1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 2 x -4 y &=& 4 \\ 3 x -y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=0, y=-1 $$

2.	Differentiation A Differentiate the following equation: $$\sin\left(\ln\left(4x\right)\right)$$ Correct Answer $$\frac{\cos\left(\ln\left(4x\right)\right)}{x}$$

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

4.	Differentiation B Differentiate the following equation: $${2}^{\left(-2 - x\right)}\left(x + 6 - \exp\left(x\right)\right)$$ Correct Answer $$(-{2}^{\left(-2 - x\right)}\ln\left(2\right)\left(x + 6 - \exp\left(x\right)\right)) + {2}^{\left(-2 - x\right)}\left(1 - \exp\left(x\right)\right)$$

5.	Integration Please carry out the following integral: $$ \int \ln\left(x + 2\right) dx$$ Correct Answer $$ \left(x + 2\right)\ln\left(x + 2\right) - \left(x + 2\right) $$

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

7.	Consider the following differential equation: $$ 5\frac{d^2y}{dx^2} + 3\frac{dy}{dx} - 2y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{2x}{5}\right) + B\exp\left((-x)\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{10} 2\left(j - 2\right) $$ What does the sum evaluate to? Correct Answer $$ 66$$

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

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