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

2.	Differentiation A Differentiate the following equation: $$\exp\left(6x\right) + \sqrt{3x}$$ Correct Answer $$6\exp\left(6x\right) + \frac{\sqrt{3}}{2\sqrt{x}}$$

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

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

5.	Integration Please carry out the following integral: $$ \int \frac{3}{-5x + 2} dx$$ Correct Answer $$ null $$

6.	Integration Please carry out the following integral: $$ \int \cos\left(x + 1\right) dx$$ Correct Answer $$ \sin\left(x + 1\right) $$

7.	Consider the following differential equation: $$ -3\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{-2x}{3}\right) + B\exp\left(2x\right) $$

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: $$\begin{eqnarray} -x +3y &=& 2 \\ 3 x +y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=1, y=1 $$

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