1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x -5 y &=& 3 \\ 2 x +4y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{27}{2}, y=-6 $$

2.	Differentiation A Differentiate the following equation: $${x}^{3.5} + \sin\left(\frac{4}{x}\right)$$ Correct Answer $$3.5{x}^{2.5} + \frac{-4\cos\left(\frac{4}{x}\right)}{{x}^{2}}$$

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

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

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

6.	Integration Please carry out the following integral: $$ \int \sqrt{-2x + 1} dx$$ Correct Answer $$ \frac{(-{\left(-2x + 1\right)}^{\frac{3}{2}})}{3} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{13} 2\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ 98$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -y &=& 1 \\ -2 x +3y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{3}{5}, y=\frac{7}{5} $$

10.	Differentiation A Differentiate the following equation: $$\exp\left({x}^{2} - \left(6 + x\right)\right)$$ Correct Answer $$\exp\left({x}^{2} - \left(6 + x\right)\right)\left(2x - 1\right)$$