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

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

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

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

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

6.	Integration Please carry out the following integral: $$ \int \cos\left(6x + 1\right) dx$$ Correct Answer $$ \frac{\sin\left(6x + 1\right)}{6} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{14} 6\left(j + 1\right) $$ What does the sum evaluate to? Correct Answer $$ 720$$

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

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