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

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

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

4.	Differentiation B Differentiate the following equation: $$\frac{\left(\sqrt{x} - \sin\left(x\right)\right)\sqrt{x}}{\sqrt{-6}}$$ Correct Answer $$\frac{\left(\frac{1}{2\sqrt{x}} - \cos\left(x\right)\right)\sqrt{x} + \frac{\sqrt{x} - \sin\left(x\right)}{2\sqrt{x}}}{\sqrt{-6}}$$

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: $$ \int \frac{-1}{2x} dx$$ Correct Answer $$ null $$

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

8.	Consider the following series: $$ \sum_{j=0}^{16} -5\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ -425$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} -x +4y &=& 2 \\ x -3 y &=& 2 \end{eqnarray}$$ Correct Answer $$ x=14, y=4 $$

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