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

2.	Differentiation A Differentiate the following equation: $$\exp\left(\frac{(-x) - 4\sqrt{x}}{4}\right)$$ Correct Answer $$\frac{\exp\left(\frac{(-x) - 4\sqrt{x}}{4}\right)\left(-1 - \frac{2}{\sqrt{x}}\right)}{4}$$

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

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

5.	Integration Please carry out the following integral: $$ \int \ln\left(-6x - 4\right) dx$$ Correct Answer $$ \frac{(-\left(\left(-6x - 4\right)\ln\left(-6x - 4\right) - \left(-6x - 4\right)\right))}{6} $$

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

7.	Consider the following differential equation: $$ 4\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + y = 0 $$ Find the general solution to the above equation. Correct Answer $$ A\exp\left(\frac{(-x)}{4}\right) + B\exp\left((-x)\right) $$

8.	Consider the following series: $$ \sum_{j=0}^{17} 4\left(j - 6\right) $$ What does the sum evaluate to? Correct Answer $$ 180$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -6 x -4 y &=& 3 \\ 6 x +6y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-13}{6}, y=\frac{5}{2} $$

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