following differential equation: $$ -5\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{(-x)}{5}\right) + B\exp\left(x\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{16} 4\left(j + 2\right) $$ What does the sum evaluate to? Correct Answer $$ 680$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x +4y &=& 2 \\ 2 x -2 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{6}{5}, y=\frac{1}{5} $$

10.	Differentiation A Differentiate the following equation: $$\exp\left(\sin\left(\ln\left(x\right)\right)\right)$$ Correct Answer $$\frac{\exp\left(\sin\left(\ln\left(x\right)\right)\right)\cos\left(\ln\left(x\right)\right)}{x}$$