1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -3 x +2y &=& 4 \\ 3 x -5 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-28}{9}, y=\frac{-8}{3} $$

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

3.	Differentiation A Differentiate the following equation: $$\left(-6 - x\right)\left(4 - x\right) + \sin\left(x + 4\right)$$ Correct Answer $$(-\left(4 - x\right)) - \left(-6 - x\right) + \cos\left(x + 4\right)$$

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

5.	Integration Please carry out the following integral: $$ \int {\left(-4x - 3\right)}^{2} dx$$ Correct Answer $$ \frac{(-{\left(-4x - 3\right)}^{3})}{12} $$

6.	Integration Please carry out the following integral: $$ \int \sqrt{6x - 4} dx$$ Correct Answer $$ \frac{{\left(6x - 4\right)}^{\frac{3}{2}}}{9} $$

7.	Consider the following differential equation: $$ -3\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + 6y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(-2x\right) + B\exp\left(x\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{13} (-\left(j + 4\right)) $$ What does the sum evaluate to? Correct Answer $$ -147$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x +3y &=& 2 \\ -6 x +4y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{-1}{10}, y=\frac{3}{5} $$

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