1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -3 x -3 y &=& 2 \\ 4 x +2y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{8}{3}, y=\frac{-10}{3} $$

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

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

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

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

6.	Integration Please carry out the following integral: $$ \int \frac{1}{2x + 2} dx$$ Correct Answer $$ null $$

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

8.	Consider the following series: $$ \sum_{j=0}^{18} -2\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ -228$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x -6 y &=& 4 \\ -5 x +6y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=8, y=\frac{22}{3} $$

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