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

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

3.	Differentiation A Differentiate the following equation: $$\cos\left({x}^{1.5}\right)$$ Correct Answer $$-1.5\sin\left({x}^{1.5}\right)\sqrt{x}$$

4.

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

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

6.	Integration Please carry out the following integral: $$ \int {\left(x + 2\right)}^{-4} dx$$ Correct Answer $$ \frac{-1}{3{\left(x + 2\right)}^{3}} $$

7.	Consider the following differential equation: $$ 4\frac{d^2y}{dx^2} + 4\frac{dy}{dx} - 3y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{x}{2}\right) + B\exp\left(\frac{-3x}{2}\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{16} 3\left(j + 3\right) $$ What does the sum evaluate to? Correct Answer $$ 561$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x -3 y &=& 2 \\ x +2y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{16}{5}, y=\frac{2}{5} $$

10.	Differentiation A Differentiate the following equation: $$\exp\left(\sin\left(x + 6\right)\right)$$ Correct Answer $$\exp\left(\sin\left(x + 6\right)\right)\cos\left(x + 6\right)$$