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

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

3.	Differentiation A Differentiate the following equation: $$\ln\left(\frac{x - 5\sqrt{x}}{5}\right)$$ Correct Answer $$\frac{1 - \frac{5}{2\sqrt{x}}}{x - 5\sqrt{x}}$$

4.	Differentiation B Differentiate the following equation: $$\left(\exp\left(x\right) - \ln\left(x\right)\right)\cos\left(5 + x\right)$$ Correct Answer $$\left(\exp\left(x\right) - \frac{1}{x}\right)\cos\left(5 + x\right) - \left(\exp\left(x\right) - \ln\left(x\right)\right)\sin\left(5 + x\right)$$

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

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

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

8.	Consider the following series: $$ \sum_{j=0}^{13} 2\left(j + 2\right) $$ What does the sum evaluate to? Correct Answer $$ 238$$

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

10.	Differentiation A Differentiate the following equation: $$\cos\left(\frac{6}{x} + x + 3\right)$$ Correct Answer $$(-\sin\left(\frac{6}{x} + x + 3\right)\left(\frac{-6}{{x}^{2}} + 1\right))$$