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

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

3.	Differentiation A Differentiate the following equation: $${\left(2x\right)}^{2} + \sin\left(\ln\left(x\right)\right)$$ Correct Answer $$8x + \frac{\cos\left(\ln\left(x\right)\right)}{x}$$

4.	Differentiation B Differentiate the following equation: $$\frac{\left(x + 6\right)\left(x - 5\right)}{{2}^{2x}}$$ Correct Answer $$\frac{2x + 1}{{2}^{2x}} - \frac{2\left(x + 6\right)\left(x - 5\right)\ln\left(2\right)}{{2}^{2x}}$$

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

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

7.	Consider the following differential equation: $$ -5\frac{d^2y}{dx^2} - 4\frac{dy}{dx} - y = 0 $$ Find the general solution to the above equation. Correct Answer $$ \exp\left(\frac{-2x}{5}\right)\left(A\sin\left(\frac{(-x)}{5}\right) + B\cos\left(\frac{(-x)}{5}\right)\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{13} 5\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ 245$$

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

10.	Differentiation A Differentiate the following equation: $$\ln\left(\sqrt{x - 3}\right)$$ Correct Answer $$\frac{1}{2\left(x - 3\right)}$$