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

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

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

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Differentiation B Differentiate the following equation: $$\frac{x - 5 - \cos\left(x\right)}{\sin\left(\sqrt{x}\right)}$$ Correct Answer $$\frac{1 + \sin\left(x\right)}{\sin\left(\sqrt{x}\right)} - \frac{\left(x - 5 - \cos\left(x\right)\right)\cos\left(\sqrt{x}\right)}{2{\sin\left(\sqrt{x}\right)}^{2}\sqrt{x}}$$

5.	Integration Please carry out the following integral: $$ \int {\left(2x - 5\right)}^{4} dx$$ Correct Answer $$ \frac{{\left(2x - 5\right)}^{5}}{10} $$

6.	Integration Please carry out the following integral: $$ \int {\left(4x\right)}^{-2} dx$$ Correct Answer $$ \frac{-1}{16x} $$

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

8.	Consider the following series: $$ \sum_{j=0}^{13} -2\left(j - 5\right) $$ What does the sum evaluate to? Correct Answer $$ -42$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +y &=& 3 \\ -6 x +3y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{8}{3}, y=\frac{17}{3} $$

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