1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x -3 y &=& 4 \\ -4 x +4y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{25}{12}, y=\frac{17}{6} $$

2.	Differentiation A Differentiate the following equation: $$\cos\left(5x - \exp\left(x\right)\right)$$ Correct Answer $$(-\sin\left(5x - \exp\left(x\right)\right)\left(5 - \exp\left(x\right)\right))$$

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

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

5.	Integration Please carry out the following integral: $$ \int \ln\left((-x) - 6\right) dx$$ Correct Answer $$ (-\left(\left((-x) - 6\right)\ln\left((-x) - 6\right) - \left((-x) - 6\right)\right)) $$

6.	Integration Please carry out the following integral: $$ \int \sqrt{5x - 4} dx$$ Correct Answer $$ \frac{2{\left(5x - 4\right)}^{\frac{3}{2}}}{15} $$

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 $$ A\exp\left(x\right) + B\exp\left(\frac{(-x)}{5}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{15} -4\left(j + 1\right) $$ What does the sum evaluate to? Correct Answer $$ -544$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x -5 y &=& 4 \\ 5 x -5 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=0, y=\frac{-4}{5} $$

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