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

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

3.	Differentiation A Differentiate the following equation: $$\sqrt{{6}^{x} + x + 6}$$ Correct Answer $$\frac{{6}^{x}\ln\left(6\right) + 1}{2\sqrt{{6}^{x} + x + 6}}$$

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

5.	Integration Please carry out the following integral: $$ \int \sqrt{-5x} dx$$ Correct Answer $$ \frac{-2{\left((-5)x\right)}^{\frac{3}{2}}}{15} $$

6.	Integration Please carry out the following integral: $$ \int \frac{-5}{-2x} dx$$ Correct Answer $$ null $$

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

8.	Consider the following series: $$ \sum_{j=0}^{19} 2\left(j - 3\right) $$ What does the sum evaluate to? Correct Answer $$ 260$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} x -5 y &=& 1 \\ -2 x +6y &=& 1 \end{eqnarray}$$ Correct Answer $$ x=\frac{-11}{4}, y=\frac{-3}{4} $$

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