1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x +y &=& 3 \\ x +5y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{13}{4}, y=\frac{-1}{4} $$

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

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

4.

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

5.	Integration Please carry out the following integral: $$ \int {\left(3x + 2\right)}^{5} dx$$ Correct Answer $$ \frac{{\left(3x + 2\right)}^{6}}{18} $$

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

7.	Consider the following differential equation: $$ -6\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 4y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{-4x}{3}\right) + B\exp\left(\frac{x}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{16} -6\left(j - 1\right) $$ What does the sum evaluate to? Correct Answer $$ -714$$

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

10.	Differentiation A Differentiate the following equation: $$\sin\left({x}^{-3} - \cos\left(x\right)\right)$$ Correct Answer $$\cos\left({x}^{-3} - \cos\left(x\right)\right)\left(\frac{-3}{{x}^{4}} + \sin\left(x\right)\right)$$