1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -5 x -2 y &=& 3 \\ -6 x -3 y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{-7}{3}, y=\frac{13}{3} $$

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: $$\sqrt{{x}^{2} + \exp\left(x\right)}$$ Correct Answer $$\frac{2x + \exp\left(x\right)}{2\sqrt{{x}^{2} + \exp\left(x\right)}}$$

4.	Differentiation B Differentiate the following equation: $$\sqrt{\frac{(-x) + 4\exp\left(x\right)}{4}}$$ Correct Answer $$\frac{4\exp\left(x\right) - 1}{4\sqrt{(-x) + 4\exp\left(x\right)}}$$

5.	Integration Please carry out the following integral: $$ \int \frac{3}{x - 6} dx$$ Correct Answer $$ null $$

6.	Integration Please carry out the following integral: $$ \int {\left(x - 3\right)}^{-6} dx$$ Correct Answer $$ \frac{-1}{5{\left(x - 3\right)}^{5}} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{14} 4\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ 780$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -4 x +y &=& 2 \\ -3 x +y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=2, y=10 $$

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