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

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

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

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

5.	Integration Please carry out the following integral: $$ \int \sqrt{-5x} dx$$ Correct Answer $$ \frac{-2{\left((-5)x\right)}^{\frac{3}{2}}}{15} $$

6.	Integration Please carry out the following integral: $$ \int {\left(x - 2\right)}^{4} dx$$ Correct Answer $$ \frac{{\left(x - 2\right)}^{5}}{5} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{11} -3\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ -414$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 5 x +y &=& 1 \\ -6 x -y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=-2, y=11 $$

10.	Differentiation A Differentiate the following equation: $$\frac{6\left(6 - x\right)}{x} + \sqrt{{x}^{-6}}$$ Correct Answer $$\frac{-6}{x} - \frac{6\left(6 - x\right)}{{x}^{2}} + \frac{-3}{{x}^{4}}$$