1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -6 x -4 y &=& 3 \\ 2 x +3y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{-21}{10}, y=\frac{12}{5} $$

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

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

4.

Differentiation B Differentiate the following equation: $$\frac{-6x - \sqrt{x}}{\sin\left(\ln\left(x\right)\right)}$$ Correct Answer $$\frac{-6 - \frac{1}{2\sqrt{x}}}{\sin\left(\ln\left(x\right)\right)} - \frac{\left(-6x - \sqrt{x}\right)\cos\left(\ln\left(x\right)\right)}{{\sin\left(\ln\left(x\right)\right)}^{2}x}$$

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

6.	Integration Please carry out the following integral: $$ \int {\left(x - 3\right)}^{5} dx$$ Correct Answer $$ \frac{{\left(x - 3\right)}^{6}}{6} $$

7.	Consider the following differential equation: $$ 3\frac{d^2y}{dx^2} + 2\frac{dy}{dx} - 5y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(x\right) + B\exp\left(\frac{-5x}{3}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{15} 6\left(j - 6\right) $$ What does the sum evaluate to? Correct Answer $$ 144$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x -y &=& 2 \\ 6 x +y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{3}{10}, y=\frac{-4}{5} $$

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