1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -4 x +5y &=& 3 \\ -3 x +4y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=-7, y=-5 $$

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

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

4.	Differentiation B Differentiate the following equation: $${2}^{\exp\left(x\right)}\left(3x - \frac{-6}{x}\right)$$ Correct Answer $${2}^{\exp\left(x\right)}\ln\left(2\right)\exp\left(x\right)\left(3x - \frac{-6}{x}\right) + {2}^{\exp\left(x\right)}\left(3 - \frac{6}{{x}^{2}}\right)$$

5.	Integration Please carry out the following integral: $$ \int \sin\left(-4x\right) dx$$ Correct Answer $$ \frac{\cos\left(-4x\right)}{4} $$

6.	Integration Please carry out the following integral: $$ \int \sqrt{x + 4} dx$$ Correct Answer $$ \frac{2{\left(x + 4\right)}^{\frac{3}{2}}}{3} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{13} 2\left(j - 2\right) $$ What does the sum evaluate to? Correct Answer $$ 126$$

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

10.	Differentiation A Differentiate the following equation: $$-6x - \ln\left(x\right) + \sqrt{\sin\left(x\right)}$$ Correct Answer $$-6 - \frac{1}{x} + \frac{\cos\left(x\right)}{2\sqrt{\sin\left(x\right)}}$$