1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 5 x +y &=& 2 \\ 3 x -y &=& 3 \end{eqnarray}$$ Correct Answer $$ x=\frac{5}{8}, y=\frac{-9}{8} $$

2.	Differentiation A Differentiate the following equation: $$\sin\left(\cos\left(2x\right)\right)$$ Correct Answer $$-2\cos\left(\cos\left(2x\right)\right)\sin\left(2x\right)$$

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

4.	Differentiation B Differentiate the following equation: $$\frac{\left(5 - x\right)\sqrt{x}}{\sqrt{\exp\left(x\right)}}$$ Correct Answer $$\frac{(-\sqrt{x}) + \frac{5 - x}{2\sqrt{x}}}{\sqrt{\exp\left(x\right)}} - \frac{\left(5 - x\right)\sqrt{x}}{2\sqrt{\exp\left(x\right)}}$$

5.	Integration Please carry out the following integral: $$ \int {\left(2x + 5\right)}^{-4} dx$$ Correct Answer $$ \frac{-1}{6{\left(2x + 5\right)}^{3}} $$

6.	Integration Please carry out the following integral: $$ \int \ln\left(x + 2\right) dx$$ Correct Answer $$ \left(x + 2\right)\ln\left(x + 2\right) - \left(x + 2\right) $$

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

8.	Consider the following series: $$ \sum_{j=0}^{17} -3\left(j + 6\right) $$ What does the sum evaluate to? Correct Answer $$ -783$$

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

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