1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x +6y &=& 3 \\ x +y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{9}{8}, y=\frac{7}{8} $$

2.	Differentiation A Differentiate the following equation: $$\ln\left(\sin\left(5x\right)\right)$$ Correct Answer $$\frac{5\cos\left(5x\right)}{\sin\left(5x\right)}$$

3.	Differentiation A Differentiate the following equation: $$\frac{5\exp\left(x\right)}{x} + \exp\left((-x)\right)$$ Correct Answer $$\frac{5\exp\left(x\right)}{x} - \frac{5\exp\left(x\right)}{{x}^{2}} - \exp\left((-x)\right)$$

4.

Differentiation B Differentiate the following equation: $$\frac{\left(x + 2\right)\ln\left(x\right)}{\sqrt{\sin\left(x\right)}}$$ Correct Answer $$\frac{\ln\left(x\right) + \frac{x + 2}{x}}{\sqrt{\sin\left(x\right)}} - \frac{\left(x + 2\right)\ln\left(x\right)\cos\left(x\right)}{2{\sin\left(x\right)}^{1.5}}$$

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: $$ \int \frac{2}{5x} dx$$ Correct Answer $$ null $$

7.	Consider the following differential equation: $$ -3\frac{d^2y}{dx^2} - \frac{dy}{dx} + 4y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{-4x}{3}\right) + B\exp\left(x\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{10} 5\left(j + 3\right) $$ What does the sum evaluate to? Correct Answer $$ 440$$

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

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