1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x +3y &=& 4 \\ -5 x -y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-10}{9}, y=\frac{32}{9} $$

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

3.	Differentiation A Differentiate the following equation: $$\exp\left(\cos\left(6 - x\right)\right)$$ Correct Answer $$\exp\left(\cos\left(6 - x\right)\right)\sin\left(6 - x\right)$$

4.	Differentiation B Differentiate the following equation: $$\frac{\sqrt{3}\exp\left(-6x\right)}{\sqrt{x}}$$ Correct Answer $$\frac{-6\sqrt{3}\exp\left(-6x\right)}{\sqrt{x}} - \frac{\sqrt{3}\exp\left(-6x\right)}{2{x}^{1.5}}$$

5.	Integration Please carry out the following integral: $$ \int \ln\left(x + 1\right) dx$$ Correct Answer $$ \left(x + 1\right)\ln\left(x + 1\right) - \left(x + 1\right) $$

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

7.	Consider the following differential equation: $$ 6\frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{x}{2}\right) + B\exp\left(\frac{-2x}{3}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{13} -3\left(j - 2\right) $$ What does the sum evaluate to? Correct Answer $$ -189$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -4 y &=& 1 \\ -2 x +3y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{7}{4}, y=\frac{3}{2} $$

10.	Differentiation A Differentiate the following equation: $$\sin\left(5x\right) - \cos\left(-6x\right)$$ Correct Answer $$5\cos\left(5x\right) - 6\sin\left(-6x\right)$$