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

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

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

4.

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

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

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

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

8.	Consider the following series: $$ \sum_{j=0}^{18} 4\left(j - 6\right) $$ What does the sum evaluate to? Correct Answer $$ 228$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 6 x -5 y &=& 4 \\ -5 x +5y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=6, y=\frac{32}{5} $$

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