1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x +6y &=& 2 \\ 4 x +4y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{1}{2}, y=0 $$

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

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

4.	Differentiation B Differentiate the following equation: $$\exp\left(4x\right)\sin\left(\frac{(-x)}{5}\right)$$ Correct Answer $$\frac{20\exp\left(4x\right)\sin\left(\frac{(-x)}{5}\right) - \exp\left(4x\right)\cos\left(\frac{(-x)}{5}\right)}{5}$$

5.	Integration Please carry out the following integral: $$ \int \frac{6}{x - 6} dx$$ Correct Answer $$ null $$

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

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

8.	Consider the following series: $$ \sum_{j=0}^{15} -6\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ -1296$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x +6y &=& 3 \\ -x -3 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{7}{2}, y=\frac{-11}{6} $$

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