1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x +2y &=& 3 \\ -2 x -3 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{17}{5}, y=\frac{-18}{5} $$

2.	Differentiation A Differentiate the following equation: $$2x\ln\left(x\right) + \cos\left(\exp\left(x\right)\right)$$ Correct Answer $$2\left(\ln\left(x\right) + 1\right) - \sin\left(\exp\left(x\right)\right)\exp\left(x\right)$$

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

4.	Differentiation B Differentiate the following equation: $$\frac{2{x}^{2}}{3\sqrt{\cos\left(x\right)}}$$ Correct Answer $$\frac{4x}{3\sqrt{\cos\left(x\right)}} - \frac{(-{x}^{2}\sin\left(x\right))}{3{\cos\left(x\right)}^{1.5}}$$

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

6.	Integration Please carry out the following integral: $$ \int \sin\left(x + 3\right) dx$$ Correct Answer $$ (-\cos\left(x + 3\right)) $$

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

8.	Consider the following series: $$ \sum_{j=0}^{14} 2\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ 60$$

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

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