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

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

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

4.	Differentiation B Differentiate the following equation: $$\frac{(-x\sin\left(x\right)) - 6\sin\left(\frac{5}{x}\right)}{6}$$ Correct Answer $$\frac{(-\left(\sin\left(x\right) + x\cos\left(x\right)\right)) - \frac{-30\cos\left(\frac{5}{x}\right)}{{x}^{2}}}{6}$$

5.	Integration Please carry out the following integral: $$ \int {\left((-x) - 4\right)}^{-1} dx$$ Correct Answer $$ (-\ln\left((-x) - 4\right)) $$

6.	Integration Please carry out the following integral: $$ \int {\left(x - 5\right)}^{1} dx$$ Correct Answer $$ \frac{{\left(x - 5\right)}^{2}}{2} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{13} 2\left(j + 4\right) $$ What does the sum evaluate to? Correct Answer $$ 294$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -5 y &=& 1 \\ -4 x +6y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{13}{2}, y=5 $$

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