1.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 3 x +3y &=& 1 \\ -2 x -6 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{3}{2}, y=\frac{-7}{6} $$

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

3.	Differentiation A Differentiate the following equation: $$\sqrt{{x}^{3.5}}$$ Correct Answer $$\frac{3.5{x}^{0.75}}{2}$$

4.	Differentiation B Differentiate the following equation: $$\exp\left(\frac{(-x) + 6\sqrt{x}}{6}\right)$$ Correct Answer $$\frac{\exp\left(\frac{(-x) + 6\sqrt{x}}{6}\right)\left(\frac{3}{\sqrt{x}} - 1\right)}{6}$$

5.	Integration Please carry out the following integral: $$ \int \frac{-3}{4x + 4} dx$$ Correct Answer $$ null $$

6.	Integration Please carry out the following integral: $$ \int \sin\left(x + 3\right) dx$$ Correct Answer $$ (-\cos\left(x + 3\right)) $$

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

8.	Consider the following series: $$ \sum_{j=0}^{18} 4\left(j + 5\right) $$ What does the sum evaluate to? Correct Answer $$ 1064$$

9.	Solution of linear equations We have the following equations: $$\begin{eqnarray} 4 x +5y &=& 3 \\ -6 x -6 y &=& 4 \end{eqnarray}$$ Correct Answer $$ x=\frac{-19}{3}, y=\frac{17}{3} $$

10.	Differentiation A Differentiate the following equation: $$\exp\left(\left(x - 5\right)\ln\left(x\right)\right)$$ Correct Answer $$\exp\left(\left(x - 5\right)\ln\left(x\right)\right)\left(\ln\left(x\right) + \frac{x - 5}{x}\right)$$