1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -6 x -4 y &=& 1 \\ 4 x +3y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=\frac{-11}{2}, y=8 $$

2.	Differentiation A Differentiate the following equation: $$\frac{2\exp\left(2x\right)}{\sqrt{x}}$$ Correct Answer $$\frac{4\exp\left(2x\right)}{\sqrt{x}} - \frac{\exp\left(2x\right)}{{x}^{1.5}}$$

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

4.

Differentiation B Differentiate the following equation: $$\frac{\left(x - 5\right)\cos\left(x\right)}{\ln\left(x - 4\right)}$$ Correct Answer $$\frac{\cos\left(x\right) - \left(x - 5\right)\sin\left(x\right)}{\ln\left(x - 4\right)} - \frac{\left(x - 5\right)\cos\left(x\right)}{{\ln\left(x - 4\right)}^{2}\left(x - 4\right)}$$

5.	Integration Please carry out the following integral: $$ \int {\left(6x - 3\right)}^{-6} dx$$ Correct Answer $$ \frac{-1}{30{\left(6x - 3\right)}^{5}} $$

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

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

8.	Consider the following series: $$ \sum_{j=0}^{16} -3\left(j + 5\right) $$ What does the sum evaluate to? Correct Answer $$ -663$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -2 x +y &=& 1 \\ -5 x +4y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=0, y=1 $$

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