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

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

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

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

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

6.	Integration Please carry out the following integral: $$ \int {\left((-3)x\right)}^{-5} dx$$ Correct Answer $$ \frac{1}{972{x}^{4}} $$

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: $$ \sum_{j=0}^{12} (-\left(j + 2\right)) $$ What does the sum evaluate to? Correct Answer $$ -104$$

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

10.	Differentiation A Differentiate the following equation: $$-4{x}^{5} + \ln\left(-1 - x\right)$$ Correct Answer $$-20{x}^{4} + \frac{-1}{-1 - x}$$